diff --git a/app.py b/app.py
index b173f2bac57e3d8ea99dc48da602cc6edc0e9a4f..a5708276eb3f4c3824fa9cde82c2876a38a743e7 100644
--- a/app.py
+++ b/app.py
@@ -1264,6 +1264,11 @@ def author_name(record: dict[str, Any]) -> str:
 
 
 def display_author(record: dict[str, Any]) -> str:
+    try:
+        if int(record.get("n") or 0) == 1:
+            return "Trivial"
+    except (TypeError, ValueError):
+        pass
     if record.get("record_type") == "reference":
         return reference_credit(record)
     author = author_name(record)
@@ -1888,9 +1893,9 @@ def leaderboard_html() -> str:
             <div>
               <h2>Leaderboard</h2>
               <p class="section-note">
-                Counts current public records by credited author. Nathan Roll is credited only when a verified
-                coordinate layout improves the displayed Friedman metric by more than 0.15%; recovered layouts
-                stay credited to the Friedman-listed finder.
+                Counts current public records by credited author. Credits follow the Friedman-listed finder for
+                recovered layouts; local Nathan Roll credit is reserved for non-image-seeded verified improvements
+                above 0.15%, and one-shape cases are credited as Trivial.
               </p>
             </div>
           </div>
diff --git a/data/evaluation_results.jsonl b/data/evaluation_results.jsonl
index 002c8c2fc1d041773ff5ee8894a79e5215a1896b..d5878fb4e6790a04422098e725b062ba687cf054 100644
--- a/data/evaluation_results.jsonl
+++ b/data/evaluation_results.jsonl
@@ -262,6 +262,7 @@
 {"case": "hexintri@17", "container": {"circumradius": 6.721674200378152, "orientation_radians": 0.0, "side_length": 11.642281226979867, "sides": 3, "type": "regular_polygon"}, "density": 0.7525303158572544, "errors": [], "item": {"circumradius": 1.0000000000000002, "side_length": 1.0, "sides": 6, "type": "regular_polygon"}, "max_boundary_excess": -1.447216764354318e-05, "max_pair_overlap_depth": -1.3408176938511929e-05, "n": 17, "ok": true, "record_id": "8137d039fd339f48", "setup": "hexintri", "side": 11.642281226979867, "solution_hash": "8137d039fd339f48", "solution_path": "data/solutions/generated/hexintri_017_8137d039fd339f48.json", "tolerance": 1e-08, "warnings": []}
 {"case": "hexintri@18", "container": {"circumradius": 6.924618334899173, "orientation_radians": 0.0, "side_length": 11.993790779068366, "sides": 3, "type": "regular_polygon"}, "density": 0.7507767554452202, "errors": [], "item": {"circumradius": 1.0000000000000002, "side_length": 1.0, "sides": 6, "type": "regular_polygon"}, "max_boundary_excess": -6.734105056962567e-06, "max_pair_overlap_depth": -5.8920104462956147e-05, "n": 18, "ok": true, "record_id": "8f10cd5e01be9029", "setup": "hexintri", "side": 11.993790779068366, "solution_hash": "8f10cd5e01be9029", "solution_path": "data/solutions/generated/hexintri_018_8f10cd5e01be9029.json", "tolerance": 1e-08, "warnings": []}
 {"case": "hexintri@19", "container": {"circumradius": 6.950404010627927, "orientation_radians": 0.0, "side_length": 12.038452879538063, "sides": 3, "type": "regular_polygon"}, "density": 0.7866173060867477, "errors": [], "item": {"circumradius": 1.0000000000000002, "side_length": 1.0, "sides": 6, "type": "regular_polygon"}, "max_boundary_excess": -8.242681221171444e-06, "max_pair_overlap_depth": -3.13088544121598e-05, "n": 19, "ok": true, "record_id": "18178ad9efaf7172", "setup": "hexintri", "side": 12.038452879538063, "solution_hash": "18178ad9efaf7172", "solution_path": "data/solutions/generated/hexintri_019_18178ad9efaf7172.json", "tolerance": 1e-08, "warnings": []}
+{"case": "hexintri@19", "container": {"circumradius": 6.928429777468251, "orientation_radians": 0.0, "side_length": 12.000392391248141, "sides": 3, "type": "regular_polygon"}, "density": 0.791614895360766, "errors": [], "item": {"circumradius": 1.0000000000000002, "side_length": 1.0, "sides": 6, "type": "regular_polygon"}, "max_boundary_excess": -6.082421874827662e-06, "max_pair_overlap_depth": -1.8024499229385427e-05, "n": 19, "ok": true, "record_id": "f5757609f28a7743", "setup": "hexintri", "side": 12.000392391248141, "solution_hash": "f5757609f28a7743", "solution_path": "data/solutions/generated/hexintri_19_f5757609f28a7743.json", "tolerance": 1e-08, "warnings": []}
 {"case": "hexintri@20", "container": {"circumradius": 7.000138571289056, "orientation_radians": 0.0, "side_length": 12.124595665495255, "sides": 3, "type": "regular_polygon"}, "density": 0.8162942117377381, "errors": [], "item": {"circumradius": 1.0000000000000002, "side_length": 1.0, "sides": 6, "type": "regular_polygon"}, "max_boundary_excess": -6.116403950810266e-06, "max_pair_overlap_depth": -3.364591626842106e-05, "n": 20, "ok": true, "record_id": "f59179c5b6665dc4", "setup": "hexintri", "side": 12.124595665495255, "solution_hash": "f59179c5b6665dc4", "solution_path": "data/solutions/generated/hexintri_020_f59179c5b6665dc4.json", "tolerance": 1e-08, "warnings": []}
 {"case": "hexintri@21", "container": {"circumradius": 7.00016054016223, "orientation_radians": 0.0, "side_length": 12.124633716699778, "sides": 3, "type": "regular_polygon"}, "density": 0.8571035425372456, "errors": [], "item": {"circumradius": 1.0000000000000002, "side_length": 1.0, "sides": 6, "type": "regular_polygon"}, "max_boundary_excess": -3.7607980864287318e-06, "max_pair_overlap_depth": -2.977721456209892e-05, "n": 21, "ok": true, "record_id": "6cf726ac83ba7d7f", "setup": "hexintri", "side": 12.124633716699778, "solution_hash": "6cf726ac83ba7d7f", "solution_path": "data/solutions/generated/hexintri_021_6cf726ac83ba7d7f.json", "tolerance": 1e-08, "warnings": []}
 {"case": "octinoct@1", "container": {"circumradius": 1.306566832523851, "orientation_radians": 0.0, "side_length": 1.0000029601692215, "sides": 8, "type": "regular_polygon"}, "density": 0.9999940796878448, "errors": [], "item": {"circumradius": 1.3065629648763766, "side_length": 1.0, "sides": 8, "type": "regular_polygon"}, "max_boundary_excess": -2.1903479056983753e-06, "max_pair_overlap_depth": 0.0, "n": 1, "ok": true, "record_id": "13c63959e19cfeb5", "setup": "octinoct", "side": 1.0000029601692215, "solution_hash": "13c63959e19cfeb5", "solution_path": "data/solutions/generated/octinoct_001_13c63959e19cfeb5.json", "tolerance": 1e-08, "warnings": []}
@@ -397,7 +398,9 @@
 {"case": "squincir@31", "container": {"radius": 3.536916321287215, "type": "circle"}, "density": 0.7887915525098625, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -2.62119976746078e-06, "max_pair_overlap_depth": -1.7231292489316985e-05, "n": 31, "ok": true, "record_id": "fdf9170d30584f4f", "setup": "squincir", "side": 7.07383264257443, "solution_hash": "fdf9170d30584f4f", "solution_path": "data/solutions/generated/squincir_031_fdf9170d30584f4f.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squincir@32", "container": {"radius": 3.5871274839526355, "type": "circle"}, "density": 0.7916012707303632, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -7.2509087862826505e-06, "max_pair_overlap_depth": -6.52310694349012e-09, "n": 32, "ok": true, "record_id": "b8bda371acb2b492", "setup": "squincir", "side": 7.174254967905271, "solution_hash": "b8bda371acb2b492", "solution_path": "data/solutions/generated/squincir_032_b8bda371acb2b492.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squincir@33", "container": {"radius": 3.606341162045688, "type": "circle"}, "density": 0.8076634866746639, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -5.493268955270025e-06, "max_pair_overlap_depth": -1.6481229587750335e-06, "n": 33, "ok": true, "record_id": "e5a9fc9a4b7235a0", "setup": "squincir", "side": 7.212682324091376, "solution_hash": "e5a9fc9a4b7235a0", "solution_path": "data/solutions/generated/squincir_033_e5a9fc9a4b7235a0.json", "tolerance": 1e-08, "warnings": []}
+{"case": "squincir@34", "container": {"radius": 3.6335692625466023, "type": "circle"}, "density": 0.8197136332658641, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -4.951833559641017e-06, "max_pair_overlap_depth": -2.1724087376329138e-05, "n": 34, "ok": true, "record_id": "8e846defa45411b2", "setup": "squincir", "side": 7.267138525093205, "solution_hash": "8e846defa45411b2", "solution_path": "data/solutions/generated/squincir_34_8e846defa45411b2.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squincir@34", "container": {"radius": 3.6341429314675135, "type": "circle"}, "density": 0.819454861319337, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -1.0151594769247652e-06, "max_pair_overlap_depth": -1.71712946250846e-07, "n": 34, "ok": true, "record_id": "9214fdf4034b8f9a", "setup": "squincir", "side": 7.268285862935027, "solution_hash": "9214fdf4034b8f9a", "solution_path": "data/solutions/generated/squincir_34_9214fdf4034b8f9a.json", "tolerance": 1e-08, "warnings": []}
+{"case": "squincir@34", "container": {"radius": 3.6315230432891554, "type": "circle"}, "density": 0.8206376457817698, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -1.1187926634015355e-06, "max_pair_overlap_depth": -1.3727466190216475e-05, "n": 34, "ok": true, "record_id": "aa2ddbda942a0ffd", "setup": "squincir", "side": 7.263046086578311, "solution_hash": "aa2ddbda942a0ffd", "solution_path": "data/solutions/generated/squincir_34_aa2ddbda942a0ffd.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squincir@35", "container": {"radius": 3.640654908255323, "type": "circle"}, "density": 0.8405414638481816, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -4.121617296348745e-07, "max_pair_overlap_depth": -2.1344301219083928e-05, "n": 35, "ok": true, "record_id": "f2d91d98b4c2ee39", "setup": "squincir", "side": 7.281309816510646, "solution_hash": "f2d91d98b4c2ee39", "solution_path": "data/solutions/generated/squincir_035_f2d91d98b4c2ee39.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squindom@1", "container": {"height": 1.0000093204700702, "type": "rectangle", "width": 2.0000186409401404}, "density": 0.499990679660235, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -3.7525252651882113e-06, "max_pair_overlap_depth": 0.0, "n": 1, "ok": true, "record_id": "557f8de873a17a8e", "setup": "squindom", "side": 2.0000186409401404, "solution_hash": "557f8de873a17a8e", "solution_path": "data/solutions/generated/squindom_001_557f8de873a17a8e.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squindom@2", "container": {"height": 1.0000058501509195, "type": "rectangle", "width": 2.000011700301839}, "density": 0.9999882998008334, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -3.463373909884382e-07, "max_pair_overlap_depth": -9.41881114351023e-06, "n": 2, "ok": true, "record_id": "7684110dce2e5290", "setup": "squindom", "side": 2.000011700301839, "solution_hash": "7684110dce2e5290", "solution_path": "data/solutions/generated/squindom_002_7684110dce2e5290.json", "tolerance": 1e-08, "warnings": []}
@@ -439,6 +442,8 @@
 {"case": "squindom@38", "container": {"height": 4.807708740683875, "type": "rectangle", "width": 9.61541748136775}, "density": 0.8220103806251009, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -4.518216488058613e-06, "max_pair_overlap_depth": -2.290026661011524e-05, "n": 38, "ok": true, "record_id": "d4d1cf6ab169d8aa", "setup": "squindom", "side": 9.61541748136775, "solution_hash": "d4d1cf6ab169d8aa", "solution_path": "data/solutions/generated/squindom_038_d4d1cf6ab169d8aa.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squindom@39", "container": {"height": 4.839387130645936, "type": "rectangle", "width": 9.678774261291872}, "density": 0.8326335013079162, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -4.790990827618913e-06, "max_pair_overlap_depth": -1.236762303413741e-05, "n": 39, "ok": true, "record_id": "a606e4f52500fa01", "setup": "squindom", "side": 9.678774261291872, "solution_hash": "a606e4f52500fa01", "solution_path": "data/solutions/generated/squindom_039_a606e4f52500fa01.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squindom@40", "container": {"height": 4.895342657342564, "type": "rectangle", "width": 9.790685314685128}, "density": 0.8345719865483486, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -1.37233266706005e-06, "max_pair_overlap_depth": -3.9677918853286975e-06, "n": 40, "ok": true, "record_id": "bb2811be04efb5ee", "setup": "squindom", "side": 9.790685314685128, "solution_hash": "bb2811be04efb5ee", "solution_path": "data/solutions/generated/squindom_040_bb2811be04efb5ee.json", "tolerance": 1e-08, "warnings": []}
+{"case": "squindom@41", "container": {"height": 5.000043288573118, "type": "rectangle", "width": 10.000086577146236}, "density": 0.8199858015324071, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -2.2531322496632813e-07, "max_pair_overlap_depth": -9.877316924367108e-07, "n": 41, "ok": true, "record_id": "5bbf9f2ba5ab11a2", "setup": "squindom", "side": 10.000086577146236, "solution_hash": "5bbf9f2ba5ab11a2", "solution_path": "data/solutions/generated/squindom_41_5bbf9f2ba5ab11a2.json", "tolerance": 1e-08, "warnings": []}
+{"case": "squindom@41", "container": {"height": 4.928216572329007, "type": "rectangle", "width": 9.856433144658014}, "density": 0.8440618888942375, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -1.8525221028298233e-06, "max_pair_overlap_depth": -8.594557442787032e-06, "n": 41, "ok": true, "record_id": "9ed000ff11bd8b55", "setup": "squindom", "side": 9.856433144658014, "solution_hash": "9ed000ff11bd8b55", "solution_path": "data/solutions/generated/squindom_41_9ed000ff11bd8b55.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squindom@41", "container": {"height": 5.000061486490366, "type": "rectangle", "width": 10.000122972980732}, "density": 0.8199798328031639, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -8.465020711057036e-07, "max_pair_overlap_depth": -6.131910444850952e-06, "n": 41, "ok": true, "record_id": "cb1462995bd3b2c0", "setup": "squindom", "side": 10.000122972980732, "solution_hash": "cb1462995bd3b2c0", "solution_path": "data/solutions/generated/squindom_41_cb1462995bd3b2c0.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squindom@42", "container": {"height": 4.978534605225135, "type": "rectangle", "width": 9.95706921045027}, "density": 0.8472590848618945, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -3.54667148005916e-06, "max_pair_overlap_depth": -1.5216861767419765e-05, "n": 42, "ok": true, "record_id": "7faea8ae450b67a1", "setup": "squindom", "side": 9.95706921045027, "solution_hash": "7faea8ae450b67a1", "solution_path": "data/solutions/generated/squindom_042_7faea8ae450b67a1.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squindom@43", "container": {"height": 5.000325272095715, "type": "rectangle", "width": 10.00065054419143}, "density": 0.859888117316887, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -5.1461540806485566e-08, "max_pair_overlap_depth": -2.005039219099558e-06, "n": 43, "ok": true, "record_id": "7f9527ccddc9d648", "setup": "squindom", "side": 10.00065054419143, "solution_hash": "7f9527ccddc9d648", "solution_path": "data/solutions/generated/squindom_043_7f9527ccddc9d648.json", "tolerance": 1e-08, "warnings": []}
@@ -470,6 +475,8 @@
 {"case": "squinhex@19", "container": {"circumradius": 2.937959654566609, "orientation_radians": 0.0, "side_length": 2.9379596545666087, "sides": 6, "type": "regular_polygon"}, "density": 0.8472470384096148, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -6.965076151420116e-06, "max_pair_overlap_depth": -7.201359447650546e-06, "n": 19, "ok": true, "record_id": "ae3850bdb0ac1880", "setup": "squinhex", "side": 2.9379596545666087, "solution_hash": "ae3850bdb0ac1880", "solution_path": "data/solutions/generated/squinhex_019_ae3850bdb0ac1880.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinhex@20", "container": {"circumradius": 3.1638559473298478, "orientation_radians": 0.0, "side_length": 3.1638559473298473, "sides": 6, "type": "regular_polygon"}, "density": 0.7690325218237841, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -2.697008230249216e-06, "max_pair_overlap_depth": -2.836652900617409e-05, "n": 20, "ok": true, "record_id": "79028917ac70723d", "setup": "squinhex", "side": 3.1638559473298473, "solution_hash": "79028917ac70723d", "solution_path": "data/solutions/generated/squinhex_020_79028917ac70723d.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinhex@21", "container": {"circumradius": 3.2382802143530665, "orientation_radians": 0.0, "side_length": 3.238280214353066, "sides": 6, "type": "regular_polygon"}, "density": 0.7707944086673769, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -3.4830527974218215e-06, "max_pair_overlap_depth": -2.662964935497389e-05, "n": 21, "ok": true, "record_id": "1d2ec517035658cd", "setup": "squinhex", "side": 3.238280214353066, "solution_hash": "1d2ec517035658cd", "solution_path": "data/solutions/generated/squinhex_21_1d2ec517035658cd.json", "tolerance": 1e-08, "warnings": []}
+{"case": "squinhex@21", "container": {"circumradius": 3.2382660883592127, "orientation_radians": 0.0, "side_length": 3.2382660883592123, "sides": 6, "type": "regular_polygon"}, "density": 0.7708011334148378, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -5.301769191883493e-06, "max_pair_overlap_depth": -1.6683459818422897e-05, "n": 21, "ok": true, "record_id": "3fb669c73e695ac9", "setup": "squinhex", "side": 3.2382660883592123, "solution_hash": "3fb669c73e695ac9", "solution_path": "data/solutions/generated/squinhex_21_3fb669c73e695ac9.json", "tolerance": 1e-08, "warnings": []}
+{"case": "squinhex@21", "container": {"circumradius": 3.236592068068801, "orientation_radians": 0.0, "side_length": 3.2365920680688007, "sides": 6, "type": "regular_polygon"}, "density": 0.7715986824430026, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -2.8602915252841952e-06, "max_pair_overlap_depth": -2.8463485488683382e-05, "n": 21, "ok": true, "record_id": "c6682411cb8007fa", "setup": "squinhex", "side": 3.2365920680688007, "solution_hash": "c6682411cb8007fa", "solution_path": "data/solutions/generated/squinhex_21_c6682411cb8007fa.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinhex@22", "container": {"circumradius": 3.3150640439651093, "orientation_radians": 0.0, "side_length": 3.315064043965109, "sides": 6, "type": "regular_polygon"}, "density": 0.770525380181529, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -2.169977234601665e-06, "max_pair_overlap_depth": -1.9814540655582746e-05, "n": 22, "ok": true, "record_id": "a1e7eaf12003fa2e", "setup": "squinhex", "side": 3.315064043965109, "solution_hash": "a1e7eaf12003fa2e", "solution_path": "data/solutions/generated/squinhex_022_a1e7eaf12003fa2e.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinhex@23", "container": {"circumradius": 3.3669876411014865, "orientation_radians": 0.0, "side_length": 3.366987641101486, "sides": 6, "type": "regular_polygon"}, "density": 0.7808954728618008, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -4.240294795076849e-06, "max_pair_overlap_depth": -2.4390771091731267e-07, "n": 23, "ok": true, "record_id": "de78b89055181fd4", "setup": "squinhex", "side": 3.366987641101486, "solution_hash": "de78b89055181fd4", "solution_path": "data/solutions/generated/squinhex_023_de78b89055181fd4.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinhex@24", "container": {"circumradius": 3.4186364158861364, "orientation_radians": 0.0, "side_length": 3.418636415886136, "sides": 6, "type": "regular_polygon"}, "density": 0.7904120022571139, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -3.0115328209217065e-06, "max_pair_overlap_depth": -2.5222031625055097e-05, "n": 24, "ok": true, "record_id": "73f1ceeaee97d32f", "setup": "squinhex", "side": 3.418636415886136, "solution_hash": "73f1ceeaee97d32f", "solution_path": "data/solutions/generated/squinhex_24_73f1ceeaee97d32f.json", "tolerance": 1e-08, "warnings": []}
@@ -484,7 +491,9 @@
 {"case": "squinhex@33", "container": {"circumradius": 3.892767355726244, "orientation_radians": 0.0, "side_length": 3.8927673557262437, "sides": 6, "type": "regular_polygon"}, "density": 0.8381951703957873, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -3.797125554432215e-06, "max_pair_overlap_depth": -8.18730119578337e-06, "n": 33, "ok": true, "record_id": "b14228e93eb45276", "setup": "squinhex", "side": 3.8927673557262437, "solution_hash": "b14228e93eb45276", "solution_path": "data/solutions/generated/squinhex_033_b14228e93eb45276.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinhex@34", "container": {"circumradius": 3.926817228886418, "orientation_radians": 0.0, "side_length": 3.9268172288864176, "sides": 6, "type": "regular_polygon"}, "density": 0.8486832973249016, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -5.30656742709778e-06, "max_pair_overlap_depth": -1.5057714820798651e-05, "n": 34, "ok": true, "record_id": "fc2f6f3b6cabd5ed", "setup": "squinhex", "side": 3.9268172288864176, "solution_hash": "fc2f6f3b6cabd5ed", "solution_path": "data/solutions/generated/squinhex_034_fc2f6f3b6cabd5ed.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinhex@35", "container": {"circumradius": 3.99755649437119, "orientation_radians": 0.0, "side_length": 3.9975564943711897, "sides": 6, "type": "regular_polygon"}, "density": 0.8429987640989463, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -3.597269939847931e-06, "max_pair_overlap_depth": -1.4652234902046146e-05, "n": 35, "ok": true, "record_id": "1ea058e93fb408a4", "setup": "squinhex", "side": 3.9975564943711897, "solution_hash": "1ea058e93fb408a4", "solution_path": "data/solutions/generated/squinhex_035_1ea058e93fb408a4.json", "tolerance": 1e-08, "warnings": []}
+{"case": "squinhex@36", "container": {"circumradius": 4.0298356750246205, "orientation_radians": 0.0, "side_length": 4.02983567502462, "sides": 6, "type": "regular_polygon"}, "density": 0.8532492984675044, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -2.1577223076817982e-06, "max_pair_overlap_depth": -9.723761702495892e-07, "n": 36, "ok": true, "record_id": "8da86e16a42a7ee1", "setup": "squinhex", "side": 4.02983567502462, "solution_hash": "8da86e16a42a7ee1", "solution_path": "data/solutions/generated/squinhex_36_8da86e16a42a7ee1.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinhex@36", "container": {"circumradius": 4.0299624719925, "orientation_radians": 0.0, "side_length": 4.029962471992499, "sides": 6, "type": "regular_polygon"}, "density": 0.8531956067904081, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -5.100230231840266e-07, "max_pair_overlap_depth": -2.2076071326537772e-07, "n": 36, "ok": true, "record_id": "b7083884dfb200c3", "setup": "squinhex", "side": 4.029962471992499, "solution_hash": "b7083884dfb200c3", "solution_path": "data/solutions/record_hunt/squinhex_36_b7083884dfb200c3.json", "tolerance": 1e-08, "warnings": []}
+{"case": "squinhex@36", "container": {"circumradius": 4.020625349363003, "orientation_radians": 0.0, "side_length": 4.020625349363002, "sides": 6, "type": "regular_polygon"}, "density": 0.8571629708269735, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -9.204501591489719e-07, "max_pair_overlap_depth": -4.634554187088469e-07, "n": 36, "ok": true, "record_id": "cbc24f56627bdbaa", "setup": "squinhex", "side": 4.020625349363002, "solution_hash": "cbc24f56627bdbaa", "solution_path": "data/solutions/generated/squinhex_36_cbc24f56627bdbaa.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinhex@37", "container": {"circumradius": 4.041527942684514, "orientation_radians": 0.0, "side_length": 4.041527942684513, "sides": 6, "type": "regular_polygon"}, "density": 0.8718839158050435, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -1.1637259667017477e-06, "max_pair_overlap_depth": -1.0162747484221413e-05, "n": 37, "ok": true, "record_id": "a455ecb05be301ad", "setup": "squinhex", "side": 4.041527942684513, "solution_hash": "a455ecb05be301ad", "solution_path": "data/solutions/generated/squinhex_037_a455ecb05be301ad.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinhex@38", "container": {"circumradius": 4.1841425436642465, "orientation_radians": 0.0, "side_length": 4.184142543664246, "sides": 6, "type": "regular_polygon"}, "density": 0.8354467372021385, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -4.3358638004937594e-07, "max_pair_overlap_depth": -2.4459335521420655e-06, "n": 38, "ok": true, "record_id": "657f5bc54656101d", "setup": "squinhex", "side": 4.184142543664246, "solution_hash": "657f5bc54656101d", "solution_path": "data/solutions/record_hunt/squinhex_38_657f5bc54656101d.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinhex@39", "container": {"circumradius": 4.259104243334675, "orientation_radians": 0.0, "side_length": 4.259104243334674, "sides": 6, "type": "regular_polygon"}, "density": 0.8275155837189719, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -3.204496689819836e-06, "max_pair_overlap_depth": -1.602842749781619e-05, "n": 39, "ok": true, "record_id": "85e7e9eb3b3b7f5f", "setup": "squinhex", "side": 4.259104243334674, "solution_hash": "85e7e9eb3b3b7f5f", "solution_path": "data/solutions/generated/squinhex_039_85e7e9eb3b3b7f5f.json", "tolerance": 1e-08, "warnings": []}
@@ -545,13 +554,20 @@
 {"case": "squinpen@24", "container": {"circumradius": 3.496826643745898, "orientation_radians": 0.0, "side_length": 4.110766262034449, "sides": 5, "type": "regular_polygon"}, "density": 0.8254992867774645, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -8.187233974203672e-07, "max_pair_overlap_depth": -1.4055675707780324e-06, "n": 24, "ok": true, "record_id": "7b6bed1452ec8f75", "setup": "squinpen", "side": 4.110766262034449, "solution_hash": "7b6bed1452ec8f75", "solution_path": "data/solutions/generated/squinpen_024_7b6bed1452ec8f75.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinpen@25", "container": {"circumradius": 3.549365855641956, "orientation_radians": 0.0, "side_length": 4.172529809873594, "sides": 5, "type": "regular_polygon"}, "density": 0.8346264431391957, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -4.8760801669609005e-06, "max_pair_overlap_depth": -9.22783607931743e-06, "n": 25, "ok": true, "record_id": "965f543dd3a1a5b2", "setup": "squinpen", "side": 4.172529809873594, "solution_hash": "965f543dd3a1a5b2", "solution_path": "data/solutions/generated/squinpen_025_965f543dd3a1a5b2.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinpen@26", "container": {"circumradius": 3.593713074674243, "orientation_radians": 0.0, "side_length": 4.224663092528319, "sides": 5, "type": "regular_polygon"}, "density": 0.846720772454187, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -5.329734777233707e-07, "max_pair_overlap_depth": -5.080948892621784e-06, "n": 26, "ok": true, "record_id": "12ea954c92ca25d9", "setup": "squinpen", "side": 4.224663092528319, "solution_hash": "12ea954c92ca25d9", "solution_path": "data/solutions/generated/squinpen_026_12ea954c92ca25d9.json", "tolerance": 1e-08, "warnings": []}
+{"case": "squinpen@27", "container": {"circumradius": 3.7023988728522115, "orientation_radians": 0.0, "side_length": 4.35243091113361, "sides": 5, "type": "regular_polygon"}, "density": 0.8284208480685643, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -5.563644238076049e-06, "max_pair_overlap_depth": -1.2401213729695826e-05, "n": 27, "ok": true, "record_id": "0b33929541015a68", "setup": "squinpen", "side": 4.35243091113361, "solution_hash": "0b33929541015a68", "solution_path": "data/solutions/generated/squinpen_27_0b33929541015a68.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinpen@27", "container": {"circumradius": 3.704305218022613, "orientation_radians": 0.0, "side_length": 4.354671954287492, "sides": 5, "type": "regular_polygon"}, "density": 0.8275684076653715, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -1.1174449550978842e-06, "max_pair_overlap_depth": -1.176344423625686e-05, "n": 27, "ok": true, "record_id": "fc7fa66fe1928440", "setup": "squinpen", "side": 4.354671954287492, "solution_hash": "fc7fa66fe1928440", "solution_path": "data/solutions/generated/squinpen_027_fc7fa66fe1928440.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinpen@28", "container": {"circumradius": 3.7605138871167676, "orientation_radians": 0.0, "side_length": 4.420749207776556, "sides": 5, "type": "regular_polygon"}, "density": 0.8327551046015365, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -3.3068707244667255e-06, "max_pair_overlap_depth": -1.2232567722092469e-05, "n": 28, "ok": true, "record_id": "81b95a9d0915b9b0", "setup": "squinpen", "side": 4.420749207776556, "solution_hash": "81b95a9d0915b9b0", "solution_path": "data/solutions/generated/squinpen_028_81b95a9d0915b9b0.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinpen@29", "container": {"circumradius": 3.827384161434449, "orientation_radians": 0.0, "side_length": 4.499359929897927, "sides": 5, "type": "regular_polygon"}, "density": 0.8326213695314967, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -3.900416840645271e-06, "max_pair_overlap_depth": -1.3857736228028994e-05, "n": 29, "ok": true, "record_id": "7cc5c6e51420a8c4", "setup": "squinpen", "side": 4.499359929897927, "solution_hash": "7cc5c6e51420a8c4", "solution_path": "data/solutions/generated/squinpen_029_7cc5c6e51420a8c4.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinpen@30", "container": {"circumradius": 3.880248035328735, "orientation_radians": 0.0, "side_length": 4.5615051408061476, "sides": 5, "type": "regular_polygon"}, "density": 0.8380230132738162, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -4.226407328203014e-06, "max_pair_overlap_depth": -5.655700288098586e-07, "n": 30, "ok": true, "record_id": "45dff6d0a270c6c5", "setup": "squinpen", "side": 4.5615051408061476, "solution_hash": "45dff6d0a270c6c5", "solution_path": "data/solutions/generated/squinpen_30_45dff6d0a270c6c5.json", "tolerance": 1e-08, "warnings": []}
+{"case": "squinpen@30", "container": {"circumradius": 3.8756674770107145, "orientation_radians": 0.0, "side_length": 4.556120371552951, "sides": 5, "type": "regular_polygon"}, "density": 0.8400050623992149, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -3.665422902102479e-06, "max_pair_overlap_depth": -2.26166097641034e-05, "n": 30, "ok": true, "record_id": "6d45a6352a0ed4b0", "setup": "squinpen", "side": 4.556120371552951, "solution_hash": "6d45a6352a0ed4b0", "solution_path": "data/solutions/generated/squinpen_30_6d45a6352a0ed4b0.json", "tolerance": 1e-08, "warnings": []}
+{"case": "squinpen@30", "container": {"circumradius": 3.8758519509947877, "orientation_radians": 0.0, "side_length": 4.556337233727491, "sides": 5, "type": "regular_polygon"}, "density": 0.8399251030020208, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -2.6577244583856583e-06, "max_pair_overlap_depth": -1.8093080493608582e-05, "n": 30, "ok": true, "record_id": "abcbdd03f9f27f35", "setup": "squinpen", "side": 4.556337233727491, "solution_hash": "abcbdd03f9f27f35", "solution_path": "data/solutions/generated/squinpen_30_abcbdd03f9f27f35.json", "tolerance": 1e-08, "warnings": []}
+{"case": "squinpen@30", "container": {"circumradius": 3.8715936028609312, "orientation_radians": 0.0, "side_length": 4.551331245263075, "sides": 5, "type": "regular_polygon"}, "density": 0.841773778692945, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -9.300402051962128e-07, "max_pair_overlap_depth": -1.6239474948775978e-05, "n": 30, "ok": true, "record_id": "c7e14ee67108e002", "setup": "squinpen", "side": 4.551331245263075, "solution_hash": "c7e14ee67108e002", "solution_path": "data/solutions/generated/squinpen_30_c7e14ee67108e002.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinpen@31", "container": {"circumradius": 3.9381000083820386, "orientation_radians": 0.0, "side_length": 4.629514213959654, "sides": 5, "type": "regular_polygon"}, "density": 0.8407016075258085, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -2.9662880539345523e-06, "max_pair_overlap_depth": -1.825266620247845e-05, "n": 31, "ok": true, "record_id": "8b17df7ad9586809", "setup": "squinpen", "side": 4.629514213959654, "solution_hash": "8b17df7ad9586809", "solution_path": "data/solutions/generated/squinpen_031_8b17df7ad9586809.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinpen@32", "container": {"circumradius": 4.005064513156432, "orientation_radians": 0.0, "side_length": 4.708235710626569, "sides": 5, "type": "regular_polygon"}, "density": 0.839043760254319, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -6.910425347385825e-07, "max_pair_overlap_depth": -1.0586072088480947e-05, "n": 32, "ok": true, "record_id": "ded24abc59c82646", "setup": "squinpen", "side": 4.708235710626569, "solution_hash": "ded24abc59c82646", "solution_path": "data/solutions/generated/squinpen_032_ded24abc59c82646.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinpen@33", "container": {"circumradius": 4.051766745121978, "orientation_radians": 0.0, "side_length": 4.763137477023549, "sides": 5, "type": "regular_polygon"}, "density": 0.8454321018371573, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -2.5906514265382727e-06, "max_pair_overlap_depth": -5.445984948337923e-06, "n": 33, "ok": true, "record_id": "a9622b0aeea26f74", "setup": "squinpen", "side": 4.763137477023549, "solution_hash": "a9622b0aeea26f74", "solution_path": "data/solutions/generated/squinpen_033_a9622b0aeea26f74.json", "tolerance": 1e-08, "warnings": []}
+{"case": "squinpen@33", "container": {"circumradius": 4.050370641067087, "orientation_radians": 0.0, "side_length": 4.761496258275288, "sides": 5, "type": "regular_polygon"}, "density": 0.8460150186653703, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -9.018172200219921e-07, "max_pair_overlap_depth": -7.073955850867009e-06, "n": 33, "ok": true, "record_id": "d93824a50e5c0a99", "setup": "squinpen", "side": 4.761496258275288, "solution_hash": "d93824a50e5c0a99", "solution_path": "data/solutions/generated/squinpen_33_d93824a50e5c0a99.json", "tolerance": 1e-08, "warnings": []}
+{"case": "squinpen@34", "container": {"circumradius": 4.107850546124187, "orientation_radians": 0.0, "side_length": 4.829067939266757, "sides": 5, "type": "regular_polygon"}, "density": 0.8474289841167177, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -3.4941000501213588e-06, "max_pair_overlap_depth": -2.3754649831841945e-05, "n": 34, "ok": true, "record_id": "7dafd61dbd636b00", "setup": "squinpen", "side": 4.829067939266757, "solution_hash": "7dafd61dbd636b00", "solution_path": "data/solutions/generated/squinpen_34_7dafd61dbd636b00.json", "tolerance": 1e-08, "warnings": []}
+{"case": "squinpen@34", "container": {"circumradius": 4.0983176143448405, "orientation_radians": 0.0, "side_length": 4.817861305844738, "sides": 5, "type": "regular_polygon"}, "density": 0.8513759101343428, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -3.6641444865908995e-06, "max_pair_overlap_depth": -7.393521151310978e-06, "n": 34, "ok": true, "record_id": "a3f4dd7d0b94e803", "setup": "squinpen", "side": 4.817861305844738, "solution_hash": "a3f4dd7d0b94e803", "solution_path": "data/solutions/generated/squinpen_34_a3f4dd7d0b94e803.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinpen@34", "container": {"circumradius": 4.109424198336639, "orientation_radians": 0.0, "side_length": 4.830917878392191, "sides": 5, "type": "regular_polygon"}, "density": 0.8467800838831615, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -9.414710391441419e-07, "max_pair_overlap_depth": -6.11976491438071e-06, "n": 34, "ok": true, "record_id": "d7af1c3ed90603fd", "setup": "squinpen", "side": 4.830917878392191, "solution_hash": "d7af1c3ed90603fd", "solution_path": "data/solutions/generated/squinpen_034_d7af1c3ed90603fd.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinpen@35", "container": {"circumradius": 4.142383397291435, "orientation_radians": 0.0, "side_length": 4.869663740538196, "sides": 5, "type": "regular_polygon"}, "density": 0.8578692979479161, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -8.74898699366526e-06, "max_pair_overlap_depth": -8.959642868955342e-06, "n": 35, "ok": true, "record_id": "d0212c88c498f951", "setup": "squinpen", "side": 4.869663740538196, "solution_hash": "d0212c88c498f951", "solution_path": "data/solutions/generated/squinpen_035_d0212c88c498f951.json", "tolerance": 1e-08, "warnings": []}
 {"case": "squinpen@36", "container": {"circumradius": 4.200125357495445, "orientation_radians": 0.0, "side_length": 4.937543485830948, "sides": 5, "type": "regular_polygon"}, "density": 0.8582852742974874, "errors": [], "item": {"circumradius": 0.7071067811865476, "side_length": 1.0, "sides": 4, "type": "regular_polygon"}, "max_boundary_excess": -8.258589189166597e-07, "max_pair_overlap_depth": -1.4614402910062552e-07, "n": 36, "ok": true, "record_id": "e43d96c031faf38c", "setup": "squinpen", "side": 4.937543485830948, "solution_hash": "e43d96c031faf38c", "solution_path": "data/solutions/record_hunt/squinpen_36_e43d96c031faf38c.json", "tolerance": 1e-08, "warnings": []}
@@ -669,6 +685,7 @@
 {"case": "triinhex@17", "container": {"circumradius": 1.8333812927758206, "orientation_radians": 0.0, "side_length": 1.8333812927758204, "sides": 6, "type": "regular_polygon"}, "density": 0.842931104392013, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -1.4990722513823532e-07, "max_pair_overlap_depth": -1.1854387088505725e-05, "n": 17, "ok": true, "record_id": "b8b9e4b4d61ec96c", "setup": "triinhex", "side": 1.8333812927758204, "solution_hash": "b8b9e4b4d61ec96c", "solution_path": "data/solutions/generated/triinhex_017_b8b9e4b4d61ec96c.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinhex@18", "container": {"circumradius": 1.8897873292238663, "orientation_radians": 0.0, "side_length": 1.889787329223866, "sides": 6, "type": "regular_polygon"}, "density": 0.8400311467465807, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -4.484924045151217e-06, "max_pair_overlap_depth": -8.796062168636709e-06, "n": 18, "ok": true, "record_id": "7671cfd644a7af24", "setup": "triinhex", "side": 1.889787329223866, "solution_hash": "7671cfd644a7af24", "solution_path": "data/solutions/generated/triinhex_018_7671cfd644a7af24.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinhex@19", "container": {"circumradius": 1.9552300191069654, "orientation_radians": 0.0, "side_length": 1.9552300191069651, "sides": 6, "type": "regular_polygon"}, "density": 0.8283361930438612, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -1.7079807782201595e-06, "max_pair_overlap_depth": -1.3478523960663846e-05, "n": 19, "ok": true, "record_id": "451018f1291a5791", "setup": "triinhex", "side": 1.9552300191069651, "solution_hash": "451018f1291a5791", "solution_path": "data/solutions/generated/triinhex_19_451018f1291a5791.json", "tolerance": 1e-08, "warnings": []}
+{"case": "triinhex@19", "container": {"circumradius": 1.954596799569544, "orientation_radians": 0.0, "side_length": 1.9545967995695437, "sides": 6, "type": "regular_polygon"}, "density": 0.828872982650555, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -2.527824635230551e-06, "max_pair_overlap_depth": -1.5640219825363566e-05, "n": 19, "ok": true, "record_id": "545ef4899aee40a3", "setup": "triinhex", "side": 1.9545967995695437, "solution_hash": "545ef4899aee40a3", "solution_path": "data/solutions/generated/triinhex_19_545ef4899aee40a3.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinhex@20", "container": {"circumradius": 1.9775009487133155, "orientation_radians": 0.0, "side_length": 1.9775009487133153, "sides": 6, "type": "regular_polygon"}, "density": 0.8524037354438128, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -3.7558573966506123e-06, "max_pair_overlap_depth": -5.2993150605473716e-06, "n": 20, "ok": true, "record_id": "388fc73ef451e99b", "setup": "triinhex", "side": 1.9775009487133153, "solution_hash": "388fc73ef451e99b", "solution_path": "data/solutions/generated/triinhex_020_388fc73ef451e99b.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinhex@21", "container": {"circumradius": 2.0000540227066215, "orientation_radians": 0.0, "side_length": 2.000054022706621, "sides": 6, "type": "regular_polygon"}, "density": 0.8749527320468723, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -8.545179480294009e-07, "max_pair_overlap_depth": -6.765642482919887e-06, "n": 21, "ok": true, "record_id": "96f74df50573bb81", "setup": "triinhex", "side": 2.000054022706621, "solution_hash": "96f74df50573bb81", "solution_path": "data/solutions/generated/triinhex_021_96f74df50573bb81.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinhex@22", "container": {"circumradius": 2.0000562934901334, "orientation_radians": 0.0, "side_length": 2.000056293490133, "sides": 6, "type": "regular_polygon"}, "density": 0.9166150664792877, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -4.91184500961419e-07, "max_pair_overlap_depth": -9.942352799940934e-07, "n": 22, "ok": true, "record_id": "38182a59461da74e", "setup": "triinhex", "side": 2.000056293490133, "solution_hash": "38182a59461da74e", "solution_path": "data/solutions/generated/triinhex_022_38182a59461da74e.json", "tolerance": 1e-08, "warnings": []}
@@ -738,6 +755,10 @@
 {"case": "triinpen@16", "container": {"circumradius": 1.8517557126631121, "orientation_radians": 0.0, "side_length": 2.1768693975034314, "sides": 5, "type": "regular_polygon"}, "density": 0.8497807683719915, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -2.337598971955443e-06, "max_pair_overlap_depth": -3.396060024770525e-05, "n": 16, "ok": true, "record_id": "852225bc33edeebe", "setup": "triinpen", "side": 2.1768693975034314, "solution_hash": "852225bc33edeebe", "solution_path": "data/solutions/generated/triinpen_016_852225bc33edeebe.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinpen@17", "container": {"circumradius": 1.9032661939510882, "orientation_radians": 0.0, "side_length": 2.237423599982551, "sides": 5, "type": "regular_polygon"}, "density": 0.8546812093159708, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -9.39992551681681e-07, "max_pair_overlap_depth": -1.7412872881594765e-05, "n": 17, "ok": true, "record_id": "a8618eee7fdaba2a", "setup": "triinpen", "side": 2.237423599982551, "solution_hash": "a8618eee7fdaba2a", "solution_path": "data/solutions/generated/triinpen_017_a8618eee7fdaba2a.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinpen@18", "container": {"circumradius": 1.9529861697880846, "orientation_radians": 0.0, "side_length": 2.2958729370652002, "sides": 5, "type": "regular_polygon"}, "density": 0.8594655455888001, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -1.4774387061990001e-05, "max_pair_overlap_depth": -2.9541451285197695e-08, "n": 18, "ok": true, "record_id": "6bf4f9b0915d39ee", "setup": "triinpen", "side": 2.2958729370652002, "solution_hash": "6bf4f9b0915d39ee", "solution_path": "data/solutions/generated/triinpen_018_6bf4f9b0915d39ee.json", "tolerance": 1e-08, "warnings": []}
+{"case": "triinpen@19", "container": {"circumradius": 1.994849109033647, "orientation_radians": 0.0, "side_length": 2.345085773677515, "sides": 5, "type": "regular_polygon"}, "density": 0.8695364674141102, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -4.742170658284962e-06, "max_pair_overlap_depth": -3.982018692783029e-06, "n": 19, "ok": true, "record_id": "16349db1062e3f6e", "setup": "triinpen", "side": 2.345085773677515, "solution_hash": "16349db1062e3f6e", "solution_path": "data/solutions/generated/triinpen_19_16349db1062e3f6e.json", "tolerance": 1e-08, "warnings": []}
+{"case": "triinpen@19", "container": {"circumradius": 1.996348109987661, "orientation_radians": 0.0, "side_length": 2.3468479549853987, "sides": 5, "type": "regular_polygon"}, "density": 0.8682311373154191, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -1.7569722225895958e-06, "max_pair_overlap_depth": -1.2055081872186513e-06, "n": 19, "ok": true, "record_id": "7110ea9122a5788e", "setup": "triinpen", "side": 2.3468479549853987, "solution_hash": "7110ea9122a5788e", "solution_path": "data/solutions/generated/triinpen_19_7110ea9122a5788e.json", "tolerance": 1e-08, "warnings": []}
+{"case": "triinpen@19", "container": {"circumradius": 1.9960191497081092, "orientation_radians": 0.0, "side_length": 2.3464612389835775, "sides": 5, "type": "regular_polygon"}, "density": 0.8685173440819363, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -1.6095450684584371e-06, "max_pair_overlap_depth": -1.2689748558725178e-05, "n": 19, "ok": true, "record_id": "875caebde6570989", "setup": "triinpen", "side": 2.3464612389835775, "solution_hash": "875caebde6570989", "solution_path": "data/solutions/generated/triinpen_19_875caebde6570989.json", "tolerance": 1e-08, "warnings": []}
+{"case": "triinpen@19", "container": {"circumradius": 1.9948244487823792, "orientation_radians": 0.0, "side_length": 2.345056783813489, "sides": 5, "type": "regular_polygon"}, "density": 0.8695579661683754, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -1.7918571290641098e-06, "max_pair_overlap_depth": -4.335928559529023e-07, "n": 19, "ok": true, "record_id": "e25d367759fc397e", "setup": "triinpen", "side": 2.345056783813489, "solution_hash": "e25d367759fc397e", "solution_path": "data/solutions/generated/triinpen_19_e25d367759fc397e.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinpen@19", "container": {"circumradius": 1.9965891518615606, "orientation_radians": 0.0, "side_length": 2.3471313167027246, "sides": 5, "type": "regular_polygon"}, "density": 0.868021512388566, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -2.9139572150349214e-06, "max_pair_overlap_depth": -1.0705368373109536e-05, "n": 19, "ok": true, "record_id": "eaa1430599d74148", "setup": "triinpen", "side": 2.3471313167027246, "solution_hash": "eaa1430599d74148", "solution_path": "data/solutions/generated/triinpen_19_eaa1430599d74148.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinpen@20", "container": {"circumradius": 2.071631162064863, "orientation_radians": 0.0, "side_length": 2.4353484905024896, "sides": 5, "type": "regular_polygon"}, "density": 0.8487102106795418, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -7.176183787084704e-07, "max_pair_overlap_depth": -8.807499014995557e-06, "n": 20, "ok": true, "record_id": "760faebc4d0b131b", "setup": "triinpen", "side": 2.4353484905024896, "solution_hash": "760faebc4d0b131b", "solution_path": "data/solutions/generated/triinpen_020_760faebc4d0b131b.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinpen@21", "container": {"circumradius": 2.1100378608614, "orientation_radians": 0.0, "side_length": 2.4804982727861766, "sides": 5, "type": "regular_polygon"}, "density": 0.8589998748063701, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -2.811024693767028e-06, "max_pair_overlap_depth": -2.8209410938284663e-06, "n": 21, "ok": true, "record_id": "115c20fad199fe9d", "setup": "triinpen", "side": 2.4804982727861766, "solution_hash": "115c20fad199fe9d", "solution_path": "data/solutions/generated/triinpen_021_115c20fad199fe9d.json", "tolerance": 1e-08, "warnings": []}
@@ -749,10 +770,12 @@
 {"case": "triinpen@27", "container": {"circumradius": 2.3979625778034013, "orientation_radians": 0.0, "side_length": 2.818974077564163, "sides": 5, "type": "regular_polygon"}, "density": 0.8551322064876743, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -5.642891580892597e-06, "max_pair_overlap_depth": -2.2253597504739986e-06, "n": 27, "ok": true, "record_id": "d6f1d3073209f163", "setup": "triinpen", "side": 2.818974077564163, "solution_hash": "d6f1d3073209f163", "solution_path": "data/solutions/generated/triinpen_027_d6f1d3073209f163.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinpen@28", "container": {"circumradius": 2.4410022778609815, "orientation_radians": 0.0, "side_length": 2.869570279478037, "sides": 5, "type": "regular_polygon"}, "density": 0.8558072548880046, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -4.305293369328324e-06, "max_pair_overlap_depth": -1.9072024115107666e-05, "n": 28, "ok": true, "record_id": "2caa877f5aa08139", "setup": "triinpen", "side": 2.869570279478037, "solution_hash": "2caa877f5aa08139", "solution_path": "data/solutions/generated/triinpen_028_2caa877f5aa08139.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinpen@29", "container": {"circumradius": 2.4720371232399, "orientation_radians": 0.0, "side_length": 2.906053928319848, "sides": 5, "type": "regular_polygon"}, "density": 0.8642558401713053, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -2.800701997238751e-06, "max_pair_overlap_depth": -5.0014115865471e-06, "n": 29, "ok": true, "record_id": "9730db96941e5b52", "setup": "triinpen", "side": 2.906053928319848, "solution_hash": "9730db96941e5b52", "solution_path": "data/solutions/generated/triinpen_29_9730db96941e5b52.json", "tolerance": 1e-08, "warnings": []}
+{"case": "triinpen@29", "container": {"circumradius": 2.471129197065864, "orientation_radians": 0.0, "side_length": 2.904986597089311, "sides": 5, "type": "regular_polygon"}, "density": 0.8648910353285495, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -1.1757076758929644e-06, "max_pair_overlap_depth": -9.047152447871909e-06, "n": 29, "ok": true, "record_id": "9da834ae740d1c15", "setup": "triinpen", "side": 2.904986597089311, "solution_hash": "9da834ae740d1c15", "solution_path": "data/solutions/generated/triinpen_29_9da834ae740d1c15.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinpen@30", "container": {"circumradius": 2.5114225358647224, "orientation_radians": 0.0, "side_length": 2.9523542577124973, "sides": 5, "type": "regular_polygon"}, "density": 0.8662355090431414, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -1.990812967166742e-06, "max_pair_overlap_depth": -2.800943013125945e-05, "n": 30, "ok": true, "record_id": "29e4e0e684891d8a", "setup": "triinpen", "side": 2.9523542577124973, "solution_hash": "29e4e0e684891d8a", "solution_path": "data/solutions/generated/triinpen_30_29e4e0e684891d8a.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinpen@31", "container": {"circumradius": 2.545376289474546, "orientation_radians": 0.0, "side_length": 2.9922692889761504, "sides": 5, "type": "regular_polygon"}, "density": 0.8713888671331285, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -2.7795814276238894e-06, "max_pair_overlap_depth": -1.3596177029562284e-05, "n": 31, "ok": true, "record_id": "44a0bb3f581e92e2", "setup": "triinpen", "side": 2.9922692889761504, "solution_hash": "44a0bb3f581e92e2", "solution_path": "data/solutions/generated/triinpen_031_44a0bb3f581e92e2.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinpen@32", "container": {"circumradius": 2.5761743553336647, "orientation_radians": 0.0, "side_length": 3.028474586798395, "sides": 5, "type": "regular_polygon"}, "density": 0.8781198099192385, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -3.877563686504985e-07, "max_pair_overlap_depth": -2.5172545809359903e-05, "n": 32, "ok": true, "record_id": "310badf403ba4fce", "setup": "triinpen", "side": 3.028474586798395, "solution_hash": "310badf403ba4fce", "solution_path": "data/solutions/generated/triinpen_032_310badf403ba4fce.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinpen@33", "container": {"circumradius": 2.618180839892074, "orientation_radians": 0.0, "side_length": 3.0778561710465637, "sides": 5, "type": "regular_polygon"}, "density": 0.8767362450469284, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -2.9579559668821387e-06, "max_pair_overlap_depth": -6.152141676318834e-06, "n": 33, "ok": true, "record_id": "2cf1b1f38810795d", "setup": "triinpen", "side": 3.0778561710465637, "solution_hash": "2cf1b1f38810795d", "solution_path": "data/solutions/generated/triinpen_033_2cf1b1f38810795d.json", "tolerance": 1e-08, "warnings": []}
+{"case": "triinpen@34", "container": {"circumradius": 2.6513814239288034, "orientation_radians": 0.0, "side_length": 3.1168857983751366, "sides": 5, "type": "regular_polygon"}, "density": 0.8808233124500154, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -1.228515372563353e-06, "max_pair_overlap_depth": -9.40092923262803e-06, "n": 34, "ok": true, "record_id": "6034a27a1d11d106", "setup": "triinpen", "side": 3.1168857983751366, "solution_hash": "6034a27a1d11d106", "solution_path": "data/solutions/generated/triinpen_34_6034a27a1d11d106.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinpen@34", "container": {"circumradius": 2.6518580305411943, "orientation_radians": 0.0, "side_length": 3.117446083050954, "sides": 5, "type": "regular_polygon"}, "density": 0.8805067280135348, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -3.4825467113644516e-07, "max_pair_overlap_depth": -8.773672566686486e-06, "n": 34, "ok": true, "record_id": "faff9872314d8b1a", "setup": "triinpen", "side": 3.117446083050954, "solution_hash": "faff9872314d8b1a", "solution_path": "data/solutions/generated/triinpen_34_faff9872314d8b1a.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinpen@35", "container": {"circumradius": 2.679818011764017, "orientation_radians": 0.0, "side_length": 3.150315012285253, "sides": 5, "type": "regular_polygon"}, "density": 0.8875886550862264, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -2.4152162741179605e-06, "max_pair_overlap_depth": -9.46789992128938e-06, "n": 35, "ok": true, "record_id": "8fe5da1df972c0b3", "setup": "triinpen", "side": 3.150315012285253, "solution_hash": "8fe5da1df972c0b3", "solution_path": "data/solutions/generated/triinpen_035_8fe5da1df972c0b3.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinpen@36", "container": {"circumradius": 2.7011924062745516, "orientation_radians": 0.0, "side_length": 3.1754421200252, "sides": 5, "type": "regular_polygon"}, "density": 0.8985572699958073, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -1.498547309348074e-07, "max_pair_overlap_depth": -2.3029919912209706e-06, "n": 36, "ok": true, "record_id": "5183a03ffc16bcf9", "setup": "triinpen", "side": 3.1754421200252, "solution_hash": "5183a03ffc16bcf9", "solution_path": "data/solutions/record_hunt/triinpen_36_5183a03ffc16bcf9.json", "tolerance": 1e-08, "warnings": []}
@@ -791,6 +814,7 @@
 {"case": "triinsqu@29", "container": {"circumradius": 2.6999496752049743, "orientation_radians": 0.0, "side_length": 3.818305448399707, "sides": 4, "type": "regular_polygon"}, "density": 0.8613056568479127, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -4.731563201531232e-06, "max_pair_overlap_depth": -2.352291984759891e-06, "n": 29, "ok": true, "record_id": "a02ae61c838755d7", "setup": "triinsqu", "side": 3.818305448399707, "solution_hash": "a02ae61c838755d7", "solution_path": "data/solutions/generated/triinsqu_029_a02ae61c838755d7.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinsqu@30", "container": {"circumradius": 2.7340349487368965, "orientation_radians": 0.0, "side_length": 3.8665093045057484, "sides": 4, "type": "regular_polygon"}, "density": 0.868927959047152, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -4.0741990212131443e-07, "max_pair_overlap_depth": -7.811820435188466e-06, "n": 30, "ok": true, "record_id": "d3cf7ea5ce255135", "setup": "triinsqu", "side": 3.8665093045057484, "solution_hash": "d3cf7ea5ce255135", "solution_path": "data/solutions/generated/triinsqu_030_d3cf7ea5ce255135.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinsqu@31", "container": {"circumradius": 2.7818510050522853, "orientation_radians": 0.0, "side_length": 3.934131419846167, "sides": 4, "type": "regular_polygon"}, "density": 0.8672905272682435, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -2.1286553127417914e-06, "max_pair_overlap_depth": -1.3206709677193729e-05, "n": 31, "ok": true, "record_id": "90f4b9b8010910a7", "setup": "triinsqu", "side": 3.934131419846167, "solution_hash": "90f4b9b8010910a7", "solution_path": "data/solutions/generated/triinsqu_031_90f4b9b8010910a7.json", "tolerance": 1e-08, "warnings": []}
+{"case": "triinsqu@32", "container": {"circumradius": 2.813776279002818, "orientation_radians": 0.0, "side_length": 3.979280575249487, "sides": 4, "type": "regular_polygon"}, "density": 0.8750673712051059, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -1.927630533637451e-06, "max_pair_overlap_depth": -1.4532438436631878e-05, "n": 32, "ok": true, "record_id": "300596cf09652b9a", "setup": "triinsqu", "side": 3.979280575249487, "solution_hash": "300596cf09652b9a", "solution_path": "data/solutions/generated/triinsqu_32_300596cf09652b9a.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinsqu@32", "container": {"circumradius": 2.8258720673212823, "orientation_radians": 0.0, "side_length": 3.996386603137053, "sides": 4, "type": "regular_polygon"}, "density": 0.8675921732131934, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -2.208596980261035e-06, "max_pair_overlap_depth": -2.3341135757526388e-06, "n": 32, "ok": true, "record_id": "f42801b713b9238d", "setup": "triinsqu", "side": 3.996386603137053, "solution_hash": "f42801b713b9238d", "solution_path": "data/solutions/generated/triinsqu_32_f42801b713b9238d.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinsqu@33", "container": {"circumradius": 2.8696820121015176, "orientation_radians": 0.0, "side_length": 4.058343221212078, "sides": 4, "type": "regular_polygon"}, "density": 0.8675949776849048, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -1.0747182587902822e-06, "max_pair_overlap_depth": -2.8024820216354662e-05, "n": 33, "ok": true, "record_id": "a6f49f2f24228d1b", "setup": "triinsqu", "side": 4.058343221212078, "solution_hash": "a6f49f2f24228d1b", "solution_path": "data/solutions/generated/triinsqu_33_a6f49f2f24228d1b.json", "tolerance": 1e-08, "warnings": []}
 {"case": "triinsqu@34", "container": {"circumradius": 2.897617160196922, "orientation_radians": 0.0, "side_length": 4.0978494865155, "sides": 4, "type": "regular_polygon"}, "density": 0.8767333914896571, "errors": [], "item": {"circumradius": 0.5773502691896258, "side_length": 1.0, "sides": 3, "type": "regular_polygon"}, "max_boundary_excess": -2.6262786795626285e-06, "max_pair_overlap_depth": -1.499292058504409e-05, "n": 34, "ok": true, "record_id": "61b4d5d6bf22a206", "setup": "triinsqu", "side": 4.0978494865155, "solution_hash": "61b4d5d6bf22a206", "solution_path": "data/solutions/generated/triinsqu_34_61b4d5d6bf22a206.json", "tolerance": 1e-08, "warnings": []}
diff --git a/data/friedman_references.jsonl b/data/friedman_references.jsonl
index d782bc1be9755cadcd1e508b245e5d667b12370c..190c7915406bf948750fdaf21a2311c1fc7983bb 100644
--- a/data/friedman_references.jsonl
+++ b/data/friedman_references.jsonl
@@ -1,842 +1,842 @@
-{"case": "triinsqu@1", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t1.gif", "id": "friedman-88198f6236e13dd4", "metric_expression": "(\u221a2+\u221a6)/4 = .965+", "metric_symbol": "s", "metric_value": 0.965, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (\u221a2+\u221a6)/4 = .965+ | Trivial.", "setup": "triinsqu", "side": 0.965, "source": "Erich Friedman Packing Center", "source_image": "t1.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@2", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t2.gif", "id": "friedman-06df28f275771178", "metric_expression": "\u221a6/2 = 1.224+", "metric_symbol": "s", "metric_value": 1.224, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a6/2 = 1.224+ | Trivial.", "setup": "triinsqu", "side": 1.224, "source": "Erich Friedman Packing Center", "source_image": "t2.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@3", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t3.gif", "id": "friedman-31fd9c05a6e4cd45", "metric_expression": "\u221a3/2+\u221a6/4 = 1.478+", "metric_symbol": "s", "metric_value": 1.478, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a3/2+\u221a6/4 = 1.478+ | Found by Erich Friedman | in 1996.", "setup": "triinsqu", "side": 1.478, "source": "Erich Friedman Packing Center", "source_image": "t3.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@4", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t4.gif", "id": "friedman-c6dea4eacbd98206", "metric_expression": "1+1/\u221a3 = 1.577+", "metric_symbol": "s", "metric_value": 1.577, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1+1/\u221a3 = 1.577+ | Found by Erich Friedman | in 1996.", "setup": "triinsqu", "side": 1.577, "source": "Erich Friedman Packing Center", "source_image": "t4.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@5", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t5.gif", "id": "friedman-a429941447ff4b85", "metric_expression": "1.803+", "metric_symbol": "s", "metric_value": 1.803, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.803+ | Found by Erich Friedman | in 1996.", "setup": "triinsqu", "side": 1.803, "source": "Erich Friedman Packing Center", "source_image": "t5.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@6", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t6.gif", "id": "friedman-57584e6cb4b7271e", "metric_expression": "9/2\u20133\u221a3/2 = 1.901+", "metric_symbol": "s", "metric_value": 1.901, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9/2\u20133\u221a3/2 = 1.901+ | Found by Erich Friedman | in 1996.", "setup": "triinsqu", "side": 1.901, "source": "Erich Friedman Packing Center", "source_image": "t6.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@7", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t7.gif", "id": "friedman-2a36fb6293e3f5fc", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Found by Erich Friedman | in 1996.", "setup": "triinsqu", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "t7.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@8", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t8.gif", "id": "friedman-b5af8f6f9326eed4", "metric_expression": "3\u221a3/2\u20131/2 = 2.098+", "metric_symbol": "s", "metric_value": 2.098, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3\u221a3/2\u20131/2 = 2.098+ | Found by Erich Friedman | in 1996.", "setup": "triinsqu", "side": 2.098, "source": "Erich Friedman Packing Center", "source_image": "t8.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@9", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t9.gif", "id": "friedman-ccb5c5c57055123b", "metric_expression": "2.287+", "metric_symbol": "s", "metric_value": 2.287, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.287+ | Found by Maurizio Morandi | in July 2008.", "setup": "triinsqu", "side": 2.287, "source": "Erich Friedman Packing Center", "source_image": "t9.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@10", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t10.gif", "id": "friedman-758d5f159bd2d072", "metric_expression": "2.377+", "metric_symbol": "s", "metric_value": 2.377, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.377+ | Found by David W. Cantrell | in July 2002.", "setup": "triinsqu", "side": 2.377, "source": "Erich Friedman Packing Center", "source_image": "t10.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@11", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t11.gif", "id": "friedman-858e61a41cc34891", "metric_expression": "2.490+", "metric_symbol": "s", "metric_value": 2.49, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.490+ | Found by Maurizio Morandi | in June 2008.", "setup": "triinsqu", "side": 2.49, "source": "Erich Friedman Packing Center", "source_image": "t11.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@12", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t12.gif", "id": "friedman-009ec6fef6d3e013", "metric_expression": "2.558+", "metric_symbol": "s", "metric_value": 2.558, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.558+ | Found by Dominik Kamp | in April 2026.", "setup": "triinsqu", "side": 2.558, "source": "Erich Friedman Packing Center", "source_image": "t12.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Dominik Kamp", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@13", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t13.gif", "id": "friedman-c3db3dd1637eb062", "metric_expression": "2.595+", "metric_symbol": "s", "metric_value": 2.595, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.595+ | Found by David W. Cantrell | in July 2002.", "setup": "triinsqu", "side": 2.595, "source": "Erich Friedman Packing Center", "source_image": "t13.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@14", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t14.gif", "id": "friedman-71db1e8bc5976aa4", "metric_expression": "2.726+", "metric_symbol": "s", "metric_value": 2.726, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.726+ | Found by David W. Cantrell | in July 2002.", "setup": "triinsqu", "side": 2.726, "source": "Erich Friedman Packing Center", "source_image": "t14.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@15", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t15.gif", "id": "friedman-935722e5b5532729", "metric_expression": "2.8299+", "metric_symbol": "s", "metric_value": 2.8299, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.8299+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 2.8299, "source": "Erich Friedman Packing Center", "source_image": "t15.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@16", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t16.gif", "id": "friedman-0efe6264aa836cbf", "metric_expression": "2.9000+", "metric_symbol": "s", "metric_value": 2.9, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.9000+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 2.9, "source": "Erich Friedman Packing Center", "source_image": "t16.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@17", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t17.gif", "id": "friedman-849f0e9c63c7a25a", "metric_expression": "2.982+", "metric_symbol": "s", "metric_value": 2.982, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.982+ | Found by Maurizio Morandi | in July 2008.", "setup": "triinsqu", "side": 2.982, "source": "Erich Friedman Packing Center", "source_image": "t17.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@18", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t18.gif", "id": "friedman-eb5d2ef9074e83ca", "metric_expression": "3.051+", "metric_symbol": "s", "metric_value": 3.051, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.051+ | Found by Maurizio Morandi | in July 2008.", "setup": "triinsqu", "side": 3.051, "source": "Erich Friedman Packing Center", "source_image": "t18.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@19", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t19.gif", "id": "friedman-31965c290ede1529", "metric_expression": "3.12930+", "metric_symbol": "s", "metric_value": 3.1293, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.12930+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 3.1293, "source": "Erich Friedman Packing Center", "source_image": "t19.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@20", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t20.gif", "id": "friedman-373ab4b3e6fed661", "metric_expression": "3.2305+", "metric_symbol": "s", "metric_value": 3.2305, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.2305+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 3.2305, "source": "Erich Friedman Packing Center", "source_image": "t20.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@21", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t21.gif", "id": "friedman-fb7783b749591f04", "metric_expression": "3.3111+", "metric_symbol": "s", "metric_value": 3.3111, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.3111+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 3.3111, "source": "Erich Friedman Packing Center", "source_image": "t21.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@22", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t22.gif", "id": "friedman-8d72959e42370da0", "metric_expression": "3.3757+", "metric_symbol": "s", "metric_value": 3.3757, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "22. | | s = 3.3757+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 3.3757, "source": "Erich Friedman Packing Center", "source_image": "t22.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@23", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t23.gif", "id": "friedman-ba92b60f8caa50c3", "metric_expression": "3.4311+", "metric_symbol": "s", "metric_value": 3.4311, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "23. | | s = 3.4311+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 3.4311, "source": "Erich Friedman Packing Center", "source_image": "t23.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@24", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t24.gif", "id": "friedman-24c98bf89d626646", "metric_expression": "3.468+", "metric_symbol": "s", "metric_value": 3.468, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "24. | | s = 3.468+ | Found by Maurizio Morandi | in August 2008.", "setup": "triinsqu", "side": 3.468, "source": "Erich Friedman Packing Center", "source_image": "t24.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@25", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t25.gif", "id": "friedman-03e709254cc5f7ae", "metric_expression": "3.537+", "metric_symbol": "s", "metric_value": 3.537, "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "25. | | s = 3.537+ | Found by David W. Cantrell | in August 2012.", "setup": "triinsqu", "side": 3.537, "source": "Erich Friedman Packing Center", "source_image": "t25.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@26", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t26.gif", "id": "friedman-85d1fd1f2e64c58e", "metric_expression": "3.575+", "metric_symbol": "s", "metric_value": 3.575, "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "26. | | s = 3.575+ | Found by Maurizio Morandi | in September 2008.", "setup": "triinsqu", "side": 3.575, "source": "Erich Friedman Packing Center", "source_image": "t26.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@27", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t27.gif", "id": "friedman-fe27f70a6f23b5b2", "metric_expression": "3.6726+", "metric_symbol": "s", "metric_value": 3.6726, "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "27. | | s = 3.6726+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 3.6726, "source": "Erich Friedman Packing Center", "source_image": "t27.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@28", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t28.gif", "id": "friedman-ed066d1905e1d8a1", "metric_expression": "3.7571+", "metric_symbol": "s", "metric_value": 3.7571, "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "28. | | s = 3.7571+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 3.7571, "source": "Erich Friedman Packing Center", "source_image": "t28.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@29", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t29.gif", "id": "friedman-5c3fb0901914dc35", "metric_expression": "3.818+", "metric_symbol": "s", "metric_value": 3.818, "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "29. | | s = 3.818+ | Found by Ignacio Vallejo | in April 2026.", "setup": "triinsqu", "side": 3.818, "source": "Erich Friedman Packing Center", "source_image": "t29.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@30", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t30.gif", "id": "friedman-5708973af114c7ec", "metric_expression": "3.8662+", "metric_symbol": "s", "metric_value": 3.8662, "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "30. | | s = 3.8662+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 3.8662, "source": "Erich Friedman Packing Center", "source_image": "t30.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@31", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t31.gif", "id": "friedman-514e8e63dccf54e9", "metric_expression": "3.936+", "metric_symbol": "s", "metric_value": 3.936, "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "31. | | s = 3.936+ | Found by Emerson Connelly | in April 2026.", "setup": "triinsqu", "side": 3.936, "source": "Erich Friedman Packing Center", "source_image": "t31.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@32", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t32.gif", "id": "friedman-1aa4833c34489e46", "metric_expression": "6\u20137\u221a3/6 = 3.979+", "metric_symbol": "s", "metric_value": 3.979, "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "32. | | s = 6\u20137\u221a3/6 = 3.979+ | Found by Maurizio Morandi | in May 2026.", "setup": "triinsqu", "side": 3.979, "source": "Erich Friedman Packing Center", "source_image": "t32.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@33", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t33.gif", "id": "friedman-944bd7cd98146437", "metric_expression": "4.058+", "metric_symbol": "s", "metric_value": 4.058, "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "33. | | s = 4.058+ | Found by Emerson Connelly | in April 2026.", "setup": "triinsqu", "side": 4.058, "source": "Erich Friedman Packing Center", "source_image": "t33.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@34", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t34.gif", "id": "friedman-dad38baedd24024a", "metric_expression": "4.098+", "metric_symbol": "s", "metric_value": 4.098, "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "34. | | s = 4.098+ | Found by Emerson Connelly | in April 2026.", "setup": "triinsqu", "side": 4.098, "source": "Erich Friedman Packing Center", "source_image": "t34.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@35", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t35.gif", "id": "friedman-33afe4505c0b2ed3", "metric_expression": "9(2\u221a3\u20133) = 4.176+", "metric_symbol": "s", "metric_value": 4.176, "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "35. | | s = 9(2\u221a3\u20133) = 4.176+ | Found by Erich Friedman | in April 2026.", "setup": "triinsqu", "side": 4.176, "source": "Erich Friedman Packing Center", "source_image": "t35.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@36", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t36.gif", "id": "friedman-e6a3d617dc0b1556", "metric_expression": "4.214+", "metric_symbol": "s", "metric_value": 4.214, "n": 36, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "36. | | s = 4.214+ | Found by Emerson Connelly | in April 2026.", "setup": "triinsqu", "side": 4.214, "source": "Erich Friedman Packing Center", "source_image": "t36.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@37", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t37.gif", "id": "friedman-62c58d2cb7e8e85c", "metric_expression": "4.27233+", "metric_symbol": "s", "metric_value": 4.27233, "n": 37, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "37. | | s = 4.27233+ | Found by Nathan Roll | in April 2026.", "setup": "triinsqu", "side": 4.27233, "source": "Erich Friedman Packing Center", "source_image": "t37.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@38", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t38.gif", "id": "friedman-fc030c65b5388c55", "metric_expression": "4.327+", "metric_symbol": "s", "metric_value": 4.327, "n": 38, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "38. | | s = 4.327+ | Found by Emerson Connelly | in April 2026.", "setup": "triinsqu", "side": 4.327, "source": "Erich Friedman Packing Center", "source_image": "t38.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@39", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t39.gif", "id": "friedman-ff9b6cccb4892504", "metric_expression": "4.383+", "metric_symbol": "s", "metric_value": 4.383, "n": 39, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "39. | | s = 4.383+ | Found by Emerson Connelly | in April 2026.", "setup": "triinsqu", "side": 4.383, "source": "Erich Friedman Packing Center", "source_image": "t39.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Squares", "verified": false}
-{"case": "triinsqu@40", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t40.gif", "id": "friedman-53a100f9bfd52ba3", "metric_expression": "4.437+", "metric_symbol": "s", "metric_value": 4.437, "n": 40, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "40. | | s = 4.437+ | Found by Emerson Connelly | in April 2026.", "setup": "triinsqu", "side": 4.437, "source": "Erich Friedman Packing Center", "source_image": "t40.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Squares", "verified": false}
-{"case": "cirinsqu@1", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs1.gif", "id": "friedman-def93353a238e00a", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial.", "setup": "cirinsqu", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "cs1.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@2", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs2.gif", "id": "friedman-2577c4d4ad595c1f", "metric_expression": "2 + \u221a2 = 3.414+", "metric_symbol": "s", "metric_value": 3.414, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + \u221a2 = 3.414+ | Trivial.", "setup": "cirinsqu", "side": 3.414, "source": "Erich Friedman Packing Center", "source_image": "cs2.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@3", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs3.gif", "id": "friedman-c6f8ea1fbc72f82f", "metric_expression": "2 + 1/\u221a2 + \u221a6/2 = 3.931+", "metric_symbol": "s", "metric_value": 3.931, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 1/\u221a2 + \u221a6/2 = 3.931+ | Trivial.", "setup": "cirinsqu", "side": 3.931, "source": "Erich Friedman Packing Center", "source_image": "cs3.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@4", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs4.gif", "id": "friedman-c4fc8f4c0a8c2885", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 | Trivial.", "setup": "cirinsqu", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "cs4.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@5", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs5.gif", "id": "friedman-b87b820b4449b1f3", "metric_expression": "2 + 2\u221a2 = 4.828+", "metric_symbol": "s", "metric_value": 4.828, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2\u221a2 = 4.828+ | Trivial.", "setup": "cirinsqu", "side": 4.828, "source": "Erich Friedman Packing Center", "source_image": "cs5.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@6", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs6.gif", "id": "friedman-9b0738e62698f43a", "metric_expression": "2 + 12/\u221a13 = 5.328+", "metric_symbol": "s", "metric_value": 5.328, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 12/\u221a13 = 5.328+ | Proved by Graham in 1963.", "setup": "cirinsqu", "side": 5.328, "source": "Erich Friedman Packing Center", "source_image": "cs6.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Graham", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@7", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs7.gif", "id": "friedman-94be4d00707d1c67", "metric_expression": "4 + \u221a3 = 5.732+", "metric_symbol": "s", "metric_value": 5.732, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + \u221a3 = 5.732+ | Proved by Schaer in 1964.", "setup": "cirinsqu", "side": 5.732, "source": "Erich Friedman Packing Center", "source_image": "cs7.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Schaer", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@8", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs8.gif", "id": "friedman-32eb1091270a5811", "metric_expression": "2 + \u221a2 + \u221a6 = 5.863+", "metric_symbol": "s", "metric_value": 5.863, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + \u221a2 + \u221a6 = 5.863+ | Proved by Schaer/Meir in 1964.", "setup": "cirinsqu", "side": 5.863, "source": "Erich Friedman Packing Center", "source_image": "cs8.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Schaer/Meir", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@9", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs9.gif", "id": "friedman-bcb79702a69e99e8", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 | Proved by Schaer in 1964.", "setup": "cirinsqu", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "cs9.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Schaer", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@10", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs10.gif", "id": "friedman-837b6988228c643c", "metric_expression": "6.747+", "metric_symbol": "s", "metric_value": 6.747, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.747+ | Proved by De Groot in 1990.", "setup": "cirinsqu", "side": 6.747, "source": "Erich Friedman Packing Center", "source_image": "cs10.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "De Groot", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@11", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs11.gif", "id": "friedman-20200084aeeb837c", "metric_expression": "7.022+", "metric_symbol": "s", "metric_value": 7.022, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.022+ | Proved by Peikert in 1991.", "setup": "cirinsqu", "side": 7.022, "source": "Erich Friedman Packing Center", "source_image": "cs11.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Peikert", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@12", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs12.gif", "id": "friedman-525876d01bcfd0e4", "metric_expression": "2 + 15\u221a(2/17) = 7.144+", "metric_symbol": "s", "metric_value": 7.144, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 15\u221a(2/17) = 7.144+ | Proved by Peikert in 1991.", "setup": "cirinsqu", "side": 7.144, "source": "Erich Friedman Packing Center", "source_image": "cs12.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Peikert", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@13", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs13.gif", "id": "friedman-77ed9e1517e08a6f", "metric_expression": "7.463+", "metric_symbol": "s", "metric_value": 7.463, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.463+ | Proved by Peikert in 1991.", "setup": "cirinsqu", "side": 7.463, "source": "Erich Friedman Packing Center", "source_image": "cs13.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Peikert", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@14", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs14.gif", "id": "friedman-aa513de257143957", "metric_expression": "6 + \u221a3 = 7.732+", "metric_symbol": "s", "metric_value": 7.732, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 + \u221a3 = 7.732+ | Proved by Wengerodt in 1987.", "setup": "cirinsqu", "side": 7.732, "source": "Erich Friedman Packing Center", "source_image": "cs14.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Wengerodt", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@15", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs15.gif", "id": "friedman-0190d4e8eff22c65", "metric_expression": "4 + \u221a2 + \u221a6 = 7.863+", "metric_symbol": "s", "metric_value": 7.863, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + \u221a2 + \u221a6 = 7.863+ | Proved by Peikert in 1991.", "setup": "cirinsqu", "side": 7.863, "source": "Erich Friedman Packing Center", "source_image": "cs15.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Peikert", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@16", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs16.gif", "id": "friedman-46edaf0a46fb32a6", "metric_expression": "8", "metric_symbol": "s", "metric_value": 8.0, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8 | Proved by Wengerodt in 1983.", "setup": "cirinsqu", "side": 8.0, "source": "Erich Friedman Packing Center", "source_image": "cs16.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Wengerodt", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@17", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs17.gif", "id": "friedman-432760f92509e0d3", "metric_expression": "8.532+", "metric_symbol": "s", "metric_value": 8.532, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8.532+ | Proved by Peikert in 1991.", "setup": "cirinsqu", "side": 8.532, "source": "Erich Friedman Packing Center", "source_image": "cs17.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Peikert", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@18", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs18.gif", "id": "friedman-43b7b2b61af81274", "metric_expression": "2 + 24/\u221a13 = 8.656+", "metric_symbol": "s", "metric_value": 8.656, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 24/\u221a13 = 8.656+ | Proved by Peikert in 1991.", "setup": "cirinsqu", "side": 8.656, "source": "Erich Friedman Packing Center", "source_image": "cs18.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Peikert", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@19", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs19.gif", "id": "friedman-af7b488e985635b9", "metric_expression": "8.907+", "metric_symbol": "s", "metric_value": 8.907, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8.907+ | Proved by Peikert in 1991.", "setup": "cirinsqu", "side": 8.907, "source": "Erich Friedman Packing Center", "source_image": "cs19.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Peikert", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@20", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs20.gif", "id": "friedman-ec1e84ac7c1bfe05", "metric_expression": "130/17 + 16/17\u221a2 = 8.978+", "metric_symbol": "s", "metric_value": 8.978, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 130/17 + 16/17\u221a2 = 8.978+ | Proved by Peikert in 1991.", "setup": "cirinsqu", "side": 8.978, "source": "Erich Friedman Packing Center", "source_image": "cs20.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Peikert", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@21", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs21.gif", "id": "friedman-8ab94bc573f7a3b9", "metric_expression": "9.358+", "metric_symbol": "s", "metric_value": 9.358, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9.358+", "setup": "cirinsqu", "side": 9.358, "source": "Erich Friedman Packing Center", "source_image": "cs21.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman Packing Center", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@22", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs22.gif", "id": "friedman-d77de0023d5029e8", "metric_expression": "9.463+", "metric_symbol": "s", "metric_value": 9.463, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9.463+", "setup": "cirinsqu", "side": 9.463, "source": "Erich Friedman Packing Center", "source_image": "cs22.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman Packing Center", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@23", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs23.gif", "id": "friedman-f3571e5edadf48f7", "metric_expression": "2 + 2\u221a2 + 2\u221a6 = 9.727+", "metric_symbol": "s", "metric_value": 9.727, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2\u221a2 + 2\u221a6 = 9.727+", "setup": "cirinsqu", "side": 9.727, "source": "Erich Friedman Packing Center", "source_image": "cs23.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman Packing Center", "title": "Circles in Squares", "verified": false}
-{"case": "cirinsqu@24", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs24.gif", "id": "friedman-8fc54b80b1eb3019", "metric_expression": "6 + \u221a2 + \u221a6 = 9.863+", "metric_symbol": "s", "metric_value": 9.863, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 + \u221a2 + \u221a6 = 9.863+", "setup": "cirinsqu", "side": 9.863, "source": "Erich Friedman Packing Center", "source_image": "cs24.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman Packing Center", "title": "Circles in Squares", "verified": false}
-{"case": "hexinsqu@1", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/1.png", "id": "friedman-f5d73e1fefe162fa", "metric_expression": "(1+\u221a3)/\u221a2 = 1.931+", "metric_symbol": "s", "metric_value": 1.931, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (1+\u221a3)/\u221a2 = 1.931+ | Trivial. |", "setup": "hexinsqu", "side": 1.931, "source": "Erich Friedman Packing Center", "source_image": "1.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@2", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/2.png", "id": "friedman-5c5e548626faab0c", "metric_expression": "(1+2\u221a3)/\u221a2 = 3.156+", "metric_symbol": "s", "metric_value": 3.156, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (1+2\u221a3)/\u221a2 = 3.156+ | Trivial. |", "setup": "hexinsqu", "side": 3.156, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@3", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/3.png", "id": "friedman-48d30c83b2cf34bc", "metric_expression": "9(6\u2013\u221a3)/11 = 3.491+", "metric_symbol": "s", "metric_value": 3.491, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9(6\u2013\u221a3)/11 = 3.491+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexinsqu", "side": 3.491, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@4", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/4.png", "id": "friedman-c26d1a7e2e23e0c3", "metric_expression": "(7\u2013\u221a3)/\u221a2 = 3.725+", "metric_symbol": "s", "metric_value": 3.725, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (7\u2013\u221a3)/\u221a2 = 3.725+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexinsqu", "side": 3.725, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@5", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/5.png", "id": "friedman-29964c51fb6474c3", "metric_expression": "7(3\u2013\u221a3)/2 = 4.437+", "metric_symbol": "s", "metric_value": 4.437, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7(3\u2013\u221a3)/2 = 4.437+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexinsqu", "side": 4.437, "source": "Erich Friedman Packing Center", "source_image": "5.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@6", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/6.png", "id": "friedman-d07a70f7b3cd945c", "metric_expression": "20(9\u20132\u221a3)/23 = 4.813+", "metric_symbol": "s", "metric_value": 4.813, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 20(9\u20132\u221a3)/23 = 4.813+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexinsqu", "side": 4.813, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@7", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/8.png", "id": "friedman-e2d3f1ba6a3361ff", "metric_expression": "3\u221a3 = 5.196+", "metric_symbol": "s", "metric_value": 5.196, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3\u221a3 = 5.196+ | Trivial. |", "setup": "hexinsqu", "side": 5.196, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@8", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/8.png", "id": "friedman-cccb6d2d687603dc", "metric_expression": "3\u221a3 = 5.196+", "metric_symbol": "s", "metric_value": 5.196, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3\u221a3 = 5.196+ | Trivial. |", "setup": "hexinsqu", "side": 5.196, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@9", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/9.png", "id": "friedman-ea6987c220904fbf", "metric_expression": "(13\u20133\u221a3)/\u221a2 = 5.518+", "metric_symbol": "s", "metric_value": 5.518, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (13\u20133\u221a3)/\u221a2 = 5.518+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexinsqu", "side": 5.518, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@10", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/10.png", "id": "friedman-99fc6b15e2732b48", "metric_expression": "6.10469+", "metric_symbol": "s", "metric_value": 6.10469, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.10469+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexinsqu", "side": 6.10469, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@11", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/11.png", "id": "friedman-97b3ee9066788a1b", "metric_expression": "6.33218+", "metric_symbol": "s", "metric_value": 6.33218, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.33218+ | Found by Maksymilian Jankowski | in April 2026.", "setup": "hexinsqu", "side": 6.33218, "source": "Erich Friedman Packing Center", "source_image": "11.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maksymilian Jankowski", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@12", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/12.png", "id": "friedman-adf2677ba7b86f45", "metric_expression": "43(5\u2013\u221a3)/22 = 6.387+", "metric_symbol": "s", "metric_value": 6.387, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 43(5\u2013\u221a3)/22 = 6.387+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexinsqu", "side": 6.387, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@13", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/13.png", "id": "friedman-004307193f41bfd8", "metric_expression": "6.75558+", "metric_symbol": "s", "metric_value": 6.75558, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.75558+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexinsqu", "side": 6.75558, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@14", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/14.png", "id": "friedman-41d4983f3cce24a4", "metric_expression": "4\u221a3 = 6.928+", "metric_symbol": "s", "metric_value": 6.928, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4\u221a3 = 6.928+ | Trivial. |", "setup": "hexinsqu", "side": 6.928, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@15", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/15.png", "id": "friedman-e63821cac755fbcb", "metric_expression": "6.96367+", "metric_symbol": "s", "metric_value": 6.96367, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.96367+ | Found by Maksymilian Jankowski | in April 2026.", "setup": "hexinsqu", "side": 6.96367, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maksymilian Jankowski", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@16", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/16.png", "id": "friedman-83804f1ad82568c2", "metric_expression": "(19\u20135\u221a3)/\u221a2 = 7.311+", "metric_symbol": "s", "metric_value": 7.311, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (19\u20135\u221a3)/\u221a2 = 7.311+ | Found by Maurizio Morandi | in April 2026.", "setup": "hexinsqu", "side": 7.311, "source": "Erich Friedman Packing Center", "source_image": "16.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@17", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/17.png", "id": "friedman-aeefaec5b0932867", "metric_expression": "6(3\u2013\u221a3) = 7.60383+", "metric_symbol": "s", "metric_value": 7.60383, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6(3\u2013\u221a3) = 7.60383+ | Found by Maksymilian Jankowski | in April 2026.", "setup": "hexinsqu", "side": 7.60383, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maksymilian Jankowski", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@18", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/18.png", "id": "friedman-276b5e5f0400948f", "metric_expression": "32(9\u20132\u221a3)/23 = 7.702+", "metric_symbol": "s", "metric_value": 7.702, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 32(9\u20132\u221a3)/23 = 7.702+ | Found by Maurizio Morandi | in April 2026.", "setup": "hexinsqu", "side": 7.702, "source": "Erich Friedman Packing Center", "source_image": "18.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@19", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/19.png", "id": "friedman-7f7f751877be8709", "metric_expression": "25(3\u2013\u221a3)/4 = 7.924+", "metric_symbol": "s", "metric_value": 7.924, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 25(3\u2013\u221a3)/4 = 7.924+ | Found by Maurizio Morandi | in April 2026.", "setup": "hexinsqu", "side": 7.924, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@20", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/20.png", "id": "friedman-40c54987415da7e2", "metric_expression": "74(21\u20134\u221a3)/131 = 7.948+", "metric_symbol": "s", "metric_value": 7.948, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 74(21\u20134\u221a3)/131 = 7.948+ | Found by Maurizio Morandi | in April 2026.", "setup": "hexinsqu", "side": 7.948, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@21", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/21.png", "id": "friedman-3017e53b816ffece", "metric_expression": "8.381+", "metric_symbol": "s", "metric_value": 8.381, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8.381+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexinsqu", "side": 8.381, "source": "Erich Friedman Packing Center", "source_image": "21.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@22", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/22.png", "id": "friedman-eca436d145a9afe3", "metric_expression": "8.568+", "metric_symbol": "s", "metric_value": 8.568, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8.568+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexinsqu", "side": 8.568, "source": "Erich Friedman Packing Center", "source_image": "22.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@23", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/23.png", "id": "friedman-17c04f47b1750509", "metric_expression": "5\u221a3 = 8.660+", "metric_symbol": "s", "metric_value": 8.66, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5\u221a3 = 8.660+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexinsqu", "side": 8.66, "source": "Erich Friedman Packing Center", "source_image": "23.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@24", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/24.png", "id": "friedman-ccd479c1f90061ad", "metric_expression": "8.795+", "metric_symbol": "s", "metric_value": 8.795, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8.795+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexinsqu", "side": 8.795, "source": "Erich Friedman Packing Center", "source_image": "24.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Squares", "verified": false}
-{"case": "hexinsqu@25", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/25.png", "id": "friedman-5d5c0dbd90a9eff3", "metric_expression": "30(4\u221a3\u20133)/13 = 9.065+", "metric_symbol": "s", "metric_value": 9.065, "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 30(4\u221a3\u20133)/13 = 9.065+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexinsqu", "side": 9.065, "source": "Erich Friedman Packing Center", "source_image": "25.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Squares", "verified": false}
-{"case": "triintri@1", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt1.gif", "id": "friedman-df9118b9ccce666c", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 | Trivial.", "setup": "triintri", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "tt1.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@2", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "id": "friedman-aeb1b4017d959f27", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial.", "setup": "triintri", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "tt4.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@3", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "id": "friedman-70245eceae59d461", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial.", "setup": "triintri", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "tt4.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@4", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "id": "friedman-6cfc39d4ac15d695", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial.", "setup": "triintri", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "tt4.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@5", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt5.gif", "id": "friedman-0cd646b14ce2224d", "metric_expression": "1 + \u221a3 = 2.732+", "metric_symbol": "s", "metric_value": 2.732, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 + \u221a3 = 2.732+ | Proved by Erich Friedman | in 1997.", "setup": "triintri", "side": 2.732, "source": "Erich Friedman Packing Center", "source_image": "tt5.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@6", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt6.gif", "id": "friedman-38e330068cdeabd2", "metric_expression": "13/8 + 3\u221a13/8 = 2.977+", "metric_symbol": "s", "metric_value": 2.977, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 13/8 + 3\u221a13/8 = 2.977+ | Found by Maurizio Morandi | in August 2008.", "setup": "triintri", "side": 2.977, "source": "Erich Friedman Packing Center", "source_image": "tt6.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@7", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "id": "friedman-ebae4a9ce826a102", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 | Trivial.", "setup": "triintri", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "tt9.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@8", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "id": "friedman-c4684b89b7d31333", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 | Trivial.", "setup": "triintri", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "tt9.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@9", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "id": "friedman-cf7a78a67aa913d1", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 | Trivial.", "setup": "triintri", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "tt9.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@10", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt10.gif", "id": "friedman-3b5caf5ce471af62", "metric_expression": "7/2 = 3.500", "metric_symbol": "s", "metric_value": 3.5, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7/2 = 3.500 | Found by Erich Friedman | in 1997.", "setup": "triintri", "side": 3.5, "source": "Erich Friedman Packing Center", "source_image": "tt10.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@11", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt11.gif", "id": "friedman-72b78146e2edb278", "metric_expression": "9/4 + 9\u221a21/28 = 3.722+", "metric_symbol": "s", "metric_value": 3.722, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9/4 + 9\u221a21/28 = 3.722+ | Found by Erich Friedman | in 1997.", "setup": "triintri", "side": 3.722, "source": "Erich Friedman Packing Center", "source_image": "tt11.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@12", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt12.gif", "id": "friedman-ed336fe52fc098ee", "metric_expression": "2 + 2cos(\u03c0/9) = 3.879+", "metric_symbol": "s", "metric_value": 3.879, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2cos(\u03c0/9) = 3.879+ | Found by David W. Cantrell | in July 2007.", "setup": "triintri", "side": 3.879, "source": "Erich Friedman Packing Center", "source_image": "tt12.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@13", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt13.gif", "id": "friedman-c55d5332fd60f0ac", "metric_expression": "3.992+", "metric_symbol": "s", "metric_value": 3.992, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.992+ | Found by Maurizio Morandi | in May 2008.", "setup": "triintri", "side": 3.992, "source": "Erich Friedman Packing Center", "source_image": "tt13.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@14", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "id": "friedman-8398fee140e7de98", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 | Trivial.", "setup": "triintri", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "tt16.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@15", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "id": "friedman-0195c1d43753e2d2", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 | Trivial.", "setup": "triintri", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "tt16.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@16", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "id": "friedman-71561fe6789fa8f2", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 | Trivial.", "setup": "triintri", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "tt16.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@17", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt17.gif", "id": "friedman-b6812065e1416baa", "metric_expression": "4.465+", "metric_symbol": "s", "metric_value": 4.465, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.465+ | Found by Maurizio Morandi | in May 2008.", "setup": "triintri", "side": 4.465, "source": "Erich Friedman Packing Center", "source_image": "tt17.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@18", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt18.gif", "id": "friedman-afd84e8a09b31318", "metric_expression": "9/2 = 4.500", "metric_symbol": "s", "metric_value": 4.5, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9/2 = 4.500 | Found by Erich Friedman | in 1997.", "setup": "triintri", "side": 4.5, "source": "Erich Friedman Packing Center", "source_image": "tt18.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@19", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt19.gif", "id": "friedman-71acd40380ab18c7", "metric_expression": "14/3 = 4.666+", "metric_symbol": "s", "metric_value": 4.666, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 14/3 = 4.666+ | Found by Maurizio Morandi | in May 2008.", "setup": "triintri", "side": 4.666, "source": "Erich Friedman Packing Center", "source_image": "tt19.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@20", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt20.gif", "id": "friedman-9261151818bd4b0a", "metric_expression": "33/8 + 9\u221a21/56 = 4.861+", "metric_symbol": "s", "metric_value": 4.861, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 33/8 + 9\u221a21/56 = 4.861+ | Found by Maurizio Morandi | in May 2008.", "setup": "triintri", "side": 4.861, "source": "Erich Friedman Packing Center", "source_image": "tt20.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@21", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt21.gif", "id": "friedman-43b248c0736fd708", "metric_expression": "4.923+", "metric_symbol": "s", "metric_value": 4.923, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.923+ | Found by Maurizio Morandi | in May 2008.", "setup": "triintri", "side": 4.923, "source": "Erich Friedman Packing Center", "source_image": "tt21.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@22", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt22.gif", "id": "friedman-0326e623c974e74a", "metric_expression": "4.996+", "metric_symbol": "s", "metric_value": 4.996, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.996+ | Found by Maurizio Morandi | in May 2008.", "setup": "triintri", "side": 4.996, "source": "Erich Friedman Packing Center", "source_image": "tt22.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@23", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "id": "friedman-447f26a1694a5fdd", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 | Trivial.", "setup": "triintri", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "tt25.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@24", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "id": "friedman-e542a08e580fdd3b", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 | Trivial.", "setup": "triintri", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "tt25.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@25", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "id": "friedman-d0073c77591ecec5", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 | Trivial.", "setup": "triintri", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "tt25.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@26", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt26.gif", "id": "friedman-b01b5221d0b238b6", "metric_expression": "5.406+", "metric_symbol": "s", "metric_value": 5.406, "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.406+ | Found by Joah Frenzley | in April 2026.", "setup": "triintri", "side": 5.406, "source": "Erich Friedman Packing Center", "source_image": "tt26.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Joah Frenzley", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@27", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "id": "friedman-c48c26640c20c9ca", "metric_expression": "11/2 = 5.500", "metric_symbol": "s", "metric_value": 5.5, "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "setup": "triintri", "side": 5.5, "source": "Erich Friedman Packing Center", "source_image": "tt28.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@28", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "id": "friedman-a654e61cacbbccd0", "metric_expression": "11/2 = 5.500", "metric_symbol": "s", "metric_value": 5.5, "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "setup": "triintri", "side": 5.5, "source": "Erich Friedman Packing Center", "source_image": "tt28.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@29", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt29.gif", "id": "friedman-0ff7372c7f0d0888", "metric_expression": "17/3 = 5.666+", "metric_symbol": "s", "metric_value": 5.666, "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 17/3 = 5.666+ | Found by David W. Cantrell | in July 2007.", "setup": "triintri", "side": 5.666, "source": "Erich Friedman Packing Center", "source_image": "tt29.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@30", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt30.gif", "id": "friedman-d5cadbd3315d9655", "metric_expression": "23/4 = 5.75", "metric_symbol": "s", "metric_value": 5.75, "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 23/4 = 5.75 | Found by Maurizio Morandi | in May 2008.", "setup": "triintri", "side": 5.75, "source": "Erich Friedman Packing Center", "source_image": "tt30.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@31", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt31.gif", "id": "friedman-01e5a2753e5c4735", "metric_expression": "5.912+", "metric_symbol": "s", "metric_value": 5.912, "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.912+ | Found by Emerson Connelly | in April 2026.", "setup": "triintri", "side": 5.912, "source": "Erich Friedman Packing Center", "source_image": "tt31.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@32", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt32.gif", "id": "friedman-0723c1b8737cc63b", "metric_expression": "5.951+", "metric_symbol": "s", "metric_value": 5.951, "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.951+ | Found by Ian Watson | in April 2026.", "setup": "triintri", "side": 5.951, "source": "Erich Friedman Packing Center", "source_image": "tt32.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@33", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "id": "friedman-2699908b012979d3", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 | Trivial. |", "setup": "triintri", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "tt36.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@34", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "id": "friedman-19fda9ea1c5069a7", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 | Trivial. |", "setup": "triintri", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "tt36.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@35", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "id": "friedman-163373bf6faa360a", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 | Trivial. |", "setup": "triintri", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "tt36.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@36", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "id": "friedman-160790c3f0b88d1e", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "n": 36, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 | Trivial. |", "setup": "triintri", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "tt36.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@37", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt37.gif", "id": "friedman-330694f3b2089601", "metric_expression": "19/3 = 6.333+", "metric_symbol": "s", "metric_value": 6.333, "n": 37, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 19/3 = 6.333+ | Found by Ian Watson | in April 2026.", "setup": "triintri", "side": 6.333, "source": "Erich Friedman Packing Center", "source_image": "tt37.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@38", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt38.gif", "id": "friedman-e2f6e745c3600f48", "metric_expression": "6.43454+", "metric_symbol": "s", "metric_value": 6.43454, "n": 38, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.43454+ | Found by Nathan Roll | in April 2026.", "setup": "triintri", "side": 6.43454, "source": "Erich Friedman Packing Center", "source_image": "tt38.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@39", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "id": "friedman-f82a2ad7a2b315df", "metric_expression": "13/2 = 6.500", "metric_symbol": "s", "metric_value": 6.5, "n": 39, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "setup": "triintri", "side": 6.5, "source": "Erich Friedman Packing Center", "source_image": "tt40.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Triangles", "verified": false}
-{"case": "triintri@40", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "id": "friedman-e625023bbb4da161", "metric_expression": "13/2 = 6.500", "metric_symbol": "s", "metric_value": 6.5, "n": 40, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "setup": "triintri", "side": 6.5, "source": "Erich Friedman Packing Center", "source_image": "tt40.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Triangles", "verified": false}
-{"case": "cirintri@1", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct1.gif", "id": "friedman-373b9d175918f2f2", "metric_expression": "2\u221a3 = 3.464+", "metric_symbol": "s", "metric_value": 3.464, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2\u221a3 = 3.464+ | Trivial.", "setup": "cirintri", "side": 3.464, "source": "Erich Friedman Packing Center", "source_image": "ct1.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Triangles", "verified": false}
-{"case": "cirintri@2", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct2.gif", "id": "friedman-a959ebb8ed72c7f9", "metric_expression": "2 + 2\u221a3 = 5.464+", "metric_symbol": "s", "metric_value": 5.464, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "setup": "cirintri", "side": 5.464, "source": "Erich Friedman Packing Center", "source_image": "ct2.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Triangles", "verified": false}
-{"case": "cirintri@3", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct3.gif", "id": "friedman-5656e051b375fc79", "metric_expression": "2 + 2\u221a3 = 5.464+", "metric_symbol": "s", "metric_value": 5.464, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "setup": "cirintri", "side": 5.464, "source": "Erich Friedman Packing Center", "source_image": "ct3.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Triangles", "verified": false}
-{"case": "cirintri@4", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct4.gif", "id": "friedman-f06ce12bcc053a39", "metric_expression": "4\u221a3 = 6.928+", "metric_symbol": "s", "metric_value": 6.928, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4\u221a3 = 6.928+ | Proved by Milano in 1987.", "setup": "cirintri", "side": 6.928, "source": "Erich Friedman Packing Center", "source_image": "ct4.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Milano", "title": "Circles in Triangles", "verified": false}
-{"case": "cirintri@5", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct5.gif", "id": "friedman-c5729987156f796f", "metric_expression": "4 + 2\u221a3 = 7.464+", "metric_symbol": "s", "metric_value": 7.464, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 2\u221a3 = 7.464+ | Proved by Milano in 1987.", "setup": "cirintri", "side": 7.464, "source": "Erich Friedman Packing Center", "source_image": "ct5.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Milano", "title": "Circles in Triangles", "verified": false}
-{"case": "cirintri@6", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct6.gif", "id": "friedman-b12c4f677ba23a05", "metric_expression": "4 + 2\u221a3 = 7.464+", "metric_symbol": "s", "metric_value": 7.464, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 2\u221a3 = 7.464+ | Proved by Oler/Groemer in 1961.", "setup": "cirintri", "side": 7.464, "source": "Erich Friedman Packing Center", "source_image": "ct6.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Oler/Groemer", "title": "Circles in Triangles", "verified": false}
-{"case": "cirintri@7", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct7.gif", "id": "friedman-c351a5cd42557637", "metric_expression": "2 + 4\u221a3 = 8.928+", "metric_symbol": "s", "metric_value": 8.928, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 4\u221a3 = 8.928+ | Proved by Melissen in 1993.", "setup": "cirintri", "side": 8.928, "source": "Erich Friedman Packing Center", "source_image": "ct7.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Melissen", "title": "Circles in Triangles", "verified": false}
-{"case": "cirintri@8", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct8.gif", "id": "friedman-60415c15b1866700", "metric_expression": "2 + 2\u221a3 + 2\u221a33/3 = 9.293+", "metric_symbol": "s", "metric_value": 9.293, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2\u221a3 + 2\u221a33/3 = 9.293+ | Proved by Melissen in 1993.", "setup": "cirintri", "side": 9.293, "source": "Erich Friedman Packing Center", "source_image": "ct8.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Melissen", "title": "Circles in Triangles", "verified": false}
-{"case": "cirintri@9", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct9.gif", "id": "friedman-fce705cb36658c35", "metric_expression": "6 + 2\u221a3 = 9.464+", "metric_symbol": "s", "metric_value": 9.464, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 + 2\u221a3 = 9.464+ | Proved by Melissen in 1993.", "setup": "cirintri", "side": 9.464, "source": "Erich Friedman Packing Center", "source_image": "ct9.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Melissen", "title": "Circles in Triangles", "verified": false}
-{"case": "cirintri@10", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct10.gif", "id": "friedman-5bc55f6e87d3e02b", "metric_expression": "6 + 2\u221a3 = 9.464+", "metric_symbol": "s", "metric_value": 9.464, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 + 2\u221a3 = 9.464+ | Proved by Oler/Groemer in 1961.", "setup": "cirintri", "side": 9.464, "source": "Erich Friedman Packing Center", "source_image": "ct10.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Oler/Groemer", "title": "Circles in Triangles", "verified": false}
-{"case": "cirintri@11", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct11.gif", "id": "friedman-7e84067fe449704a", "metric_expression": "4 + 2\u221a3 + 4\u221a6/3 = 10.730+", "metric_symbol": "s", "metric_value": 10.73, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 2\u221a3 + 4\u221a6/3 = 10.730+ | Proved by Melissen in 1993.", "setup": "cirintri", "side": 10.73, "source": "Erich Friedman Packing Center", "source_image": "ct11.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Melissen", "title": "Circles in Triangles", "verified": false}
-{"case": "cirintri@12", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct12.gif", "id": "friedman-0a283852fe1098a4", "metric_expression": "4 + 4\u221a3 = 10.928+", "metric_symbol": "s", "metric_value": 10.928, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 4\u221a3 = 10.928+ | Proved by Melissen in 1994.", "setup": "cirintri", "side": 10.928, "source": "Erich Friedman Packing Center", "source_image": "ct12.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Melissen", "title": "Circles in Triangles", "verified": false}
-{"case": "cirintri@13", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct13.gif", "id": "friedman-13ddd5fef6e95420", "metric_expression": "4 + 2\u221a6/3 + 10\u221a3/3 = 11.406+", "metric_symbol": "s", "metric_value": 11.406, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 2\u221a6/3 + 10\u221a3/3 = 11.406+ | Found by Melissen in 1993.", "setup": "cirintri", "side": 11.406, "source": "Erich Friedman Packing Center", "source_image": "ct13.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Melissen", "title": "Circles in Triangles", "verified": false}
-{"case": "cirintri@14", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct14.gif", "id": "friedman-93af76ed87316ae0", "metric_expression": "8 + 2\u221a3 = 11.464+", "metric_symbol": "s", "metric_value": 11.464, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8 + 2\u221a3 = 11.464+ | Found by Erd\u0151s/Oler in 1961.", "setup": "cirintri", "side": 11.464, "source": "Erich Friedman Packing Center", "source_image": "ct14.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Erd\u0151s/Oler", "title": "Circles in Triangles", "verified": false}
-{"case": "cirintri@15", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct15.gif", "id": "friedman-04c5e2fe2e9c9fd4", "metric_expression": "8 + 2\u221a3 = 11.464+", "metric_symbol": "s", "metric_value": 11.464, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8 + 2\u221a3 = 11.464+ | Proved by Erd\u0151s/Groemer in 1961.", "setup": "cirintri", "side": 11.464, "source": "Erich Friedman Packing Center", "source_image": "ct15.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Erd\u0151s/Groemer", "title": "Circles in Triangles", "verified": false}
-{"case": "squintri@1", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts1.gif", "id": "friedman-252bd3d74dba4cb7", "metric_expression": "1 + 2 / \u221a3 = 2.154+", "metric_symbol": "s", "metric_value": 2.154, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 + 2 / \u221a3 = 2.154+ | Trivial.", "setup": "squintri", "side": 2.154, "source": "Erich Friedman Packing Center", "source_image": "ts1.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@2", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts2.gif", "id": "friedman-fe76c6578fd87ee5", "metric_expression": "2 + 2 / \u221a3 = 3.154+", "metric_symbol": "s", "metric_value": 3.154, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2 / \u221a3 = 3.154+ | Trivial.", "setup": "squintri", "side": 3.154, "source": "Erich Friedman Packing Center", "source_image": "ts2.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@3", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts3.gif", "id": "friedman-e13c02a1c322601b", "metric_expression": "3 / 2 + \u221a3 = 3.232+", "metric_symbol": "s", "metric_value": 3.232, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 / 2 + \u221a3 = 3.232+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 3.232, "source": "Erich Friedman Packing Center", "source_image": "ts3.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@4", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts4.gif", "id": "friedman-2cf44f3dd3edf72d", "metric_expression": "3 + 2 / \u221a3 = 4.154+", "metric_symbol": "s", "metric_value": 4.154, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 + 2 / \u221a3 = 4.154+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 4.154, "source": "Erich Friedman Packing Center", "source_image": "ts4.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@5", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts6.gif", "id": "friedman-3e74e575e12c12f9", "metric_expression": "2 + 4 / \u221a3 = 4.309+", "metric_symbol": "s", "metric_value": 4.309, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 4 / \u221a3 = 4.309+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 4.309, "source": "Erich Friedman Packing Center", "source_image": "ts6.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@6", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts6.gif", "id": "friedman-0c1dc53a7025f255", "metric_expression": "2 + 4 / \u221a3 = 4.309+", "metric_symbol": "s", "metric_value": 4.309, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 4 / \u221a3 = 4.309+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 4.309, "source": "Erich Friedman Packing Center", "source_image": "ts6.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@7", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts7.gif", "id": "friedman-24fd1e5bd65f4ad8", "metric_expression": "4 + 2 / \u221a3 = 5.154+", "metric_symbol": "s", "metric_value": 5.154, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 2 / \u221a3 = 5.154+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 5.154, "source": "Erich Friedman Packing Center", "source_image": "ts7.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@8", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts8.gif", "id": "friedman-58de376746beeb9a", "metric_expression": "5.301+", "metric_symbol": "s", "metric_value": 5.301, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.301+ | Found by David W. Cantrell | in July 2002.", "setup": "squintri", "side": 5.301, "source": "Erich Friedman Packing Center", "source_image": "ts8.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@9", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts9.gif", "id": "friedman-b485f09747e7e5c6", "metric_expression": "3 + 4 / \u221a3 = 5.309+", "metric_symbol": "s", "metric_value": 5.309, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 + 4 / \u221a3 = 5.309+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 5.309, "source": "Erich Friedman Packing Center", "source_image": "ts9.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@10", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts10.gif", "id": "friedman-c6dc14a24cd917ac", "metric_expression": "2 + 2 \u221a3 = 5.464+", "metric_symbol": "s", "metric_value": 5.464, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2 \u221a3 = 5.464+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 5.464, "source": "Erich Friedman Packing Center", "source_image": "ts10.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@11", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts11.gif", "id": "friedman-6209c847fa1f31ae", "metric_expression": "5 + 2 / \u221a3 = 6.154+", "metric_symbol": "s", "metric_value": 6.154, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 + 2 / \u221a3 = 6.154+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 6.154, "source": "Erich Friedman Packing Center", "source_image": "ts11.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@12", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts12.gif", "id": "friedman-2043aa54c7c9a732", "metric_expression": "6.301+", "metric_symbol": "s", "metric_value": 6.301, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.301+ | Found by David W. Cantrell | in July 2002.", "setup": "squintri", "side": 6.301, "source": "Erich Friedman Packing Center", "source_image": "ts12.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@13", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts13.gif", "id": "friedman-4b945aba75ec065e", "metric_expression": "4 + 4 / \u221a3 = 6.309+", "metric_symbol": "s", "metric_value": 6.309, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 4 / \u221a3 = 6.309+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 6.309, "source": "Erich Friedman Packing Center", "source_image": "ts13.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@14", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts15.gif", "id": "friedman-e1fe8a5a00d4d3a9", "metric_expression": "3 + 2 \u221a3 = 6.464+", "metric_symbol": "s", "metric_value": 6.464, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 + 2 \u221a3 = 6.464+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 6.464, "source": "Erich Friedman Packing Center", "source_image": "ts15.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@15", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts15.gif", "id": "friedman-5e450eea66553cab", "metric_expression": "3 + 2 \u221a3 = 6.464+", "metric_symbol": "s", "metric_value": 6.464, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 + 2 \u221a3 = 6.464+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 6.464, "source": "Erich Friedman Packing Center", "source_image": "ts15.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@16", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts16.gif", "id": "friedman-b5af71c140885928", "metric_expression": "6 + 2 / \u221a3 = 7.154+", "metric_symbol": "s", "metric_value": 7.154, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 + 2 / \u221a3 = 7.154+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 7.154, "source": "Erich Friedman Packing Center", "source_image": "ts16.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@17", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts17.gif", "id": "friedman-83f30539d05ff1ea", "metric_expression": "7.301+", "metric_symbol": "s", "metric_value": 7.301, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.301+ | Found by David W. Cantrell | in July 2002.", "setup": "squintri", "side": 7.301, "source": "Erich Friedman Packing Center", "source_image": "ts17.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@18", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts18.gif", "id": "friedman-f306cfcbae8a7f8e", "metric_expression": "5 + 4 / \u221a3 = 7.309+", "metric_symbol": "s", "metric_value": 7.309, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 + 4 / \u221a3 = 7.309+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 7.309, "source": "Erich Friedman Packing Center", "source_image": "ts18.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@19", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts19.gif", "id": "friedman-e19f0be0f2dc8df2", "metric_expression": "4 + 2 \u221a3 = 7.464+", "metric_symbol": "s", "metric_value": 7.464, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 2 \u221a3 = 7.464+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 7.464, "source": "Erich Friedman Packing Center", "source_image": "ts19.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@20", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "id": "friedman-3d64213c7a5836f5", "metric_expression": "3 + 8 / \u221a3 = 7.618+", "metric_symbol": "s", "metric_value": 7.618, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 7.618, "source": "Erich Friedman Packing Center", "source_image": "ts21.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@21", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "id": "friedman-f8ef85a53da23bd0", "metric_expression": "3 + 8 / \u221a3 = 7.618+", "metric_symbol": "s", "metric_value": 7.618, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 7.618, "source": "Erich Friedman Packing Center", "source_image": "ts21.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@22", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts22.gif", "id": "friedman-242218d9342fa48e", "metric_expression": "7 + 2 / \u221a3 = 8.154+", "metric_symbol": "s", "metric_value": 8.154, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7 + 2 / \u221a3 = 8.154+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 8.154, "source": "Erich Friedman Packing Center", "source_image": "ts22.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@23", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts23.gif", "id": "friedman-3befb4edaec3c6b2", "metric_expression": "8.301+", "metric_symbol": "s", "metric_value": 8.301, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8.301+ | Found by David W. Cantrell | in July 2002.", "setup": "squintri", "side": 8.301, "source": "Erich Friedman Packing Center", "source_image": "ts23.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@24", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts24.gif", "id": "friedman-bd7d307154faf055", "metric_expression": "6 + 4 / \u221a3 = 8.309+", "metric_symbol": "s", "metric_value": 8.309, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 + 4 / \u221a3 = 8.309+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 8.309, "source": "Erich Friedman Packing Center", "source_image": "ts24.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@25", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts25.gif", "id": "friedman-0b6595cd97166f90", "metric_expression": "5 + 2 \u221a3 = 8.464+", "metric_symbol": "s", "metric_value": 8.464, "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 + 2 \u221a3 = 8.464+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 8.464, "source": "Erich Friedman Packing Center", "source_image": "ts25.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@26", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "id": "friedman-a6bf8a53768051a7", "metric_expression": "4 + 8 / \u221a3 = 8.618+", "metric_symbol": "s", "metric_value": 8.618, "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 8.618, "source": "Erich Friedman Packing Center", "source_image": "ts27.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@27", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "id": "friedman-5917db90a1b78e6a", "metric_expression": "4 + 8 / \u221a3 = 8.618+", "metric_symbol": "s", "metric_value": 8.618, "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 8.618, "source": "Erich Friedman Packing Center", "source_image": "ts27.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@28", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts28.gif", "id": "friedman-4b96aad075724908", "metric_expression": "3 + 10 / \u221a3 = 8.773+", "metric_symbol": "s", "metric_value": 8.773, "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 + 10 / \u221a3 = 8.773+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 8.773, "source": "Erich Friedman Packing Center", "source_image": "ts28.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@29", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts29.gif", "id": "friedman-7ee971f1094bebb8", "metric_expression": "8 + 2 / \u221a3 = 9.154+", "metric_symbol": "s", "metric_value": 9.154, "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8 + 2 / \u221a3 = 9.154+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 9.154, "source": "Erich Friedman Packing Center", "source_image": "ts29.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@30", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts30.gif", "id": "friedman-75a268a52b7b18d2", "metric_expression": "9.301+", "metric_symbol": "s", "metric_value": 9.301, "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9.301+ | Found by David W. Cantrell | in July 2002.", "setup": "squintri", "side": 9.301, "source": "Erich Friedman Packing Center", "source_image": "ts30.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@31", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts31.gif", "id": "friedman-3c1a52eb3bb8d2bb", "metric_expression": "7 + 4 / \u221a3 = 9.309+", "metric_symbol": "s", "metric_value": 9.309, "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7 + 4 / \u221a3 = 9.309+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 9.309, "source": "Erich Friedman Packing Center", "source_image": "ts31.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@32", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts32.gif", "id": "friedman-f6d4517fe4e9ed0e", "metric_expression": "6 + 2 \u221a3 = 9.464+", "metric_symbol": "s", "metric_value": 9.464, "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 + 2 \u221a3 = 9.464+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 9.464, "source": "Erich Friedman Packing Center", "source_image": "ts32.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@33", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "id": "friedman-8a42501b6cf579b5", "metric_expression": "5 + 8 / \u221a3 = 9.618+", "metric_symbol": "s", "metric_value": 9.618, "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 9.618, "source": "Erich Friedman Packing Center", "source_image": "ts34.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@34", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "id": "friedman-b52bb6f382575b48", "metric_expression": "5 + 8 / \u221a3 = 9.618+", "metric_symbol": "s", "metric_value": 9.618, "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 9.618, "source": "Erich Friedman Packing Center", "source_image": "ts34.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@35", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "id": "friedman-57a8cb93a77e91d4", "metric_expression": "4 + 10 / \u221a3 = 9.773+", "metric_symbol": "s", "metric_value": 9.773, "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 9.773, "source": "Erich Friedman Packing Center", "source_image": "ts36.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@36", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "id": "friedman-4994eda0bbf77702", "metric_expression": "4 + 10 / \u221a3 = 9.773+", "metric_symbol": "s", "metric_value": 9.773, "n": 36, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 9.773, "source": "Erich Friedman Packing Center", "source_image": "ts36.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@37", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts37.gif", "id": "friedman-e715f0132930826c", "metric_expression": "10.154+", "metric_symbol": "s", "metric_value": 10.154, "n": 37, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 10.154+ | Found by Emerson Connelly | in April 2026.", "setup": "squintri", "side": 10.154, "source": "Erich Friedman Packing Center", "source_image": "ts37.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@38", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts38.gif", "id": "friedman-7bcee7c16e556bd5", "metric_expression": "10.309+", "metric_symbol": "s", "metric_value": 10.309, "n": 38, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 10.309+ | Found by Emerson Connelly | in April 2026.", "setup": "squintri", "side": 10.309, "source": "Erich Friedman Packing Center", "source_image": "ts38.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@39", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts39.gif", "id": "friedman-df36f7577447ec3d", "metric_expression": "10.310+", "metric_symbol": "s", "metric_value": 10.31, "n": 39, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 10.310+ | Found by Emerson Connelly | in April 2026.", "setup": "squintri", "side": 10.31, "source": "Erich Friedman Packing Center", "source_image": "ts39.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Triangles", "verified": false}
-{"case": "squintri@40", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts40.gif", "id": "friedman-5711f10b48735b21", "metric_expression": "10.46426+", "metric_symbol": "s", "metric_value": 10.46426, "n": 40, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 10.46426+ | Found by Nathan Roll | in April 2026.", "setup": "squintri", "side": 10.46426, "source": "Erich Friedman Packing Center", "source_image": "ts40.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Squares in Triangles", "verified": false}
-{"case": "hexintri@1", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/1.gif", "id": "friedman-1aafd6d3b9d56f10", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 | Trivial.", "setup": "hexintri", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@2", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "id": "friedman-6de94aa5c70c1d66", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 | Trivial.", "setup": "hexintri", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@3", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "id": "friedman-6120335c9c51cee6", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 | Trivial.", "setup": "hexintri", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@4", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/4.gif", "id": "friedman-138e781034e01a76", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 | Trivial.", "setup": "hexintri", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@5", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/5.gif", "id": "friedman-ed187d080d03acd0", "metric_expression": "5(1+\u221a3)/2 = 6.8301+", "metric_symbol": "s", "metric_value": 6.8301, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5(1+\u221a3)/2 = 6.8301+ | Found by Maurizio Morandi | in April 2015.", "setup": "hexintri", "side": 6.8301, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@6", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/6.gif", "id": "friedman-b1c9c240f6559f22", "metric_expression": "2(1+\u221a6) = 6.89897+", "metric_symbol": "s", "metric_value": 6.89897, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2(1+\u221a6) = 6.89897+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexintri", "side": 6.89897, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@7", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/7.gif", "id": "friedman-29a6dc59323a9611", "metric_expression": "8", "metric_symbol": "s", "metric_value": 8.0, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8 | Trivial. |", "setup": "hexintri", "side": 8.0, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@8", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/8.gif", "id": "friedman-7b09f11b760f0fc7", "metric_expression": "25/3 = 8.3333+", "metric_symbol": "s", "metric_value": 8.3333, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 25/3 = 8.3333+ | Found by Erich Friedman | in April 2015.", "setup": "hexintri", "side": 8.3333, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@9", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/10.gif", "id": "friedman-00ecad6b4501c825", "metric_expression": "5\u221a3 = 8.6602+", "metric_symbol": "s", "metric_value": 8.6602, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5\u221a3 = 8.6602+ | Trivial. |", "setup": "hexintri", "side": 8.6602, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@10", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/10.gif", "id": "friedman-c49e6b68a9f1f880", "metric_expression": "5\u221a3 = 8.6602+", "metric_symbol": "s", "metric_value": 8.6602, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5\u221a3 = 8.6602+ | Trivial. |", "setup": "hexintri", "side": 8.6602, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@11", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/11.gif", "id": "friedman-e0d55b3ab8be7571", "metric_expression": "9.54823+", "metric_symbol": "s", "metric_value": 9.54823, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9.54823+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexintri", "side": 9.54823, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@12", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/12.gif", "id": "friedman-999280a4c324d258", "metric_expression": "10", "metric_symbol": "s", "metric_value": 10.0, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 10 | Trivial. |", "setup": "hexintri", "side": 10.0, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@13", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "id": "friedman-ed5c141d4256363a", "metric_expression": "6\u221a3 = 10.3923+", "metric_symbol": "s", "metric_value": 10.3923, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "setup": "hexintri", "side": 10.3923, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@14", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "id": "friedman-d3b2202bbf8b650f", "metric_expression": "6\u221a3 = 10.3923+", "metric_symbol": "s", "metric_value": 10.3923, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "setup": "hexintri", "side": 10.3923, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@15", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "id": "friedman-1a13545718e93d73", "metric_expression": "6\u221a3 = 10.3923+", "metric_symbol": "s", "metric_value": 10.3923, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "setup": "hexintri", "side": 10.3923, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@16", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/16.gif", "id": "friedman-0943623f6ed7001f", "metric_expression": "11.36599+", "metric_symbol": "s", "metric_value": 11.36599, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 11.36599+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexintri", "side": 11.36599, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@17", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/17.gif", "id": "friedman-1d735af9489b44cb", "metric_expression": "11.63457+", "metric_symbol": "s", "metric_value": 11.63457, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 11.63457+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexintri", "side": 11.63457, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@18", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "id": "friedman-907d6855ada30327", "metric_expression": "12", "metric_symbol": "s", "metric_value": 12.0, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 12 | Trivial. |", "setup": "hexintri", "side": 12.0, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@19", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "id": "friedman-4ee9a5df05ced0ef", "metric_expression": "12", "metric_symbol": "s", "metric_value": 12.0, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 12 | Trivial. |", "setup": "hexintri", "side": 12.0, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@20", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "id": "friedman-4084fe628f219c86", "metric_expression": "7\u221a3 = 12.1243+", "metric_symbol": "s", "metric_value": 12.1243, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "setup": "hexintri", "side": 12.1243, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
-{"case": "hexintri@21", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "id": "friedman-85cc61ddf2bd9f7a", "metric_expression": "7\u221a3 = 12.1243+", "metric_symbol": "s", "metric_value": 12.1243, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "setup": "hexintri", "side": 12.1243, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
-{"case": "triincir@1", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc1.gif", "id": "friedman-bee5966c0befdafd", "metric_expression": "1/\u221a3 = .577+", "metric_symbol": "r", "metric_value": 0.577, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1/\u221a3 = .577+ | Trivial.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc1.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@2", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc2.gif", "id": "friedman-4d6984dddc7f791b", "metric_expression": "\u221a3/2 = .866+", "metric_symbol": "r", "metric_value": 0.866, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a3/2 = .866+ | Trivial.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc2.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@3", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc3.gif", "id": "friedman-ce49d5f28e5c0e43", "metric_expression": "3\u221a3 - 3\u221a2 = .953+", "metric_symbol": "r", "metric_value": 0.953, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3\u221a3 - 3\u221a2 = .953+ | Found by Erich Friedman | in 1997.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc3.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@4", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc4.gif", "id": "friedman-44542e32bbf59f07", "metric_expression": ".980+", "metric_symbol": "r", "metric_value": 0.98, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = .980+ | Found by Erich Friedman | in 1997.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc4.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@5", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc5.gif", "id": "friedman-76722ed16e528e08", "metric_expression": "1", "metric_symbol": "r", "metric_value": 1.0, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1 | Trivial.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc5.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@6", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc6.gif", "id": "friedman-a685fb07bbba025a", "metric_expression": "1", "metric_symbol": "r", "metric_value": 1.0, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1 | Trivial.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc6.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@7", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc7.gif", "id": "friedman-a34a6123847bdb93", "metric_expression": "1.152+", "metric_symbol": "r", "metric_value": 1.152, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.152+ | Found by Erich Friedman | in 1997.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc7.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@8", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc8.gif", "id": "friedman-3aeb5ecbe4b569a8", "metric_expression": "1.263+", "metric_symbol": "r", "metric_value": 1.263, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.263+ | Found by Maurizio Morandi | in April 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc8.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@9", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc9.gif", "id": "friedman-4e4a46b1cf98b4af", "metric_expression": "1.314+", "metric_symbol": "r", "metric_value": 1.314, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.314+ | Found by David W. Cantrell | in July 2002.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc9.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@10", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc10.gif", "id": "friedman-5c2676f2d6cd1814", "metric_expression": "1.385+", "metric_symbol": "r", "metric_value": 1.385, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.385+ | Found by David W. Cantrell | in July 2002.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc10.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@11", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc11.gif", "id": "friedman-b5ac4dbd01d673af", "metric_expression": "1.466+", "metric_symbol": "r", "metric_value": 1.466, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.466+ | Found by DC after MM | in August 2012.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc11.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell after Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@12", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc12.gif", "id": "friedman-5ffcd0ec27882e30", "metric_expression": "1.507+", "metric_symbol": "r", "metric_value": 1.507, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.507+ | Found by David W. Cantrell | in October 2005.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc12.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@13", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc13.gif", "id": "friedman-2c79a2e843091421", "metric_expression": "\u221a(7/3) = 1.527+", "metric_symbol": "r", "metric_value": 1.527, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a(7/3) = 1.527+ | Found by Erich Friedman | in 1997.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc13.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@14", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc14.gif", "id": "friedman-3142158c9944d32b", "metric_expression": "1.609+", "metric_symbol": "r", "metric_value": 1.609, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.609+ | Found by DC after MM | in August 2012.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc14.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell after Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@15", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc15.gif", "id": "friedman-cd323abc0be756c7", "metric_expression": "1.636+", "metric_symbol": "r", "metric_value": 1.636, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.636+ | Found by David W. Cantrell | in July 2002.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc15.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@16", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc16.gif", "id": "friedman-f633ad5d6e281a55", "metric_expression": "1.687+", "metric_symbol": "r", "metric_value": 1.687, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.687+ | Found by Maurizio Morandi | in April 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc16.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@17", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc17.gif", "id": "friedman-39a25d3dcd24ac29", "metric_expression": "1.730+", "metric_symbol": "r", "metric_value": 1.73, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.730+ | Found by David W. Cantrell | in July 2005.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc17.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@18", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc18.gif", "id": "friedman-4cac381fafba2e73", "metric_expression": "\u221a13/2 = 1.802+", "metric_symbol": "r", "metric_value": 1.802, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a13/2 = 1.802+ | Found by Erich Friedman | in 1997.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc18.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@19", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc19.gif", "id": "friedman-09240ee047e9b02e", "metric_expression": "\u221a(10/3) = 1.825+", "metric_symbol": "r", "metric_value": 1.825, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a(10/3) = 1.825+ | Found by Haym Hirsh | in August 2019.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc19.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Haym Hirsh", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@20", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc20.gif", "id": "friedman-11894bd2ae50e21d", "metric_expression": "1.874+", "metric_symbol": "r", "metric_value": 1.874, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.874+ | Found by Erich Friedman | in 1997.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc20.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@21", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc21.gif", "id": "friedman-2c6cdef8b7760ab2", "metric_expression": "1.910+", "metric_symbol": "r", "metric_value": 1.91, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.910+ | Found by Maurizio Morandi | in May 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc21.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@22", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc22.gif", "id": "friedman-c4d8c6a51fc99d06", "metric_expression": "1.943+", "metric_symbol": "r", "metric_value": 1.943, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.943+ | Found by Maurizio Morandi | in June 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc22.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@23", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc23.gif", "id": "friedman-5971a993b0db6da9", "metric_expression": "1.988+", "metric_symbol": "r", "metric_value": 1.988, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.988+ | Found by Maurizio Morandi | in June 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc23.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@24", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc24.gif", "id": "friedman-50aba5c38741ed94", "metric_expression": "2", "metric_symbol": "r", "metric_value": 2.0, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2 | Trivial.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc24.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@25", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc25.gif", "id": "friedman-3687974ed51eedf3", "metric_expression": "2.055+", "metric_symbol": "r", "metric_value": 2.055, "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.055+ | Found by David W. Cantrell | in July 2005.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc25.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@26", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc26.gif", "id": "friedman-a6793ae8c3171099", "metric_expression": "2.109+", "metric_symbol": "r", "metric_value": 2.109, "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.109+ | Found by Maurizio Morandi | in April 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc26.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@27", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc27.gif", "id": "friedman-fe685ce08e30ecac", "metric_expression": "2.138+", "metric_symbol": "r", "metric_value": 2.138, "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.138+ | Found by David W. Cantrell | in July 2005.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc27.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@28", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc28.gif", "id": "friedman-daf0f91a5db8d01c", "metric_expression": "2.191+", "metric_symbol": "r", "metric_value": 2.191, "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.191+ | Found by David W. Cantrell | in July 2005.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc28.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@29", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc29.gif", "id": "friedman-91e468ecae8e00df", "metric_expression": "2.215+", "metric_symbol": "r", "metric_value": 2.215, "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.215+ | Found by Maurizio Morandi | in June 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc29.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@30", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc30.gif", "id": "friedman-1d8fd1d8acfcc649", "metric_expression": "2.258+", "metric_symbol": "r", "metric_value": 2.258, "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.258+ | Found by Maurizio Morandi | in July 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc30.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
-{"case": "triincir@31", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc31.gif", "id": "friedman-3151b3ff6842a945", "metric_expression": "2.272+", "metric_symbol": "r", "metric_value": 2.272, "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.272+ | Found by Maurizio Morandi | in July 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc31.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
-{"case": "cirincir@1", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc1.gif", "id": "friedman-a9224170994c2db7", "metric_expression": "1", "metric_symbol": "r", "metric_value": 1.0, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1 | Trivial.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc1.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@2", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc2.gif", "id": "friedman-d0526dd85e67bcc5", "metric_expression": "2", "metric_symbol": "r", "metric_value": 2.0, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2 | Trivial.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc2.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@3", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc3.gif", "id": "friedman-8a18e25e4448bdf6", "metric_expression": "1 + 2 / \u221a3 = 2.154+", "metric_symbol": "r", "metric_value": 2.154, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1 + 2 / \u221a3 = 2.154+ | Trivial.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc3.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@4", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc4.gif", "id": "friedman-1f89ac0d8425a177", "metric_expression": "1 + \u221a2 = 2.414+", "metric_symbol": "r", "metric_value": 2.414, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1 + \u221a2 = 2.414+ | Trivial.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc4.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@5", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc5.gif", "id": "friedman-77e9a21fe2dbf0ec", "metric_expression": "2.701+", "metric_symbol": "r", "metric_value": 2.701, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.701+ | Proved by Graham in 1968.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc5.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Graham", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@6", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc6.gif", "id": "friedman-c22f64ca3a4b2997", "metric_expression": "3", "metric_symbol": "r", "metric_value": 3.0, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3 | Proved by Graham in 1968.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc6.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Graham", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@7", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc7.gif", "id": "friedman-ebd074e73c455d00", "metric_expression": "3", "metric_symbol": "r", "metric_value": 3.0, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3 | Proved by Graham in 1968.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc7.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Graham", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@8", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc8.gif", "id": "friedman-64038cce97e05aac", "metric_expression": "3.304+", "metric_symbol": "r", "metric_value": 3.304, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.304+ | Proved by Braaksma in 1963.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc8.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Braaksma", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@9", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc9.gif", "id": "friedman-ce6041f680ff2644", "metric_expression": "3.613+", "metric_symbol": "r", "metric_value": 3.613, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.613+ | Proved by Pirl in 1969.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc9.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Pirl", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@10", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc10.gif", "id": "friedman-248f9c5d338e3645", "metric_expression": "3.813+", "metric_symbol": "r", "metric_value": 3.813, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.813+ | Proved by Pirl in 1969.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc10.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Pirl", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@11", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc11.gif", "id": "friedman-68c8f3aded0a06cc", "metric_expression": "3.923+", "metric_symbol": "r", "metric_value": 3.923, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.923+ | Proved by Melissen in 1994.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc11.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Melissen", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@12", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc12.gif", "id": "friedman-7754f3598b4ae15f", "metric_expression": "4.029+", "metric_symbol": "r", "metric_value": 4.029, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.029+ | Found by Kravitz in 1967.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc12.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Kravitz", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@13", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc13.gif", "id": "friedman-c43ded19f288094a", "metric_expression": "2 + \u221a5 = 4.236+", "metric_symbol": "r", "metric_value": 4.236, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2 + \u221a5 = 4.236+ | Proved by F. Fodor in 2003.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc13.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "F. Fodor", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@14", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc14.gif", "id": "friedman-6c3aaffa9b755646", "metric_expression": "4.328+", "metric_symbol": "r", "metric_value": 4.328, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.328+ | Found by Goldberg in 1971.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc14.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Goldberg", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@15", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc15.gif", "id": "friedman-e2482d27b978ed53", "metric_expression": "4.521+", "metric_symbol": "r", "metric_value": 4.521, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.521+ | Found by Kravitz in 1967.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc15.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Kravitz", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@16", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc16.gif", "id": "friedman-c9d37cb5558adc7c", "metric_expression": "4.615+", "metric_symbol": "r", "metric_value": 4.615, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.615+ | Found by Goldberg in 1971.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc16.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Goldberg", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@17", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc17.gif", "id": "friedman-94d6b7610c98379e", "metric_expression": "4.792+", "metric_symbol": "r", "metric_value": 4.792, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.792+ | Found by Reis in 1975.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc17.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Reis", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@18", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc18.gif", "id": "friedman-cfd342d4610e6900", "metric_expression": "1 + \u221a2 + \u221a6 = 4.863+", "metric_symbol": "r", "metric_value": 4.863, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1 + \u221a2 + \u221a6 = 4.863+ | Found by Kravitz in 1967.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc18.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Kravitz", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@19", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc19.gif", "id": "friedman-34c45545a7a83759", "metric_expression": "1 + \u221a2 + \u221a6 = 4.863+", "metric_symbol": "r", "metric_value": 4.863, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1 + \u221a2 + \u221a6 = 4.863+ | Proved by F. Fodor in 1999.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc19.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "F. Fodor", "title": "Circles in Circles", "verified": false}
-{"case": "cirincir@20", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc20.gif", "id": "friedman-3c6aef83d624cd46", "metric_expression": "5.122+", "metric_symbol": "r", "metric_value": 5.122, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 5.122+ | Found by Goldberg in 1971.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc20.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Goldberg", "title": "Circles in Circles", "verified": false}
-{"case": "squincir@1", "external_image_url": "https://erich-friedman.github.io/packing/squincir/1.gif", "id": "friedman-5869e84b3591c27f", "metric_expression": "\u221a2 / 2 = .707+", "metric_symbol": "r", "metric_value": 0.707, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a2 / 2 = .707+ | Trivial.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@2", "external_image_url": "https://erich-friedman.github.io/packing/squincir/2.gif", "id": "friedman-0e4ee169173f3134", "metric_expression": "\u221a5 / 2 = 1.118+", "metric_symbol": "r", "metric_value": 1.118, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a5 / 2 = 1.118+ | Trivial.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@3", "external_image_url": "https://erich-friedman.github.io/packing/squincir/3.gif", "id": "friedman-b224ef527f65192e", "metric_expression": "5 \u221a17 / 16 = 1.288+", "metric_symbol": "r", "metric_value": 1.288, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 5 \u221a17 / 16 = 1.288+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@4", "external_image_url": "https://erich-friedman.github.io/packing/squincir/4.gif", "id": "friedman-f3807b78d909da78", "metric_expression": "\u221a2 = 1.414+", "metric_symbol": "r", "metric_value": 1.414, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a2 = 1.414+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@5", "external_image_url": "https://erich-friedman.github.io/packing/squincir/5.gif", "id": "friedman-88294a7216094c59", "metric_expression": "\u221a10 / 2 = 1.581+", "metric_symbol": "r", "metric_value": 1.581, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a10 / 2 = 1.581+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@6", "external_image_url": "https://erich-friedman.github.io/packing/squincir/6.gif", "id": "friedman-65e8d793b348932d", "metric_expression": "1.688+ *", "metric_symbol": "r", "metric_value": 1.688, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.688+ * | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@7", "external_image_url": "https://erich-friedman.github.io/packing/squincir/7.gif", "id": "friedman-a59f56f1b2674418", "metric_expression": "\u221a13 / 2 = 1.802+", "metric_symbol": "r", "metric_value": 1.802, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a13 / 2 = 1.802+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@8", "external_image_url": "https://erich-friedman.github.io/packing/squincir/8.gif", "id": "friedman-43a8cc87dd562e65", "metric_expression": "1.978+ *", "metric_symbol": "r", "metric_value": 1.978, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.978+ * | Found by David W. Cantrell | in March 2002.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@9", "external_image_url": "https://erich-friedman.github.io/packing/squincir/9.gif", "id": "friedman-86ca41fcbeeb5e27", "metric_expression": "\u221a1105 / 16 = 2.077+", "metric_symbol": "r", "metric_value": 2.077, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a1105 / 16 = 2.077+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@10", "external_image_url": "https://erich-friedman.github.io/packing/squincir/10.gif", "id": "friedman-6355730efda78cb7", "metric_expression": "3 \u221a2 / 2 = 2.121+", "metric_symbol": "r", "metric_value": 2.121, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3 \u221a2 / 2 = 2.121+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@11", "external_image_url": "https://erich-friedman.github.io/packing/squincir/11.gif", "id": "friedman-c1b8b1c58054d915", "metric_expression": "2.214+", "metric_symbol": "r", "metric_value": 2.214, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.214+ | Found by David W. Cantrell | in March 2002.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@12", "external_image_url": "https://erich-friedman.github.io/packing/squincir/12.gif", "id": "friedman-9977a2eaf2805d65", "metric_expression": "\u221a5 = 2.236+", "metric_symbol": "r", "metric_value": 2.236, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a5 = 2.236+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@13", "external_image_url": "https://erich-friedman.github.io/packing/squincir/13.gif", "id": "friedman-cb0c99e6f49a3a7c", "metric_expression": "2.3607+", "metric_symbol": "r", "metric_value": 2.3607, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.3607+ | Found by David W. Cantrell | in November 2010.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@14", "external_image_url": "https://erich-friedman.github.io/packing/squincir/14.gif", "id": "friedman-9db264d6fbd56f88", "metric_expression": "2.5", "metric_symbol": "r", "metric_value": 2.5, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.5 | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "14.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@15", "external_image_url": "https://erich-friedman.github.io/packing/squincir/15.gif", "id": "friedman-7a18753406988317", "metric_expression": "2.533+", "metric_symbol": "r", "metric_value": 2.533, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.533+ | Found by by David W. Cantrell | in June 2002.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@16", "external_image_url": "https://erich-friedman.github.io/packing/squincir/16.gif", "id": "friedman-5ad570c477b4ac2e", "metric_expression": "\u221a11009 / 40 = 2.623+", "metric_symbol": "r", "metric_value": 2.623, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a11009 / 40 = 2.623+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@17", "external_image_url": "https://erich-friedman.github.io/packing/squincir/17.gif", "id": "friedman-d4f47c876c439469", "metric_expression": "2.677+", "metric_symbol": "r", "metric_value": 2.677, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.677+ | Found by Maurizio Morandi | in December 2010.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@18", "external_image_url": "https://erich-friedman.github.io/packing/squincir/18.gif", "id": "friedman-d3d2c90ab2ff01be", "metric_expression": "\u221a481 / 8 = 2.741+", "metric_symbol": "r", "metric_value": 2.741, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a481 / 8 = 2.741+ | Found by David W. Cantrell | in March 2002.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@19", "external_image_url": "https://erich-friedman.github.io/packing/squincir/19.gif", "id": "friedman-345374d2edaefdb5", "metric_expression": "2.802+", "metric_symbol": "r", "metric_value": 2.802, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.802+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@20", "external_image_url": "https://erich-friedman.github.io/packing/squincir/20.gif", "id": "friedman-9d8656f915990a3a", "metric_expression": "2.893+", "metric_symbol": "r", "metric_value": 2.893, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.893+ | Found by David W. Cantrell | in June 2002.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "20.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@21", "external_image_url": "https://erich-friedman.github.io/packing/squincir/21.gif", "id": "friedman-9cd3149db57e66f9", "metric_expression": "\u221a34 / 2 = 2.915+", "metric_symbol": "r", "metric_value": 2.915, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a34 / 2 = 2.915+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@22", "external_image_url": "https://erich-friedman.github.io/packing/squincir/22.gif", "id": "friedman-ebe3742a355dd42c", "metric_expression": "3.033+", "metric_symbol": "r", "metric_value": 3.033, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.033+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "22.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@23", "external_image_url": "https://erich-friedman.github.io/packing/squincir/23.gif", "id": "friedman-4348f331eb35d40c", "metric_expression": "3.073+", "metric_symbol": "r", "metric_value": 3.073, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.073+ | Found by David W. Cantrell | in June 2002.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "23.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@24", "external_image_url": "https://erich-friedman.github.io/packing/squincir/24.gif", "id": "friedman-4d57352fc22cdfc6", "metric_expression": "3.110+", "metric_symbol": "r", "metric_value": 3.11, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.110+ | Found by Maurizio Morandi | in October 2010.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@25", "external_image_url": "https://erich-friedman.github.io/packing/squincir/25.gif", "id": "friedman-68b34ad5c97761b2", "metric_expression": "\u221a5809 / 24 = 3.175+", "metric_symbol": "r", "metric_value": 3.175, "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a5809 / 24 = 3.175+ | Found by David W. Cantrell | in April 2002.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@26", "external_image_url": "https://erich-friedman.github.io/packing/squincir/26.gif", "id": "friedman-b6a112efa3684477", "metric_expression": "\u221a41 / 2 = 3.201+", "metric_symbol": "r", "metric_value": 3.201, "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a41 / 2 = 3.201+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@27", "external_image_url": "https://erich-friedman.github.io/packing/squincir/27.gif", "id": "friedman-7dcca59d45647799", "metric_expression": "13\u221a145/48 = 3.261+", "metric_symbol": "r", "metric_value": 3.261, "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 13\u221a145/48 = 3.261+ | Found by Maurizio Morandi | in September 2010.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "27.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@28", "external_image_url": "https://erich-friedman.github.io/packing/squincir/28.gif", "id": "friedman-76c15924023fc9c9", "metric_expression": "3.333+", "metric_symbol": "r", "metric_value": 3.333, "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.333+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "28.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@29", "external_image_url": "https://erich-friedman.github.io/packing/squincir/29.gif", "id": "friedman-1269da4cc3a8081b", "metric_expression": "3.401+", "metric_symbol": "r", "metric_value": 3.401, "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.401+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "29.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@30", "external_image_url": "https://erich-friedman.github.io/packing/squincir/30.gif", "id": "friedman-376088620cfc99d9", "metric_expression": "3.472+", "metric_symbol": "r", "metric_value": 3.472, "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.472+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "30.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@31", "external_image_url": "https://erich-friedman.github.io/packing/squincir/31.gif", "id": "friedman-14370ff874d2cb2d", "metric_expression": "5 \u221a2 / 2 = 3.535+", "metric_symbol": "r", "metric_value": 3.535, "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 5 \u221a2 / 2 = 3.535+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "31.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@32", "external_image_url": "https://erich-friedman.github.io/packing/squincir/32.gif", "id": "friedman-64ecaa354f0fa4c4", "metric_expression": "3.584+", "metric_symbol": "r", "metric_value": 3.584, "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.584+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@33", "external_image_url": "https://erich-friedman.github.io/packing/squincir/33.gif", "id": "friedman-d05dcfdf1ac4c4fe", "metric_expression": "\u221a13 = 3.605+", "metric_symbol": "r", "metric_value": 3.605, "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in June 2010.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "33.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@34", "external_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif", "id": "friedman-e762304582c78701", "metric_expression": "3.629+", "metric_symbol": "r", "metric_value": 3.629, "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "34.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Circles", "verified": false}
-{"case": "squincir@35", "external_image_url": "https://erich-friedman.github.io/packing/squincir/35.gif", "id": "friedman-2149f75e4bd65fbf", "metric_expression": "\u221a53 / 2 = 3.640+", "metric_symbol": "r", "metric_value": 3.64, "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a53 / 2 = 3.640+ | Found by David Eppstein | in March 2002.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "35.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David Eppstein", "title": "Squares in Circles", "verified": false}
-{"case": "hexincir@1", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/1.png", "id": "friedman-f4365a8237f4d536", "metric_expression": "1", "metric_symbol": "r", "metric_value": 1.0, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1 | Trivial.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "1.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@2", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/2.png", "id": "friedman-161cd75eb6ba9ba4", "metric_expression": "\u221a13/2 = 1.802+", "metric_symbol": "r", "metric_value": 1.802, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a13/2 = 1.802+ | Trivial.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@3", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/3.png", "id": "friedman-907e870939be554d", "metric_expression": "2", "metric_symbol": "r", "metric_value": 2.0, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2 | Trivial.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@4", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/4.png", "id": "friedman-c1a3d7df20036b35", "metric_expression": "(21\u2013\u221a145)/4 = 2.239+", "metric_symbol": "r", "metric_value": 2.239, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = (21\u2013\u221a145)/4 = 2.239+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@5", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/5.png", "id": "friedman-d5d1894268994287", "metric_expression": "2.471+", "metric_symbol": "r", "metric_value": 2.471, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.471+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "5.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@6", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/7.png", "id": "friedman-0f6175719a014590", "metric_expression": "\u221a7 = 2.645+", "metric_symbol": "r", "metric_value": 2.645, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a7 = 2.645+ | Trivial. |", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@7", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/7.png", "id": "friedman-ce7782e664eb3509", "metric_expression": "\u221a7 = 2.645+", "metric_symbol": "r", "metric_value": 2.645, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a7 = 2.645+ | Trivial. |", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@8", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/8.png", "id": "friedman-8f9fd353f3c39f8f", "metric_expression": "2.984+", "metric_symbol": "r", "metric_value": 2.984, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.984+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@9", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/9.png", "id": "friedman-ce7d1705ae35759e", "metric_expression": "3.301+", "metric_symbol": "r", "metric_value": 3.301, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.301+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@10", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/10.png", "id": "friedman-29b086edb1679805", "metric_expression": "7/2 = 3.5", "metric_symbol": "r", "metric_value": 3.5, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 7/2 = 3.5 | Found by Maurizio Morandi | in March 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@11", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/12.png", "id": "friedman-ac95a15bac80aada", "metric_expression": "\u221a13 = 3.605+", "metric_symbol": "r", "metric_value": 3.605, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@12", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/12.png", "id": "friedman-3376d2ccb3372ee0", "metric_expression": "\u221a13 = 3.605+", "metric_symbol": "r", "metric_value": 3.605, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@13", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/13.png", "id": "friedman-96ae4e9094430c50", "metric_expression": "3.82298+", "metric_symbol": "r", "metric_value": 3.82298, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.82298+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@14", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/14.png", "id": "friedman-df66c818ec0fcb21", "metric_expression": "\u221a(109\u20139\u221a109) = 3.877+", "metric_symbol": "r", "metric_value": 3.877, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a(109\u20139\u221a109) = 3.877+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@15", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/15.png", "id": "friedman-1b8f3d32de4efd85", "metric_expression": "4.08174+", "metric_symbol": "r", "metric_value": 4.08174, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.08174+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@16", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/16.png", "id": "friedman-984915062df8aaf9", "metric_expression": "4.13966+", "metric_symbol": "r", "metric_value": 4.13966, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.13966+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "16.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@17", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/17.png", "id": "friedman-d2e9447ad7d3e656", "metric_expression": "4.30170+", "metric_symbol": "r", "metric_value": 4.3017, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.30170+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@18", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "id": "friedman-aaa107cfaf93d0b6", "metric_expression": "\u221a19 = 4.35889+", "metric_symbol": "r", "metric_value": 4.35889, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@19", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "id": "friedman-a90f0ec81a1e11a5", "metric_expression": "\u221a19 = 4.35889+", "metric_symbol": "r", "metric_value": 4.35889, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@20", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/20.png", "id": "friedman-d422aef11edc8b4e", "metric_expression": "4.62598+", "metric_symbol": "r", "metric_value": 4.62598, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.62598+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Circles", "verified": false}
-{"case": "hexincir@21", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/21.png", "id": "friedman-29ad6735609174be", "metric_expression": "4.68339+", "metric_symbol": "r", "metric_value": 4.68339, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.68339+ | Found by Enea Victor | in April 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "21.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Enea Victor", "title": "Hexagons in Circles", "verified": false}
-{"case": "triinhex@1", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/1.gif", "id": "friedman-3da8e7e1948e6736", "metric_expression": "1/\u221a3 = .577+", "metric_symbol": "s", "metric_value": 0.577, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1/\u221a3 = .577+ | Trivial.", "setup": "triinhex", "side": 0.577, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@2", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/2.gif", "id": "friedman-6a37d09ba95769ef", "metric_expression": "\u221a3/2 = .866+", "metric_symbol": "s", "metric_value": 0.866, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a3/2 = .866+ | Trivial.", "setup": "triinhex", "side": 0.866, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@3", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/3.gif", "id": "friedman-2e8c6ffd77fd1caa", "metric_expression": "\u221a((6+\u221a33)/12) = .989+", "metric_symbol": "s", "metric_value": 0.989, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a((6+\u221a33)/12) = .989+ | Found by Erich Friedman | in April 2005.", "setup": "triinhex", "side": 0.989, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@4", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/4.gif", "id": "friedman-4801232c424f2df0", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 | Trivial.", "setup": "triinhex", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@5", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/5.gif", "id": "friedman-a98b7b2f0609831c", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 | Trivial.", "setup": "triinhex", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@6", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/6.gif", "id": "friedman-344dc5b961d22a74", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 | Trivial.", "setup": "triinhex", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@7", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/7.gif", "id": "friedman-1cfc719fa74e4895", "metric_expression": "1.277+", "metric_symbol": "s", "metric_value": 1.277, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.277+ | Found by David W. Cantrell | in May 2005.", "setup": "triinhex", "side": 1.277, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@8", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/8.gif", "id": "friedman-1026f883709bd7d3", "metric_expression": "1.356+", "metric_symbol": "s", "metric_value": 1.356, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.356+ | Found by David W. Cantrell | in July 2012.", "setup": "triinhex", "side": 1.356, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@9", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/9.gif", "id": "friedman-878211b91c2cd25f", "metric_expression": "1.434+", "metric_symbol": "s", "metric_value": 1.434, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.434+ | Found by Erich Friedman | in April 2005.", "setup": "triinhex", "side": 1.434, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@10", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/10.gif", "id": "friedman-3f524f23d82a3765", "metric_expression": "1.497+", "metric_symbol": "s", "metric_value": 1.497, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.497+ | Found by Timo Berthold et al | in January 2026.", "setup": "triinhex", "side": 1.497, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@11", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/11.gif", "id": "friedman-d8daa892bdde901b", "metric_expression": "3/2 = 1.500", "metric_symbol": "s", "metric_value": 1.5, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3/2 = 1.500 | Found by Erich Friedman | in April 2005.", "setup": "triinhex", "side": 1.5, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@12", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/12.gif", "id": "friedman-e69ae6a58b2340ae", "metric_expression": "1.623+", "metric_symbol": "s", "metric_value": 1.623, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.623+ | Found by Timo Berthold et al | in January 2026.", "setup": "triinhex", "side": 1.623, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@13", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/13.gif", "id": "friedman-b44ea2e121113705", "metric_expression": "\u221a(587+51\u221a17)/12\u221a2 = 1.663829+", "metric_symbol": "s", "metric_value": 1.663829, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a(587+51\u221a17)/12\u221a2 = 1.663829+ | Found by Ian Watson | in April 2026.", "setup": "triinhex", "side": 1.663829, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@14", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/14.gif", "id": "friedman-a3f46ac5df4272b1", "metric_expression": "1.725+", "metric_symbol": "s", "metric_value": 1.725, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.725+ | Found by David W. Cantrell | in August 2012.", "setup": "triinhex", "side": 1.725, "source": "Erich Friedman Packing Center", "source_image": "14.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@15", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/15.gif", "id": "friedman-f1d60e3a404c89fa", "metric_expression": "7/4 = 1.750", "metric_symbol": "s", "metric_value": 1.75, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7/4 = 1.750 | Found by Erich Friedman | in April 2005.", "setup": "triinhex", "side": 1.75, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@16", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/16.gif", "id": "friedman-7fac796b89bce5ba", "metric_expression": "9/5 = 1.800", "metric_symbol": "s", "metric_value": 1.8, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9/5 = 1.800 | Found by Maurizio Morandi | in April 2008.", "setup": "triinhex", "side": 1.8, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@17", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/17.gif", "id": "friedman-32b5ba5889634179", "metric_expression": "11/6 = 1.833+", "metric_symbol": "s", "metric_value": 1.833, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 11/6 = 1.833+ | Found by Maurizio Morandi | in April 2008.", "setup": "triinhex", "side": 1.833, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@18", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/18.gif", "id": "friedman-6fe52b2c6562a1a5", "metric_expression": "17/9 = 1.888+", "metric_symbol": "s", "metric_value": 1.888, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 17/9 = 1.888+ | Found by Maurizio Morandi | in April 2008.", "setup": "triinhex", "side": 1.888, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@19", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/19.gif", "id": "friedman-ae881bae597b1582", "metric_expression": "1.953+", "metric_symbol": "s", "metric_value": 1.953, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.953+ | Found by Alex Adri\u00e1n Nieto | in April 2026.", "setup": "triinhex", "side": 1.953, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Alex Adri\u00e1n Nieto", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@20", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/20.gif", "id": "friedman-e09e2731ede2b818", "metric_expression": "1.97591+", "metric_symbol": "s", "metric_value": 1.97591, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.97591+ | Found by Aaden Abraham | in April 2026.", "setup": "triinhex", "side": 1.97591, "source": "Erich Friedman Packing Center", "source_image": "20.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Aaden Abraham", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@21", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/21.gif", "id": "friedman-6a5c03a69b1a0944", "metric_expression": "1.99878+", "metric_symbol": "s", "metric_value": 1.99878, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.99878+ | Found by Ian Watson | in April 2026.", "setup": "triinhex", "side": 1.99878, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@22", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "id": "friedman-f4b5e7f94a8cb2d9", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial. |", "setup": "triinhex", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@23", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "id": "friedman-98ecf39e2c10f60b", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial. |", "setup": "triinhex", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@24", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "id": "friedman-848e5e014bbb1c07", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial. |", "setup": "triinhex", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@25", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/25.gif", "id": "friedman-0669c70e4fbc9795", "metric_expression": "13/6 = 2.166+", "metric_symbol": "s", "metric_value": 2.166, "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 13/6 = 2.166+ | Found by Ignacio Vallejo | in April 2026.", "setup": "triinhex", "side": 2.166, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@26", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/26.gif", "id": "friedman-be91cb98d802160b", "metric_expression": "2.21991+", "metric_symbol": "s", "metric_value": 2.21991, "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.21991+ | Found by Ian Watson | in April 2026.", "setup": "triinhex", "side": 2.21991, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@27", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/27.gif", "id": "friedman-de6536d86c63771d", "metric_expression": "2.29541+", "metric_symbol": "s", "metric_value": 2.29541, "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.29541+ | Found by Ian Watson | in April 2026.", "setup": "triinhex", "side": 2.29541, "source": "Erich Friedman Packing Center", "source_image": "27.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@28", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/28.gif", "id": "friedman-84527b93fa221d9a", "metric_expression": "2.32289+", "metric_symbol": "s", "metric_value": 2.32289, "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.32289+ | Found by Ian Watson | in April 2026.", "setup": "triinhex", "side": 2.32289, "source": "Erich Friedman Packing Center", "source_image": "28.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@29", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/29.gif", "id": "friedman-760c159820f8d745", "metric_expression": "7/3 = 2.333+", "metric_symbol": "s", "metric_value": 2.333, "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7/3 = 2.333+ | Found by Ignacio Vallejo | in April 2026.", "setup": "triinhex", "side": 2.333, "source": "Erich Friedman Packing Center", "source_image": "29.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@30", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/30.gif", "id": "friedman-b4d9e24006eac400", "metric_expression": "19/8 = 2.375", "metric_symbol": "s", "metric_value": 2.375, "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 19/8 = 2.375 | Found by Ignacio Vallejo | in April 2026.", "setup": "triinhex", "side": 2.375, "source": "Erich Friedman Packing Center", "source_image": "30.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@31", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/31.gif", "id": "friedman-f86fde748b4194e9", "metric_expression": "12/5 = 2.400", "metric_symbol": "s", "metric_value": 2.4, "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 12/5 = 2.400 | Found by Emerson Connelly | in April 2026.", "setup": "triinhex", "side": 2.4, "source": "Erich Friedman Packing Center", "source_image": "31.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@32", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/32.gif", "id": "friedman-3dd51f0f97b0b151", "metric_expression": "2.465+", "metric_symbol": "s", "metric_value": 2.465, "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.465+ | Found by Emerson Connelly | in April 2026.", "setup": "triinhex", "side": 2.465, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@33", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/33.gif", "id": "friedman-eef0a3d7d3d42660", "metric_expression": "2.498+", "metric_symbol": "s", "metric_value": 2.498, "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.498+ | Found by Emerson Connelly | in April 2026.", "setup": "triinhex", "side": 2.498, "source": "Erich Friedman Packing Center", "source_image": "33.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@34", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "id": "friedman-0d6413d764fd130a", "metric_expression": "5/2 = 2.500", "metric_symbol": "s", "metric_value": 2.5, "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "setup": "triinhex", "side": 2.5, "source": "Erich Friedman Packing Center", "source_image": "35.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@35", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "id": "friedman-3f36e9a7b3ccf62a", "metric_expression": "5/2 = 2.500", "metric_symbol": "s", "metric_value": 2.5, "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "setup": "triinhex", "side": 2.5, "source": "Erich Friedman Packing Center", "source_image": "35.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@36", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/36.gif", "id": "friedman-5a3e047914e4c52e", "metric_expression": "2.59123+", "metric_symbol": "s", "metric_value": 2.59123, "n": 36, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.59123+ | Found by Nathan Roll | in April 2026.", "setup": "triinhex", "side": 2.59123, "source": "Erich Friedman Packing Center", "source_image": "36.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@37", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/37.gif", "id": "friedman-88d93da6bb76b1b1", "metric_expression": "2.61943+", "metric_symbol": "s", "metric_value": 2.61943, "n": 37, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.61943+ | Found by Nathan Roll | in April 2026.", "setup": "triinhex", "side": 2.61943, "source": "Erich Friedman Packing Center", "source_image": "37.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@38", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "id": "friedman-c5101afcc06aa9b6", "metric_expression": "8/3 = 2.666+", "metric_symbol": "s", "metric_value": 2.666, "n": 38, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "setup": "triinhex", "side": 2.666, "source": "Erich Friedman Packing Center", "source_image": "39.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@39", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "id": "friedman-fe6d3925c241e54c", "metric_expression": "8/3 = 2.666+", "metric_symbol": "s", "metric_value": 2.666, "n": 39, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "setup": "triinhex", "side": 2.666, "source": "Erich Friedman Packing Center", "source_image": "39.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Hexagons", "verified": false}
-{"case": "triinhex@40", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/40.gif", "id": "friedman-664d8ab6cb5c8368", "metric_expression": "2.71622+", "metric_symbol": "s", "metric_value": 2.71622, "n": 40, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.71622+ | Found by Nathan Roll | in April 2026.", "setup": "triinhex", "side": 2.71622, "source": "Erich Friedman Packing Center", "source_image": "40.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Triangles in Hexagons", "verified": false}
-{"case": "cirinhex@1", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc1.gif", "id": "friedman-770d235be87f7626", "metric_expression": "2/\u221a3 = 1.154+", "metric_symbol": "s", "metric_value": 1.154, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2/\u221a3 = 1.154+ | Trivial.", "setup": "cirinhex", "side": 1.154, "source": "Erich Friedman Packing Center", "source_image": "hc1.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@2", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc2.gif", "id": "friedman-73fd4a5a73841e9b", "metric_expression": "1 + 2/\u221a3 = 2.154+", "metric_symbol": "s", "metric_value": 2.154, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 + 2/\u221a3 = 2.154+ | Trivial.", "setup": "cirinhex", "side": 2.154, "source": "Erich Friedman Packing Center", "source_image": "hc2.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@3", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc3.gif", "id": "friedman-79ade9f886ed48ae", "metric_expression": "4/\u221a3 = 2.309+", "metric_symbol": "s", "metric_value": 2.309, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4/\u221a3 = 2.309+ | Trivial.", "setup": "cirinhex", "side": 2.309, "source": "Erich Friedman Packing Center", "source_image": "hc3.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@4", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc4.gif", "id": "friedman-bac6d855bac20369", "metric_expression": "2/\u221a3 + 4/\u221a7 = 2.666+", "metric_symbol": "s", "metric_value": 2.666, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2/\u221a3 + 4/\u221a7 = 2.666+ | Found by Shahriar Manzoor | in April 2002.", "setup": "cirinhex", "side": 2.666, "source": "Erich Friedman Packing Center", "source_image": "hc4.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Shahriar Manzoor", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@5", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc5.gif", "id": "friedman-fd320f8f6c6e941f", "metric_expression": "2.999+", "metric_symbol": "s", "metric_value": 2.999, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.999+ | Found by Erich Friedman | in 1999.", "setup": "cirinhex", "side": 2.999, "source": "Erich Friedman Packing Center", "source_image": "hc5.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@6", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc6.gif", "id": "friedman-0fda7696de625f14", "metric_expression": "2 + 2/\u221a3 = 3.154+", "metric_symbol": "s", "metric_value": 3.154, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2/\u221a3 = 3.154+ | Trivial. |", "setup": "cirinhex", "side": 3.154, "source": "Erich Friedman Packing Center", "source_image": "hc6.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@7", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc7.gif", "id": "friedman-ed3a018f5ec225be", "metric_expression": "2 + 2/\u221a3 = 3.154+", "metric_symbol": "s", "metric_value": 3.154, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2/\u221a3 = 3.154+ | Trivial. |", "setup": "cirinhex", "side": 3.154, "source": "Erich Friedman Packing Center", "source_image": "hc7.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@8", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc8.gif", "id": "friedman-993ee06d15d5ed36", "metric_expression": "3.709+", "metric_symbol": "s", "metric_value": 3.709, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.709+ | Found by David W. Cantrell | in July 2002.", "setup": "cirinhex", "side": 3.709, "source": "Erich Friedman Packing Center", "source_image": "hc8.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@9", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc9.gif", "id": "friedman-c3af9c95b34d4eae", "metric_expression": "20/7 + 2/\u221a3 = 4.011+", "metric_symbol": "s", "metric_value": 4.011, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 20/7 + 2/\u221a3 = 4.011+ | Found by David W. Cantrell | in July 2002.", "setup": "cirinhex", "side": 4.011, "source": "Erich Friedman Packing Center", "source_image": "hc9.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@10", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc10.gif", "id": "friedman-059d42e7a7094200", "metric_expression": "4.119+", "metric_symbol": "s", "metric_value": 4.119, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.119+ | Found by David W. Cantrell | in July 2002.", "setup": "cirinhex", "side": 4.119, "source": "Erich Friedman Packing Center", "source_image": "hc10.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@11", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc11.gif", "id": "friedman-d8761b35cf44d4b6", "metric_expression": "2 + 4/\u221a3 = 4.309+", "metric_symbol": "s", "metric_value": 4.309, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 4/\u221a3 = 4.309+ | Found by Erich Friedman | in 1999.", "setup": "cirinhex", "side": 4.309, "source": "Erich Friedman Packing Center", "source_image": "hc11.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@12", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc12.gif", "id": "friedman-72b7d9ef3a1d1eb3", "metric_expression": "2 + 4/\u221a3 = 4.309+", "metric_symbol": "s", "metric_value": 4.309, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 4/\u221a3 = 4.309+ | Found by Erich Friedman | in 1999.", "setup": "cirinhex", "side": 4.309, "source": "Erich Friedman Packing Center", "source_image": "hc12.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@13", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc13.gif", "id": "friedman-050ca63d878798db", "metric_expression": "8/\u221a3 = 4.618+", "metric_symbol": "s", "metric_value": 4.618, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8/\u221a3 = 4.618+ | Found by Erich Friedman | in 1999.", "setup": "cirinhex", "side": 4.618, "source": "Erich Friedman Packing Center", "source_image": "hc13.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@14", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc14.gif", "id": "friedman-16d5278528a0de05", "metric_expression": "2 + 2/\u221a3 + 4/\u221a7 = 4.666+", "metric_symbol": "s", "metric_value": 4.666, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2/\u221a3 + 4/\u221a7 = 4.666+ | Found by David W. Cantrell | in July 2002.", "setup": "cirinhex", "side": 4.666, "source": "Erich Friedman Packing Center", "source_image": "hc14.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@15", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc15.gif", "id": "friedman-cbd8c577436a2f32", "metric_expression": "4.961+", "metric_symbol": "s", "metric_value": 4.961, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.961+ | Found by David W. Cantrell | in January 2006.", "setup": "cirinhex", "side": 4.961, "source": "Erich Friedman Packing Center", "source_image": "hc15.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@16", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc16.gif", "id": "friedman-b904921ad4239ae1", "metric_expression": "4.999+", "metric_symbol": "s", "metric_value": 4.999, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.999+ | Found by David W. Cantrell | in July 2002.", "setup": "cirinhex", "side": 4.999, "source": "Erich Friedman Packing Center", "source_image": "hc16.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@17", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc17.gif", "id": "friedman-a809c6c673ff63e9", "metric_expression": "5.133+", "metric_symbol": "s", "metric_value": 5.133, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.133+ | Found by David W. Cantrell | in January 2006.", "setup": "cirinhex", "side": 5.133, "source": "Erich Friedman Packing Center", "source_image": "hc17.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@18", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc18.gif", "id": "friedman-fee81833ed47e1c7", "metric_expression": "4 + 2/\u221a3 = 5.154+", "metric_symbol": "s", "metric_value": 5.154, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "setup": "cirinhex", "side": 5.154, "source": "Erich Friedman Packing Center", "source_image": "hc18.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@19", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc19.gif", "id": "friedman-2008aa727face205", "metric_expression": "4 + 2/\u221a3 = 5.154+", "metric_symbol": "s", "metric_value": 5.154, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "setup": "cirinhex", "side": 5.154, "source": "Erich Friedman Packing Center", "source_image": "hc19.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@20", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc20.gif", "id": "friedman-05e6d5eff9cc57c1", "metric_expression": "5.676+", "metric_symbol": "s", "metric_value": 5.676, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.676+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinhex", "side": 5.676, "source": "Erich Friedman Packing Center", "source_image": "hc20.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@21", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc21.gif", "id": "friedman-1fbed3d4da59c92b", "metric_expression": "5.709+", "metric_symbol": "s", "metric_value": 5.709, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.709+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinhex", "side": 5.709, "source": "Erich Friedman Packing Center", "source_image": "hc21.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@22", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc22.gif", "id": "friedman-97ac6750b723bc99", "metric_expression": "5.952+", "metric_symbol": "s", "metric_value": 5.952, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.952+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinhex", "side": 5.952, "source": "Erich Friedman Packing Center", "source_image": "hc22.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@23", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc23.gif", "id": "friedman-416e07b086cdb41c", "metric_expression": "34/7 + 2/\u221a3 = 6.011+", "metric_symbol": "s", "metric_value": 6.011, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 34/7 + 2/\u221a3 = 6.011+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinhex", "side": 6.011, "source": "Erich Friedman Packing Center", "source_image": "hc23.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
-{"case": "cirinhex@24", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc24.gif", "id": "friedman-f836a33ba94ecd25", "metric_expression": "6.117+", "metric_symbol": "s", "metric_value": 6.117, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.117+ | Found by Rob Pratt | in March 2020.", "setup": "cirinhex", "side": 6.117, "source": "Erich Friedman Packing Center", "source_image": "hc24.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Rob Pratt", "title": "Circles in Hexagons", "verified": false}
-{"case": "squinhex@1", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/1.png", "id": "friedman-aa882c20c2730808", "metric_expression": "(3+\u221a3)/6 = 0.778+", "metric_symbol": "s", "metric_value": 0.778, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (3+\u221a3)/6 = 0.778+ | Trivial. |", "setup": "squinhex", "side": 0.778, "source": "Erich Friedman Packing Center", "source_image": "1.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@2", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/2.png", "id": "friedman-c9575101dedb956d", "metric_expression": "2/\u221a3 = 1.154+", "metric_symbol": "s", "metric_value": 1.154, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2/\u221a3 = 1.154+ | Trivial. |", "setup": "squinhex", "side": 1.154, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@3", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/3.png", "id": "friedman-65d767684918c83c", "metric_expression": "(1+\u221a3)/2 = 1.366+", "metric_symbol": "s", "metric_value": 1.366, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (1+\u221a3)/2 = 1.366+ | Found by Maurizio Morandi | in March 2026.", "setup": "squinhex", "side": 1.366, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@4", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/4.png", "id": "friedman-7f3c951c602c858c", "metric_expression": "2/3 1/4 = 1.519+", "metric_symbol": "s", "metric_value": 1.519, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2/3 1/4 = 1.519+ | Found by Maurizio Morandi | in March 2026.", "setup": "squinhex", "side": 1.519, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@5", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/5.png", "id": "friedman-059fe44f20dafce7", "metric_expression": "\u221a3 = 1.732+", "metric_symbol": "s", "metric_value": 1.732, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a3 = 1.732+ | Trivial. |", "setup": "squinhex", "side": 1.732, "source": "Erich Friedman Packing Center", "source_image": "5.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@6", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/6.png", "id": "friedman-e9e76992ebfd0eea", "metric_expression": "1.821+", "metric_symbol": "s", "metric_value": 1.821, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.821+ | Found by Maurizio Morandi | in March 2026.", "setup": "squinhex", "side": 1.821, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@7", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/7.png", "id": "friedman-917aa74cad64acc9", "metric_expression": "(\u221a2)3 1/4 = 1.861+", "metric_symbol": "s", "metric_value": 1.861, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (\u221a2)3 1/4 = 1.861+ | Found by Maurizio Morandi | in March 2026.", "setup": "squinhex", "side": 1.861, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@8", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/8.png", "id": "friedman-37c209606b5d0be8", "metric_expression": "2.15378+", "metric_symbol": "s", "metric_value": 2.15378, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.15378+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 2.15378, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@9", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/9.png", "id": "friedman-6ed5a97a8522fe9f", "metric_expression": "1/2+\u221a3 = 2.23205+", "metric_symbol": "s", "metric_value": 2.23205, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1/2+\u221a3 = 2.23205+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squinhex", "side": 2.23205, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@10", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/10.png", "id": "friedman-5698b9a145008429", "metric_expression": "4/\u221a3 = 2.309+", "metric_symbol": "s", "metric_value": 2.309, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4/\u221a3 = 2.309+ | Trivial. |", "setup": "squinhex", "side": 2.309, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@11", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/11.png", "id": "friedman-e4f42dd9bad6e9ae", "metric_expression": "2.40944+", "metric_symbol": "s", "metric_value": 2.40944, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.40944+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squinhex", "side": 2.40944, "source": "Erich Friedman Packing Center", "source_image": "11.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@12", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/12.png", "id": "friedman-158e465d78189aab", "metric_expression": "1+5\u221a3/6 = 2.443+", "metric_symbol": "s", "metric_value": 2.443, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1+5\u221a3/6 = 2.443+ | Found by Maurizio Morandi | in March 2026.", "setup": "squinhex", "side": 2.443, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@13", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/13.png", "id": "friedman-31834b23bb74454b", "metric_expression": "2.572+", "metric_symbol": "s", "metric_value": 2.572, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.572+ | Found by Maurizio Morandi | in April 2026.", "setup": "squinhex", "side": 2.572, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@14", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/14.png", "id": "friedman-7402434f1a7eae36", "metric_expression": "2.62126+", "metric_symbol": "s", "metric_value": 2.62126, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.62126+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squinhex", "side": 2.62126, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@15", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/15.png", "id": "friedman-9114dd3f206761d1", "metric_expression": "2.75365+", "metric_symbol": "s", "metric_value": 2.75365, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.75365+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 2.75365, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@16", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/16.png", "id": "friedman-a30a52e06c253a1b", "metric_expression": "2.82004+", "metric_symbol": "s", "metric_value": 2.82004, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.82004+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 2.82004, "source": "Erich Friedman Packing Center", "source_image": "16.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@17", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/17.png", "id": "friedman-84da5ab39ba704e9", "metric_expression": "5/\u221a3 = 2.88675+", "metric_symbol": "s", "metric_value": 2.88675, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5/\u221a3 = 2.88675+ | Trivial. |", "setup": "squinhex", "side": 2.88675, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@18", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/18.png", "id": "friedman-35051601e3c9e057", "metric_expression": "2.92111+", "metric_symbol": "s", "metric_value": 2.92111, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.92111+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 2.92111, "source": "Erich Friedman Packing Center", "source_image": "18.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@19", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/19.png", "id": "friedman-231ad19a0b0cd36c", "metric_expression": "2.93511+", "metric_symbol": "s", "metric_value": 2.93511, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.93511+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 2.93511, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@20", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/20.png", "id": "friedman-1cfab8de587ba4c6", "metric_expression": "3.16123+", "metric_symbol": "s", "metric_value": 3.16123, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.16123+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.16123, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@21", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png", "id": "friedman-e865847c64403456", "metric_expression": "3.23496+", "metric_symbol": "s", "metric_value": 3.23496, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.23496, "source": "Erich Friedman Packing Center", "source_image": "21.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@22", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/22.png", "id": "friedman-66d1403e8b5dee87", "metric_expression": "3.31573+", "metric_symbol": "s", "metric_value": 3.31573, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.31573+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.31573, "source": "Erich Friedman Packing Center", "source_image": "22.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@23", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/23.png", "id": "friedman-26ed1439200c2bbc", "metric_expression": "3.36437+", "metric_symbol": "s", "metric_value": 3.36437, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.36437+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.36437, "source": "Erich Friedman Packing Center", "source_image": "23.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@24", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/24.png", "id": "friedman-584ac536e92babf7", "metric_expression": "3.41524+", "metric_symbol": "s", "metric_value": 3.41524, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.41524+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.41524, "source": "Erich Friedman Packing Center", "source_image": "24.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@25", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/25.png", "id": "friedman-65226018eb6187d3", "metric_expression": "2\u221a3 = 3.46410+", "metric_symbol": "s", "metric_value": 3.4641, "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2\u221a3 = 3.46410+ | Trivial. |", "setup": "squinhex", "side": 3.4641, "source": "Erich Friedman Packing Center", "source_image": "25.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@26", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/26.png", "id": "friedman-f94dfa7915aa6316", "metric_expression": "3.4939927+", "metric_symbol": "s", "metric_value": 3.4939927, "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.4939927+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.4939927, "source": "Erich Friedman Packing Center", "source_image": "26.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@27", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/27.png", "id": "friedman-e777b2b5ac8c6ea9", "metric_expression": "(9+7\u221a3)/6 = 3.52072+", "metric_symbol": "s", "metric_value": 3.52072, "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (9+7\u221a3)/6 = 3.52072+ | Found by Erich Friedman | in April 2026.", "setup": "squinhex", "side": 3.52072, "source": "Erich Friedman Packing Center", "source_image": "27.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@28", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/28.png", "id": "friedman-81a1a54a931ce32e", "metric_expression": "3.62565+", "metric_symbol": "s", "metric_value": 3.62565, "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.62565+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.62565, "source": "Erich Friedman Packing Center", "source_image": "28.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@29", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/29.png", "id": "friedman-2aab609feceb8fed", "metric_expression": "3.66437+", "metric_symbol": "s", "metric_value": 3.66437, "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.66437+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.66437, "source": "Erich Friedman Packing Center", "source_image": "29.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@30", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/30.png", "id": "friedman-04182f5877400446", "metric_expression": "3.69554+", "metric_symbol": "s", "metric_value": 3.69554, "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.69554+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.69554, "source": "Erich Friedman Packing Center", "source_image": "30.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@31", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/31.png", "id": "friedman-c8d8192a6b8559d5", "metric_expression": "3.78410+", "metric_symbol": "s", "metric_value": 3.7841, "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.78410+ | Found by Emerson Connelly | in April 2026.", "setup": "squinhex", "side": 3.7841, "source": "Erich Friedman Packing Center", "source_image": "31.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@32", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/32.png", "id": "friedman-6939c4e529869605", "metric_expression": "3.84795+", "metric_symbol": "s", "metric_value": 3.84795, "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.84795+ | Found by Emerson Connelly | in April 2026.", "setup": "squinhex", "side": 3.84795, "source": "Erich Friedman Packing Center", "source_image": "32.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@33", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/33.png", "id": "friedman-8d87a9abaccdff08", "metric_expression": "3.88897+", "metric_symbol": "s", "metric_value": 3.88897, "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.88897+ | Found by Emerson Connelly | in April 2026.", "setup": "squinhex", "side": 3.88897, "source": "Erich Friedman Packing Center", "source_image": "33.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@34", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/34.png", "id": "friedman-da7dc94b7823a116", "metric_expression": "3.92704+", "metric_symbol": "s", "metric_value": 3.92704, "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.92704+ | Found by Emerson Connelly | in April 2026.", "setup": "squinhex", "side": 3.92704, "source": "Erich Friedman Packing Center", "source_image": "34.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@35", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/35.png", "id": "friedman-7ac34820b3e6a7cb", "metric_expression": "3.99833+", "metric_symbol": "s", "metric_value": 3.99833, "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.99833+ | Found by Emerson Connelly | in April 2026.", "setup": "squinhex", "side": 3.99833, "source": "Erich Friedman Packing Center", "source_image": "35.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@36", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png", "id": "friedman-5c2db381bec4d142", "metric_expression": "2+7\u221a3/6 = 4.02072+", "metric_symbol": "s", "metric_value": 4.02072, "n": 36, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+7\u221a3/6 = 4.02072+ | Found by Maurizio Morandi | in May 2026.", "setup": "squinhex", "side": 4.02072, "source": "Erich Friedman Packing Center", "source_image": "36.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@37", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/37.png", "id": "friedman-581729fe5a584193", "metric_expression": "7/\u221a3 = 4.04145+", "metric_symbol": "s", "metric_value": 4.04145, "n": 37, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7/\u221a3 = 4.04145+ | Trivial. |", "setup": "squinhex", "side": 4.04145, "source": "Erich Friedman Packing Center", "source_image": "37.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@38", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/38.png", "id": "friedman-df13cc746b03b8e0", "metric_expression": "4.18476+", "metric_symbol": "s", "metric_value": 4.18476, "n": 38, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.18476+ | Found by Emerson Connelly | in April 2026.", "setup": "squinhex", "side": 4.18476, "source": "Erich Friedman Packing Center", "source_image": "38.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@39", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/39.png", "id": "friedman-1c5ebd8a6ef4b69a", "metric_expression": "4.25744+", "metric_symbol": "s", "metric_value": 4.25744, "n": 39, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.25744+ | Found by Emerson Connelly | in April 2026.", "setup": "squinhex", "side": 4.25744, "source": "Erich Friedman Packing Center", "source_image": "39.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Hexagons", "verified": false}
-{"case": "squinhex@40", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/40.png", "id": "friedman-5c31be5fb74fc454", "metric_expression": "4.31157+", "metric_symbol": "s", "metric_value": 4.31157, "n": 40, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.31157+ | Found by Emerson Connelly | in April 2026.", "setup": "squinhex", "side": 4.31157, "source": "Erich Friedman Packing Center", "source_image": "40.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Hexagons", "verified": false}
-{"case": "hexinhex@1", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/1.gif", "id": "friedman-7d2fc81f3a8500ae", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "1. | | s = 1 | Trivial.", "setup": "hexinhex", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@2", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/2.gif", "id": "friedman-f14de263d1f7d57c", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "2. | | s = 2 | Trivial.", "setup": "hexinhex", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@3", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/3.gif", "id": "friedman-79e22bfc8102054c", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "3. | | s = 2 | Trivial.", "setup": "hexinhex", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@4", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/4.gif", "id": "friedman-ccccf1fc8a7da443", "metric_expression": "7/3 = 2.333+", "metric_symbol": "s", "metric_value": 2.333, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "4. | | s = 7/3 = 2.333+ | Trivial.", "setup": "hexinhex", "side": 2.333, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@5", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/5.gif", "id": "friedman-6ac4c984e4376c53", "metric_expression": "8/3 = 2.666+", "metric_symbol": "s", "metric_value": 2.666, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "5. | | s = 8/3 = 2.666+ | Found by Erich Friedman | in March 2015.", "setup": "hexinhex", "side": 2.666, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@6", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/7.gif", "id": "friedman-588ca2766605f010", "metric_expression": "5/\u221a3 = 2.886+", "metric_symbol": "s", "metric_value": 2.886, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "6-7. | | s = 5/\u221a3 = 2.886+ | Found by Maurizio Morandi | in April 2015.", "setup": "hexinhex", "side": 2.886, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@7", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/7.gif", "id": "friedman-db440f9c50e5ab80", "metric_expression": "5/\u221a3 = 2.886+", "metric_symbol": "s", "metric_value": 2.886, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "6-7. | | s = 5/\u221a3 = 2.886+ | Found by Maurizio Morandi | in April 2015.", "setup": "hexinhex", "side": 2.886, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@8", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/8.gif", "id": "friedman-20dcb9522b47625e", "metric_expression": "(51+5\u221a3)/18 = 3.314+", "metric_symbol": "s", "metric_value": 3.314, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "8. | | s = (51+5\u221a3)/18 = 3.314+ | Found by Maurizio Morandi | in April 2015.", "setup": "hexinhex", "side": 3.314, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@9", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/9.gif", "id": "friedman-2085529f48890bb9", "metric_expression": "(24+5\u221a3)/9 = 3.628+", "metric_symbol": "s", "metric_value": 3.628, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "9. | | s = (24+5\u221a3)/9 = 3.628+ | Found by Maurizio Morandi | in April 2015.", "setup": "hexinhex", "side": 3.628, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@10", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/10.gif", "id": "friedman-cc2c8d74be6eabc4", "metric_expression": "2 + \u221a3 = 3.732+", "metric_symbol": "s", "metric_value": 3.732, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "10. | | s = 2 + \u221a3 = 3.732+ | Found by Maurizio Morandi | in April 2015.", "setup": "hexinhex", "side": 3.732, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@11", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/11.gif", "id": "friedman-f57107a4580db9bd", "metric_expression": "2+10/3\u221a3 = 3.92450+", "metric_symbol": "s", "metric_value": 3.9245, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "11. | | s = 2+10/3\u221a3 = 3.92450+ | Found by Johann Schellhorn | in July 2025. | | | |", "setup": "hexinhex", "side": 3.9245, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Johann Schellhorn", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@12", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/12.gif", "id": "friedman-1d7855153f4426af", "metric_expression": "3.94164+", "metric_symbol": "s", "metric_value": 3.94164, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "12. | | s = 3.94164+ | Found by Alexander Novikov et al | in June 2025. | Improved slightly by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 3.94164, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Alexander Novikov et al", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@13", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/13.gif", "id": "friedman-d5e613d60ea5a121", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "13 | | s = 4 | Trivial. | | | | |", "setup": "hexinhex", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@14", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/14.gif", "id": "friedman-7227925526080a56", "metric_expression": "4.26899+", "metric_symbol": "s", "metric_value": 4.26899, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14. | | s = 4.26899+ | Found by Dominik Kamp | in April 2026.", "setup": "hexinhex", "side": 4.26899, "source": "Erich Friedman Packing Center", "source_image": "14.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Dominik Kamp", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@15", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/15.gif", "id": "friedman-fd72d6e91face17f", "metric_expression": "4.44727+", "metric_symbol": "s", "metric_value": 4.44727, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "15. | | s = 4.44727+ | Found by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 4.44727, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@16", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/16.gif", "id": "friedman-2607d8e05843091b", "metric_expression": "4.52746+", "metric_symbol": "s", "metric_value": 4.52746, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "16. | | s = 4.52746+ | Found by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 4.52746, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@17", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/17.gif", "id": "friedman-4a0e3382c2f91341", "metric_expression": "4.6136+", "metric_symbol": "s", "metric_value": 4.6136, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "17. | | s = 4.6136+ | Found by Timo Berthold et al | and Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 4.6136, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@18", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "id": "friedman-5d106d7a584d2e4a", "metric_expression": "8/\u221a3 = 4.618+", "metric_symbol": "s", "metric_value": 4.618, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "setup": "hexinhex", "side": 4.618, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@19", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "id": "friedman-e8163d17d47f75c5", "metric_expression": "8/\u221a3 = 4.618+", "metric_symbol": "s", "metric_value": 4.618, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "setup": "hexinhex", "side": 4.618, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@20", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "id": "friedman-b9b934450972f3f2", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "20-21. | | s = 5 | Trivial. | |", "setup": "hexinhex", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@21", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "id": "friedman-36b066565def6e80", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "20-21. | | s = 5 | Trivial. | |", "setup": "hexinhex", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@22", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/22.gif", "id": "friedman-e23498b5cf150f95", "metric_expression": "(39+8\u221a3)/10 = 5.285+", "metric_symbol": "s", "metric_value": 5.285, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "22. | | s = (39+8\u221a3)/10 = 5.285+ | Found by Maurizio Morandi | in April 2015.", "setup": "hexinhex", "side": 5.285, "source": "Erich Friedman Packing Center", "source_image": "22.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@23", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/23.gif", "id": "friedman-d9dbeab4d45e7737", "metric_expression": "5.400+", "metric_symbol": "s", "metric_value": 5.4, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "23. | | s = 5.400+ | Found by Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 5.4, "source": "Erich Friedman Packing Center", "source_image": "23.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Alex Kravatsky et al", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@24", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/24.gif", "id": "friedman-0e3c1a70fd02d7a3", "metric_expression": "19\u221a3/6 = 5.484+", "metric_symbol": "s", "metric_value": 5.484, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "24. | | s = 19\u221a3/6 = 5.484+ | Found by Maurizio Morandi | in April 2015.", "setup": "hexinhex", "side": 5.484, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@25", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/25.gif", "id": "friedman-276cf845aacff93e", "metric_expression": "5.62390+", "metric_symbol": "s", "metric_value": 5.6239, "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "25. | | s = 5.62390+ | Found by Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 5.6239, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Alex Kravatsky et al", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@26", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/26.gif", "id": "friedman-e4991ec3392395d2", "metric_expression": "5.70972+", "metric_symbol": "s", "metric_value": 5.70972, "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "26. | | s = 5.70972+ | Found by Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 5.70972, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Alex Kravatsky et al", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@27", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/27.gif", "id": "friedman-a33e4890e2d48b81", "metric_expression": "5.71415+", "metric_symbol": "s", "metric_value": 5.71415, "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "27. | | s = 5.71415+ | Found by Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 5.71415, "source": "Erich Friedman Packing Center", "source_image": "27.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Alex Kravatsky et al", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@28", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/28.gif", "id": "friedman-746003537392c940", "metric_expression": "5.90893+", "metric_symbol": "s", "metric_value": 5.90893, "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "28. | | s = 5.90893+ | Found by Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 5.90893, "source": "Erich Friedman Packing Center", "source_image": "28.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Alex Kravatsky et al", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@29", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "id": "friedman-0ceba4dddc547424", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "29-31. | | s = 6 | Trivial. |", "setup": "hexinhex", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "31.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@30", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "id": "friedman-67ef09edf0264a3d", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "29-31. | | s = 6 | Trivial. |", "setup": "hexinhex", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "31.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "hexinhex@31", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "id": "friedman-ce339bb897e95790", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "29-31. | | s = 6 | Trivial. |", "setup": "hexinhex", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "31.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
-{"case": "triinpen@1", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/1.gif", "id": "friedman-96279e2107a71452", "metric_expression": ".781+", "metric_symbol": "s", "metric_value": 0.781, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = cos(42\u00b0) / cos(18\u00b0) | s = .781+ | Trivial. |", "setup": "triinpen", "side": 0.781, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@2", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/2.gif", "id": "friedman-bfca58c6417586ac", "metric_expression": "1.070+", "metric_symbol": "s", "metric_value": 1.07, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a(6/(3+\u221a5)) | s = 1.070+ | Trivial. |", "setup": "triinpen", "side": 1.07, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@3", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/3.gif", "id": "friedman-c9e48380c0c277f4", "metric_expression": "1.143+", "metric_symbol": "s", "metric_value": 1.143, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.143+ | Found by Maurizio Morandi | in August 2012. |", "setup": "triinpen", "side": 1.143, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@4", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/4.gif", "id": "friedman-d9bb9327e072f65a", "metric_expression": "1.199+", "metric_symbol": "s", "metric_value": 1.199, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.199+ | Found by Maurizio Morandi | in July 2012. |", "setup": "triinpen", "side": 1.199, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@5", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/5.gif", "id": "friedman-30b99f667d0390f5", "metric_expression": "1.240+", "metric_symbol": "s", "metric_value": 1.24, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 + 2sin(12\u00b0)/\u221a3 | s = 1.240+ | Found by Erich Friedman | in March 2012.", "setup": "triinpen", "side": 1.24, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@6", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/6.gif", "id": "friedman-e333c306ac117d09", "metric_expression": "1.393+", "metric_symbol": "s", "metric_value": 1.393, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.393+ | Found by Dominik Kamp | in April 2026.", "setup": "triinpen", "side": 1.393, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Dominik Kamp", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@7", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/7.gif", "id": "friedman-06eee10277647397", "metric_expression": "1.581+", "metric_symbol": "s", "metric_value": 1.581, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.581+ | Found by David W. Cantrell | in July 2012.", "setup": "triinpen", "side": 1.581, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@8", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/8.gif", "id": "friedman-9b9197f5eec0793b", "metric_expression": "1.659+", "metric_symbol": "s", "metric_value": 1.659, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.659+ | Found by Maurizio Morandi | in July 2012.", "setup": "triinpen", "side": 1.659, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@9", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/9.gif", "id": "friedman-59a5b99b8f4f188b", "metric_expression": "1.767+", "metric_symbol": "s", "metric_value": 1.767, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.767+ | Found by Maurizio Morandi in July 2012. | Improved slightly by David W. Cantrell in August 2012.", "setup": "triinpen", "side": 1.767, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@10", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/10.gif", "id": "friedman-bd353f3981693157", "metric_expression": "1.815+", "metric_symbol": "s", "metric_value": 1.815, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.815+ | Found by Timo Berthold et al | in January 2026.", "setup": "triinpen", "side": 1.815, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@11", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/11.gif", "id": "friedman-a80f917c602437b6", "metric_expression": "1.871+", "metric_symbol": "s", "metric_value": 1.871, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.871+ | Found by Timo Berthold et al | in January 2026.", "setup": "triinpen", "side": 1.871, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@12", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/12.gif", "id": "friedman-e9a5008b814199d6", "metric_expression": "1.973+", "metric_symbol": "s", "metric_value": 1.973, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.973+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinpen", "side": 1.973, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@13", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/13.gif", "id": "friedman-81819cbb2d23f978", "metric_expression": "2.017+", "metric_symbol": "s", "metric_value": 2.017, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.017+ | Found by Timo Berthold et al | in January 2026.", "setup": "triinpen", "side": 2.017, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@14", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/14.gif", "id": "friedman-d6a7a899bd38f561", "metric_expression": "2.088+", "metric_symbol": "s", "metric_value": 2.088, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.088+ | Found by Ignacio Vallejo | in April 2026.", "setup": "triinpen", "side": 2.088, "source": "Erich Friedman Packing Center", "source_image": "14.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@15", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/15.gif", "id": "friedman-f66ac4e6cfdf6828", "metric_expression": "2.123+", "metric_symbol": "s", "metric_value": 2.123, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.123+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinpen", "side": 2.123, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@16", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/16.gif", "id": "friedman-64493990df5f4f6e", "metric_expression": "2.17598+", "metric_symbol": "s", "metric_value": 2.17598, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.17598+ | Found by Ian Watson | in April 2026.", "setup": "triinpen", "side": 2.17598, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@17", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/17.gif", "id": "friedman-f512cdf042b69a86", "metric_expression": "2.23658+", "metric_symbol": "s", "metric_value": 2.23658, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.23658+ | Found by Ian Watson | in April 2026.", "setup": "triinpen", "side": 2.23658, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@18", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/18.gif", "id": "friedman-85070b7792557c87", "metric_expression": "2.29382+", "metric_symbol": "s", "metric_value": 2.29382, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.29382+ | Found by Ian Watson | in April 2026.", "setup": "triinpen", "side": 2.29382, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@19", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "id": "friedman-eda74c98590f31cb", "metric_expression": "2.344+", "metric_symbol": "s", "metric_value": 2.344, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinpen", "side": 2.344, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@20", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/20.gif", "id": "friedman-06a2b02781d0120e", "metric_expression": "2.43350+", "metric_symbol": "s", "metric_value": 2.4335, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.43350+ | Found by Ian Watson | in April 2026.", "setup": "triinpen", "side": 2.4335, "source": "Erich Friedman Packing Center", "source_image": "20.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@21", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/21.gif", "id": "friedman-eb992ca5bc125b67", "metric_expression": "2.479+", "metric_symbol": "s", "metric_value": 2.479, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.479+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinpen", "side": 2.479, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@22", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/22.gif", "id": "friedman-6840d8a6ac2c5c99", "metric_expression": "2.56740+", "metric_symbol": "s", "metric_value": 2.5674, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.56740+ | Found by Ian Watson | in April 2026.", "setup": "triinpen", "side": 2.5674, "source": "Erich Friedman Packing Center", "source_image": "22.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@23", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/23.gif", "id": "friedman-a4967e0e8babb771", "metric_expression": "2.61831+", "metric_symbol": "s", "metric_value": 2.61831, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.61831+ | Found by Ian Watson | in April 2026.", "setup": "triinpen", "side": 2.61831, "source": "Erich Friedman Packing Center", "source_image": "23.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@24", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/24.gif", "id": "friedman-d47afc4cb7695168", "metric_expression": "2.66641+", "metric_symbol": "s", "metric_value": 2.66641, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.66641+ | Found by Ian Watson | in April 2026.", "setup": "triinpen", "side": 2.66641, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@25", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/25.gif", "id": "friedman-2b180c3a0e8120c9", "metric_expression": "2.720+", "metric_symbol": "s", "metric_value": 2.72, "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.720+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinpen", "side": 2.72, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@26", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/26.gif", "id": "friedman-79bcdb6fc92c72f5", "metric_expression": "2.771+", "metric_symbol": "s", "metric_value": 2.771, "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.771+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinpen", "side": 2.771, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@27", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/27.gif", "id": "friedman-b9beeccef0536c60", "metric_expression": "2.81761+", "metric_symbol": "s", "metric_value": 2.81761, "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.81761+ | Found by Ian Watson | in April 2026.", "setup": "triinpen", "side": 2.81761, "source": "Erich Friedman Packing Center", "source_image": "27.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@28", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/28.gif", "id": "friedman-055b2cf1505d3817", "metric_expression": "2.868+", "metric_symbol": "s", "metric_value": 2.868, "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.868+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinpen", "side": 2.868, "source": "Erich Friedman Packing Center", "source_image": "28.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@29", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/29.gif", "id": "friedman-45bc6376621f11ac", "metric_expression": "2.903+", "metric_symbol": "s", "metric_value": 2.903, "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.903+ | Found by Ignacio Vallejo | in April 2026.", "setup": "triinpen", "side": 2.903, "source": "Erich Friedman Packing Center", "source_image": "29.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@30", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/30.gif", "id": "friedman-9bbeddaa7856bd2b", "metric_expression": "2.952+", "metric_symbol": "s", "metric_value": 2.952, "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.952+ | Found by Ignacio Vallejo | in April 2026.", "setup": "triinpen", "side": 2.952, "source": "Erich Friedman Packing Center", "source_image": "30.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@31", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/31.gif", "id": "friedman-591672036688db40", "metric_expression": "2.992+", "metric_symbol": "s", "metric_value": 2.992, "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.992+ | Found by Emerson Connelly | in April 2026.", "setup": "triinpen", "side": 2.992, "source": "Erich Friedman Packing Center", "source_image": "31.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@32", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/32.gif", "id": "friedman-31e29416ce2c1316", "metric_expression": "3.029+", "metric_symbol": "s", "metric_value": 3.029, "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.029+ | Found by Emerson Connelly | in April 2026.", "setup": "triinpen", "side": 3.029, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@33", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/33.gif", "id": "friedman-a8c79f30a396724c", "metric_expression": "3.078+", "metric_symbol": "s", "metric_value": 3.078, "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.078+ | Found by Emerson Connelly | in April 2026.", "setup": "triinpen", "side": 3.078, "source": "Erich Friedman Packing Center", "source_image": "33.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@34", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/34.gif", "id": "friedman-8b0dda58d5153d92", "metric_expression": "3.114+", "metric_symbol": "s", "metric_value": 3.114, "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.114+ | Found by Emerson Connelly | in April 2026.", "setup": "triinpen", "side": 3.114, "source": "Erich Friedman Packing Center", "source_image": "34.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@35", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/35.gif", "id": "friedman-1cb318bc9b8161c4", "metric_expression": "3.150+", "metric_symbol": "s", "metric_value": 3.15, "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.150+ | Found by Emerson Connelly | in April 2026.", "setup": "triinpen", "side": 3.15, "source": "Erich Friedman Packing Center", "source_image": "35.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@36", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/36.gif", "id": "friedman-fe8ce057b8d651f6", "metric_expression": "3.177+", "metric_symbol": "s", "metric_value": 3.177, "n": 36, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.177+ | Found by Emerson Connelly | in April 2026.", "setup": "triinpen", "side": 3.177, "source": "Erich Friedman Packing Center", "source_image": "36.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@37", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/37.gif", "id": "friedman-c5eee355e150d7d2", "metric_expression": "3.21529+", "metric_symbol": "s", "metric_value": 3.21529, "n": 37, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.21529+ | Found by Nathan Roll | in April 2026.", "setup": "triinpen", "side": 3.21529, "source": "Erich Friedman Packing Center", "source_image": "37.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@38", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/38.gif", "id": "friedman-be90f7181b1b549b", "metric_expression": "3.25877+", "metric_symbol": "s", "metric_value": 3.25877, "n": 38, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.25877+ | Found by Nathan Roll | in April 2026.", "setup": "triinpen", "side": 3.25877, "source": "Erich Friedman Packing Center", "source_image": "38.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@39", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/39.gif", "id": "friedman-7f092aea9b7120aa", "metric_expression": "3.295+", "metric_symbol": "s", "metric_value": 3.295, "n": 39, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.295+ | Found by Emerson Connelly | in April 2026.", "setup": "triinpen", "side": 3.295, "source": "Erich Friedman Packing Center", "source_image": "39.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Pentagons", "verified": false}
-{"case": "triinpen@40", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/40.gif", "id": "friedman-a15498f8116a7bcc", "metric_expression": "3.32786+", "metric_symbol": "s", "metric_value": 3.32786, "n": 40, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.32786+ | Found by Nathan Roll | in April 2026.", "setup": "triinpen", "side": 3.32786, "source": "Erich Friedman Packing Center", "source_image": "40.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Triangles in Pentagons", "verified": false}
-{"case": "cirinpen@1", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.1.png", "id": "friedman-c9f2bcf3f1dbe7c5", "metric_expression": "1.453+", "metric_symbol": "s", "metric_value": 1.453, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2tan(36\u00b0) | s = 1.453+ | Trivial.", "setup": "cirinpen", "side": 1.453, "source": "Erich Friedman Packing Center", "source_image": "pent.1.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@2", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.2.png", "id": "friedman-ed9c0d76bc77ea1a", "metric_expression": "2.689+", "metric_symbol": "s", "metric_value": 2.689, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2tan(36\u00b0) + \u221a5 - 1 | s = 2.689+ | Trivial.", "setup": "cirinpen", "side": 2.689, "source": "Erich Friedman Packing Center", "source_image": "pent.2.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@3", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.3.png", "id": "friedman-26644edcfdfec30c", "metric_expression": "3.015+", "metric_symbol": "s", "metric_value": 3.015, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.015+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 3.015, "source": "Erich Friedman Packing Center", "source_image": "pent.3.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@4", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.4.png", "id": "friedman-9156e410455106ef", "metric_expression": "3.314+", "metric_symbol": "s", "metric_value": 3.314, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.314+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 3.314, "source": "Erich Friedman Packing Center", "source_image": "pent.4.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@5", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.5.png", "id": "friedman-d66ba0c1e7a08c8b", "metric_expression": "3.453+", "metric_symbol": "s", "metric_value": 3.453, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2tan(36\u00b0) + 2 | s = 3.453+ | Trivial.", "setup": "cirinpen", "side": 3.453, "source": "Erich Friedman Packing Center", "source_image": "pent.5.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@6", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.6.png", "id": "friedman-4864d7bb2c47dcf5", "metric_expression": "3.804+", "metric_symbol": "s", "metric_value": 3.804, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2tan(36\u00b0) + 4sin(36\u00b0) | s = 3.804+ | Trivial.", "setup": "cirinpen", "side": 3.804, "source": "Erich Friedman Packing Center", "source_image": "pent.6.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@7", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.7.png", "id": "friedman-e0d62c06e228a431", "metric_expression": "4.236+", "metric_symbol": "s", "metric_value": 4.236, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.236+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 4.236, "source": "Erich Friedman Packing Center", "source_image": "pent.7.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@8", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.8.png", "id": "friedman-f94cccc6d82b2ff2", "metric_expression": "4.564+", "metric_symbol": "s", "metric_value": 4.564, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.564+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 4.564, "source": "Erich Friedman Packing Center", "source_image": "pent.8.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@9", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.9.png", "id": "friedman-0941f9b189caab02", "metric_expression": "4.825+", "metric_symbol": "s", "metric_value": 4.825, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.825+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 4.825, "source": "Erich Friedman Packing Center", "source_image": "pent.9.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@10", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.10.png", "id": "friedman-7f3d81e4662c4616", "metric_expression": "5.095+", "metric_symbol": "s", "metric_value": 5.095, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.095+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 5.095, "source": "Erich Friedman Packing Center", "source_image": "pent.10.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@11", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.11.gif", "id": "friedman-b4a88a8ece9f21cb", "metric_expression": "5.240+", "metric_symbol": "s", "metric_value": 5.24, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.240+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 5.24, "source": "Erich Friedman Packing Center", "source_image": "pent.11.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@12", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.12.png", "id": "friedman-734cfcf308e1e9d2", "metric_expression": "5.407+", "metric_symbol": "s", "metric_value": 5.407, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.407+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 5.407, "source": "Erich Friedman Packing Center", "source_image": "pent.12.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@13", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.13.png", "id": "friedman-ce3600f54e22eb20", "metric_expression": "5.651+", "metric_symbol": "s", "metric_value": 5.651, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.651+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 5.651, "source": "Erich Friedman Packing Center", "source_image": "pent.13.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@14", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.14.png", "id": "friedman-158eb3bf8601d310", "metric_expression": "5.808+", "metric_symbol": "s", "metric_value": 5.808, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.808+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 5.808, "source": "Erich Friedman Packing Center", "source_image": "pent.14.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@15", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.15.gif", "id": "friedman-6a72351047bc84a7", "metric_expression": "5.945+", "metric_symbol": "s", "metric_value": 5.945, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.945+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 5.945, "source": "Erich Friedman Packing Center", "source_image": "pent.15.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@16", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.16.png", "id": "friedman-208c860fd242dac6", "metric_expression": "6.129+", "metric_symbol": "s", "metric_value": 6.129, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.129+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 6.129, "source": "Erich Friedman Packing Center", "source_image": "pent.16.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@17", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.17.gif", "id": "friedman-26afa89c5f7c2ad0", "metric_expression": "6.419+", "metric_symbol": "s", "metric_value": 6.419, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.419+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 6.419, "source": "Erich Friedman Packing Center", "source_image": "pent.17.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@18", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.18.gif", "id": "friedman-101cf81d62f95e87", "metric_expression": "6.586+", "metric_symbol": "s", "metric_value": 6.586, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.586+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 6.586, "source": "Erich Friedman Packing Center", "source_image": "pent.18.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@19", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.19.gif", "id": "friedman-59bf470092f01cbc", "metric_expression": "6.777+", "metric_symbol": "s", "metric_value": 6.777, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.777+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 6.777, "source": "Erich Friedman Packing Center", "source_image": "pent.19.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@20", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.20.gif", "id": "friedman-3a1d065c11ca84de", "metric_expression": "6.944+", "metric_symbol": "s", "metric_value": 6.944, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.944+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 6.944, "source": "Erich Friedman Packing Center", "source_image": "pent.20.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@21", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.21.gif", "id": "friedman-ed29424aa41ad1b1", "metric_expression": "7.107+", "metric_symbol": "s", "metric_value": 7.107, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.107+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 7.107, "source": "Erich Friedman Packing Center", "source_image": "pent.21.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@22", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.22.gif", "id": "friedman-46ff6d83528fa7a5", "metric_expression": "7.271+", "metric_symbol": "s", "metric_value": 7.271, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.271+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 7.271, "source": "Erich Friedman Packing Center", "source_image": "pent.22.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@23", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.23.gif", "id": "friedman-84460262a31d0fdc", "metric_expression": "7.397+", "metric_symbol": "s", "metric_value": 7.397, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.397+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 7.397, "source": "Erich Friedman Packing Center", "source_image": "pent.23.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
-{"case": "cirinpen@24", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.24.gif", "id": "friedman-dbf693fd05289ccf", "metric_expression": "7.534+", "metric_symbol": "s", "metric_value": 7.534, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.534+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 7.534, "source": "Erich Friedman Packing Center", "source_image": "pent.24.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
-{"case": "squinpen@1", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/1.gif", "id": "friedman-d7ef2119776f0d12", "metric_expression": ".936+", "metric_symbol": "s", "metric_value": 0.936, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = cos(27\u00b0) / cos(18\u00b0) | s = .936+ | Trivial. |", "setup": "squinpen", "side": 0.936, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@2", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/2.gif", "id": "friedman-3f4163ac8dcdd1b9", "metric_expression": "1.535+", "metric_symbol": "s", "metric_value": 1.535, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4\u221a(1\u20132/\u221a5)+\u221a5\u20132 | s = 1.535+ | Found by Erich Friedman | in March 2012.", "setup": "squinpen", "side": 1.535, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@3", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/3.gif", "id": "friedman-49f61cc055ea2c87", "metric_expression": "1.695+", "metric_symbol": "s", "metric_value": 1.695, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.695+ | Found by David W. Cantrell | in July 2012. |", "setup": "squinpen", "side": 1.695, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@4", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/4.gif", "id": "friedman-ef16cdaf2d6a02bd", "metric_expression": "1.861+", "metric_symbol": "s", "metric_value": 1.861, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.861+ | Found by Maurizio Morandi | in July 2012. |", "setup": "squinpen", "side": 1.861, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@5", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/5.gif", "id": "friedman-7f70dc3990e182fa", "metric_expression": "1.951+", "metric_symbol": "s", "metric_value": 1.951, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 + cos(18\u00b0) | s = 1.951+ | Found by Erich Friedman | in March 2012.", "setup": "squinpen", "side": 1.951, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@6", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/6.gif", "id": "friedman-e7afd9e46316bcc1", "metric_expression": "2.185+", "metric_symbol": "s", "metric_value": 2.185, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6\u221a(1\u20132/\u221a5)+\u221a5\u20132 | s = 2.185+ | Found by Erich Friedman | in March 2012.", "setup": "squinpen", "side": 2.185, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@7", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/7.gif", "id": "friedman-2ecddf9cbfa1f173", "metric_expression": "2.421+", "metric_symbol": "s", "metric_value": 2.421, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6\u221a(1\u20132/\u221a5)+2\u221a5\u20134 | s = 2.421+ | Found by Erich Friedman | in July 2012.", "setup": "squinpen", "side": 2.421, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@8", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/8.gif", "id": "friedman-6a3b223ab63c2947", "metric_expression": "2.565+", "metric_symbol": "s", "metric_value": 2.565, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.565+ | Found by David W. Cantrell | in July 2012. |", "setup": "squinpen", "side": 2.565, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@9", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/9.gif", "id": "friedman-a6c2b0197783eee5", "metric_expression": "2.693+", "metric_symbol": "s", "metric_value": 2.693, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.693+ | Found by Timo Berthold et al | in January 2026. |", "setup": "squinpen", "side": 2.693, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@10", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/10.gif", "id": "friedman-ccbbb98ad3054d40", "metric_expression": "2.793+", "metric_symbol": "s", "metric_value": 2.793, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.793+ | Found by Timo Berthold et al | in January 2026.", "setup": "squinpen", "side": 2.793, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@11", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/11.gif", "id": "friedman-12d57458705ce4cb", "metric_expression": "2.890+", "metric_symbol": "s", "metric_value": 2.89, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.890+ | Found by Timo Berthold et al | in January 2026.", "setup": "squinpen", "side": 2.89, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@12", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/12.gif", "id": "friedman-2be59682b4c2e87c", "metric_expression": "2.969+", "metric_symbol": "s", "metric_value": 2.969, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.969+ | Found by Timo Berthold et al | in January 2026.", "setup": "squinpen", "side": 2.969, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@13", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/13.gif", "id": "friedman-3d3e0b87fcbe50c3", "metric_expression": "3.121+", "metric_symbol": "s", "metric_value": 3.121, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2\u221a(1\u20132/\u221a5)+2\u221a5\u20132 | s = 3.121+ | Found by David W. Cantrell | in July 2012.", "setup": "squinpen", "side": 3.121, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@14", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/14.gif", "id": "friedman-02be1bc530651adb", "metric_expression": "3.187+", "metric_symbol": "s", "metric_value": 3.187, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.187+ | Found by David W. Cantrell | in July 2012. |", "setup": "squinpen", "side": 3.187, "source": "Erich Friedman Packing Center", "source_image": "14.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@15", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/15.gif", "id": "friedman-a43dcbc6943d141b", "metric_expression": "3.284+", "metric_symbol": "s", "metric_value": 3.284, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (\u221a(125\u201338\u221a5)+8\u20132\u221a5)/3 | s = 3.284+ | Found by David W. Cantrell | in July 2012.", "setup": "squinpen", "side": 3.284, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@16", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/16.gif", "id": "friedman-c6a1e8cb1e0deddf", "metric_expression": "3.480+", "metric_symbol": "s", "metric_value": 3.48, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.480+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinpen", "side": 3.48, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@17", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/17.gif", "id": "friedman-3456245654cc9b9f", "metric_expression": "3.541+", "metric_symbol": "s", "metric_value": 3.541, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.541+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinpen", "side": 3.541, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@18", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/18.gif", "id": "friedman-2ffc826ecadac301", "metric_expression": "3.626+", "metric_symbol": "s", "metric_value": 3.626, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.626+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinpen", "side": 3.626, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@19", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/19.gif", "id": "friedman-c9abe1676a142edd", "metric_expression": "3.710+", "metric_symbol": "s", "metric_value": 3.71, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.710+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinpen", "side": 3.71, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@20", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/20.gif", "id": "friedman-288106ba840a58c8", "metric_expression": "3.802+", "metric_symbol": "s", "metric_value": 3.802, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.802+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinpen", "side": 3.802, "source": "Erich Friedman Packing Center", "source_image": "20.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@21", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/21.gif", "id": "friedman-2b3be1a404d9d1a5", "metric_expression": "3.864+", "metric_symbol": "s", "metric_value": 3.864, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.864+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 3.864, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@22", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/22.gif", "id": "friedman-8f8027ed0a740da0", "metric_expression": "3.937+", "metric_symbol": "s", "metric_value": 3.937, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.937+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 3.937, "source": "Erich Friedman Packing Center", "source_image": "22.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@23", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/23.gif", "id": "friedman-8590a862cf3736dc", "metric_expression": "4.002+", "metric_symbol": "s", "metric_value": 4.002, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.002+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 4.002, "source": "Erich Friedman Packing Center", "source_image": "23.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@24", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/24.gif", "id": "friedman-44eadd0b8f885d67", "metric_expression": "4.107+", "metric_symbol": "s", "metric_value": 4.107, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.107+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 4.107, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@25", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/25.gif", "id": "friedman-8a9d49a64c978c0f", "metric_expression": "4.169+", "metric_symbol": "s", "metric_value": 4.169, "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.169+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 4.169, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@26", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/26.gif", "id": "friedman-b29bdc83b0d065b8", "metric_expression": "4.223+", "metric_symbol": "s", "metric_value": 4.223, "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.223+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 4.223, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@27", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/27.gif", "id": "friedman-da78765113e89e22", "metric_expression": "4.350+", "metric_symbol": "s", "metric_value": 4.35, "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.350+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 4.35, "source": "Erich Friedman Packing Center", "source_image": "27.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@28", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/28.gif", "id": "friedman-6b34ec50ffe92fbb", "metric_expression": "4.421+", "metric_symbol": "s", "metric_value": 4.421, "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.421+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 4.421, "source": "Erich Friedman Packing Center", "source_image": "28.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@29", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/29.gif", "id": "friedman-21c659f8071b2b16", "metric_expression": "4.499+", "metric_symbol": "s", "metric_value": 4.499, "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.499+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 4.499, "source": "Erich Friedman Packing Center", "source_image": "29.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@30", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif", "id": "friedman-7173d82201ed6e3c", "metric_expression": "4.550+", "metric_symbol": "s", "metric_value": 4.55, "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 4.55, "source": "Erich Friedman Packing Center", "source_image": "30.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@31", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/31.gif", "id": "friedman-dd2cd3babb384303", "metric_expression": "4.63041+", "metric_symbol": "s", "metric_value": 4.63041, "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.63041+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 4.63041, "source": "Erich Friedman Packing Center", "source_image": "31.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@32", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/32.gif", "id": "friedman-2d92e9603ee41a64", "metric_expression": "4.70774+", "metric_symbol": "s", "metric_value": 4.70774, "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.70774+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 4.70774, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@33", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/33.gif", "id": "friedman-63f93454f18c250d", "metric_expression": "4.75774+", "metric_symbol": "s", "metric_value": 4.75774, "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.75774+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 4.75774, "source": "Erich Friedman Packing Center", "source_image": "33.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@34", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif", "id": "friedman-eeb6149a86c27680", "metric_expression": "4.81817+", "metric_symbol": "s", "metric_value": 4.81817, "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 4.81817, "source": "Erich Friedman Packing Center", "source_image": "34.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@35", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/35.gif", "id": "friedman-e3a828c2c58bf45d", "metric_expression": "4.86994+", "metric_symbol": "s", "metric_value": 4.86994, "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.86994+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 4.86994, "source": "Erich Friedman Packing Center", "source_image": "35.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@36", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/36.gif", "id": "friedman-c86ce8a81dccfffd", "metric_expression": "4.93902+", "metric_symbol": "s", "metric_value": 4.93902, "n": 36, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.93902+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 4.93902, "source": "Erich Friedman Packing Center", "source_image": "36.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@37", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/37.gif", "id": "friedman-8941d727017dcd77", "metric_expression": "4.98234+", "metric_symbol": "s", "metric_value": 4.98234, "n": 37, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.98234+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 4.98234, "source": "Erich Friedman Packing Center", "source_image": "37.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@38", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/38.gif", "id": "friedman-12e2bcc7445aa5de", "metric_expression": "5.05233+", "metric_symbol": "s", "metric_value": 5.05233, "n": 38, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.05233+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 5.05233, "source": "Erich Friedman Packing Center", "source_image": "38.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@39", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/39.gif", "id": "friedman-298c40434327f042", "metric_expression": "5.13846+", "metric_symbol": "s", "metric_value": 5.13846, "n": 39, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.13846+ | Found by Nathan Roll | in April 2026.", "setup": "squinpen", "side": 5.13846, "source": "Erich Friedman Packing Center", "source_image": "39.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinpen@40", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/40.gif", "id": "friedman-4af74e832ea9a0b5", "metric_expression": "5.17250+", "metric_symbol": "s", "metric_value": 5.1725, "n": 40, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.17250+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 5.1725, "source": "Erich Friedman Packing Center", "source_image": "40.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
-{"case": "squinoct@1", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/1.gif", "id": "friedman-da5933f6713060f4", "metric_expression": "1/\u221a(2+\u221a2) = .54119+", "metric_symbol": "s", "metric_value": 0.54119, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1/\u221a(2+\u221a2) = .54119+ | Trivial. |", "setup": "squinoct", "side": 0.54119, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@2", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/2.gif", "id": "friedman-b25c78ae72aa7537", "metric_expression": ".87667+", "metric_symbol": "s", "metric_value": 0.87667, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = .87667+ | Found by Maurizio Morandi | in December 2013.", "setup": "squinoct", "side": 0.87667, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@3", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/3.gif", "id": "friedman-151639396050713e", "metric_expression": "18 \u2013 12\u221a2 = 1.02940+", "metric_symbol": "s", "metric_value": 1.0294, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 18 \u2013 12\u221a2 = 1.02940+ | Found by Erich Friedman | in December 2013.", "setup": "squinoct", "side": 1.0294, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@4", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/4.gif", "id": "friedman-d6bbf9f56c231029", "metric_expression": "\u221a(4\u20132\u221a2) = 1.08239+", "metric_symbol": "s", "metric_value": 1.08239, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a(4\u20132\u221a2) = 1.08239+ | Trivial. |", "setup": "squinoct", "side": 1.08239, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@5", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/5.gif", "id": "friedman-f0ab9071f835b471", "metric_expression": "3\u221a2 \u2013 3 = 1.24261+", "metric_symbol": "s", "metric_value": 1.24261, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3\u221a2 \u2013 3 = 1.24261+ | Trivial. |", "setup": "squinoct", "side": 1.24261, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@6", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/6.gif", "id": "friedman-c1e40d7ffb11aded", "metric_expression": "7 \u2013 4\u221a2 = 1.34314+", "metric_symbol": "s", "metric_value": 1.34314, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7 \u2013 4\u221a2 = 1.34314+ | Found by Maurizio Morandi | in December 2013.", "setup": "squinoct", "side": 1.34314, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@7", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/7.gif", "id": "friedman-809d1257bba66448", "metric_expression": "1.43691+", "metric_symbol": "s", "metric_value": 1.43691, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.43691+ | Found by Maurizio Morandi | in December 2013.", "setup": "squinoct", "side": 1.43691, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@8", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/8.gif", "id": "friedman-e0291935714d1fb4", "metric_expression": "1.56967+", "metric_symbol": "s", "metric_value": 1.56967, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.56967+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 1.56967, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@9", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/9.gif", "id": "friedman-38c5ae1e73ee6676", "metric_expression": "3/\u221a(2+\u221a2) = 1.62358+", "metric_symbol": "s", "metric_value": 1.62358, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3/\u221a(2+\u221a2) = 1.62358+ | Trivial. |", "setup": "squinoct", "side": 1.62358, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@10", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/10.gif", "id": "friedman-427a7450f2d1f4bd", "metric_expression": "2^(3/4) = 1.68179+", "metric_symbol": "s", "metric_value": 1.68179, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2^(3/4) = 1.68179+ | Found by Maurizio Morandi | in December 2013.", "setup": "squinoct", "side": 1.68179, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@11", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/11.gif", "id": "friedman-f1ab48e521317a08", "metric_expression": "1.73180+", "metric_symbol": "s", "metric_value": 1.7318, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.73180+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 1.7318, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@12", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/12.gif", "id": "friedman-9d5e02cc2f15620f", "metric_expression": "1.7533+", "metric_symbol": "s", "metric_value": 1.7533, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.7533+ | Found by Maurizio Morandi | in December 2013.", "setup": "squinoct", "side": 1.7533, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@13", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/13.gif", "id": "friedman-7ea27340e360e857", "metric_expression": "1.89760+", "metric_symbol": "s", "metric_value": 1.8976, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.89760+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 1.8976, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@14", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/14.gif", "id": "friedman-06836a0d72a778f5", "metric_expression": "1.98350+", "metric_symbol": "s", "metric_value": 1.9835, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.98350+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 1.9835, "source": "Erich Friedman Packing Center", "source_image": "14.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@15", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/15.gif", "id": "friedman-ecf0183547a74f37", "metric_expression": "2.03259+", "metric_symbol": "s", "metric_value": 2.03259, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.03259+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.03259, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@16", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/16.gif", "id": "friedman-7b509f9f550de0c6", "metric_expression": "5\u221a2 \u2013 5 = 2.07106+", "metric_symbol": "s", "metric_value": 2.07106, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5\u221a2 \u2013 5 = 2.07106+ | Trivial. |", "setup": "squinoct", "side": 2.07106, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@17", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/17.gif", "id": "friedman-68b2751e38b5b755", "metric_expression": "5\u221a2 \u2013 5 = 2.07106+", "metric_symbol": "s", "metric_value": 2.07106, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5\u221a2 \u2013 5 = 2.07106+ | Trivial. |", "setup": "squinoct", "side": 2.07106, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@18", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/18.gif", "id": "friedman-c94a124453f64dbf", "metric_expression": "2.16778+", "metric_symbol": "s", "metric_value": 2.16778, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.16778+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.16778, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@19", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/19.gif", "id": "friedman-c262f3b0ebec245f", "metric_expression": "2.22823+", "metric_symbol": "s", "metric_value": 2.22823, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.22823+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.22823, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@20", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/20.gif", "id": "friedman-7f4081be3aa060a1", "metric_expression": "2.28730+", "metric_symbol": "s", "metric_value": 2.2873, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.28730+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.2873, "source": "Erich Friedman Packing Center", "source_image": "20.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@21", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/21.gif", "id": "friedman-76036df6d6b85434", "metric_expression": "2.32167+", "metric_symbol": "s", "metric_value": 2.32167, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.32167+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.32167, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@22", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/22.gif", "id": "friedman-ce6b9a629b4d15aa", "metric_expression": "2.41811+", "metric_symbol": "s", "metric_value": 2.41811, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.41811+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.41811, "source": "Erich Friedman Packing Center", "source_image": "22.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@23", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/23.gif", "id": "friedman-c7dfc422fd6ddfcf", "metric_expression": "2.47329+", "metric_symbol": "s", "metric_value": 2.47329, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.47329+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.47329, "source": "Erich Friedman Packing Center", "source_image": "23.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@24", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/24.gif", "id": "friedman-dddbad94b92c6c05", "metric_expression": "6\u221a2 \u2013 6 = 2.48528+", "metric_symbol": "s", "metric_value": 2.48528, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6\u221a2 \u2013 6 = 2.48528+ | Trivial.", "setup": "squinoct", "side": 2.48528, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@25", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/25.gif", "id": "friedman-0ae45c561bb3fc32", "metric_expression": "11/(3+\u221a2) = 2.49195+", "metric_symbol": "s", "metric_value": 2.49195, "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 11/(3+\u221a2) = 2.49195+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.49195, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@26", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/26.gif", "id": "friedman-36057ce571f3b782", "metric_expression": "2.52841+", "metric_symbol": "s", "metric_value": 2.52841, "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.52841+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.52841, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@27", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/27.gif", "id": "friedman-8164ac63cdc325e5", "metric_expression": "2.58695+", "metric_symbol": "s", "metric_value": 2.58695, "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.58695+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.58695, "source": "Erich Friedman Packing Center", "source_image": "27.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@28", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/28.gif", "id": "friedman-bddf4849ff3a31f0", "metric_expression": "2.63116+", "metric_symbol": "s", "metric_value": 2.63116, "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.63116+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.63116, "source": "Erich Friedman Packing Center", "source_image": "28.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@29", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/29.gif", "id": "friedman-fd024b7869011606", "metric_expression": "2.70811+", "metric_symbol": "s", "metric_value": 2.70811, "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.70811+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.70811, "source": "Erich Friedman Packing Center", "source_image": "29.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
-{"case": "squinoct@30", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/30.gif", "id": "friedman-bc947d974efc5caa", "metric_expression": "2.74220+", "metric_symbol": "s", "metric_value": 2.7422, "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.74220+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.7422, "source": "Erich Friedman Packing Center", "source_image": "30.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
-{"case": "triinoct@1", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/1.gif", "id": "friedman-c8efc6f47945c67c", "metric_expression": ".46470+", "metric_symbol": "s", "metric_value": 0.4647, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = .46470+ | Trivial. |", "setup": "triinoct", "side": 0.4647, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@2", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/2.gif", "id": "friedman-181b58c3365d23a6", "metric_expression": "\u221a3/\u221a(4+2\u221a2) = .66282+", "metric_symbol": "s", "metric_value": 0.66282, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a3/\u221a(4+2\u221a2) = .66282+ | Trivial. |", "setup": "triinoct", "side": 0.66282, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@3", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/3.gif", "id": "friedman-f7af9ac1be8fe735", "metric_expression": ".73651+", "metric_symbol": "s", "metric_value": 0.73651, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = .73651+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 0.73651, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@4", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/4.gif", "id": "friedman-939870266bcc0da1", "metric_expression": ".77733+", "metric_symbol": "s", "metric_value": 0.77733, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = .77733+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 0.77733, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@5", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/5.gif", "id": "friedman-8a3c42dfa07403fd", "metric_expression": ".80367+", "metric_symbol": "s", "metric_value": 0.80367, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = .80367+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 0.80367, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@6", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/6.gif", "id": "friedman-7e71647ac3920a91", "metric_expression": ".81574+", "metric_symbol": "s", "metric_value": 0.81574, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = .81574+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 0.81574, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@7", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/7.gif", "id": "friedman-6e01773283efdfcd", "metric_expression": ".92453+", "metric_symbol": "s", "metric_value": 0.92453, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = .92453+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 0.92453, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@8", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/8.gif", "id": "friedman-02c221fe120e674c", "metric_expression": ".98782+", "metric_symbol": "s", "metric_value": 0.98782, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = .98782+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 0.98782, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@9", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/9.gif", "id": "friedman-0f68ee9b37f799d1", "metric_expression": "1.00875+", "metric_symbol": "s", "metric_value": 1.00875, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.00875+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.00875, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@10", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/10.gif", "id": "friedman-a31443a9888942ad", "metric_expression": "1.07565+", "metric_symbol": "s", "metric_value": 1.07565, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.07565+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.07565, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@11", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/11.gif", "id": "friedman-e21c3a21adbaaabc", "metric_expression": "1.14571+", "metric_symbol": "s", "metric_value": 1.14571, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.14571+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.14571, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@12", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/12.gif", "id": "friedman-a7daf48cc0b7521a", "metric_expression": "1.19929+", "metric_symbol": "s", "metric_value": 1.19929, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.19929+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.19929, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@13", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/13.gif", "id": "friedman-2c82036dc0fc3460", "metric_expression": "1.23759+", "metric_symbol": "s", "metric_value": 1.23759, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.23759+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.23759, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@14", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/14.gif", "id": "friedman-82b661560c998f1a", "metric_expression": "1.27677+", "metric_symbol": "s", "metric_value": 1.27677, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.27677+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.27677, "source": "Erich Friedman Packing Center", "source_image": "14.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@15", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/15.gif", "id": "friedman-175875dadd122feb", "metric_expression": "1.30275+", "metric_symbol": "s", "metric_value": 1.30275, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.30275+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.30275, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@16", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/16.gif", "id": "friedman-4c5ccc91a35d1a01", "metric_expression": "1.34584+", "metric_symbol": "s", "metric_value": 1.34584, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.34584+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.34584, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@17", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/17.gif", "id": "friedman-b81f6f653f27ba0a", "metric_expression": "1.38964+", "metric_symbol": "s", "metric_value": 1.38964, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.38964+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.38964, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@18", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/18.gif", "id": "friedman-d47d8c67dc8ae82f", "metric_expression": "1.41836+", "metric_symbol": "s", "metric_value": 1.41836, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.41836+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.41836, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@19", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/19.gif", "id": "friedman-8795b2bf292490f1", "metric_expression": "1.46749+", "metric_symbol": "s", "metric_value": 1.46749, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.46749+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.46749, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@20", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/20.gif", "id": "friedman-a30713bb98715f4e", "metric_expression": "1.49832+", "metric_symbol": "s", "metric_value": 1.49832, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.49832+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.49832, "source": "Erich Friedman Packing Center", "source_image": "20.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@21", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/21.gif", "id": "friedman-dedc662d5dbfec33", "metric_expression": "1.52615+", "metric_symbol": "s", "metric_value": 1.52615, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.52615+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.52615, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@22", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/22.gif", "id": "friedman-818e75465f9d922a", "metric_expression": "1.55545+", "metric_symbol": "s", "metric_value": 1.55545, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.55545+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.55545, "source": "Erich Friedman Packing Center", "source_image": "22.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@23", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/23.gif", "id": "friedman-2b90bd6917df7354", "metric_expression": "1.58458+", "metric_symbol": "s", "metric_value": 1.58458, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.58458+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.58458, "source": "Erich Friedman Packing Center", "source_image": "23.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@24", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/24.gif", "id": "friedman-4144217c1c64407b", "metric_expression": "1.60261+", "metric_symbol": "s", "metric_value": 1.60261, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.60261+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.60261, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@25", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/25.gif", "id": "friedman-c4b6e206182f6656", "metric_expression": "1.63797+", "metric_symbol": "s", "metric_value": 1.63797, "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.63797+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.63797, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@26", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/26.gif", "id": "friedman-b5025e53f93dd7df", "metric_expression": "1.67666+", "metric_symbol": "s", "metric_value": 1.67666, "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.67666+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.67666, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@27", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/27.gif", "id": "friedman-6b67435ae7c5d63b", "metric_expression": "1.70882+", "metric_symbol": "s", "metric_value": 1.70882, "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.70882+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.70882, "source": "Erich Friedman Packing Center", "source_image": "27.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@28", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/28.gif", "id": "friedman-480aa33577c942b6", "metric_expression": "1.73954+", "metric_symbol": "s", "metric_value": 1.73954, "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.73954+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.73954, "source": "Erich Friedman Packing Center", "source_image": "28.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@29", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/29.gif", "id": "friedman-98dd78ff4d6f199d", "metric_expression": "1.75576+", "metric_symbol": "s", "metric_value": 1.75576, "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.75576+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.75576, "source": "Erich Friedman Packing Center", "source_image": "29.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "triinoct@30", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/30.gif", "id": "friedman-4e400c77bc6203b7", "metric_expression": "1.78101+", "metric_symbol": "s", "metric_value": 1.78101, "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.78101+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.78101, "source": "Erich Friedman Packing Center", "source_image": "30.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
-{"case": "octinoct@1", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/1.gif", "id": "friedman-b24674da59558d1e", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 | Trivial. |", "setup": "octinoct", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@2", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/2.gif", "id": "friedman-0f39a906713cff4f", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial. |", "setup": "octinoct", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@3", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/3.gif", "id": "friedman-5b836fbc06fd414e", "metric_expression": "5\u20132\u221a2 = 2.17157+", "metric_symbol": "s", "metric_value": 2.17157, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5\u20132\u221a2 = 2.17157+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 2.17157, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@4", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/4.gif", "id": "friedman-e11eef2c6244ac4b", "metric_expression": "\u221a(5+1/\u221a2) = 2.38895+", "metric_symbol": "s", "metric_value": 2.38895, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a(5+1/\u221a2) = 2.38895+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 2.38895, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@5", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/5.gif", "id": "friedman-bd10f4529feec332", "metric_expression": "2+1/\u221a2 = 2.70710+", "metric_symbol": "s", "metric_value": 2.7071, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+1/\u221a2 = 2.70710+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 2.7071, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@6", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/6.gif", "id": "friedman-f7ac307d81b19162", "metric_expression": "2.98915+", "metric_symbol": "s", "metric_value": 2.98915, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.98915+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 2.98915, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@7", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/7.gif", "id": "friedman-0afa616b2a3243c2", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 | Trivial. |", "setup": "octinoct", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@8", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/8.gif", "id": "friedman-b639b315fc5e4d08", "metric_expression": "3.27526+", "metric_symbol": "s", "metric_value": 3.27526, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.27526+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 3.27526, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@9", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/9.gif", "id": "friedman-f0800ed60969527f", "metric_expression": "2+\u221a2 = 3.41421+", "metric_symbol": "s", "metric_value": 3.41421, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+\u221a2 = 3.41421+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 3.41421, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@10", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/10.gif", "id": "friedman-98ee7aa5c63524d5", "metric_expression": "3+1/\u221a2 = 3.70710+", "metric_symbol": "s", "metric_value": 3.7071, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3+1/\u221a2 = 3.70710+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 3.7071, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@11", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/11.gif", "id": "friedman-0172a8cf71826939", "metric_expression": "3.93270+", "metric_symbol": "s", "metric_value": 3.9327, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.93270+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 3.9327, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@12", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/12.gif", "id": "friedman-90c1d80bdc44c46d", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 | Trivial. |", "setup": "octinoct", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@13", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/13.gif", "id": "friedman-611052921fc0aead", "metric_expression": "7\u20132\u221a2 = 4.17157+", "metric_symbol": "s", "metric_value": 4.17157, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7\u20132\u221a2 = 4.17157+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 4.17157, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@14", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/14.gif", "id": "friedman-9bdc29340ab79bc6", "metric_expression": "4.28155+", "metric_symbol": "s", "metric_value": 4.28155, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.28155+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 4.28155, "source": "Erich Friedman Packing Center", "source_image": "14.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@15", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/15.gif", "id": "friedman-6bd941204bb86cc2", "metric_expression": "4.45594+", "metric_symbol": "s", "metric_value": 4.45594, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.45594+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 4.45594, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@16", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/16.gif", "id": "friedman-c1282f4d01a2ddef", "metric_expression": "4.59824+", "metric_symbol": "s", "metric_value": 4.59824, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.59824+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 4.59824, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@17", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/17.gif", "id": "friedman-67f790dcd2d7aedf", "metric_expression": "4.75741+", "metric_symbol": "s", "metric_value": 4.75741, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.75741+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 4.75741, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@18", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/18.gif", "id": "friedman-bc52e524d7f1dc6a", "metric_expression": "4.85717+", "metric_symbol": "s", "metric_value": 4.85717, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.85717+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 4.85717, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@19", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/19.gif", "id": "friedman-7f8d435e7e75742a", "metric_expression": "4.93586+", "metric_symbol": "s", "metric_value": 4.93586, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.93586+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 4.93586, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@20", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/20.gif", "id": "friedman-6c5a60f7a5b99e14", "metric_expression": "5.06781+", "metric_symbol": "s", "metric_value": 5.06781, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.06781+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.06781, "source": "Erich Friedman Packing Center", "source_image": "20.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@21", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/21.gif", "id": "friedman-62b042a9c4160f76", "metric_expression": "5.19715+", "metric_symbol": "s", "metric_value": 5.19715, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.19715+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.19715, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@22", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/22.gif", "id": "friedman-fa85f57ef3ad9e9e", "metric_expression": "5.35750+", "metric_symbol": "s", "metric_value": 5.3575, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.35750+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.3575, "source": "Erich Friedman Packing Center", "source_image": "22.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@23", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/23.gif", "id": "friedman-007965e1f7c3b3a8", "metric_expression": "5.41440+", "metric_symbol": "s", "metric_value": 5.4144, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.41440+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.4144, "source": "Erich Friedman Packing Center", "source_image": "23.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@24", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/24.gif", "id": "friedman-c97db9b3738a229d", "metric_expression": "5.55464+", "metric_symbol": "s", "metric_value": 5.55464, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.55464+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.55464, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@25", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/25.gif", "id": "friedman-8c0f88c0b7b2ce6f", "metric_expression": "5.65593+", "metric_symbol": "s", "metric_value": 5.65593, "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.65593+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.65593, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@26", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/26.gif", "id": "friedman-bc05afd85bd1c220", "metric_expression": "5.73940+", "metric_symbol": "s", "metric_value": 5.7394, "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.73940+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.7394, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@27", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/27.gif", "id": "friedman-6eda0588045826bc", "metric_expression": "5.81238+", "metric_symbol": "s", "metric_value": 5.81238, "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.81238+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.81238, "source": "Erich Friedman Packing Center", "source_image": "27.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@28", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/28.gif", "id": "friedman-692f872700d246c9", "metric_expression": "3+2\u221a2 = 5.82842+", "metric_symbol": "s", "metric_value": 5.82842, "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3+2\u221a2 = 5.82842+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.82842, "source": "Erich Friedman Packing Center", "source_image": "28.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@29", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/29.gif", "id": "friedman-9d7906d7782ebbc1", "metric_expression": "6.05746+", "metric_symbol": "s", "metric_value": 6.05746, "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.05746+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 6.05746, "source": "Erich Friedman Packing Center", "source_image": "29.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "octinoct@30", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/30.gif", "id": "friedman-99e7b695be48aeea", "metric_expression": "6.15432+", "metric_symbol": "s", "metric_value": 6.15432, "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.15432+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 6.15432, "source": "Erich Friedman Packing Center", "source_image": "30.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
-{"case": "domintri@1", "external_image_url": "https://erich-friedman.github.io/packing/domintri/1.png", "id": "friedman-0c092c16e65ef91c", "metric_expression": "2+2/\u221a3 = 3.15470+", "metric_symbol": "s", "metric_value": 3.1547, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+2/\u221a3 = 3.15470+ | Trivial.", "setup": "domintri", "side": 3.1547, "source": "Erich Friedman Packing Center", "source_image": "1.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@2", "external_image_url": "https://erich-friedman.github.io/packing/domintri/2.png", "id": "friedman-a15bc7dfac6ef1a7", "metric_expression": "2+4/\u221a3 = 4.30940+", "metric_symbol": "s", "metric_value": 4.3094, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+4/\u221a3 = 4.30940+ | Trivial.", "setup": "domintri", "side": 4.3094, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@3", "external_image_url": "https://erich-friedman.github.io/packing/domintri/3.png", "id": "friedman-70e897d9bfc25e33", "metric_expression": "2+4/\u221a3 = 4.30934+", "metric_symbol": "s", "metric_value": 4.30934, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+4/\u221a3 = 4.30934+ | Trivial.", "setup": "domintri", "side": 4.30934, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@4", "external_image_url": "https://erich-friedman.github.io/packing/domintri/4.png", "id": "friedman-d81827e82f0d5304", "metric_expression": "5.38188+", "metric_symbol": "s", "metric_value": 5.38188, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.38188+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 5.38188, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@5", "external_image_url": "https://erich-friedman.github.io/packing/domintri/5.png", "id": "friedman-fdda6ecdc3a976e8", "metric_expression": "2+2\u221a3 = 5.46410+", "metric_symbol": "s", "metric_value": 5.4641, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+2\u221a3 = 5.46410+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 5.4641, "source": "Erich Friedman Packing Center", "source_image": "5.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@6", "external_image_url": "https://erich-friedman.github.io/packing/domintri/6.png", "id": "friedman-98b3407b42e56d92", "metric_expression": "4+4/\u221a3 = 6.30940+", "metric_symbol": "s", "metric_value": 6.3094, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4+4/\u221a3 = 6.30940+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 6.3094, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@7", "external_image_url": "https://erich-friedman.github.io/packing/domintri/7.png", "id": "friedman-95970e29a4251c10", "metric_expression": "6.61409+", "metric_symbol": "s", "metric_value": 6.61409, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.61409+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 6.61409, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@8", "external_image_url": "https://erich-friedman.github.io/packing/domintri/8.png", "id": "friedman-1a13d6a472aa7bee", "metric_expression": "6+2/\u221a3 = 7.15470+", "metric_symbol": "s", "metric_value": 7.1547, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6+2/\u221a3 = 7.15470+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 7.1547, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@9", "external_image_url": "https://erich-friedman.github.io/packing/domintri/9.png", "id": "friedman-0e81766811a88057", "metric_expression": "5+4/\u221a3 = 7.30940+", "metric_symbol": "s", "metric_value": 7.3094, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5+4/\u221a3 = 7.30940+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 7.3094, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@10", "external_image_url": "https://erich-friedman.github.io/packing/domintri/10.png", "id": "friedman-6e457e60eeab7f0c", "metric_expression": "3+8/\u221a3 = 7.61885+", "metric_symbol": "s", "metric_value": 7.61885, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3+8/\u221a3 = 7.61885+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 7.61885, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@11", "external_image_url": "https://erich-friedman.github.io/packing/domintri/11.png", "id": "friedman-52e1b51216b50748", "metric_expression": "7+2/\u221a3 = 8.15470+", "metric_symbol": "s", "metric_value": 8.1547, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7+2/\u221a3 = 8.15470+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 8.1547, "source": "Erich Friedman Packing Center", "source_image": "11.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@12", "external_image_url": "https://erich-friedman.github.io/packing/domintri/12.png", "id": "friedman-844f628390e4c5f4", "metric_expression": "6+4/\u221a3 = 8.30940+", "metric_symbol": "s", "metric_value": 8.3094, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6+4/\u221a3 = 8.30940+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 8.3094, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@13", "external_image_url": "https://erich-friedman.github.io/packing/domintri/13.png", "id": "friedman-922f258e8787be46", "metric_expression": "4+8/\u221a3 = 8.61885+", "metric_symbol": "s", "metric_value": 8.61885, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4+8/\u221a3 = 8.61885+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 8.61885, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@14", "external_image_url": "https://erich-friedman.github.io/packing/domintri/14.png", "id": "friedman-3b37cfa994994ce2", "metric_expression": "3+10/\u221a3 = 8.77350+", "metric_symbol": "s", "metric_value": 8.7735, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3+10/\u221a3 = 8.77350+ | Found by Maurizio Morandi | in April 2026.", "setup": "domintri", "side": 8.7735, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@15", "external_image_url": "https://erich-friedman.github.io/packing/domintri/15.png", "id": "friedman-5353651e0a25321c", "metric_expression": "7+4/\u221a3 = 9.30940+", "metric_symbol": "s", "metric_value": 9.3094, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7+4/\u221a3 = 9.30940+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 9.3094, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@16", "external_image_url": "https://erich-friedman.github.io/packing/domintri/16.png", "id": "friedman-fb928d23da3debe6", "metric_expression": "6+2\u221a3 = 9.46410+", "metric_symbol": "s", "metric_value": 9.4641, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6+2\u221a3 = 9.46410+ | Found by Maurizio Morandi | in April 2026.", "setup": "domintri", "side": 9.4641, "source": "Erich Friedman Packing Center", "source_image": "16.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@17", "external_image_url": "https://erich-friedman.github.io/packing/domintri/17.png", "id": "friedman-032a49fde439e321", "metric_expression": "4+10/\u221a3 = 9.77350+", "metric_symbol": "s", "metric_value": 9.7735, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4+10/\u221a3 = 9.77350+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 9.7735, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@18", "external_image_url": "https://erich-friedman.github.io/packing/domintri/18.png", "id": "friedman-5cecc605aaf6b720", "metric_expression": "3+4\u221a3 = 9.92820+", "metric_symbol": "s", "metric_value": 9.9282, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3+4\u221a3 = 9.92820+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 9.9282, "source": "Erich Friedman Packing Center", "source_image": "18.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@19", "external_image_url": "https://erich-friedman.github.io/packing/domintri/19.png", "id": "friedman-4f9c928d94b3ffd2", "metric_expression": "8+4/\u221a3 = 10.30940+", "metric_symbol": "s", "metric_value": 10.3094, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8+4/\u221a3 = 10.30940+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 10.3094, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@20", "external_image_url": "https://erich-friedman.github.io/packing/domintri/20.png", "id": "friedman-babeccb1f91a5e4e", "metric_expression": "7+2\u221a3 = 10.46410+", "metric_symbol": "s", "metric_value": 10.4641, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7+2\u221a3 = 10.46410+ | Found by Maurizio Morandi | in April 2026.", "setup": "domintri", "side": 10.4641, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@21", "external_image_url": "https://erich-friedman.github.io/packing/domintri/21.png", "id": "friedman-d3880ffccb6fbbf0", "metric_expression": "2+5\u221a3 = 10.66025+", "metric_symbol": "s", "metric_value": 10.66025, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+5\u221a3 = 10.66025+ | Found by Maurizio Morandi | in April 2026.", "setup": "domintri", "side": 10.66025, "source": "Erich Friedman Packing Center", "source_image": "21.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@22", "external_image_url": "https://erich-friedman.github.io/packing/domintri/22.png", "id": "friedman-ffa257a36540a61e", "metric_expression": "4(1+\u221a3) = 10.92820+", "metric_symbol": "s", "metric_value": 10.9282, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4(1+\u221a3) = 10.92820+ | Found by Maurizio Morandi | in April 2026.", "setup": "domintri", "side": 10.9282, "source": "Erich Friedman Packing Center", "source_image": "22.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@23", "external_image_url": "https://erich-friedman.github.io/packing/domintri/23.png", "id": "friedman-454e14ef9a5ce734", "metric_expression": "10+2/\u221a3 = 11.15470+", "metric_symbol": "s", "metric_value": 11.1547, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 10+2/\u221a3 = 11.15470+ | Found by Maurizio Morandi | in April 2026.", "setup": "domintri", "side": 11.1547, "source": "Erich Friedman Packing Center", "source_image": "23.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Triangles", "verified": false}
-{"case": "domintri@24", "external_image_url": "https://erich-friedman.github.io/packing/domintri/24.png", "id": "friedman-29114dd835ba2559", "metric_expression": "9+4/\u221a3 = 11.30940+", "metric_symbol": "s", "metric_value": 11.3094, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9+4/\u221a3 = 11.30940+ | Found by Maurizio Morandi | in April 2026.", "setup": "domintri", "side": 11.3094, "source": "Erich Friedman Packing Center", "source_image": "24.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Triangles", "verified": false}
-{"case": "squindom@1", "external_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "id": "friedman-5014797fdaddc695", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "1-2. | | s = 1 | Trivial. |", "setup": "squindom", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@2", "external_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "id": "friedman-757770ad1f8b5cc0", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "1-2. | | s = 1 | Trivial. |", "setup": "squindom", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@3", "external_image_url": "https://erich-friedman.github.io/packing/squindom/3.gif", "id": "friedman-a44d8b6d6f0e9f52", "metric_expression": "3/2 = 1.5", "metric_symbol": "s", "metric_value": 1.5, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "3. | | s = 3/2 = 1.5 | Trivial. |", "setup": "squindom", "side": 1.5, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@4", "external_image_url": "https://erich-friedman.github.io/packing/squindom/4.gif", "id": "friedman-d5b324bb4da5564f", "metric_expression": "1.930+", "metric_symbol": "s", "metric_value": 1.93, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "4. | | s = 1.930+ | Found by Evert Stenlund | in June 2010.", "setup": "squindom", "side": 1.93, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Evert Stenlund", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@5", "external_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "id": "friedman-eb7f1f6a68787eb8", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "5-8. | | s = 2 | Trivial. |", "setup": "squindom", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@6", "external_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "id": "friedman-26d4d607db286852", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "5-8. | | s = 2 | Trivial. |", "setup": "squindom", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@7", "external_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "id": "friedman-26d2174cf47693e2", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "5-8. | | s = 2 | Trivial. |", "setup": "squindom", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@8", "external_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "id": "friedman-770447a5fa93bcce", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "5-8. | | s = 2 | Trivial. |", "setup": "squindom", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@9", "external_image_url": "https://erich-friedman.github.io/packing/squindom/9.gif", "id": "friedman-911b5ee29fe3308b", "metric_expression": "2 + \u221a2/3 = 2.471+", "metric_symbol": "s", "metric_value": 2.471, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "9. | | s = 2 + \u221a2/3 = 2.471+ | Found by Evert Stenlund | in June 2010.", "setup": "squindom", "side": 2.471, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Evert Stenlund", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@10", "external_image_url": "https://erich-friedman.github.io/packing/squindom/10.gif", "id": "friedman-ec07df79d37cfd19", "metric_expression": "5/2 = 2.5", "metric_symbol": "s", "metric_value": 2.5, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "10. | | s = 5/2 = 2.5 | Trivial. |", "setup": "squindom", "side": 2.5, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@11", "external_image_url": "https://erich-friedman.github.io/packing/squindom/11.gif", "id": "friedman-f84588ec5a02cbec", "metric_expression": "2.779+", "metric_symbol": "s", "metric_value": 2.779, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "11. | | s = 2.779+ | Found by Evert Stenlund | in June 2010. |", "setup": "squindom", "side": 2.779, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Evert Stenlund", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@12", "external_image_url": "https://erich-friedman.github.io/packing/squindom/12.gif", "id": "friedman-15eb4c3098fcb692", "metric_expression": "6 (1 + \u221a2) / 5 = 2.897+", "metric_symbol": "s", "metric_value": 2.897, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "12. | | s = 6 (1 + \u221a2) / 5 = 2.897+ | Found by Maurizio Morandi | in June 2010. |", "setup": "squindom", "side": 2.897, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@13", "external_image_url": "https://erich-friedman.github.io/packing/squindom/13.gif", "id": "friedman-24cddd09aa88a137", "metric_expression": "2.976+", "metric_symbol": "s", "metric_value": 2.976, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "13. | | s = 2.976+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)", "setup": "squindom", "side": 2.976, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@14", "external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "id": "friedman-31da3a9cc8386278", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14-18. | | s = 3 | Trivial. |", "setup": "squindom", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@15", "external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "id": "friedman-2d2c7495b99e6c10", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14-18. | | s = 3 | Trivial. |", "setup": "squindom", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@16", "external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "id": "friedman-4e8a4fa1e52bd953", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14-18. | | s = 3 | Trivial. |", "setup": "squindom", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@17", "external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "id": "friedman-c77c38f2962c132b", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14-18. | | s = 3 | Trivial. |", "setup": "squindom", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@18", "external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "id": "friedman-abc916e48c35716f", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14-18. | | s = 3 | Trivial. |", "setup": "squindom", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@19", "external_image_url": "https://erich-friedman.github.io/packing/squindom/19.gif", "id": "friedman-67d27c6311c73bae", "metric_expression": "3 + 1/\u221a5 = 3.447+", "metric_symbol": "s", "metric_value": 3.447, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "19. | | s = 3 + 1/\u221a5 = 3.447+ | Found by Maurizio Morandi | in June 2010.", "setup": "squindom", "side": 3.447, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@20", "external_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "id": "friedman-b1853e9c65016dd9", "metric_expression": "7/2 = 3.5", "metric_symbol": "s", "metric_value": 3.5, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "setup": "squindom", "side": 3.5, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@21", "external_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "id": "friedman-2e90bf9b358b7411", "metric_expression": "7/2 = 3.5", "metric_symbol": "s", "metric_value": 3.5, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "setup": "squindom", "side": 3.5, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@22", "external_image_url": "https://erich-friedman.github.io/packing/squindom/22.gif", "id": "friedman-c7cdc02320008438", "metric_expression": "3.745+", "metric_symbol": "s", "metric_value": 3.745, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "22. | | s = 3.745+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)", "setup": "squindom", "side": 3.745, "source": "Erich Friedman Packing Center", "source_image": "22.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@23", "external_image_url": "https://erich-friedman.github.io/packing/squindom/23.gif", "id": "friedman-ec1ade482aa1a7fd", "metric_expression": "3.849+", "metric_symbol": "s", "metric_value": 3.849, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "23. | | s = 3.849+ | Found by Maurizio Morandi | in June 2010. |", "setup": "squindom", "side": 3.849, "source": "Erich Friedman Packing Center", "source_image": "23.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@24", "external_image_url": "https://erich-friedman.github.io/packing/squindom/24.gif", "id": "friedman-44afa839c5d4e499", "metric_expression": "3.882+", "metric_symbol": "s", "metric_value": 3.882, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "24. | | s = 3.882+ | Found by DC after MM | in August 2012. |", "setup": "squindom", "side": 3.882, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "David W. Cantrell after Maurizio Morandi", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@25", "external_image_url": "https://erich-friedman.github.io/packing/squindom/25.gif", "id": "friedman-f4a086f1320dfc36", "metric_expression": "3.939+", "metric_symbol": "s", "metric_value": 3.939, "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "25. | | s = 3.939+ | Found by DC after MM | in August 2012. |", "setup": "squindom", "side": 3.939, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "David W. Cantrell after Maurizio Morandi", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@26", "external_image_url": "https://erich-friedman.github.io/packing/squindom/26.gif", "id": "friedman-50a558ebf9de8bab", "metric_expression": "3.981+", "metric_symbol": "s", "metric_value": 3.981, "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "26. | | s = 3.981+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in July 2012.)", "setup": "squindom", "side": 3.981, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@27", "external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "id": "friedman-16ff90552c02c33d", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "27-32. | | s = 4 | Trivial. | |", "setup": "squindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@28", "external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "id": "friedman-2b582527ece8934e", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "27-32. | | s = 4 | Trivial. | |", "setup": "squindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@29", "external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "id": "friedman-46309bc7457b0cfe", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "27-32. | | s = 4 | Trivial. | |", "setup": "squindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@30", "external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "id": "friedman-88ebdc8d7b60ef88", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "27-32. | | s = 4 | Trivial. | |", "setup": "squindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@31", "external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "id": "friedman-65ea5574d4dd0878", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "27-32. | | s = 4 | Trivial. | |", "setup": "squindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@32", "external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "id": "friedman-020cc762b911b6b6", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "27-32. | | s = 4 | Trivial. | |", "setup": "squindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@33", "external_image_url": "https://erich-friedman.github.io/packing/squindom/33.gif", "id": "friedman-f71ebd16ddf3d624", "metric_expression": "3 + \u221a2 = 4.414+", "metric_symbol": "s", "metric_value": 4.414, "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "33. | | s = 3 + \u221a2 = 4.414+ | Found by Maurizio Morandi | in July 2012.", "setup": "squindom", "side": 4.414, "source": "Erich Friedman Packing Center", "source_image": "33.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@34", "external_image_url": "https://erich-friedman.github.io/packing/squindom/34.gif", "id": "friedman-9278a960daf8d32f", "metric_expression": "4 + \u221a2/3 = 4.471+", "metric_symbol": "s", "metric_value": 4.471, "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "34. | | s = 4 + \u221a2/3 = 4.471+ | Found by David W. Cantrell | in July 2012.", "setup": "squindom", "side": 4.471, "source": "Erich Friedman Packing Center", "source_image": "34.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@35", "external_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "id": "friedman-f71f478216853ec9", "metric_expression": "9/2 = 4.5", "metric_symbol": "s", "metric_value": 4.5, "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "setup": "squindom", "side": 4.5, "source": "Erich Friedman Packing Center", "source_image": "36.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@36", "external_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "id": "friedman-0816f27e30f718f7", "metric_expression": "9/2 = 4.5", "metric_symbol": "s", "metric_value": 4.5, "n": 36, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "setup": "squindom", "side": 4.5, "source": "Erich Friedman Packing Center", "source_image": "36.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@37", "external_image_url": "https://erich-friedman.github.io/packing/squindom/37.gif", "id": "friedman-de32dfcf3ec55123", "metric_expression": "10 / 3 + \u221a2 = 4.747+", "metric_symbol": "s", "metric_value": 4.747, "n": 37, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "37. | | s = 10 / 3 + \u221a2 = 4.747+ | Found by Maurizio Morandi | in August 2012.", "setup": "squindom", "side": 4.747, "source": "Erich Friedman Packing Center", "source_image": "37.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@38", "external_image_url": "https://erich-friedman.github.io/packing/squindom/38.gif", "id": "friedman-72a9e74eacdae400", "metric_expression": "(13 + \u221a2) / 3 = 4.804+", "metric_symbol": "s", "metric_value": 4.804, "n": 38, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "38. | | s = (13 + \u221a2) / 3 = 4.804+ | Found by Maurizio Morandi | in August 2012.", "setup": "squindom", "side": 4.804, "source": "Erich Friedman Packing Center", "source_image": "38.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@39", "external_image_url": "https://erich-friedman.github.io/packing/squindom/39.gif", "id": "friedman-e3ba16dca355ea1e", "metric_expression": "4.839+", "metric_symbol": "s", "metric_value": 4.839, "n": 39, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "39. | | s = 4.839+ | Found by David W. Cantrell | in August 2012.", "setup": "squindom", "side": 4.839, "source": "Erich Friedman Packing Center", "source_image": "39.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@40", "external_image_url": "https://erich-friedman.github.io/packing/squindom/40.gif", "id": "friedman-ca00577d0d0551b5", "metric_expression": "4.895+", "metric_symbol": "s", "metric_value": 4.895, "n": 40, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "40. | | s = 4.895+ | Found by Sigvart Brendberg | in June 2023.", "setup": "squindom", "side": 4.895, "source": "Erich Friedman Packing Center", "source_image": "40.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Sigvart Brendberg", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@41", "external_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif", "id": "friedman-e8c33cfe5bb26c8e", "metric_expression": "4.927+", "metric_symbol": "s", "metric_value": 4.927, "n": 41, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.", "setup": "squindom", "side": 4.927, "source": "Erich Friedman Packing Center", "source_image": "41.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Sigvart Brendberg", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@42", "external_image_url": "https://erich-friedman.github.io/packing/squindom/42.gif", "id": "friedman-f0e1ef88792ca2f0", "metric_expression": "4.989+", "metric_symbol": "s", "metric_value": 4.989, "n": 42, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "42. | | s = 4.989+ | Found by David W. Cantrell | in August 2012.", "setup": "squindom", "side": 4.989, "source": "Erich Friedman Packing Center", "source_image": "42.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@43", "external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "id": "friedman-dc3910f178baa82e", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "n": 43, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "43-50. | | s = 5 | Trivial. |", "setup": "squindom", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "50.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@44", "external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "id": "friedman-dc0442edd8b13f81", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "n": 44, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "43-50. | | s = 5 | Trivial. |", "setup": "squindom", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "50.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@45", "external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "id": "friedman-92203de7a78a89e0", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "n": 45, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "43-50. | | s = 5 | Trivial. |", "setup": "squindom", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "50.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@46", "external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "id": "friedman-8bc8251fb17bd0a4", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "n": 46, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "43-50. | | s = 5 | Trivial. |", "setup": "squindom", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "50.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@47", "external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "id": "friedman-6f799588ad84ce0f", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "n": 47, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "43-50. | | s = 5 | Trivial. |", "setup": "squindom", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "50.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@48", "external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "id": "friedman-ac8b979d645373c3", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "n": 48, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "43-50. | | s = 5 | Trivial. |", "setup": "squindom", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "50.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@49", "external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "id": "friedman-f8b2f277dc699002", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "n": 49, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "43-50. | | s = 5 | Trivial. |", "setup": "squindom", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "50.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "squindom@50", "external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "id": "friedman-0655ad47f55fec32", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "n": 50, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "43-50. | | s = 5 | Trivial. |", "setup": "squindom", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "50.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
-{"case": "domindom@1", "external_image_url": "https://erich-friedman.github.io/packing/domindom/1.gif", "id": "friedman-fe5074fb42926405", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "1. | | s = 1 | Trivial.", "setup": "domindom", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
-{"case": "domindom@2", "external_image_url": "https://erich-friedman.github.io/packing/domindom/2.gif", "id": "friedman-c285aa9cd5d12a71", "metric_expression": "(2+\u221a2)/\u221a3 = 1.971+", "metric_symbol": "s", "metric_value": 1.971, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "2. | | s = (2+\u221a2)/\u221a3 = 1.971+ | Found by Erich Friedman in April 2026.", "setup": "domindom", "side": 1.971, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Dominoes in Dominoes", "verified": false}
-{"case": "domindom@3", "external_image_url": "https://erich-friedman.github.io/packing/domindom/4.gif", "id": "friedman-a40b473968b13df2", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "3.-4. | | s = 2 | Trivial.", "setup": "domindom", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
-{"case": "domindom@4", "external_image_url": "https://erich-friedman.github.io/packing/domindom/4.gif", "id": "friedman-35c8c1dcb75aaa80", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "3.-4. | | s = 2 | Trivial.", "setup": "domindom", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
-{"case": "domindom@5", "external_image_url": "https://erich-friedman.github.io/packing/domindom/5.gif", "id": "friedman-8fe8d537307854a7", "metric_expression": "5/2 = 2.5", "metric_symbol": "s", "metric_value": 2.5, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "5. | | s = 5/2 = 2.5 | Trivial.", "setup": "domindom", "side": 2.5, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
-{"case": "domindom@6", "external_image_url": "https://erich-friedman.github.io/packing/domindom/6.gif", "id": "friedman-82b5ac658d668d43", "metric_expression": "2.916+", "metric_symbol": "s", "metric_value": 2.916, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "6. | | s = 2.916+ | Found by Erich Friedman in April 2026.", "setup": "domindom", "side": 2.916, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Dominoes in Dominoes", "verified": false}
-{"case": "domindom@7", "external_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "id": "friedman-b6ff64c8ec34d9e5", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "7.-9. | | s = 3 | Trivial.", "setup": "domindom", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
-{"case": "domindom@8", "external_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "id": "friedman-f7a6ac29d49b90a3", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "7.-9. | | s = 3 | Trivial.", "setup": "domindom", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
-{"case": "domindom@9", "external_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "id": "friedman-c66f72045cce92b7", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "7.-9. | | s = 3 | Trivial.", "setup": "domindom", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
-{"case": "domindom@10", "external_image_url": "https://erich-friedman.github.io/packing/domindom/10.gif", "id": "friedman-7632a523c5e58279", "metric_expression": "7/2 = 3.5", "metric_symbol": "s", "metric_value": 3.5, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "10. | | s = 7/2 = 3.5 | Trivial.", "setup": "domindom", "side": 3.5, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
-{"case": "domindom@11", "external_image_url": "https://erich-friedman.github.io/packing/domindom/11.gif", "id": "friedman-3428de772f6a382f", "metric_expression": "(5+\u221a41)/3 = 3.801+", "metric_symbol": "s", "metric_value": 3.801, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "11. | | s = (5+\u221a41)/3 = 3.801+ | Found by Maurizio Morandi in April 2026.", "setup": "domindom", "side": 3.801, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Dominoes", "verified": false}
-{"case": "domindom@12", "external_image_url": "https://erich-friedman.github.io/packing/domindom/12.gif", "id": "friedman-f23035aabd01a5b7", "metric_expression": "5/2+\u221a2 = 3.914+", "metric_symbol": "s", "metric_value": 3.914, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "12. | | s = 5/2+\u221a2 = 3.914+ | Found by Maurizio Morandi in April 2026.", "setup": "domindom", "side": 3.914, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Dominoes", "verified": false}
-{"case": "domindom@14", "external_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "id": "friedman-b1aa68da6c91ef71", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14.-16 | | s = 4 | Trivial.", "setup": "domindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
-{"case": "domindom@15", "external_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "id": "friedman-a6466cde31e289b0", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14.-16 | | s = 4 | Trivial.", "setup": "domindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
-{"case": "domindom@16", "external_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "id": "friedman-63618f5cbe16b7ba", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14.-16 | | s = 4 | Trivial.", "setup": "domindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
-{"case": "domindom@17", "external_image_url": "https://erich-friedman.github.io/packing/domindom/18.gif", "id": "friedman-88637958ab2f0bd2", "metric_expression": "9/2 = 4.5", "metric_symbol": "s", "metric_value": 4.5, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "17.-18 | | s = 9/2 = 4.5 | Trivial.", "setup": "domindom", "side": 4.5, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
-{"case": "domindom@18", "external_image_url": "https://erich-friedman.github.io/packing/domindom/18.gif", "id": "friedman-d53361ac7a36e5b8", "metric_expression": "9/2 = 4.5", "metric_symbol": "s", "metric_value": 4.5, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "17.-18 | | s = 9/2 = 4.5 | Trivial.", "setup": "domindom", "side": 4.5, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
-{"case": "triindom@1", "external_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "id": "friedman-6b448902241352f2", "metric_expression": "\u221a3/2", "metric_symbol": "s", "metric_value": 0.8660254037844386, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "setup": "triindom", "side": 0.8660254037844386, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@2", "external_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "id": "friedman-3631b27632253615", "metric_expression": "\u221a3/2", "metric_symbol": "s", "metric_value": 0.8660254037844386, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "setup": "triindom", "side": 0.8660254037844386, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@3", "external_image_url": "https://erich-friedman.github.io/packing/triindom/3.png", "id": "friedman-1455255ba68cde92", "metric_expression": ".96796+", "metric_symbol": "s", "metric_value": 0.96796, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "3. | | s = .96796+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 0.96796, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@4", "external_image_url": "https://erich-friedman.github.io/packing/triindom/4.png", "id": "friedman-0417703b28057480", "metric_expression": "1.12036+", "metric_symbol": "s", "metric_value": 1.12036, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "4. | | s = 1.12036+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.12036, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@5", "external_image_url": "https://erich-friedman.github.io/packing/triindom/5.png", "id": "friedman-debd0a7c19c484e1", "metric_expression": "1.26315+", "metric_symbol": "s", "metric_value": 1.26315, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "5. | | s = 1.26315+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.26315, "source": "Erich Friedman Packing Center", "source_image": "5.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@6", "external_image_url": "https://erich-friedman.github.io/packing/triindom/6.png", "id": "friedman-34403ff3ad786191", "metric_expression": "1.37629+", "metric_symbol": "s", "metric_value": 1.37629, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "6. | | s = 1.37629+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.37629, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@7", "external_image_url": "https://erich-friedman.github.io/packing/triindom/7.png", "id": "friedman-945df93d80c9c3d2", "metric_expression": "1.49076+", "metric_symbol": "s", "metric_value": 1.49076, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "7. | | s = 1.49076+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.49076, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@8", "external_image_url": "https://erich-friedman.github.io/packing/triindom/8.png", "id": "friedman-dfa7a589fe07b565", "metric_expression": "1.56293+", "metric_symbol": "s", "metric_value": 1.56293, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "8. | | s = 1.56293+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.56293, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@9", "external_image_url": "https://erich-friedman.github.io/packing/triindom/9.png", "id": "friedman-c53aecbe04dfab59", "metric_expression": "1.64908+", "metric_symbol": "s", "metric_value": 1.64908, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "9. | | s = 1.64908+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.64908, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@10", "external_image_url": "https://erich-friedman.github.io/packing/triindom/10.png", "id": "friedman-c9503bfc16e9a2ba", "metric_expression": "1.68303+", "metric_symbol": "s", "metric_value": 1.68303, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "10. | | s = 1.68303+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.68303, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@11", "external_image_url": "https://erich-friedman.github.io/packing/triindom/11.png", "id": "friedman-c915dc3af9332ca3", "metric_expression": "1.73127+", "metric_symbol": "s", "metric_value": 1.73127, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "11. | | s = 1.73127+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.73127, "source": "Erich Friedman Packing Center", "source_image": "11.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@12", "external_image_url": "https://erich-friedman.github.io/packing/triindom/12.png", "id": "friedman-eea7c6944997f18c", "metric_expression": "1.74040+", "metric_symbol": "s", "metric_value": 1.7404, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "12. | | s = 1.74040+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.7404, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@13", "external_image_url": "https://erich-friedman.github.io/packing/triindom/13.png", "id": "friedman-d3e1a59ca736eabf", "metric_expression": "1.85319+", "metric_symbol": "s", "metric_value": 1.85319, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "13. | | s = 1.85319+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.85319, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@14", "external_image_url": "https://erich-friedman.github.io/packing/triindom/14.png", "id": "friedman-ce118ec85cf41825", "metric_expression": "3(3\u2013\u221a3)/2 = 1.90192+", "metric_symbol": "s", "metric_value": 1.90192, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14. | | s = 3(3\u2013\u221a3)/2 = 1.90192+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.90192, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@15", "external_image_url": "https://erich-friedman.github.io/packing/triindom/15.png", "id": "friedman-08d901dffb40a794", "metric_expression": "1.97950+", "metric_symbol": "s", "metric_value": 1.9795, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "15. | | s = 1.97950+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.9795, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@16", "external_image_url": "https://erich-friedman.github.io/packing/triindom/16.png", "id": "friedman-1f6e1fe57c5f2442", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "16. | | s = 2 | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "16.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@17", "external_image_url": "https://erich-friedman.github.io/packing/triindom/17.png", "id": "friedman-5d31f2162dd84c17", "metric_expression": "2.10306+", "metric_symbol": "s", "metric_value": 2.10306, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "17. | | s = 2.10306+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 2.10306, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@18", "external_image_url": "https://erich-friedman.github.io/packing/triindom/18.png", "id": "friedman-02be21094cf7b39a", "metric_expression": "2.14913.+", "metric_symbol": "s", "metric_value": 2.14913, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "18. | | s = 2.14913.+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 2.14913, "source": "Erich Friedman Packing Center", "source_image": "18.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@19", "external_image_url": "https://erich-friedman.github.io/packing/triindom/19.png", "id": "friedman-b2d8895e526d7303", "metric_expression": "2.24848+", "metric_symbol": "s", "metric_value": 2.24848, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "19. | | s = 2.24848+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 2.24848, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "triindom@20", "external_image_url": "https://erich-friedman.github.io/packing/triindom/20.png", "id": "friedman-6398e99b9a2f63fa", "metric_expression": "2.29730+", "metric_symbol": "s", "metric_value": 2.2973, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "20. | | s = 2.29730+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 2.2973, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
-{"case": "hexindom@1", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/1.png", "id": "friedman-1461f42fd98f7a6a", "metric_expression": "\u221a3 = 1.73205+", "metric_symbol": "s", "metric_value": 1.73205, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "1. | | s = \u221a3 = 1.73205+ | Trivial.", "setup": "hexindom", "side": 1.73205, "source": "Erich Friedman Packing Center", "source_image": "1.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@2", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/2.png", "id": "friedman-7d5e1327de198c15", "metric_expression": "1.8946+", "metric_symbol": "s", "metric_value": 1.8946, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "2. | | s = 1.8946+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 1.8946, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@3", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/3.png", "id": "friedman-d90bd8f82b040166", "metric_expression": "6\u20132\u221a3 = 2.53589+", "metric_symbol": "s", "metric_value": 2.53589, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "3. | | s = 6\u20132\u221a3 = 2.53589+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 2.53589, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@4", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/4.png", "id": "friedman-28ca5ddf4b39fa00", "metric_expression": "22\u201311\u221a3 = 2.94744+", "metric_symbol": "s", "metric_value": 2.94744, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "4. | | s = 22\u201311\u221a3 = 2.94744+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 2.94744, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@5", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/5.png", "id": "friedman-cf482f91d8c8bce5", "metric_expression": "7(2\u221a3\u20133) = 3.24871+", "metric_symbol": "s", "metric_value": 3.24871, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "5. | | s = 7(2\u221a3\u20133) = 3.24871+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 3.24871, "source": "Erich Friedman Packing Center", "source_image": "5.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@6", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/6.png", "id": "friedman-5aeee784110012c1", "metric_expression": "21(15\u20132\u221a3)/71 = 3.41202+", "metric_symbol": "s", "metric_value": 3.41202, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "6. | | s = 21(15\u20132\u221a3)/71 = 3.41202+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 3.41202, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@7", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/7.png", "id": "friedman-2a9436ef5fcff759", "metric_expression": "3.4873+", "metric_symbol": "s", "metric_value": 3.4873, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "7. | | s = 3.4873+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 3.4873, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@8", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/8.png", "id": "friedman-ed40f04ec723e8e5", "metric_expression": "3.6906+", "metric_symbol": "s", "metric_value": 3.6906, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "8. | | s = 3.6906+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 3.6906, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@9", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/9.png", "id": "friedman-dea7c54e25c3fa0a", "metric_expression": "(36+5\u221a3)/11 = 4.06002+", "metric_symbol": "s", "metric_value": 4.06002, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "9. | | s = (36+5\u221a3)/11 = 4.06002+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 4.06002, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@10", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/10.png", "id": "friedman-7a8236d7b304056d", "metric_expression": "9(2\u221a3\u20133) = 4.17691+", "metric_symbol": "s", "metric_value": 4.17691, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "10. | | s = 9(2\u221a3\u20133) = 4.17691+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 4.17691, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@11", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/11.png", "id": "friedman-23dad7daa2ff8934", "metric_expression": "4.5036+", "metric_symbol": "s", "metric_value": 4.5036, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "11. | | s = 4.5036+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 4.5036, "source": "Erich Friedman Packing Center", "source_image": "11.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@12", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/12.png", "id": "friedman-5a47dfb6b80a6234", "metric_expression": "41(18\u20135\u221a3)/83 = 4.6136+", "metric_symbol": "s", "metric_value": 4.6136, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "12. | | s = 41(18\u20135\u221a3)/83 = 4.6136+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 4.6136, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@13", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/13.png", "id": "friedman-bb2ef399bf9176f5", "metric_expression": "4.8137+", "metric_symbol": "s", "metric_value": 4.8137, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "13. | | s = 4.8137+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 4.8137, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@14", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/14.png", "id": "friedman-62cc49b91435c7ec", "metric_expression": "25(6\u2013\u221a3)/22 = 4.84994+", "metric_symbol": "s", "metric_value": 4.84994, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14. | | s = 25(6\u2013\u221a3)/22 = 4.84994+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 4.84994, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@15", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/15.png", "id": "friedman-d667d7fb283e5388", "metric_expression": "56(27\u20134\u221a3)/227 = 4.95163+", "metric_symbol": "s", "metric_value": 4.95163, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "15. | | s = 56(27\u20134\u221a3)/227 = 4.95163+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 4.95163, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@16", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/17.png", "id": "friedman-dca43056adc15966", "metric_expression": "3\u221a3 = 5.19615+", "metric_symbol": "s", "metric_value": 5.19615, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "16.-17. | | s = 3\u221a3 = 5.19615+ | Trivial.", "setup": "hexindom", "side": 5.19615, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@17", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/17.png", "id": "friedman-db297820cc5a8688", "metric_expression": "3\u221a3 = 5.19615+", "metric_symbol": "s", "metric_value": 5.19615, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "16.-17. | | s = 3\u221a3 = 5.19615+ | Trivial.", "setup": "hexindom", "side": 5.19615, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@18", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/18.png", "id": "friedman-7800a531b4789b9f", "metric_expression": "31(4\u2013\u221a3)/13 = 5.40818+", "metric_symbol": "s", "metric_value": 5.40818, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "18. | | s = 31(4\u2013\u221a3)/13 = 5.40818+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 5.40818, "source": "Erich Friedman Packing Center", "source_image": "18.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@19", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/19.png", "id": "friedman-b7d670339a43ec6b", "metric_expression": "5.6530+", "metric_symbol": "s", "metric_value": 5.653, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "19. | | s = 5.6530+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 5.653, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "hexindom@20", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/20.png", "id": "friedman-f39e5484db44fdfe", "metric_expression": "5.8012+", "metric_symbol": "s", "metric_value": 5.8012, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "20. | | s = 5.8012+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 5.8012, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
-{"case": "peninsqu@1", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/1.png", "id": "friedman-7e15ce644e4f9c5a", "metric_expression": "(3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+", "metric_symbol": "s", "metric_value": 1.59811, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+ | Trivial. |", "setup": "peninsqu", "side": 1.59811, "source": "Erich Friedman Packing Center", "source_image": "1.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@2", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/2.png", "id": "friedman-24eb94771b341380", "metric_expression": "2.46345+", "metric_symbol": "s", "metric_value": 2.46345, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.46345+ | Trivial. |", "setup": "peninsqu", "side": 2.46345, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@3", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/3.png", "id": "friedman-99cdebf50cc70a7b", "metric_expression": "2.90812+", "metric_symbol": "s", "metric_value": 2.90812, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.90812+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 2.90812, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@4", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/4.png", "id": "friedman-3b6b6b416d6a90ab", "metric_expression": "3.10252+", "metric_symbol": "s", "metric_value": 3.10252, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.10252+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 3.10252, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@5", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/5.png", "id": "friedman-b7d5a744e282c95a", "metric_expression": "3.54903+", "metric_symbol": "s", "metric_value": 3.54903, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.54903+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 3.54903, "source": "Erich Friedman Packing Center", "source_image": "5.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@6", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/6.png", "id": "friedman-68649f95f43f5c9b", "metric_expression": "3.88300+", "metric_symbol": "s", "metric_value": 3.883, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.88300+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 3.883, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@7", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/7.png", "id": "friedman-cc971af6673d00d8", "metric_expression": "4.18038+", "metric_symbol": "s", "metric_value": 4.18038, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.18038+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 4.18038, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@8", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/8.png", "id": "friedman-59e36ba91686eefb", "metric_expression": "4.38191+", "metric_symbol": "s", "metric_value": 4.38191, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.38191+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 4.38191, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@9", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/9.png", "id": "friedman-2ce3a5fe408a3dfd", "metric_expression": "4.60033+", "metric_symbol": "s", "metric_value": 4.60033, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.60033+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 4.60033, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@10", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/10.png", "id": "friedman-5182d89ad3c76f97", "metric_expression": "4.90584+", "metric_symbol": "s", "metric_value": 4.90584, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.90584+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 4.90584, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@11", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/11.png", "id": "friedman-81b654bc5e2cbb88", "metric_expression": "5.11557+", "metric_symbol": "s", "metric_value": 5.11557, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.11557+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 5.11557, "source": "Erich Friedman Packing Center", "source_image": "11.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@12", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/12.png", "id": "friedman-277b0b7ca884a6e6", "metric_expression": "5.23250+", "metric_symbol": "s", "metric_value": 5.2325, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.23250+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 5.2325, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@13", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/13.png", "id": "friedman-2188f40153726aa1", "metric_expression": "5.52183+", "metric_symbol": "s", "metric_value": 5.52183, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.52183+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 5.52183, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@14", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/14.png", "id": "friedman-50a67ef59b0e0b84", "metric_expression": "5.69775+", "metric_symbol": "s", "metric_value": 5.69775, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.69775+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 5.69775, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@15", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/15.png", "id": "friedman-cc27ef00c2ecb2cd", "metric_expression": "5.91106+", "metric_symbol": "s", "metric_value": 5.91106, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.91106+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 5.91106, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@16", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/16.png", "id": "friedman-bd78c96c0c713b24", "metric_expression": "6.11021+", "metric_symbol": "s", "metric_value": 6.11021, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.11021+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 6.11021, "source": "Erich Friedman Packing Center", "source_image": "16.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@17", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/17.png", "id": "friedman-46003f0493f05d4c", "metric_expression": "6.26466+", "metric_symbol": "s", "metric_value": 6.26466, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.26466+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 6.26466, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@18", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/18.png", "id": "friedman-ea74d2b6fe45f281", "metric_expression": "6.33632+", "metric_symbol": "s", "metric_value": 6.33632, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.33632+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 6.33632, "source": "Erich Friedman Packing Center", "source_image": "18.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@19", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/19.png", "id": "friedman-315fd8b234cd54b2", "metric_expression": "6.55939+", "metric_symbol": "s", "metric_value": 6.55939, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.55939+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 6.55939, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@20", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/20.png", "id": "friedman-b4ebac20ab7a97c2", "metric_expression": "6.69588+", "metric_symbol": "s", "metric_value": 6.69588, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.69588+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 6.69588, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@21", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/21.png", "id": "friedman-471bdfdb778fab95", "metric_expression": "6.85540+", "metric_symbol": "s", "metric_value": 6.8554, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.85540+ | Found by Emerson Connelly | in April 2026.", "setup": "peninsqu", "side": 6.8554, "source": "Erich Friedman Packing Center", "source_image": "21.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@22", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/22.png", "id": "friedman-d63a5d0588c65ab3", "metric_expression": "7.04532+", "metric_symbol": "s", "metric_value": 7.04532, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.04532+ | Found by Teodors Smith | in April 2026.", "setup": "peninsqu", "side": 7.04532, "source": "Erich Friedman Packing Center", "source_image": "22.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Teodors Smith", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@23", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/23.png", "id": "friedman-04176d404ee2c823", "metric_expression": "7.20731+", "metric_symbol": "s", "metric_value": 7.20731, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.20731+ | Found by Emerson Connelly | in April 2026.", "setup": "peninsqu", "side": 7.20731, "source": "Erich Friedman Packing Center", "source_image": "23.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Pentagons in Squares", "verified": false}
-{"case": "peninsqu@24", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/24.png", "id": "friedman-605e0d56f6df289f", "metric_expression": "7.33823+", "metric_symbol": "s", "metric_value": 7.33823, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.33823+ | Found by Emerson Connelly | in April 2026.", "setup": "peninsqu", "side": 7.33823, "source": "Erich Friedman Packing Center", "source_image": "24.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Pentagons in Squares", "verified": false}
-{"case": "penincir@1", "external_image_url": "https://erich-friedman.github.io/packing/penincir/1.png", "id": "friedman-d406bb60cb04bec8", "metric_expression": "\u221a((5+\u221a5)/10) = .86065+", "metric_symbol": "r", "metric_value": 0.86065, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a((5+\u221a5)/10) = .86065+ | Trivial.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "1.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@2", "external_image_url": "https://erich-friedman.github.io/packing/penincir/2.png", "id": "friedman-c1d311342820e254", "metric_expression": "\u221a(5+2\u221a5)/2 = 1.53884+", "metric_symbol": "r", "metric_value": 1.53884, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a(5+2\u221a5)/2 = 1.53884+ | Trivial.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@3", "external_image_url": "https://erich-friedman.github.io/packing/penincir/3.png", "id": "friedman-584001d603a8d226", "metric_expression": "(1+\u221a5)/2 = 1.61803+", "metric_symbol": "r", "metric_value": 1.61803, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = (1+\u221a5)/2 = 1.61803+ | Trivial.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@4", "external_image_url": "https://erich-friedman.github.io/packing/penincir/4.png", "id": "friedman-afcd1b3f0d4b1f0d", "metric_expression": "1.82971+", "metric_symbol": "r", "metric_value": 1.82971, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.82971+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@5", "external_image_url": "https://erich-friedman.github.io/packing/penincir/5.png", "id": "friedman-1ad57916719a9a56", "metric_expression": "2.03271+", "metric_symbol": "r", "metric_value": 2.03271, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.03271+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "5.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@6", "external_image_url": "https://erich-friedman.github.io/packing/penincir/6.png", "id": "friedman-12822fdb89455dab", "metric_expression": "\u221a((25+11\u221a5)/10) = 2.22703+", "metric_symbol": "r", "metric_value": 2.22703, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a((25+11\u221a5)/10) = 2.22703+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@7", "external_image_url": "https://erich-friedman.github.io/packing/penincir/7.png", "id": "friedman-162c0670b694ad7e", "metric_expression": "2.29474+", "metric_symbol": "r", "metric_value": 2.29474, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.29474+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@8", "external_image_url": "https://erich-friedman.github.io/packing/penincir/8.png", "id": "friedman-fe0a52f918bd5917", "metric_expression": "2.48128+", "metric_symbol": "r", "metric_value": 2.48128, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.48128+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@9", "external_image_url": "https://erich-friedman.github.io/packing/penincir/9.png", "id": "friedman-437b0288e72edf4b", "metric_expression": "2.70171+", "metric_symbol": "r", "metric_value": 2.70171, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.70171+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@10", "external_image_url": "https://erich-friedman.github.io/packing/penincir/10.png", "id": "friedman-dd5f3170e3194179", "metric_expression": "2.79768+", "metric_symbol": "r", "metric_value": 2.79768, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.79768+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@11", "external_image_url": "https://erich-friedman.github.io/packing/penincir/11.png", "id": "friedman-8f226f7fca76de25", "metric_expression": "2.90180+", "metric_symbol": "r", "metric_value": 2.9018, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.90180+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "11.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@12", "external_image_url": "https://erich-friedman.github.io/packing/penincir/12.png", "id": "friedman-1cb1d1196a113e11", "metric_expression": "3.01826+", "metric_symbol": "r", "metric_value": 3.01826, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.01826+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@13", "external_image_url": "https://erich-friedman.github.io/packing/penincir/13.png", "id": "friedman-e2b856e3113c6a69", "metric_expression": "\u221a(5+2\u221a5)/2 =3.07769+", "metric_symbol": "r", "metric_value": 3.07769, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a(5+2\u221a5)/2 =3.07769+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@14", "external_image_url": "https://erich-friedman.github.io/packing/penincir/14.png", "id": "friedman-3616fa5406506d9f", "metric_expression": "3.23385+", "metric_symbol": "r", "metric_value": 3.23385, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.23385+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@15", "external_image_url": "https://erich-friedman.github.io/packing/penincir/15.png", "id": "friedman-6ea0be20a21123dc", "metric_expression": "3.33911+", "metric_symbol": "r", "metric_value": 3.33911, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.33911+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@16", "external_image_url": "https://erich-friedman.github.io/packing/penincir/16.png", "id": "friedman-3d2f175a3fc14f29", "metric_expression": "3.43657+", "metric_symbol": "r", "metric_value": 3.43657, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.43657+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "16.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@17", "external_image_url": "https://erich-friedman.github.io/packing/penincir/17.png", "id": "friedman-b012044b6051ffc2", "metric_expression": "3.50958+", "metric_symbol": "r", "metric_value": 3.50958, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.50958+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@18", "external_image_url": "https://erich-friedman.github.io/packing/penincir/18.png", "id": "friedman-dd71777879a485ed", "metric_expression": "3.62080+", "metric_symbol": "r", "metric_value": 3.6208, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.62080+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "18.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@19", "external_image_url": "https://erich-friedman.github.io/packing/penincir/19.png", "id": "friedman-17041aab438560fc", "metric_expression": "3.67287+", "metric_symbol": "r", "metric_value": 3.67287, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.67287+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@20", "external_image_url": "https://erich-friedman.github.io/packing/penincir/20.png", "id": "friedman-12e982d92f646f18", "metric_expression": "3.80415+", "metric_symbol": "r", "metric_value": 3.80415, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.80415+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
-{"case": "penincir@21", "external_image_url": "https://erich-friedman.github.io/packing/penincir/21.png", "id": "friedman-201ad4373d160900", "metric_expression": "3.90735+", "metric_symbol": "r", "metric_value": 3.90735, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.90735+ | Found by Cyril Summerfield | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "21.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Cyril Summerfield", "title": "Pentagons in Circles", "verified": false}
-{"case": "peninpen@1", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/1.png", "id": "friedman-f9f52c1e8d515658", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 | Trivial.", "setup": "peninpen", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "1.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@2", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/2.png", "id": "friedman-a4081ac98088edfc", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial.", "setup": "peninpen", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@3", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/3.png", "id": "friedman-5046d857d2856fcc", "metric_expression": "\u221a5 = 2.23606+", "metric_symbol": "s", "metric_value": 2.23606, "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a5 = 2.23606+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 2.23606, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@4", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/4.png", "id": "friedman-4db0f711f785c6c8", "metric_expression": "2.44719+", "metric_symbol": "s", "metric_value": 2.44719, "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.44719+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 2.44719, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@5", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/6.png", "id": "friedman-07b4275bce72d2f8", "metric_expression": "(3+\u221a5)/2 = 2.61803+", "metric_symbol": "s", "metric_value": 2.61803, "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (3+\u221a5)/2 = 2.61803+ | Trivial.", "setup": "peninpen", "side": 2.61803, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@6", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/6.png", "id": "friedman-05e9eb87f4d4588a", "metric_expression": "(3+\u221a5)/2 = 2.61803+", "metric_symbol": "s", "metric_value": 2.61803, "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (3+\u221a5)/2 = 2.61803+ | Trivial.", "setup": "peninpen", "side": 2.61803, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@7", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/7.png", "id": "friedman-070578b8cff8b55e", "metric_expression": "3.07866+", "metric_symbol": "s", "metric_value": 3.07866, "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.07866+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 3.07866, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@8", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/8.png", "id": "friedman-dcc9fda4fbc43032", "metric_expression": "3.33514+", "metric_symbol": "s", "metric_value": 3.33514, "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.33514+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 3.33514, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@9", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/9.png", "id": "friedman-bcb280dc7cd22f84", "metric_expression": "3.44956+", "metric_symbol": "s", "metric_value": 3.44956, "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.44956+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 3.44956, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@10", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/10.png", "id": "friedman-d80c616dfa0aaa49", "metric_expression": "3.68324+", "metric_symbol": "s", "metric_value": 3.68324, "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.68324+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 3.68324, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@11", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/11.png", "id": "friedman-1282da0f3edc0bd9", "metric_expression": "3.79704+", "metric_symbol": "s", "metric_value": 3.79704, "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.79704+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 3.79704, "source": "Erich Friedman Packing Center", "source_image": "11.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@12", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/12.png", "id": "friedman-8b914755a9f1e439", "metric_expression": "3.96926+", "metric_symbol": "s", "metric_value": 3.96926, "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.96926+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 3.96926, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@13", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/13.png", "id": "friedman-5e9a9ce0bec89084", "metric_expression": "4.06523+", "metric_symbol": "s", "metric_value": 4.06523, "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.06523+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 4.06523, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@14", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/14.png", "id": "friedman-3afcc3dd8f832d7e", "metric_expression": "4.21120+", "metric_symbol": "s", "metric_value": 4.2112, "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.21120+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 4.2112, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@15", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/15.png", "id": "friedman-939f351e8fd006a2", "metric_expression": "2+\u221a5 = 4.23606+", "metric_symbol": "s", "metric_value": 4.23606, "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+\u221a5 = 4.23606+ | Trivial.", "setup": "peninpen", "side": 4.23606, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@16", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/16.png", "id": "friedman-01bc819429ff8629", "metric_expression": "4.41636+", "metric_symbol": "s", "metric_value": 4.41636, "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.41636+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 4.41636, "source": "Erich Friedman Packing Center", "source_image": "16.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@17", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/17.png", "id": "friedman-76f0cb13a9a97cb4", "metric_expression": "4.65561+", "metric_symbol": "s", "metric_value": 4.65561, "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.65561+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 4.65561, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@18", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/18.png", "id": "friedman-4c9b35e62cec039a", "metric_expression": "4.77541+", "metric_symbol": "s", "metric_value": 4.77541, "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.77541+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 4.77541, "source": "Erich Friedman Packing Center", "source_image": "18.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@19", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/19.png", "id": "friedman-f86fad763d9b64f5", "metric_expression": "4.95269+", "metric_symbol": "s", "metric_value": 4.95269, "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.95269+ | Found by Ian Watson in April 2026.", "setup": "peninpen", "side": 4.95269, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@20", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/20.png", "id": "friedman-2f420c79190960f4", "metric_expression": "5.04154+", "metric_symbol": "s", "metric_value": 5.04154, "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.04154+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 5.04154, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@21", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/21.png", "id": "friedman-8db20f7456e53f2c", "metric_expression": "5.15948+", "metric_symbol": "s", "metric_value": 5.15948, "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.15948+ | Found by Ignacio Vallejo in April 2026.", "setup": "peninpen", "side": 5.15948, "source": "Erich Friedman Packing Center", "source_image": "21.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@22", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/22.png", "id": "friedman-26aaee8ebea05fc0", "metric_expression": "5.26740+", "metric_symbol": "s", "metric_value": 5.2674, "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.26740+ | Found by Ignacio Vallejo in April 2026.", "setup": "peninpen", "side": 5.2674, "source": "Erich Friedman Packing Center", "source_image": "22.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@23", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/23.png", "id": "friedman-cdba463397eebb91", "metric_expression": "5.34794+", "metric_symbol": "s", "metric_value": 5.34794, "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.34794+ | Found by Ignacio Vallejo in April 2026.", "setup": "peninpen", "side": 5.34794, "source": "Erich Friedman Packing Center", "source_image": "23.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@24", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/24.png", "id": "friedman-7f618eb1ea83663a", "metric_expression": "5.49241+", "metric_symbol": "s", "metric_value": 5.49241, "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.49241+ | Found by Ignacio Vallejo in April 2026.", "setup": "peninpen", "side": 5.49241, "source": "Erich Friedman Packing Center", "source_image": "24.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Pentagons in Pentagons", "verified": false}
-{"case": "peninpen@25", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/25.png", "id": "friedman-811ff41caea519c7", "metric_expression": "5.58370+", "metric_symbol": "s", "metric_value": 5.5837, "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.58370+ | Found by Ignacio Vallejo in April 2026.", "setup": "peninpen", "side": 5.5837, "source": "Erich Friedman Packing Center", "source_image": "25.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "triinsqu@1", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t1.gif", "friedman_display_metric_value": 0.965, "id": "friedman-88198f6236e13dd4", "metric_expression": "(\u221a2+\u221a6)/4 = .965+", "metric_formula_parsed": "( sqrt 2+ sqrt 6)/4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.9659258262890683, "metric_value_source": "exact_expression", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (\u221a2+\u221a6)/4 = .965+ | Trivial.", "setup": "triinsqu", "side": 0.9659258262890683, "source": "Erich Friedman Packing Center", "source_image": "t1.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@2", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t2.gif", "friedman_display_metric_value": 1.224, "id": "friedman-06df28f275771178", "metric_expression": "\u221a6/2 = 1.224+", "metric_formula_parsed": "sqrt 6/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.224744871391589, "metric_value_source": "exact_expression", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a6/2 = 1.224+ | Trivial.", "setup": "triinsqu", "side": 1.224744871391589, "source": "Erich Friedman Packing Center", "source_image": "t2.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@3", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t3.gif", "friedman_display_metric_value": 1.478, "id": "friedman-31fd9c05a6e4cd45", "metric_expression": "\u221a3/2+\u221a6/4 = 1.478+", "metric_formula_parsed": "sqrt 3/2+ sqrt 6/4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.478397839480233, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a3/2+\u221a6/4 = 1.478+ | Found by Erich Friedman | in 1996.", "setup": "triinsqu", "side": 1.478397839480233, "source": "Erich Friedman Packing Center", "source_image": "t3.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@4", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t4.gif", "friedman_display_metric_value": 1.577, "id": "friedman-c6dea4eacbd98206", "metric_expression": "1+1/\u221a3 = 1.577+", "metric_formula_parsed": "1+1/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.5773502691896257, "metric_value_source": "exact_expression", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1+1/\u221a3 = 1.577+ | Found by Erich Friedman | in 1996.", "setup": "triinsqu", "side": 1.5773502691896257, "source": "Erich Friedman Packing Center", "source_image": "t4.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@5", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t5.gif", "friedman_display_metric_value": 1.803, "id": "friedman-a429941447ff4b85", "metric_expression": "1.803+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.803, "metric_value_source": "reported_decimal", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.803+ | Found by Erich Friedman | in 1996.", "setup": "triinsqu", "side": 1.803, "source": "Erich Friedman Packing Center", "source_image": "t5.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@6", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t6.gif", "friedman_display_metric_value": 1.901, "id": "friedman-57584e6cb4b7271e", "metric_expression": "9/2\u20133\u221a3/2 = 1.901+", "metric_formula_parsed": "9/2-3 sqrt 3/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.901923788646684, "metric_value_source": "exact_expression", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9/2\u20133\u221a3/2 = 1.901+ | Found by Erich Friedman | in 1996.", "setup": "triinsqu", "side": 1.901923788646684, "source": "Erich Friedman Packing Center", "source_image": "t6.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@7", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t7.gif", "friedman_display_metric_value": 2.0, "id": "friedman-2a36fb6293e3f5fc", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Found by Erich Friedman | in 1996.", "setup": "triinsqu", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "t7.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@8", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t8.gif", "friedman_display_metric_value": 2.098, "id": "friedman-b5af8f6f9326eed4", "metric_expression": "3\u221a3/2\u20131/2 = 2.098+", "metric_formula_parsed": "3 sqrt 3/2-1/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.098076211353316, "metric_value_source": "exact_expression", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3\u221a3/2\u20131/2 = 2.098+ | Found by Erich Friedman | in 1996.", "setup": "triinsqu", "side": 2.098076211353316, "source": "Erich Friedman Packing Center", "source_image": "t8.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@9", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t9.gif", "friedman_display_metric_value": 2.287, "id": "friedman-ccb5c5c57055123b", "metric_expression": "2.287+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.287, "metric_value_source": "reported_decimal", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.287+ | Found by Maurizio Morandi | in July 2008.", "setup": "triinsqu", "side": 2.287, "source": "Erich Friedman Packing Center", "source_image": "t9.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@10", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t10.gif", "friedman_display_metric_value": 2.377, "id": "friedman-758d5f159bd2d072", "metric_expression": "2.377+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.377, "metric_value_source": "reported_decimal", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.377+ | Found by David W. Cantrell | in July 2002.", "setup": "triinsqu", "side": 2.377, "source": "Erich Friedman Packing Center", "source_image": "t10.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@11", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t11.gif", "friedman_display_metric_value": 2.49, "id": "friedman-858e61a41cc34891", "metric_expression": "2.490+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.49, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.490+ | Found by Maurizio Morandi | in June 2008.", "setup": "triinsqu", "side": 2.49, "source": "Erich Friedman Packing Center", "source_image": "t11.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@12", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t12.gif", "friedman_display_metric_value": 2.558, "id": "friedman-009ec6fef6d3e013", "metric_expression": "2.558+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.558, "metric_value_source": "reported_decimal", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.558+ | Found by Dominik Kamp | in April 2026.", "setup": "triinsqu", "side": 2.558, "source": "Erich Friedman Packing Center", "source_image": "t12.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Dominik Kamp", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@13", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t13.gif", "friedman_display_metric_value": 2.595, "id": "friedman-c3db3dd1637eb062", "metric_expression": "2.595+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.595, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.595+ | Found by David W. Cantrell | in July 2002.", "setup": "triinsqu", "side": 2.595, "source": "Erich Friedman Packing Center", "source_image": "t13.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@14", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t14.gif", "friedman_display_metric_value": 2.726, "id": "friedman-71db1e8bc5976aa4", "metric_expression": "2.726+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.726, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.726+ | Found by David W. Cantrell | in July 2002.", "setup": "triinsqu", "side": 2.726, "source": "Erich Friedman Packing Center", "source_image": "t14.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@15", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t15.gif", "friedman_display_metric_value": 2.8299, "id": "friedman-935722e5b5532729", "metric_expression": "2.8299+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.8299, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.8299+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 2.8299, "source": "Erich Friedman Packing Center", "source_image": "t15.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@16", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t16.gif", "friedman_display_metric_value": 2.9, "id": "friedman-0efe6264aa836cbf", "metric_expression": "2.9000+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.9, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.9000+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 2.9, "source": "Erich Friedman Packing Center", "source_image": "t16.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@17", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t17.gif", "friedman_display_metric_value": 2.982, "id": "friedman-849f0e9c63c7a25a", "metric_expression": "2.982+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.982, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.982+ | Found by Maurizio Morandi | in July 2008.", "setup": "triinsqu", "side": 2.982, "source": "Erich Friedman Packing Center", "source_image": "t17.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@18", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t18.gif", "friedman_display_metric_value": 3.051, "id": "friedman-eb5d2ef9074e83ca", "metric_expression": "3.051+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.051, "metric_value_source": "reported_decimal", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.051+ | Found by Maurizio Morandi | in July 2008.", "setup": "triinsqu", "side": 3.051, "source": "Erich Friedman Packing Center", "source_image": "t18.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@19", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t19.gif", "friedman_display_metric_value": 3.1293, "id": "friedman-31965c290ede1529", "metric_expression": "3.12930+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.1293, "metric_value_source": "reported_decimal", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.12930+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 3.1293, "source": "Erich Friedman Packing Center", "source_image": "t19.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@20", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t20.gif", "friedman_display_metric_value": 3.2305, "id": "friedman-373ab4b3e6fed661", "metric_expression": "3.2305+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.2305, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.2305+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 3.2305, "source": "Erich Friedman Packing Center", "source_image": "t20.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@21", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t21.gif", "friedman_display_metric_value": 3.3111, "id": "friedman-fb7783b749591f04", "metric_expression": "3.3111+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.3111, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.3111+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 3.3111, "source": "Erich Friedman Packing Center", "source_image": "t21.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@22", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t22.gif", "friedman_display_metric_value": 3.3757, "id": "friedman-8d72959e42370da0", "metric_expression": "3.3757+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.3757, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "22. | | s = 3.3757+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 3.3757, "source": "Erich Friedman Packing Center", "source_image": "t22.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@23", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t23.gif", "friedman_display_metric_value": 3.4311, "id": "friedman-ba92b60f8caa50c3", "metric_expression": "3.4311+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.4311, "metric_value_source": "reported_decimal", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "23. | | s = 3.4311+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 3.4311, "source": "Erich Friedman Packing Center", "source_image": "t23.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@24", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t24.gif", "friedman_display_metric_value": 3.468, "id": "friedman-24c98bf89d626646", "metric_expression": "3.468+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.468, "metric_value_source": "reported_decimal", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "24. | | s = 3.468+ | Found by Maurizio Morandi | in August 2008.", "setup": "triinsqu", "side": 3.468, "source": "Erich Friedman Packing Center", "source_image": "t24.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@25", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t25.gif", "friedman_display_metric_value": 3.537, "id": "friedman-03e709254cc5f7ae", "metric_expression": "3.537+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.537, "metric_value_source": "reported_decimal", "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "25. | | s = 3.537+ | Found by David W. Cantrell | in August 2012.", "setup": "triinsqu", "side": 3.537, "source": "Erich Friedman Packing Center", "source_image": "t25.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@26", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t26.gif", "friedman_display_metric_value": 3.575, "id": "friedman-85d1fd1f2e64c58e", "metric_expression": "3.575+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.575, "metric_value_source": "reported_decimal", "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "26. | | s = 3.575+ | Found by Maurizio Morandi | in September 2008.", "setup": "triinsqu", "side": 3.575, "source": "Erich Friedman Packing Center", "source_image": "t26.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@27", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t27.gif", "friedman_display_metric_value": 3.6726, "id": "friedman-fe27f70a6f23b5b2", "metric_expression": "3.6726+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.6726, "metric_value_source": "reported_decimal", "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "27. | | s = 3.6726+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 3.6726, "source": "Erich Friedman Packing Center", "source_image": "t27.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@28", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t28.gif", "friedman_display_metric_value": 3.7571, "id": "friedman-ed066d1905e1d8a1", "metric_expression": "3.7571+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.7571, "metric_value_source": "reported_decimal", "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "28. | | s = 3.7571+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 3.7571, "source": "Erich Friedman Packing Center", "source_image": "t28.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@29", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t29.gif", "friedman_display_metric_value": 3.818, "id": "friedman-5c3fb0901914dc35", "metric_expression": "3.818+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.818, "metric_value_source": "reported_decimal", "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "29. | | s = 3.818+ | Found by Ignacio Vallejo | in April 2026.", "setup": "triinsqu", "side": 3.818, "source": "Erich Friedman Packing Center", "source_image": "t29.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@30", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t30.gif", "friedman_display_metric_value": 3.8662, "id": "friedman-5708973af114c7ec", "metric_expression": "3.8662+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.8662, "metric_value_source": "reported_decimal", "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "30. | | s = 3.8662+ | Found by Ian Watson | in April 2026.", "setup": "triinsqu", "side": 3.8662, "source": "Erich Friedman Packing Center", "source_image": "t30.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@31", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t31.gif", "friedman_display_metric_value": 3.936, "id": "friedman-514e8e63dccf54e9", "metric_expression": "3.936+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.936, "metric_value_source": "reported_decimal", "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "31. | | s = 3.936+ | Found by Emerson Connelly | in April 2026.", "setup": "triinsqu", "side": 3.936, "source": "Erich Friedman Packing Center", "source_image": "t31.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@32", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t32.gif", "friedman_display_metric_value": 3.979, "id": "friedman-1aa4833c34489e46", "metric_expression": "6\u20137\u221a3/6 = 3.979+", "metric_formula_parsed": "6-7 sqrt 3/6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.9792740578363097, "metric_value_source": "exact_expression", "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "32. | | s = 6\u20137\u221a3/6 = 3.979+ | Found by Maurizio Morandi | in May 2026.", "setup": "triinsqu", "side": 3.9792740578363097, "source": "Erich Friedman Packing Center", "source_image": "t32.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@33", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t33.gif", "friedman_display_metric_value": 4.058, "id": "friedman-944bd7cd98146437", "metric_expression": "4.058+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.058, "metric_value_source": "reported_decimal", "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "33. | | s = 4.058+ | Found by Emerson Connelly | in April 2026.", "setup": "triinsqu", "side": 4.058, "source": "Erich Friedman Packing Center", "source_image": "t33.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@34", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t34.gif", "friedman_display_metric_value": 4.098, "id": "friedman-dad38baedd24024a", "metric_expression": "4.098+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.098, "metric_value_source": "reported_decimal", "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "34. | | s = 4.098+ | Found by Emerson Connelly | in April 2026.", "setup": "triinsqu", "side": 4.098, "source": "Erich Friedman Packing Center", "source_image": "t34.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@35", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t35.gif", "friedman_display_metric_value": 4.176, "id": "friedman-33afe4505c0b2ed3", "metric_expression": "9(2\u221a3\u20133) = 4.176+", "metric_formula_parsed": "9(2 sqrt 3-3)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.176914536239791, "metric_value_source": "exact_expression", "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "35. | | s = 9(2\u221a3\u20133) = 4.176+ | Found by Erich Friedman | in April 2026.", "setup": "triinsqu", "side": 4.176914536239791, "source": "Erich Friedman Packing Center", "source_image": "t35.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@36", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t36.gif", "friedman_display_metric_value": 4.214, "id": "friedman-e6a3d617dc0b1556", "metric_expression": "4.214+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.214, "metric_value_source": "reported_decimal", "n": 36, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "36. | | s = 4.214+ | Found by Emerson Connelly | in April 2026.", "setup": "triinsqu", "side": 4.214, "source": "Erich Friedman Packing Center", "source_image": "t36.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@37", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t37.gif", "friedman_display_metric_value": 4.27233, "id": "friedman-62c58d2cb7e8e85c", "metric_expression": "4.27233+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.27233, "metric_value_source": "reported_decimal", "n": 37, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "37. | | s = 4.27233+ | Found by Nathan Roll | in April 2026.", "setup": "triinsqu", "side": 4.27233, "source": "Erich Friedman Packing Center", "source_image": "t37.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@38", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t38.gif", "friedman_display_metric_value": 4.327, "id": "friedman-fc030c65b5388c55", "metric_expression": "4.327+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.327, "metric_value_source": "reported_decimal", "n": 38, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "38. | | s = 4.327+ | Found by Emerson Connelly | in April 2026.", "setup": "triinsqu", "side": 4.327, "source": "Erich Friedman Packing Center", "source_image": "t38.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@39", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t39.gif", "friedman_display_metric_value": 4.383, "id": "friedman-ff9b6cccb4892504", "metric_expression": "4.383+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.383, "metric_value_source": "reported_decimal", "n": 39, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "39. | | s = 4.383+ | Found by Emerson Connelly | in April 2026.", "setup": "triinsqu", "side": 4.383, "source": "Erich Friedman Packing Center", "source_image": "t39.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Squares", "verified": false}
+{"case": "triinsqu@40", "external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t40.gif", "friedman_display_metric_value": 4.437, "id": "friedman-53a100f9bfd52ba3", "metric_expression": "4.437+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.437, "metric_value_source": "reported_decimal", "n": 40, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "40. | | s = 4.437+ | Found by Emerson Connelly | in April 2026.", "setup": "triinsqu", "side": 4.437, "source": "Erich Friedman Packing Center", "source_image": "t40.gif", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Squares", "verified": false}
+{"case": "cirinsqu@1", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs1.gif", "friedman_display_metric_value": 2.0, "id": "friedman-def93353a238e00a", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial.", "setup": "cirinsqu", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "cs1.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@2", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs2.gif", "friedman_display_metric_value": 3.414, "id": "friedman-2577c4d4ad595c1f", "metric_expression": "2 + \u221a2 = 3.414+", "metric_formula_parsed": "2 + sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.414213562373095, "metric_value_source": "exact_expression", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + \u221a2 = 3.414+ | Trivial.", "setup": "cirinsqu", "side": 3.414213562373095, "source": "Erich Friedman Packing Center", "source_image": "cs2.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@3", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs3.gif", "friedman_display_metric_value": 3.931, "id": "friedman-c6f8ea1fbc72f82f", "metric_expression": "2 + 1/\u221a2 + \u221a6/2 = 3.931+", "metric_formula_parsed": "2 + 1/ sqrt 2 + sqrt 6/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.9318516525781364, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 1/\u221a2 + \u221a6/2 = 3.931+ | Trivial.", "setup": "cirinsqu", "side": 3.9318516525781364, "source": "Erich Friedman Packing Center", "source_image": "cs3.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@4", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs4.gif", "friedman_display_metric_value": 4.0, "id": "friedman-c4fc8f4c0a8c2885", "metric_expression": "4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "metric_value_source": "reported_decimal", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 | Trivial.", "setup": "cirinsqu", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "cs4.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@5", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs5.gif", "friedman_display_metric_value": 4.828, "id": "friedman-b87b820b4449b1f3", "metric_expression": "2 + 2\u221a2 = 4.828+", "metric_formula_parsed": "2 + 2 sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.82842712474619, "metric_value_source": "exact_expression", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2\u221a2 = 4.828+ | Trivial.", "setup": "cirinsqu", "side": 4.82842712474619, "source": "Erich Friedman Packing Center", "source_image": "cs5.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@6", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs6.gif", "friedman_display_metric_value": 5.328, "id": "friedman-9b0738e62698f43a", "metric_expression": "2 + 12/\u221a13 = 5.328+", "metric_formula_parsed": "2 + 12/ sqrt 13", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.328201177351374, "metric_value_source": "exact_expression", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 12/\u221a13 = 5.328+ | Proved by Graham in 1963.", "setup": "cirinsqu", "side": 5.328201177351374, "source": "Erich Friedman Packing Center", "source_image": "cs6.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Graham", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@7", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs7.gif", "friedman_display_metric_value": 5.732, "id": "friedman-94be4d00707d1c67", "metric_expression": "4 + \u221a3 = 5.732+", "metric_formula_parsed": "4 + sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.732050807568878, "metric_value_source": "exact_expression", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + \u221a3 = 5.732+ | Proved by Schaer in 1964.", "setup": "cirinsqu", "side": 5.732050807568878, "source": "Erich Friedman Packing Center", "source_image": "cs7.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Schaer", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@8", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs8.gif", "friedman_display_metric_value": 5.863, "id": "friedman-32eb1091270a5811", "metric_expression": "2 + \u221a2 + \u221a6 = 5.863+", "metric_formula_parsed": "2 + sqrt 2 + sqrt 6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.863703305156273, "metric_value_source": "exact_expression", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + \u221a2 + \u221a6 = 5.863+ | Proved by Schaer/Meir in 1964.", "setup": "cirinsqu", "side": 5.863703305156273, "source": "Erich Friedman Packing Center", "source_image": "cs8.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Schaer/Meir", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@9", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs9.gif", "friedman_display_metric_value": 6.0, "id": "friedman-bcb79702a69e99e8", "metric_expression": "6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.0, "metric_value_source": "reported_decimal", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 | Proved by Schaer in 1964.", "setup": "cirinsqu", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "cs9.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Schaer", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@10", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs10.gif", "friedman_display_metric_value": 6.747, "id": "friedman-837b6988228c643c", "metric_expression": "6.747+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.747, "metric_value_source": "reported_decimal", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.747+ | Proved by De Groot in 1990.", "setup": "cirinsqu", "side": 6.747, "source": "Erich Friedman Packing Center", "source_image": "cs10.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "De Groot", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@11", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs11.gif", "friedman_display_metric_value": 7.022, "id": "friedman-20200084aeeb837c", "metric_expression": "7.022+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.022, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.022+ | Proved by Peikert in 1991.", "setup": "cirinsqu", "side": 7.022, "source": "Erich Friedman Packing Center", "source_image": "cs11.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Peikert", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@12", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs12.gif", "friedman_display_metric_value": 7.144, "id": "friedman-525876d01bcfd0e4", "metric_expression": "2 + 15\u221a(2/17) = 7.144+", "metric_formula_parsed": "2 + 15 sqrt (2/17)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.1449575542752655, "metric_value_source": "exact_expression", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 15\u221a(2/17) = 7.144+ | Proved by Peikert in 1991.", "setup": "cirinsqu", "side": 7.1449575542752655, "source": "Erich Friedman Packing Center", "source_image": "cs12.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Peikert", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@13", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs13.gif", "friedman_display_metric_value": 7.463, "id": "friedman-77ed9e1517e08a6f", "metric_expression": "7.463+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.463, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.463+ | Proved by Peikert in 1991.", "setup": "cirinsqu", "side": 7.463, "source": "Erich Friedman Packing Center", "source_image": "cs13.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Peikert", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@14", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs14.gif", "friedman_display_metric_value": 7.732, "id": "friedman-aa513de257143957", "metric_expression": "6 + \u221a3 = 7.732+", "metric_formula_parsed": "6 + sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.732050807568878, "metric_value_source": "exact_expression", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 + \u221a3 = 7.732+ | Proved by Wengerodt in 1987.", "setup": "cirinsqu", "side": 7.732050807568878, "source": "Erich Friedman Packing Center", "source_image": "cs14.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Wengerodt", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@15", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs15.gif", "friedman_display_metric_value": 7.863, "id": "friedman-0190d4e8eff22c65", "metric_expression": "4 + \u221a2 + \u221a6 = 7.863+", "metric_formula_parsed": "4 + sqrt 2 + sqrt 6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.863703305156273, "metric_value_source": "exact_expression", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + \u221a2 + \u221a6 = 7.863+ | Proved by Peikert in 1991.", "setup": "cirinsqu", "side": 7.863703305156273, "source": "Erich Friedman Packing Center", "source_image": "cs15.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Peikert", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@16", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs16.gif", "friedman_display_metric_value": 8.0, "id": "friedman-46edaf0a46fb32a6", "metric_expression": "8", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.0, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8 | Proved by Wengerodt in 1983.", "setup": "cirinsqu", "side": 8.0, "source": "Erich Friedman Packing Center", "source_image": "cs16.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Wengerodt", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@17", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs17.gif", "friedman_display_metric_value": 8.532, "id": "friedman-432760f92509e0d3", "metric_expression": "8.532+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.532, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8.532+ | Proved by Peikert in 1991.", "setup": "cirinsqu", "side": 8.532, "source": "Erich Friedman Packing Center", "source_image": "cs17.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Peikert", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@18", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs18.gif", "friedman_display_metric_value": 8.656, "id": "friedman-43b7b2b61af81274", "metric_expression": "2 + 24/\u221a13 = 8.656+", "metric_formula_parsed": "2 + 24/ sqrt 13", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.656402354702749, "metric_value_source": "exact_expression", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 24/\u221a13 = 8.656+ | Proved by Peikert in 1991.", "setup": "cirinsqu", "side": 8.656402354702749, "source": "Erich Friedman Packing Center", "source_image": "cs18.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Peikert", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@19", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs19.gif", "friedman_display_metric_value": 8.907, "id": "friedman-af7b488e985635b9", "metric_expression": "8.907+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.907, "metric_value_source": "reported_decimal", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8.907+ | Proved by Peikert in 1991.", "setup": "cirinsqu", "side": 8.907, "source": "Erich Friedman Packing Center", "source_image": "cs19.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Peikert", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@20", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs20.gif", "friedman_display_metric_value": 8.978, "id": "friedman-ec1e84ac7c1bfe05", "metric_expression": "130/17 + 16/17\u221a2 = 8.978+", "metric_formula_parsed": "130/17 + 16/17 sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.978083352821736, "metric_value_source": "exact_expression", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 130/17 + 16/17\u221a2 = 8.978+ | Proved by Peikert in 1991.", "setup": "cirinsqu", "side": 8.978083352821736, "source": "Erich Friedman Packing Center", "source_image": "cs20.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Peikert", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@21", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs21.gif", "friedman_display_metric_value": 9.358, "id": "friedman-8ab94bc573f7a3b9", "metric_expression": "9.358+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.358, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9.358+", "setup": "cirinsqu", "side": 9.358, "source": "Erich Friedman Packing Center", "source_image": "cs21.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman Packing Center", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@22", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs22.gif", "friedman_display_metric_value": 9.463, "id": "friedman-d77de0023d5029e8", "metric_expression": "9.463+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.463, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9.463+", "setup": "cirinsqu", "side": 9.463, "source": "Erich Friedman Packing Center", "source_image": "cs22.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman Packing Center", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@23", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs23.gif", "friedman_display_metric_value": 9.727, "id": "friedman-f3571e5edadf48f7", "metric_expression": "2 + 2\u221a2 + 2\u221a6 = 9.727+", "metric_formula_parsed": "2 + 2 sqrt 2 + 2 sqrt 6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.727406610312546, "metric_value_source": "exact_expression", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2\u221a2 + 2\u221a6 = 9.727+", "setup": "cirinsqu", "side": 9.727406610312546, "source": "Erich Friedman Packing Center", "source_image": "cs23.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman Packing Center", "title": "Circles in Squares", "verified": false}
+{"case": "cirinsqu@24", "external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs24.gif", "friedman_display_metric_value": 9.863, "id": "friedman-8fc54b80b1eb3019", "metric_expression": "6 + \u221a2 + \u221a6 = 9.863+", "metric_formula_parsed": "6 + sqrt 2 + sqrt 6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.863703305156273, "metric_value_source": "exact_expression", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 + \u221a2 + \u221a6 = 9.863+", "setup": "cirinsqu", "side": 9.863703305156273, "source": "Erich Friedman Packing Center", "source_image": "cs24.gif", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "", "submitted_by": "Erich Friedman Packing Center", "title": "Circles in Squares", "verified": false}
+{"case": "hexinsqu@1", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/1.png", "friedman_display_metric_value": 1.931, "id": "friedman-f5d73e1fefe162fa", "metric_expression": "(1+\u221a3)/\u221a2 = 1.931+", "metric_formula_parsed": "(1+ sqrt 3)/ sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.9318516525781366, "metric_value_source": "exact_expression", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (1+\u221a3)/\u221a2 = 1.931+ | Trivial. |", "setup": "hexinsqu", "side": 1.9318516525781366, "source": "Erich Friedman Packing Center", "source_image": "1.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@2", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/2.png", "friedman_display_metric_value": 3.156, "id": "friedman-5c5e548626faab0c", "metric_expression": "(1+2\u221a3)/\u221a2 = 3.156+", "metric_formula_parsed": "(1+2 sqrt 3)/ sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.156596523969726, "metric_value_source": "exact_expression", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (1+2\u221a3)/\u221a2 = 3.156+ | Trivial. |", "setup": "hexinsqu", "side": 3.156596523969726, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@3", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/3.png", "friedman_display_metric_value": 3.491, "id": "friedman-48d30c83b2cf34bc", "metric_expression": "9(6\u2013\u221a3)/11 = 3.491+", "metric_formula_parsed": "9(6- sqrt 3)/11", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.491958430170919, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9(6\u2013\u221a3)/11 = 3.491+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexinsqu", "side": 3.491958430170919, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@4", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/4.png", "friedman_display_metric_value": 3.725, "id": "friedman-c26d1a7e2e23e0c3", "metric_expression": "(7\u2013\u221a3)/\u221a2 = 3.725+", "metric_formula_parsed": "(7- sqrt 3)/ sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.7250025969142437, "metric_value_source": "exact_expression", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (7\u2013\u221a3)/\u221a2 = 3.725+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexinsqu", "side": 3.7250025969142437, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@5", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/5.png", "friedman_display_metric_value": 4.437, "id": "friedman-29964c51fb6474c3", "metric_expression": "7(3\u2013\u221a3)/2 = 4.437+", "metric_formula_parsed": "7(3- sqrt 3)/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.43782217350893, "metric_value_source": "exact_expression", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7(3\u2013\u221a3)/2 = 4.437+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexinsqu", "side": 4.43782217350893, "source": "Erich Friedman Packing Center", "source_image": "5.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@6", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/6.png", "friedman_display_metric_value": 4.813, "id": "friedman-d07a70f7b3cd945c", "metric_expression": "20(9\u20132\u221a3)/23 = 4.813+", "metric_formula_parsed": "20(9-2 sqrt 3)/23", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.813824682488909, "metric_value_source": "exact_expression", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 20(9\u20132\u221a3)/23 = 4.813+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexinsqu", "side": 4.813824682488909, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@7", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/8.png", "friedman_display_metric_value": 5.196, "id": "friedman-e2d3f1ba6a3361ff", "metric_expression": "3\u221a3 = 5.196+", "metric_formula_parsed": "3 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.196152422706632, "metric_value_source": "exact_expression", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3\u221a3 = 5.196+ | Trivial. |", "setup": "hexinsqu", "side": 5.196152422706632, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@8", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/8.png", "friedman_display_metric_value": 5.196, "id": "friedman-cccb6d2d687603dc", "metric_expression": "3\u221a3 = 5.196+", "metric_formula_parsed": "3 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.196152422706632, "metric_value_source": "exact_expression", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3\u221a3 = 5.196+ | Trivial. |", "setup": "hexinsqu", "side": 5.196152422706632, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@9", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/9.png", "friedman_display_metric_value": 5.518, "id": "friedman-ea6987c220904fbf", "metric_expression": "(13\u20133\u221a3)/\u221a2 = 5.518+", "metric_formula_parsed": "(13-3 sqrt 3)/ sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.518153541250351, "metric_value_source": "exact_expression", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (13\u20133\u221a3)/\u221a2 = 5.518+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexinsqu", "side": 5.518153541250351, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@10", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/10.png", "friedman_display_metric_value": 6.10469, "id": "friedman-99fc6b15e2732b48", "metric_expression": "6.10469+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.10469, "metric_value_source": "reported_decimal", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.10469+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexinsqu", "side": 6.10469, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@11", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/11.png", "friedman_display_metric_value": 6.33218, "id": "friedman-97b3ee9066788a1b", "metric_expression": "6.33218+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.33218, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.33218+ | Found by Maksymilian Jankowski | in April 2026.", "setup": "hexinsqu", "side": 6.33218, "source": "Erich Friedman Packing Center", "source_image": "11.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maksymilian Jankowski", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@12", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/12.png", "friedman_display_metric_value": 6.387, "id": "friedman-adf2677ba7b86f45", "metric_expression": "43(5\u2013\u221a3)/22 = 6.387+", "metric_formula_parsed": "43(5- sqrt 3)/22", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.38735523975174, "metric_value_source": "exact_expression", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 43(5\u2013\u221a3)/22 = 6.387+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexinsqu", "side": 6.38735523975174, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@13", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/13.png", "friedman_display_metric_value": 6.75558, "id": "friedman-004307193f41bfd8", "metric_expression": "6.75558+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.75558, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.75558+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexinsqu", "side": 6.75558, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@14", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/14.png", "friedman_display_metric_value": 6.928, "id": "friedman-41d4983f3cce24a4", "metric_expression": "4\u221a3 = 6.928+", "metric_formula_parsed": "4 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.928203230275509, "metric_value_source": "exact_expression", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4\u221a3 = 6.928+ | Trivial. |", "setup": "hexinsqu", "side": 6.928203230275509, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@15", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/15.png", "friedman_display_metric_value": 6.96367, "id": "friedman-e63821cac755fbcb", "metric_expression": "6.96367+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.96367, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.96367+ | Found by Maksymilian Jankowski | in April 2026.", "setup": "hexinsqu", "side": 6.96367, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maksymilian Jankowski", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@16", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/16.png", "friedman_display_metric_value": 7.311, "id": "friedman-83804f1ad82568c2", "metric_expression": "(19\u20135\u221a3)/\u221a2 = 7.311+", "metric_formula_parsed": "(19-5 sqrt 3)/ sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.311304485586458, "metric_value_source": "exact_expression", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (19\u20135\u221a3)/\u221a2 = 7.311+ | Found by Maurizio Morandi | in April 2026.", "setup": "hexinsqu", "side": 7.311304485586458, "source": "Erich Friedman Packing Center", "source_image": "16.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@17", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/17.png", "friedman_display_metric_value": 7.60383, "id": "friedman-aeefaec5b0932867", "metric_expression": "6(3\u2013\u221a3) = 7.60383+", "metric_formula_parsed": "6(3- sqrt 3)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.607695154586736, "metric_value_source": "exact_expression", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6(3\u2013\u221a3) = 7.60383+ | Found by Maksymilian Jankowski | in April 2026.", "setup": "hexinsqu", "side": 7.607695154586736, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maksymilian Jankowski", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@18", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/18.png", "friedman_display_metric_value": 7.702, "id": "friedman-276b5e5f0400948f", "metric_expression": "32(9\u20132\u221a3)/23 = 7.702+", "metric_formula_parsed": "32(9-2 sqrt 3)/23", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.702119491982255, "metric_value_source": "exact_expression", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 32(9\u20132\u221a3)/23 = 7.702+ | Found by Maurizio Morandi | in April 2026.", "setup": "hexinsqu", "side": 7.702119491982255, "source": "Erich Friedman Packing Center", "source_image": "18.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@19", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/19.png", "friedman_display_metric_value": 7.924, "id": "friedman-7f7f751877be8709", "metric_expression": "25(3\u2013\u221a3)/4 = 7.924+", "metric_formula_parsed": "25(3- sqrt 3)/4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.924682452694517, "metric_value_source": "exact_expression", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 25(3\u2013\u221a3)/4 = 7.924+ | Found by Maurizio Morandi | in April 2026.", "setup": "hexinsqu", "side": 7.924682452694517, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@20", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/20.png", "friedman_display_metric_value": 7.948, "id": "friedman-40c54987415da7e2", "metric_expression": "74(21\u20134\u221a3)/131 = 7.948+", "metric_formula_parsed": "74(21-4 sqrt 3)/131", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.948953900455056, "metric_value_source": "exact_expression", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 74(21\u20134\u221a3)/131 = 7.948+ | Found by Maurizio Morandi | in April 2026.", "setup": "hexinsqu", "side": 7.948953900455056, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@21", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/21.png", "friedman_display_metric_value": 8.381, "id": "friedman-3017e53b816ffece", "metric_expression": "8.381+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.381, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8.381+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexinsqu", "side": 8.381, "source": "Erich Friedman Packing Center", "source_image": "21.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@22", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/22.png", "friedman_display_metric_value": 8.568, "id": "friedman-eca436d145a9afe3", "metric_expression": "8.568+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.568, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8.568+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexinsqu", "side": 8.568, "source": "Erich Friedman Packing Center", "source_image": "22.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@23", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/23.png", "friedman_display_metric_value": 8.66, "id": "friedman-17c04f47b1750509", "metric_expression": "5\u221a3 = 8.660+", "metric_formula_parsed": "5 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.660254037844387, "metric_value_source": "exact_expression", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5\u221a3 = 8.660+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexinsqu", "side": 8.660254037844387, "source": "Erich Friedman Packing Center", "source_image": "23.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@24", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/24.png", "friedman_display_metric_value": 8.795, "id": "friedman-ccd479c1f90061ad", "metric_expression": "8.795+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.795, "metric_value_source": "reported_decimal", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8.795+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexinsqu", "side": 8.795, "source": "Erich Friedman Packing Center", "source_image": "24.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Squares", "verified": false}
+{"case": "hexinsqu@25", "external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/25.png", "friedman_display_metric_value": 9.065, "id": "friedman-5d5c0dbd90a9eff3", "metric_expression": "30(4\u221a3\u20133)/13 = 9.065+", "metric_formula_parsed": "30(4 sqrt 3-3)/13", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.065084377558867, "metric_value_source": "exact_expression", "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 30(4\u221a3\u20133)/13 = 9.065+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexinsqu", "side": 9.065084377558867, "source": "Erich Friedman Packing Center", "source_image": "25.png", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Squares", "verified": false}
+{"case": "triintri@1", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt1.gif", "friedman_display_metric_value": 1.0, "id": "friedman-df9118b9ccce666c", "metric_expression": "1", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0, "metric_value_source": "reported_decimal", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 | Trivial.", "setup": "triintri", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "tt1.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@2", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "friedman_display_metric_value": 2.0, "id": "friedman-aeb1b4017d959f27", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial.", "setup": "triintri", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "tt4.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@3", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "friedman_display_metric_value": 2.0, "id": "friedman-70245eceae59d461", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial.", "setup": "triintri", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "tt4.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@4", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "friedman_display_metric_value": 2.0, "id": "friedman-6cfc39d4ac15d695", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial.", "setup": "triintri", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "tt4.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@5", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt5.gif", "friedman_display_metric_value": 2.732, "id": "friedman-0cd646b14ce2224d", "metric_expression": "1 + \u221a3 = 2.732+", "metric_formula_parsed": "1 + sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.732050807568877, "metric_value_source": "exact_expression", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 + \u221a3 = 2.732+ | Proved by Erich Friedman | in 1997.", "setup": "triintri", "side": 2.732050807568877, "source": "Erich Friedman Packing Center", "source_image": "tt5.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@6", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt6.gif", "friedman_display_metric_value": 2.977, "id": "friedman-38e330068cdeabd2", "metric_expression": "13/8 + 3\u221a13/8 = 2.977+", "metric_formula_parsed": "13/8 + 3 sqrt 13/8", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.977081728298996, "metric_value_source": "exact_expression", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 13/8 + 3\u221a13/8 = 2.977+ | Found by Maurizio Morandi | in August 2008.", "setup": "triintri", "side": 2.977081728298996, "source": "Erich Friedman Packing Center", "source_image": "tt6.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@7", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "friedman_display_metric_value": 3.0, "id": "friedman-ebae4a9ce826a102", "metric_expression": "3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 | Trivial.", "setup": "triintri", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "tt9.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@8", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "friedman_display_metric_value": 3.0, "id": "friedman-c4684b89b7d31333", "metric_expression": "3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 | Trivial.", "setup": "triintri", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "tt9.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@9", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "friedman_display_metric_value": 3.0, "id": "friedman-cf7a78a67aa913d1", "metric_expression": "3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0, "metric_value_source": "reported_decimal", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 | Trivial.", "setup": "triintri", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "tt9.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@10", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt10.gif", "friedman_display_metric_value": 3.5, "id": "friedman-3b5caf5ce471af62", "metric_expression": "7/2 = 3.500", "metric_formula_parsed": "7/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.5, "metric_value_source": "exact_expression", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7/2 = 3.500 | Found by Erich Friedman | in 1997.", "setup": "triintri", "side": 3.5, "source": "Erich Friedman Packing Center", "source_image": "tt10.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@11", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt11.gif", "friedman_display_metric_value": 3.722, "id": "friedman-72b78146e2edb278", "metric_expression": "9/4 + 9\u221a21/28 = 3.722+", "metric_formula_parsed": "9/4 + 9 sqrt 21/28", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.7229707590929486, "metric_value_source": "exact_expression", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9/4 + 9\u221a21/28 = 3.722+ | Found by Erich Friedman | in 1997.", "setup": "triintri", "side": 3.7229707590929486, "source": "Erich Friedman Packing Center", "source_image": "tt11.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@12", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt12.gif", "friedman_display_metric_value": 3.879, "id": "friedman-ed336fe52fc098ee", "metric_expression": "2 + 2cos(\u03c0/9) = 3.879+", "metric_formula_parsed": "2 + 2cos(pi/9)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.879385241571817, "metric_value_source": "exact_expression", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2cos(\u03c0/9) = 3.879+ | Found by David W. Cantrell | in July 2007.", "setup": "triintri", "side": 3.879385241571817, "source": "Erich Friedman Packing Center", "source_image": "tt12.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@13", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt13.gif", "friedman_display_metric_value": 3.992, "id": "friedman-c55d5332fd60f0ac", "metric_expression": "3.992+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.992, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.992+ | Found by Maurizio Morandi | in May 2008.", "setup": "triintri", "side": 3.992, "source": "Erich Friedman Packing Center", "source_image": "tt13.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@14", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "friedman_display_metric_value": 4.0, "id": "friedman-8398fee140e7de98", "metric_expression": "4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 | Trivial.", "setup": "triintri", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "tt16.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@15", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "friedman_display_metric_value": 4.0, "id": "friedman-0195c1d43753e2d2", "metric_expression": "4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 | Trivial.", "setup": "triintri", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "tt16.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@16", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "friedman_display_metric_value": 4.0, "id": "friedman-71561fe6789fa8f2", "metric_expression": "4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 | Trivial.", "setup": "triintri", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "tt16.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@17", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt17.gif", "friedman_display_metric_value": 4.465, "id": "friedman-b6812065e1416baa", "metric_expression": "4.465+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.465, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.465+ | Found by Maurizio Morandi | in May 2008.", "setup": "triintri", "side": 4.465, "source": "Erich Friedman Packing Center", "source_image": "tt17.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@18", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt18.gif", "friedman_display_metric_value": 4.5, "id": "friedman-afd84e8a09b31318", "metric_expression": "9/2 = 4.500", "metric_formula_parsed": "9/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.5, "metric_value_source": "exact_expression", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9/2 = 4.500 | Found by Erich Friedman | in 1997.", "setup": "triintri", "side": 4.5, "source": "Erich Friedman Packing Center", "source_image": "tt18.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@19", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt19.gif", "friedman_display_metric_value": 4.666, "id": "friedman-71acd40380ab18c7", "metric_expression": "14/3 = 4.666+", "metric_formula_parsed": "14/3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.666666666666667, "metric_value_source": "exact_expression", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 14/3 = 4.666+ | Found by Maurizio Morandi | in May 2008.", "setup": "triintri", "side": 4.666666666666667, "source": "Erich Friedman Packing Center", "source_image": "tt19.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@20", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt20.gif", "friedman_display_metric_value": 4.861, "id": "friedman-9261151818bd4b0a", "metric_expression": "33/8 + 9\u221a21/56 = 4.861+", "metric_formula_parsed": "33/8 + 9 sqrt 21/56", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.861485379546474, "metric_value_source": "exact_expression", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 33/8 + 9\u221a21/56 = 4.861+ | Found by Maurizio Morandi | in May 2008.", "setup": "triintri", "side": 4.861485379546474, "source": "Erich Friedman Packing Center", "source_image": "tt20.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@21", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt21.gif", "friedman_display_metric_value": 4.923, "id": "friedman-43b248c0736fd708", "metric_expression": "4.923+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.923, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.923+ | Found by Maurizio Morandi | in May 2008.", "setup": "triintri", "side": 4.923, "source": "Erich Friedman Packing Center", "source_image": "tt21.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@22", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt22.gif", "friedman_display_metric_value": 4.996, "id": "friedman-0326e623c974e74a", "metric_expression": "4.996+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.996, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.996+ | Found by Maurizio Morandi | in May 2008.", "setup": "triintri", "side": 4.996, "source": "Erich Friedman Packing Center", "source_image": "tt22.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@23", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "friedman_display_metric_value": 5.0, "id": "friedman-447f26a1694a5fdd", "metric_expression": "5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "metric_value_source": "reported_decimal", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 | Trivial.", "setup": "triintri", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "tt25.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@24", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "friedman_display_metric_value": 5.0, "id": "friedman-e542a08e580fdd3b", "metric_expression": "5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "metric_value_source": "reported_decimal", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 | Trivial.", "setup": "triintri", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "tt25.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@25", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "friedman_display_metric_value": 5.0, "id": "friedman-d0073c77591ecec5", "metric_expression": "5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "metric_value_source": "reported_decimal", "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 | Trivial.", "setup": "triintri", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "tt25.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@26", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt26.gif", "friedman_display_metric_value": 5.406, "id": "friedman-b01b5221d0b238b6", "metric_expression": "5.406+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.406, "metric_value_source": "reported_decimal", "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.406+ | Found by Joah Frenzley | in April 2026.", "setup": "triintri", "side": 5.406, "source": "Erich Friedman Packing Center", "source_image": "tt26.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Joah Frenzley", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@27", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "friedman_display_metric_value": 5.5, "id": "friedman-c48c26640c20c9ca", "metric_expression": "11/2 = 5.500", "metric_formula_parsed": "11/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.5, "metric_value_source": "exact_expression", "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "setup": "triintri", "side": 5.5, "source": "Erich Friedman Packing Center", "source_image": "tt28.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@28", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "friedman_display_metric_value": 5.5, "id": "friedman-a654e61cacbbccd0", "metric_expression": "11/2 = 5.500", "metric_formula_parsed": "11/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.5, "metric_value_source": "exact_expression", "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "setup": "triintri", "side": 5.5, "source": "Erich Friedman Packing Center", "source_image": "tt28.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@29", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt29.gif", "friedman_display_metric_value": 5.666, "id": "friedman-0ff7372c7f0d0888", "metric_expression": "17/3 = 5.666+", "metric_formula_parsed": "17/3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.666666666666667, "metric_value_source": "exact_expression", "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 17/3 = 5.666+ | Found by David W. Cantrell | in July 2007.", "setup": "triintri", "side": 5.666666666666667, "source": "Erich Friedman Packing Center", "source_image": "tt29.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@30", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt30.gif", "friedman_display_metric_value": 5.75, "id": "friedman-d5cadbd3315d9655", "metric_expression": "23/4 = 5.75", "metric_formula_parsed": "23/4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.75, "metric_value_source": "exact_expression", "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 23/4 = 5.75 | Found by Maurizio Morandi | in May 2008.", "setup": "triintri", "side": 5.75, "source": "Erich Friedman Packing Center", "source_image": "tt30.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@31", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt31.gif", "friedman_display_metric_value": 5.912, "id": "friedman-01e5a2753e5c4735", "metric_expression": "5.912+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.912, "metric_value_source": "reported_decimal", "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.912+ | Found by Emerson Connelly | in April 2026.", "setup": "triintri", "side": 5.912, "source": "Erich Friedman Packing Center", "source_image": "tt31.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@32", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt32.gif", "friedman_display_metric_value": 5.951, "id": "friedman-0723c1b8737cc63b", "metric_expression": "5.951+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.951, "metric_value_source": "reported_decimal", "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.951+ | Found by Ian Watson | in April 2026.", "setup": "triintri", "side": 5.951, "source": "Erich Friedman Packing Center", "source_image": "tt32.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@33", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_display_metric_value": 6.0, "id": "friedman-2699908b012979d3", "metric_expression": "6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.0, "metric_value_source": "reported_decimal", "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 | Trivial. |", "setup": "triintri", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "tt36.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@34", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_display_metric_value": 6.0, "id": "friedman-19fda9ea1c5069a7", "metric_expression": "6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.0, "metric_value_source": "reported_decimal", "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 | Trivial. |", "setup": "triintri", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "tt36.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@35", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_display_metric_value": 6.0, "id": "friedman-163373bf6faa360a", "metric_expression": "6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.0, "metric_value_source": "reported_decimal", "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 | Trivial. |", "setup": "triintri", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "tt36.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@36", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_display_metric_value": 6.0, "id": "friedman-160790c3f0b88d1e", "metric_expression": "6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.0, "metric_value_source": "reported_decimal", "n": 36, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 | Trivial. |", "setup": "triintri", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "tt36.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@37", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt37.gif", "friedman_display_metric_value": 6.333, "id": "friedman-330694f3b2089601", "metric_expression": "19/3 = 6.333+", "metric_formula_parsed": "19/3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.333333333333333, "metric_value_source": "exact_expression", "n": 37, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 19/3 = 6.333+ | Found by Ian Watson | in April 2026.", "setup": "triintri", "side": 6.333333333333333, "source": "Erich Friedman Packing Center", "source_image": "tt37.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@38", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt38.gif", "friedman_display_metric_value": 6.43454, "id": "friedman-e2f6e745c3600f48", "metric_expression": "6.43454+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.43454, "metric_value_source": "reported_decimal", "n": 38, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.43454+ | Found by Nathan Roll | in April 2026.", "setup": "triintri", "side": 6.43454, "source": "Erich Friedman Packing Center", "source_image": "tt38.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@39", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "friedman_display_metric_value": 6.5, "id": "friedman-f82a2ad7a2b315df", "metric_expression": "13/2 = 6.500", "metric_formula_parsed": "13/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.5, "metric_value_source": "exact_expression", "n": 39, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "setup": "triintri", "side": 6.5, "source": "Erich Friedman Packing Center", "source_image": "tt40.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Triangles", "verified": false}
+{"case": "triintri@40", "external_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "friedman_display_metric_value": 6.5, "id": "friedman-e625023bbb4da161", "metric_expression": "13/2 = 6.500", "metric_formula_parsed": "13/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.5, "metric_value_source": "exact_expression", "n": 40, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "setup": "triintri", "side": 6.5, "source": "Erich Friedman Packing Center", "source_image": "tt40.gif", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Triangles", "verified": false}
+{"case": "cirintri@1", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct1.gif", "friedman_display_metric_value": 3.464, "id": "friedman-373b9d175918f2f2", "metric_expression": "2\u221a3 = 3.464+", "metric_formula_parsed": "2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.4641016151377544, "metric_value_source": "exact_expression", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2\u221a3 = 3.464+ | Trivial.", "setup": "cirintri", "side": 3.4641016151377544, "source": "Erich Friedman Packing Center", "source_image": "ct1.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Triangles", "verified": false}
+{"case": "cirintri@2", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct2.gif", "friedman_display_metric_value": 5.464, "id": "friedman-a959ebb8ed72c7f9", "metric_expression": "2 + 2\u221a3 = 5.464+", "metric_formula_parsed": "2 + 2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.464101615137754, "metric_value_source": "exact_expression", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "setup": "cirintri", "side": 5.464101615137754, "source": "Erich Friedman Packing Center", "source_image": "ct2.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Triangles", "verified": false}
+{"case": "cirintri@3", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct3.gif", "friedman_display_metric_value": 5.464, "id": "friedman-5656e051b375fc79", "metric_expression": "2 + 2\u221a3 = 5.464+", "metric_formula_parsed": "2 + 2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.464101615137754, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "setup": "cirintri", "side": 5.464101615137754, "source": "Erich Friedman Packing Center", "source_image": "ct3.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Triangles", "verified": false}
+{"case": "cirintri@4", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct4.gif", "friedman_display_metric_value": 6.928, "id": "friedman-f06ce12bcc053a39", "metric_expression": "4\u221a3 = 6.928+", "metric_formula_parsed": "4 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.928203230275509, "metric_value_source": "exact_expression", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4\u221a3 = 6.928+ | Proved by Milano in 1987.", "setup": "cirintri", "side": 6.928203230275509, "source": "Erich Friedman Packing Center", "source_image": "ct4.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Milano", "title": "Circles in Triangles", "verified": false}
+{"case": "cirintri@5", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct5.gif", "friedman_display_metric_value": 7.464, "id": "friedman-c5729987156f796f", "metric_expression": "4 + 2\u221a3 = 7.464+", "metric_formula_parsed": "4 + 2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.464101615137754, "metric_value_source": "exact_expression", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 2\u221a3 = 7.464+ | Proved by Milano in 1987.", "setup": "cirintri", "side": 7.464101615137754, "source": "Erich Friedman Packing Center", "source_image": "ct5.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Milano", "title": "Circles in Triangles", "verified": false}
+{"case": "cirintri@6", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct6.gif", "friedman_display_metric_value": 7.464, "id": "friedman-b12c4f677ba23a05", "metric_expression": "4 + 2\u221a3 = 7.464+", "metric_formula_parsed": "4 + 2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.464101615137754, "metric_value_source": "exact_expression", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 2\u221a3 = 7.464+ | Proved by Oler/Groemer in 1961.", "setup": "cirintri", "side": 7.464101615137754, "source": "Erich Friedman Packing Center", "source_image": "ct6.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Oler/Groemer", "title": "Circles in Triangles", "verified": false}
+{"case": "cirintri@7", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct7.gif", "friedman_display_metric_value": 8.928, "id": "friedman-c351a5cd42557637", "metric_expression": "2 + 4\u221a3 = 8.928+", "metric_formula_parsed": "2 + 4 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.928203230275509, "metric_value_source": "exact_expression", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 4\u221a3 = 8.928+ | Proved by Melissen in 1993.", "setup": "cirintri", "side": 8.928203230275509, "source": "Erich Friedman Packing Center", "source_image": "ct7.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Melissen", "title": "Circles in Triangles", "verified": false}
+{"case": "cirintri@8", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct8.gif", "friedman_display_metric_value": 9.293, "id": "friedman-60415c15b1866700", "metric_expression": "2 + 2\u221a3 + 2\u221a33/3 = 9.293+", "metric_formula_parsed": "2 + 2 sqrt 3 + 2 sqrt 33/3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.293810046163108, "metric_value_source": "exact_expression", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2\u221a3 + 2\u221a33/3 = 9.293+ | Proved by Melissen in 1993.", "setup": "cirintri", "side": 9.293810046163108, "source": "Erich Friedman Packing Center", "source_image": "ct8.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Melissen", "title": "Circles in Triangles", "verified": false}
+{"case": "cirintri@9", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct9.gif", "friedman_display_metric_value": 9.464, "id": "friedman-fce705cb36658c35", "metric_expression": "6 + 2\u221a3 = 9.464+", "metric_formula_parsed": "6 + 2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.464101615137755, "metric_value_source": "exact_expression", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 + 2\u221a3 = 9.464+ | Proved by Melissen in 1993.", "setup": "cirintri", "side": 9.464101615137755, "source": "Erich Friedman Packing Center", "source_image": "ct9.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Melissen", "title": "Circles in Triangles", "verified": false}
+{"case": "cirintri@10", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct10.gif", "friedman_display_metric_value": 9.464, "id": "friedman-5bc55f6e87d3e02b", "metric_expression": "6 + 2\u221a3 = 9.464+", "metric_formula_parsed": "6 + 2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.464101615137755, "metric_value_source": "exact_expression", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 + 2\u221a3 = 9.464+ | Proved by Oler/Groemer in 1961.", "setup": "cirintri", "side": 9.464101615137755, "source": "Erich Friedman Packing Center", "source_image": "ct10.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Oler/Groemer", "title": "Circles in Triangles", "verified": false}
+{"case": "cirintri@11", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct11.gif", "friedman_display_metric_value": 10.73, "id": "friedman-7e84067fe449704a", "metric_expression": "4 + 2\u221a3 + 4\u221a6/3 = 10.730+", "metric_formula_parsed": "4 + 2 sqrt 3 + 4 sqrt 6/3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.730087938848659, "metric_value_source": "exact_expression", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 2\u221a3 + 4\u221a6/3 = 10.730+ | Proved by Melissen in 1993.", "setup": "cirintri", "side": 10.730087938848659, "source": "Erich Friedman Packing Center", "source_image": "ct11.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Melissen", "title": "Circles in Triangles", "verified": false}
+{"case": "cirintri@12", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct12.gif", "friedman_display_metric_value": 10.928, "id": "friedman-0a283852fe1098a4", "metric_expression": "4 + 4\u221a3 = 10.928+", "metric_formula_parsed": "4 + 4 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.928203230275509, "metric_value_source": "exact_expression", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 4\u221a3 = 10.928+ | Proved by Melissen in 1994.", "setup": "cirintri", "side": 10.928203230275509, "source": "Erich Friedman Packing Center", "source_image": "ct12.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Melissen", "title": "Circles in Triangles", "verified": false}
+{"case": "cirintri@13", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct13.gif", "friedman_display_metric_value": 11.406, "id": "friedman-13ddd5fef6e95420", "metric_expression": "4 + 2\u221a6/3 + 10\u221a3/3 = 11.406+", "metric_formula_parsed": "4 + 2 sqrt 6/3 + 10 sqrt 3/3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 11.406495853751709, "metric_value_source": "exact_expression", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 2\u221a6/3 + 10\u221a3/3 = 11.406+ | Found by Melissen in 1993.", "setup": "cirintri", "side": 11.406495853751709, "source": "Erich Friedman Packing Center", "source_image": "ct13.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Melissen", "title": "Circles in Triangles", "verified": false}
+{"case": "cirintri@14", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct14.gif", "friedman_display_metric_value": 11.464, "id": "friedman-93af76ed87316ae0", "metric_expression": "8 + 2\u221a3 = 11.464+", "metric_formula_parsed": "8 + 2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 11.464101615137755, "metric_value_source": "exact_expression", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8 + 2\u221a3 = 11.464+ | Found by Erd\u0151s/Oler in 1961.", "setup": "cirintri", "side": 11.464101615137755, "source": "Erich Friedman Packing Center", "source_image": "ct14.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Erd\u0151s/Oler", "title": "Circles in Triangles", "verified": false}
+{"case": "cirintri@15", "external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct15.gif", "friedman_display_metric_value": 11.464, "id": "friedman-04c5e2fe2e9c9fd4", "metric_expression": "8 + 2\u221a3 = 11.464+", "metric_formula_parsed": "8 + 2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 11.464101615137755, "metric_value_source": "exact_expression", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8 + 2\u221a3 = 11.464+ | Proved by Erd\u0151s/Groemer in 1961.", "setup": "cirintri", "side": 11.464101615137755, "source": "Erich Friedman Packing Center", "source_image": "ct15.gif", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "", "submitted_by": "Erd\u0151s/Groemer", "title": "Circles in Triangles", "verified": false}
+{"case": "squintri@1", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts1.gif", "friedman_display_metric_value": 2.154, "id": "friedman-252bd3d74dba4cb7", "metric_expression": "1 + 2 / \u221a3 = 2.154+", "metric_formula_parsed": "1 + 2 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.1547005383792515, "metric_value_source": "exact_expression", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 + 2 / \u221a3 = 2.154+ | Trivial.", "setup": "squintri", "side": 2.1547005383792515, "source": "Erich Friedman Packing Center", "source_image": "ts1.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@2", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts2.gif", "friedman_display_metric_value": 3.154, "id": "friedman-fe76c6578fd87ee5", "metric_expression": "2 + 2 / \u221a3 = 3.154+", "metric_formula_parsed": "2 + 2 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.1547005383792515, "metric_value_source": "exact_expression", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2 / \u221a3 = 3.154+ | Trivial.", "setup": "squintri", "side": 3.1547005383792515, "source": "Erich Friedman Packing Center", "source_image": "ts2.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@3", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts3.gif", "friedman_display_metric_value": 3.232, "id": "friedman-e13c02a1c322601b", "metric_expression": "3 / 2 + \u221a3 = 3.232+", "metric_formula_parsed": "3 / 2 + sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.232050807568877, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 / 2 + \u221a3 = 3.232+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 3.232050807568877, "source": "Erich Friedman Packing Center", "source_image": "ts3.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@4", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts4.gif", "friedman_display_metric_value": 4.154, "id": "friedman-2cf44f3dd3edf72d", "metric_expression": "3 + 2 / \u221a3 = 4.154+", "metric_formula_parsed": "3 + 2 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.1547005383792515, "metric_value_source": "exact_expression", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 + 2 / \u221a3 = 4.154+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 4.1547005383792515, "source": "Erich Friedman Packing Center", "source_image": "ts4.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@5", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts6.gif", "friedman_display_metric_value": 4.309, "id": "friedman-3e74e575e12c12f9", "metric_expression": "2 + 4 / \u221a3 = 4.309+", "metric_formula_parsed": "2 + 4 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.309401076758503, "metric_value_source": "exact_expression", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 4 / \u221a3 = 4.309+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 4.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "ts6.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@6", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts6.gif", "friedman_display_metric_value": 4.309, "id": "friedman-0c1dc53a7025f255", "metric_expression": "2 + 4 / \u221a3 = 4.309+", "metric_formula_parsed": "2 + 4 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.309401076758503, "metric_value_source": "exact_expression", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 4 / \u221a3 = 4.309+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 4.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "ts6.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@7", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts7.gif", "friedman_display_metric_value": 5.154, "id": "friedman-24fd1e5bd65f4ad8", "metric_expression": "4 + 2 / \u221a3 = 5.154+", "metric_formula_parsed": "4 + 2 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.1547005383792515, "metric_value_source": "exact_expression", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 2 / \u221a3 = 5.154+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 5.1547005383792515, "source": "Erich Friedman Packing Center", "source_image": "ts7.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@8", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts8.gif", "friedman_display_metric_value": 5.301, "id": "friedman-58de376746beeb9a", "metric_expression": "5.301+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.301, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.301+ | Found by David W. Cantrell | in July 2002.", "setup": "squintri", "side": 5.301, "source": "Erich Friedman Packing Center", "source_image": "ts8.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@9", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts9.gif", "friedman_display_metric_value": 5.309, "id": "friedman-b485f09747e7e5c6", "metric_expression": "3 + 4 / \u221a3 = 5.309+", "metric_formula_parsed": "3 + 4 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.309401076758503, "metric_value_source": "exact_expression", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 + 4 / \u221a3 = 5.309+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 5.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "ts9.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@10", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts10.gif", "friedman_display_metric_value": 5.464, "id": "friedman-c6dc14a24cd917ac", "metric_expression": "2 + 2 \u221a3 = 5.464+", "metric_formula_parsed": "2 + 2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.464101615137754, "metric_value_source": "exact_expression", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2 \u221a3 = 5.464+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 5.464101615137754, "source": "Erich Friedman Packing Center", "source_image": "ts10.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@11", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts11.gif", "friedman_display_metric_value": 6.154, "id": "friedman-6209c847fa1f31ae", "metric_expression": "5 + 2 / \u221a3 = 6.154+", "metric_formula_parsed": "5 + 2 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.1547005383792515, "metric_value_source": "exact_expression", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 + 2 / \u221a3 = 6.154+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 6.1547005383792515, "source": "Erich Friedman Packing Center", "source_image": "ts11.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@12", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts12.gif", "friedman_display_metric_value": 6.301, "id": "friedman-2043aa54c7c9a732", "metric_expression": "6.301+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.301, "metric_value_source": "reported_decimal", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.301+ | Found by David W. Cantrell | in July 2002.", "setup": "squintri", "side": 6.301, "source": "Erich Friedman Packing Center", "source_image": "ts12.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@13", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts13.gif", "friedman_display_metric_value": 6.309, "id": "friedman-4b945aba75ec065e", "metric_expression": "4 + 4 / \u221a3 = 6.309+", "metric_formula_parsed": "4 + 4 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.309401076758503, "metric_value_source": "exact_expression", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 4 / \u221a3 = 6.309+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 6.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "ts13.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@14", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts15.gif", "friedman_display_metric_value": 6.464, "id": "friedman-e1fe8a5a00d4d3a9", "metric_expression": "3 + 2 \u221a3 = 6.464+", "metric_formula_parsed": "3 + 2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.464101615137754, "metric_value_source": "exact_expression", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 + 2 \u221a3 = 6.464+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 6.464101615137754, "source": "Erich Friedman Packing Center", "source_image": "ts15.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@15", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts15.gif", "friedman_display_metric_value": 6.464, "id": "friedman-5e450eea66553cab", "metric_expression": "3 + 2 \u221a3 = 6.464+", "metric_formula_parsed": "3 + 2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.464101615137754, "metric_value_source": "exact_expression", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 + 2 \u221a3 = 6.464+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 6.464101615137754, "source": "Erich Friedman Packing Center", "source_image": "ts15.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@16", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts16.gif", "friedman_display_metric_value": 7.154, "id": "friedman-b5af71c140885928", "metric_expression": "6 + 2 / \u221a3 = 7.154+", "metric_formula_parsed": "6 + 2 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.1547005383792515, "metric_value_source": "exact_expression", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 + 2 / \u221a3 = 7.154+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 7.1547005383792515, "source": "Erich Friedman Packing Center", "source_image": "ts16.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@17", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts17.gif", "friedman_display_metric_value": 7.301, "id": "friedman-83f30539d05ff1ea", "metric_expression": "7.301+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.301, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.301+ | Found by David W. Cantrell | in July 2002.", "setup": "squintri", "side": 7.301, "source": "Erich Friedman Packing Center", "source_image": "ts17.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@18", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts18.gif", "friedman_display_metric_value": 7.309, "id": "friedman-f306cfcbae8a7f8e", "metric_expression": "5 + 4 / \u221a3 = 7.309+", "metric_formula_parsed": "5 + 4 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.309401076758503, "metric_value_source": "exact_expression", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 + 4 / \u221a3 = 7.309+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 7.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "ts18.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@19", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts19.gif", "friedman_display_metric_value": 7.464, "id": "friedman-e19f0be0f2dc8df2", "metric_expression": "4 + 2 \u221a3 = 7.464+", "metric_formula_parsed": "4 + 2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.464101615137754, "metric_value_source": "exact_expression", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 2 \u221a3 = 7.464+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 7.464101615137754, "source": "Erich Friedman Packing Center", "source_image": "ts19.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@20", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "friedman_display_metric_value": 7.618, "id": "friedman-3d64213c7a5836f5", "metric_expression": "3 + 8 / \u221a3 = 7.618+", "metric_formula_parsed": "3 + 8 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.618802153517006, "metric_value_source": "exact_expression", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 7.618802153517006, "source": "Erich Friedman Packing Center", "source_image": "ts21.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@21", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "friedman_display_metric_value": 7.618, "id": "friedman-f8ef85a53da23bd0", "metric_expression": "3 + 8 / \u221a3 = 7.618+", "metric_formula_parsed": "3 + 8 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.618802153517006, "metric_value_source": "exact_expression", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 7.618802153517006, "source": "Erich Friedman Packing Center", "source_image": "ts21.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@22", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts22.gif", "friedman_display_metric_value": 8.154, "id": "friedman-242218d9342fa48e", "metric_expression": "7 + 2 / \u221a3 = 8.154+", "metric_formula_parsed": "7 + 2 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.154700538379252, "metric_value_source": "exact_expression", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7 + 2 / \u221a3 = 8.154+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 8.154700538379252, "source": "Erich Friedman Packing Center", "source_image": "ts22.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@23", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts23.gif", "friedman_display_metric_value": 8.301, "id": "friedman-3befb4edaec3c6b2", "metric_expression": "8.301+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.301, "metric_value_source": "reported_decimal", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8.301+ | Found by David W. Cantrell | in July 2002.", "setup": "squintri", "side": 8.301, "source": "Erich Friedman Packing Center", "source_image": "ts23.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@24", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts24.gif", "friedman_display_metric_value": 8.309, "id": "friedman-bd7d307154faf055", "metric_expression": "6 + 4 / \u221a3 = 8.309+", "metric_formula_parsed": "6 + 4 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.309401076758503, "metric_value_source": "exact_expression", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 + 4 / \u221a3 = 8.309+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 8.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "ts24.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@25", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts25.gif", "friedman_display_metric_value": 8.464, "id": "friedman-0b6595cd97166f90", "metric_expression": "5 + 2 \u221a3 = 8.464+", "metric_formula_parsed": "5 + 2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.464101615137755, "metric_value_source": "exact_expression", "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 + 2 \u221a3 = 8.464+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 8.464101615137755, "source": "Erich Friedman Packing Center", "source_image": "ts25.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@26", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "friedman_display_metric_value": 8.618, "id": "friedman-a6bf8a53768051a7", "metric_expression": "4 + 8 / \u221a3 = 8.618+", "metric_formula_parsed": "4 + 8 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.618802153517006, "metric_value_source": "exact_expression", "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 8.618802153517006, "source": "Erich Friedman Packing Center", "source_image": "ts27.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@27", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "friedman_display_metric_value": 8.618, "id": "friedman-5917db90a1b78e6a", "metric_expression": "4 + 8 / \u221a3 = 8.618+", "metric_formula_parsed": "4 + 8 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.618802153517006, "metric_value_source": "exact_expression", "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 8.618802153517006, "source": "Erich Friedman Packing Center", "source_image": "ts27.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@28", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts28.gif", "friedman_display_metric_value": 8.773, "id": "friedman-4b96aad075724908", "metric_expression": "3 + 10 / \u221a3 = 8.773+", "metric_formula_parsed": "3 + 10 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.773502691896258, "metric_value_source": "exact_expression", "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 + 10 / \u221a3 = 8.773+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 8.773502691896258, "source": "Erich Friedman Packing Center", "source_image": "ts28.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@29", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts29.gif", "friedman_display_metric_value": 9.154, "id": "friedman-7ee971f1094bebb8", "metric_expression": "8 + 2 / \u221a3 = 9.154+", "metric_formula_parsed": "8 + 2 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.154700538379252, "metric_value_source": "exact_expression", "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8 + 2 / \u221a3 = 9.154+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 9.154700538379252, "source": "Erich Friedman Packing Center", "source_image": "ts29.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@30", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts30.gif", "friedman_display_metric_value": 9.301, "id": "friedman-75a268a52b7b18d2", "metric_expression": "9.301+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.301, "metric_value_source": "reported_decimal", "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9.301+ | Found by David W. Cantrell | in July 2002.", "setup": "squintri", "side": 9.301, "source": "Erich Friedman Packing Center", "source_image": "ts30.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@31", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts31.gif", "friedman_display_metric_value": 9.309, "id": "friedman-3c1a52eb3bb8d2bb", "metric_expression": "7 + 4 / \u221a3 = 9.309+", "metric_formula_parsed": "7 + 4 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.309401076758503, "metric_value_source": "exact_expression", "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7 + 4 / \u221a3 = 9.309+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 9.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "ts31.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@32", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts32.gif", "friedman_display_metric_value": 9.464, "id": "friedman-f6d4517fe4e9ed0e", "metric_expression": "6 + 2 \u221a3 = 9.464+", "metric_formula_parsed": "6 + 2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.464101615137755, "metric_value_source": "exact_expression", "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 + 2 \u221a3 = 9.464+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 9.464101615137755, "source": "Erich Friedman Packing Center", "source_image": "ts32.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@33", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "friedman_display_metric_value": 9.618, "id": "friedman-8a42501b6cf579b5", "metric_expression": "5 + 8 / \u221a3 = 9.618+", "metric_formula_parsed": "5 + 8 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.618802153517006, "metric_value_source": "exact_expression", "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 9.618802153517006, "source": "Erich Friedman Packing Center", "source_image": "ts34.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@34", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "friedman_display_metric_value": 9.618, "id": "friedman-b52bb6f382575b48", "metric_expression": "5 + 8 / \u221a3 = 9.618+", "metric_formula_parsed": "5 + 8 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.618802153517006, "metric_value_source": "exact_expression", "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 9.618802153517006, "source": "Erich Friedman Packing Center", "source_image": "ts34.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@35", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "friedman_display_metric_value": 9.773, "id": "friedman-57a8cb93a77e91d4", "metric_expression": "4 + 10 / \u221a3 = 9.773+", "metric_formula_parsed": "4 + 10 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.773502691896258, "metric_value_source": "exact_expression", "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 9.773502691896258, "source": "Erich Friedman Packing Center", "source_image": "ts36.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@36", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "friedman_display_metric_value": 9.773, "id": "friedman-4994eda0bbf77702", "metric_expression": "4 + 10 / \u221a3 = 9.773+", "metric_formula_parsed": "4 + 10 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.773502691896258, "metric_value_source": "exact_expression", "n": 36, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "setup": "squintri", "side": 9.773502691896258, "source": "Erich Friedman Packing Center", "source_image": "ts36.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@37", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts37.gif", "friedman_display_metric_value": 10.154, "id": "friedman-e715f0132930826c", "metric_expression": "10.154+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.154, "metric_value_source": "reported_decimal", "n": 37, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 10.154+ | Found by Emerson Connelly | in April 2026.", "setup": "squintri", "side": 10.154, "source": "Erich Friedman Packing Center", "source_image": "ts37.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@38", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts38.gif", "friedman_display_metric_value": 10.309, "id": "friedman-7bcee7c16e556bd5", "metric_expression": "10.309+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.309, "metric_value_source": "reported_decimal", "n": 38, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 10.309+ | Found by Emerson Connelly | in April 2026.", "setup": "squintri", "side": 10.309, "source": "Erich Friedman Packing Center", "source_image": "ts38.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@39", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts39.gif", "friedman_display_metric_value": 10.31, "id": "friedman-df36f7577447ec3d", "metric_expression": "10.310+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.31, "metric_value_source": "reported_decimal", "n": 39, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 10.310+ | Found by Emerson Connelly | in April 2026.", "setup": "squintri", "side": 10.31, "source": "Erich Friedman Packing Center", "source_image": "ts39.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Triangles", "verified": false}
+{"case": "squintri@40", "external_image_url": "https://erich-friedman.github.io/packing/squintri/ts40.gif", "friedman_display_metric_value": 10.46426, "id": "friedman-5711f10b48735b21", "metric_expression": "10.46426+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.46426, "metric_value_source": "reported_decimal", "n": 40, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 10.46426+ | Found by Nathan Roll | in April 2026.", "setup": "squintri", "side": 10.46426, "source": "Erich Friedman Packing Center", "source_image": "ts40.gif", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Squares in Triangles", "verified": false}
+{"case": "hexintri@1", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/1.gif", "friedman_display_metric_value": 3.0, "id": "friedman-1aafd6d3b9d56f10", "metric_expression": "3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0, "metric_value_source": "reported_decimal", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 | Trivial.", "setup": "hexintri", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@2", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "friedman_display_metric_value": 5.0, "id": "friedman-6de94aa5c70c1d66", "metric_expression": "5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "metric_value_source": "reported_decimal", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 | Trivial.", "setup": "hexintri", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@3", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "friedman_display_metric_value": 5.0, "id": "friedman-6120335c9c51cee6", "metric_expression": "5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "metric_value_source": "reported_decimal", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5 | Trivial.", "setup": "hexintri", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@4", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/4.gif", "friedman_display_metric_value": 6.0, "id": "friedman-138e781034e01a76", "metric_expression": "6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.0, "metric_value_source": "reported_decimal", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6 | Trivial.", "setup": "hexintri", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@5", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/5.gif", "friedman_display_metric_value": 6.8301, "id": "friedman-ed187d080d03acd0", "metric_expression": "5(1+\u221a3)/2 = 6.8301+", "metric_formula_parsed": "5(1+ sqrt 3)/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.830127018922194, "metric_value_source": "exact_expression", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5(1+\u221a3)/2 = 6.8301+ | Found by Maurizio Morandi | in April 2015.", "setup": "hexintri", "side": 6.830127018922194, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@6", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/6.gif", "friedman_display_metric_value": 6.89897, "id": "friedman-b1c9c240f6559f22", "metric_expression": "2(1+\u221a6) = 6.89897+", "metric_formula_parsed": "2(1+ sqrt 6)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.898979485566356, "metric_value_source": "exact_expression", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2(1+\u221a6) = 6.89897+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexintri", "side": 6.898979485566356, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@7", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/7.gif", "friedman_display_metric_value": 8.0, "id": "friedman-29a6dc59323a9611", "metric_expression": "8", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.0, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8 | Trivial. |", "setup": "hexintri", "side": 8.0, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@8", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/8.gif", "friedman_display_metric_value": 8.3333, "id": "friedman-7b09f11b760f0fc7", "metric_expression": "25/3 = 8.3333+", "metric_formula_parsed": "25/3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.333333333333334, "metric_value_source": "exact_expression", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 25/3 = 8.3333+ | Found by Erich Friedman | in April 2015.", "setup": "hexintri", "side": 8.333333333333334, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@9", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/10.gif", "friedman_display_metric_value": 8.6602, "id": "friedman-00ecad6b4501c825", "metric_expression": "5\u221a3 = 8.6602+", "metric_formula_parsed": "5 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.660254037844387, "metric_value_source": "exact_expression", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5\u221a3 = 8.6602+ | Trivial. |", "setup": "hexintri", "side": 8.660254037844387, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@10", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/10.gif", "friedman_display_metric_value": 8.6602, "id": "friedman-c49e6b68a9f1f880", "metric_expression": "5\u221a3 = 8.6602+", "metric_formula_parsed": "5 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.660254037844387, "metric_value_source": "exact_expression", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5\u221a3 = 8.6602+ | Trivial. |", "setup": "hexintri", "side": 8.660254037844387, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@11", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/11.gif", "friedman_display_metric_value": 9.54823, "id": "friedman-e0d55b3ab8be7571", "metric_expression": "9.54823+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.54823, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9.54823+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexintri", "side": 9.54823, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@12", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/12.gif", "friedman_display_metric_value": 10.0, "id": "friedman-999280a4c324d258", "metric_expression": "10", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.0, "metric_value_source": "reported_decimal", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 10 | Trivial. |", "setup": "hexintri", "side": 10.0, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@13", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "friedman_display_metric_value": 10.3923, "id": "friedman-ed5c141d4256363a", "metric_expression": "6\u221a3 = 10.3923+", "metric_formula_parsed": "6 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.392304845413264, "metric_value_source": "exact_expression", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "setup": "hexintri", "side": 10.392304845413264, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@14", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "friedman_display_metric_value": 10.3923, "id": "friedman-d3b2202bbf8b650f", "metric_expression": "6\u221a3 = 10.3923+", "metric_formula_parsed": "6 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.392304845413264, "metric_value_source": "exact_expression", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "setup": "hexintri", "side": 10.392304845413264, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@15", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "friedman_display_metric_value": 10.3923, "id": "friedman-1a13545718e93d73", "metric_expression": "6\u221a3 = 10.3923+", "metric_formula_parsed": "6 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.392304845413264, "metric_value_source": "exact_expression", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "setup": "hexintri", "side": 10.392304845413264, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@16", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/16.gif", "friedman_display_metric_value": 11.36599, "id": "friedman-0943623f6ed7001f", "metric_expression": "11.36599+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 11.36599, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 11.36599+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexintri", "side": 11.36599, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@17", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/17.gif", "friedman_display_metric_value": 11.63457, "id": "friedman-1d735af9489b44cb", "metric_expression": "11.63457+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 11.63457, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 11.63457+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexintri", "side": 11.63457, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@18", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "friedman_display_metric_value": 12.0, "id": "friedman-907d6855ada30327", "metric_expression": "12", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 12.0, "metric_value_source": "reported_decimal", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 12 | Trivial. |", "setup": "hexintri", "side": 12.0, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@19", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "friedman_display_metric_value": 12.0, "id": "friedman-4ee9a5df05ced0ef", "metric_expression": "12", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 12.0, "metric_value_source": "reported_decimal", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 12 | Trivial. |", "setup": "hexintri", "side": 12.0, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@20", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "friedman_display_metric_value": 12.1243, "id": "friedman-4084fe628f219c86", "metric_expression": "7\u221a3 = 12.1243+", "metric_formula_parsed": "7 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 12.12435565298214, "metric_value_source": "exact_expression", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "setup": "hexintri", "side": 12.12435565298214, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
+{"case": "hexintri@21", "external_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "friedman_display_metric_value": 12.1243, "id": "friedman-85cc61ddf2bd9f7a", "metric_expression": "7\u221a3 = 12.1243+", "metric_formula_parsed": "7 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 12.12435565298214, "metric_value_source": "exact_expression", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "setup": "hexintri", "side": 12.12435565298214, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Triangles", "verified": false}
+{"case": "triincir@1", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc1.gif", "friedman_display_metric_value": 0.577, "id": "friedman-bee5966c0befdafd", "metric_expression": "1/\u221a3 = .577+", "metric_formula_parsed": "1/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 0.5773502691896257, "metric_value_source": "exact_expression", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1/\u221a3 = .577+ | Trivial.", "setup": "triincir", "side": 0.5773502691896257, "source": "Erich Friedman Packing Center", "source_image": "tc1.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@2", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc2.gif", "friedman_display_metric_value": 0.866, "id": "friedman-4d6984dddc7f791b", "metric_expression": "\u221a3/2 = .866+", "metric_formula_parsed": "sqrt 3/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 0.8660254037844386, "metric_value_source": "exact_expression", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a3/2 = .866+ | Trivial.", "setup": "triincir", "side": 0.8660254037844386, "source": "Erich Friedman Packing Center", "source_image": "tc2.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@3", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc3.gif", "friedman_display_metric_value": 0.953, "id": "friedman-ce49d5f28e5c0e43", "metric_expression": "3\u221a3 - 3\u221a2 = .953+", "metric_formula_parsed": "3 sqrt 3 - 3 sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 0.9535117355873467, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3\u221a3 - 3\u221a2 = .953+ | Found by Erich Friedman | in 1997.", "setup": "triincir", "side": 0.9535117355873467, "source": "Erich Friedman Packing Center", "source_image": "tc3.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@4", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc4.gif", "friedman_display_metric_value": 0.98, "id": "friedman-44542e32bbf59f07", "metric_expression": ".980+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 0.98, "metric_value_source": "reported_decimal", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = .980+ | Found by Erich Friedman | in 1997.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc4.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@5", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc5.gif", "friedman_display_metric_value": 1.0, "id": "friedman-76722ed16e528e08", "metric_expression": "1", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.0, "metric_value_source": "reported_decimal", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1 | Trivial.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc5.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@6", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc6.gif", "friedman_display_metric_value": 1.0, "id": "friedman-a685fb07bbba025a", "metric_expression": "1", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.0, "metric_value_source": "reported_decimal", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1 | Trivial.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc6.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@7", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc7.gif", "friedman_display_metric_value": 1.152, "id": "friedman-a34a6123847bdb93", "metric_expression": "1.152+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.152, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.152+ | Found by Erich Friedman | in 1997.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc7.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@8", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc8.gif", "friedman_display_metric_value": 1.263, "id": "friedman-3aeb5ecbe4b569a8", "metric_expression": "1.263+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.263, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.263+ | Found by Maurizio Morandi | in April 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc8.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@9", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc9.gif", "friedman_display_metric_value": 1.314, "id": "friedman-4e4a46b1cf98b4af", "metric_expression": "1.314+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.314, "metric_value_source": "reported_decimal", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.314+ | Found by David W. Cantrell | in July 2002.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc9.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@10", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc10.gif", "friedman_display_metric_value": 1.385, "id": "friedman-5c2676f2d6cd1814", "metric_expression": "1.385+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.385, "metric_value_source": "reported_decimal", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.385+ | Found by David W. Cantrell | in July 2002.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc10.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@11", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc11.gif", "friedman_display_metric_value": 1.466, "id": "friedman-b5ac4dbd01d673af", "metric_expression": "1.466+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.466, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.466+ | Found by DC after MM | in August 2012.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc11.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell after Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@12", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc12.gif", "friedman_display_metric_value": 1.507, "id": "friedman-5ffcd0ec27882e30", "metric_expression": "1.507+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.507, "metric_value_source": "reported_decimal", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.507+ | Found by David W. Cantrell | in October 2005.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc12.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@13", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc13.gif", "friedman_display_metric_value": 1.527, "id": "friedman-2c79a2e843091421", "metric_expression": "\u221a(7/3) = 1.527+", "metric_formula_parsed": "sqrt (7/3)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.5275252316519468, "metric_value_source": "exact_expression", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a(7/3) = 1.527+ | Found by Erich Friedman | in 1997.", "setup": "triincir", "side": 1.5275252316519468, "source": "Erich Friedman Packing Center", "source_image": "tc13.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@14", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc14.gif", "friedman_display_metric_value": 1.609, "id": "friedman-3142158c9944d32b", "metric_expression": "1.609+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.609, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.609+ | Found by DC after MM | in August 2012.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc14.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell after Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@15", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc15.gif", "friedman_display_metric_value": 1.636, "id": "friedman-cd323abc0be756c7", "metric_expression": "1.636+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.636, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.636+ | Found by David W. Cantrell | in July 2002.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc15.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@16", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc16.gif", "friedman_display_metric_value": 1.687, "id": "friedman-f633ad5d6e281a55", "metric_expression": "1.687+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.687, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.687+ | Found by Maurizio Morandi | in April 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc16.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@17", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc17.gif", "friedman_display_metric_value": 1.73, "id": "friedman-39a25d3dcd24ac29", "metric_expression": "1.730+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.73, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.730+ | Found by David W. Cantrell | in July 2005.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc17.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@18", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc18.gif", "friedman_display_metric_value": 1.802, "id": "friedman-4cac381fafba2e73", "metric_expression": "\u221a13/2 = 1.802+", "metric_formula_parsed": "sqrt 13/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.8027756377319946, "metric_value_source": "exact_expression", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a13/2 = 1.802+ | Found by Erich Friedman | in 1997.", "setup": "triincir", "side": 1.8027756377319946, "source": "Erich Friedman Packing Center", "source_image": "tc18.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@19", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc19.gif", "friedman_display_metric_value": 1.825, "id": "friedman-09240ee047e9b02e", "metric_expression": "\u221a(10/3) = 1.825+", "metric_formula_parsed": "sqrt (10/3)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.8257418583505538, "metric_value_source": "exact_expression", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a(10/3) = 1.825+ | Found by Haym Hirsh | in August 2019.", "setup": "triincir", "side": 1.8257418583505538, "source": "Erich Friedman Packing Center", "source_image": "tc19.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Haym Hirsh", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@20", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc20.gif", "friedman_display_metric_value": 1.874, "id": "friedman-11894bd2ae50e21d", "metric_expression": "1.874+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.874, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.874+ | Found by Erich Friedman | in 1997.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc20.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@21", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc21.gif", "friedman_display_metric_value": 1.91, "id": "friedman-2c6cdef8b7760ab2", "metric_expression": "1.910+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.91, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.910+ | Found by Maurizio Morandi | in May 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc21.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@22", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc22.gif", "friedman_display_metric_value": 1.943, "id": "friedman-c4d8c6a51fc99d06", "metric_expression": "1.943+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.943, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.943+ | Found by Maurizio Morandi | in June 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc22.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@23", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc23.gif", "friedman_display_metric_value": 1.988, "id": "friedman-5971a993b0db6da9", "metric_expression": "1.988+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.988, "metric_value_source": "reported_decimal", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.988+ | Found by Maurizio Morandi | in June 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc23.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@24", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc24.gif", "friedman_display_metric_value": 2.0, "id": "friedman-50aba5c38741ed94", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2 | Trivial.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc24.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@25", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc25.gif", "friedman_display_metric_value": 2.055, "id": "friedman-3687974ed51eedf3", "metric_expression": "2.055+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.055, "metric_value_source": "reported_decimal", "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.055+ | Found by David W. Cantrell | in July 2005.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc25.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@26", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc26.gif", "friedman_display_metric_value": 2.109, "id": "friedman-a6793ae8c3171099", "metric_expression": "2.109+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.109, "metric_value_source": "reported_decimal", "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.109+ | Found by Maurizio Morandi | in April 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc26.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@27", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc27.gif", "friedman_display_metric_value": 2.138, "id": "friedman-fe685ce08e30ecac", "metric_expression": "2.138+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.138, "metric_value_source": "reported_decimal", "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.138+ | Found by David W. Cantrell | in July 2005.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc27.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@28", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc28.gif", "friedman_display_metric_value": 2.191, "id": "friedman-daf0f91a5db8d01c", "metric_expression": "2.191+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.191, "metric_value_source": "reported_decimal", "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.191+ | Found by David W. Cantrell | in July 2005.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc28.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@29", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc29.gif", "friedman_display_metric_value": 2.215, "id": "friedman-91e468ecae8e00df", "metric_expression": "2.215+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.215, "metric_value_source": "reported_decimal", "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.215+ | Found by Maurizio Morandi | in June 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc29.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@30", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc30.gif", "friedman_display_metric_value": 2.258, "id": "friedman-1d8fd1d8acfcc649", "metric_expression": "2.258+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.258, "metric_value_source": "reported_decimal", "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.258+ | Found by Maurizio Morandi | in July 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc30.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
+{"case": "triincir@31", "external_image_url": "https://erich-friedman.github.io/packing/triincir/tc31.gif", "friedman_display_metric_value": 2.272, "id": "friedman-3151b3ff6842a945", "metric_expression": "2.272+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.272, "metric_value_source": "reported_decimal", "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.272+ | Found by Maurizio Morandi | in July 2008.", "setup": "triincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "tc31.gif", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Circles", "verified": false}
+{"case": "cirincir@1", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc1.gif", "friedman_display_metric_value": 1.0, "id": "friedman-a9224170994c2db7", "metric_expression": "1", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.0, "metric_value_source": "reported_decimal", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1 | Trivial.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc1.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@2", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc2.gif", "friedman_display_metric_value": 2.0, "id": "friedman-d0526dd85e67bcc5", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2 | Trivial.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc2.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@3", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc3.gif", "friedman_display_metric_value": 2.154, "id": "friedman-8a18e25e4448bdf6", "metric_expression": "1 + 2 / \u221a3 = 2.154+", "metric_formula_parsed": "1 + 2 / sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.1547005383792515, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1 + 2 / \u221a3 = 2.154+ | Trivial.", "setup": "cirincir", "side": 2.1547005383792515, "source": "Erich Friedman Packing Center", "source_image": "ccc3.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@4", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc4.gif", "friedman_display_metric_value": 2.414, "id": "friedman-1f89ac0d8425a177", "metric_expression": "1 + \u221a2 = 2.414+", "metric_formula_parsed": "1 + sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.414213562373095, "metric_value_source": "exact_expression", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1 + \u221a2 = 2.414+ | Trivial.", "setup": "cirincir", "side": 2.414213562373095, "source": "Erich Friedman Packing Center", "source_image": "ccc4.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@5", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc5.gif", "friedman_display_metric_value": 2.701, "id": "friedman-77e9a21fe2dbf0ec", "metric_expression": "2.701+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.701, "metric_value_source": "reported_decimal", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.701+ | Proved by Graham in 1968.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc5.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Graham", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@6", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc6.gif", "friedman_display_metric_value": 3.0, "id": "friedman-c22f64ca3a4b2997", "metric_expression": "3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.0, "metric_value_source": "reported_decimal", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3 | Proved by Graham in 1968.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc6.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Graham", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@7", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc7.gif", "friedman_display_metric_value": 3.0, "id": "friedman-ebd074e73c455d00", "metric_expression": "3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.0, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3 | Proved by Graham in 1968.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc7.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Graham", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@8", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc8.gif", "friedman_display_metric_value": 3.304, "id": "friedman-64038cce97e05aac", "metric_expression": "3.304+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.304, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.304+ | Proved by Braaksma in 1963.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc8.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Braaksma", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@9", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc9.gif", "friedman_display_metric_value": 3.613, "id": "friedman-ce6041f680ff2644", "metric_expression": "3.613+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.613, "metric_value_source": "reported_decimal", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.613+ | Proved by Pirl in 1969.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc9.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Pirl", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@10", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc10.gif", "friedman_display_metric_value": 3.813, "id": "friedman-248f9c5d338e3645", "metric_expression": "3.813+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.813, "metric_value_source": "reported_decimal", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.813+ | Proved by Pirl in 1969.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc10.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Pirl", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@11", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc11.gif", "friedman_display_metric_value": 3.923, "id": "friedman-68c8f3aded0a06cc", "metric_expression": "3.923+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.923, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.923+ | Proved by Melissen in 1994.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc11.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Melissen", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@12", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc12.gif", "friedman_display_metric_value": 4.029, "id": "friedman-7754f3598b4ae15f", "metric_expression": "4.029+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.029, "metric_value_source": "reported_decimal", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.029+ | Found by Kravitz in 1967.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc12.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Kravitz", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@13", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc13.gif", "friedman_display_metric_value": 4.236, "id": "friedman-c43ded19f288094a", "metric_expression": "2 + \u221a5 = 4.236+", "metric_formula_parsed": "2 + sqrt 5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.23606797749979, "metric_value_source": "exact_expression", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2 + \u221a5 = 4.236+ | Proved by F. Fodor in 2003.", "setup": "cirincir", "side": 4.23606797749979, "source": "Erich Friedman Packing Center", "source_image": "ccc13.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "F. Fodor", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@14", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc14.gif", "friedman_display_metric_value": 4.328, "id": "friedman-6c3aaffa9b755646", "metric_expression": "4.328+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.328, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.328+ | Found by Goldberg in 1971.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc14.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Goldberg", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@15", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc15.gif", "friedman_display_metric_value": 4.521, "id": "friedman-e2482d27b978ed53", "metric_expression": "4.521+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.521, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.521+ | Found by Kravitz in 1967.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc15.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Kravitz", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@16", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc16.gif", "friedman_display_metric_value": 4.615, "id": "friedman-c9d37cb5558adc7c", "metric_expression": "4.615+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.615, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.615+ | Found by Goldberg in 1971.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc16.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Goldberg", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@17", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc17.gif", "friedman_display_metric_value": 4.792, "id": "friedman-94d6b7610c98379e", "metric_expression": "4.792+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.792, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.792+ | Found by Reis in 1975.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc17.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Reis", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@18", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc18.gif", "friedman_display_metric_value": 4.863, "id": "friedman-cfd342d4610e6900", "metric_expression": "1 + \u221a2 + \u221a6 = 4.863+", "metric_formula_parsed": "1 + sqrt 2 + sqrt 6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.863703305156273, "metric_value_source": "exact_expression", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1 + \u221a2 + \u221a6 = 4.863+ | Found by Kravitz in 1967.", "setup": "cirincir", "side": 4.863703305156273, "source": "Erich Friedman Packing Center", "source_image": "ccc18.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Kravitz", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@19", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc19.gif", "friedman_display_metric_value": 4.863, "id": "friedman-34c45545a7a83759", "metric_expression": "1 + \u221a2 + \u221a6 = 4.863+", "metric_formula_parsed": "1 + sqrt 2 + sqrt 6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.863703305156273, "metric_value_source": "exact_expression", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1 + \u221a2 + \u221a6 = 4.863+ | Proved by F. Fodor in 1999.", "setup": "cirincir", "side": 4.863703305156273, "source": "Erich Friedman Packing Center", "source_image": "ccc19.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "F. Fodor", "title": "Circles in Circles", "verified": false}
+{"case": "cirincir@20", "external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc20.gif", "friedman_display_metric_value": 5.122, "id": "friedman-3c6aef83d624cd46", "metric_expression": "5.122+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 5.122, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 5.122+ | Found by Goldberg in 1971.", "setup": "cirincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "ccc20.gif", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "", "submitted_by": "Goldberg", "title": "Circles in Circles", "verified": false}
+{"case": "squincir@1", "external_image_url": "https://erich-friedman.github.io/packing/squincir/1.gif", "friedman_display_metric_value": 0.707, "id": "friedman-5869e84b3591c27f", "metric_expression": "\u221a2 / 2 = .707+", "metric_formula_parsed": "sqrt 2 / 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 0.7071067811865476, "metric_value_source": "exact_expression", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a2 / 2 = .707+ | Trivial.", "setup": "squincir", "side": 0.7071067811865476, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@2", "external_image_url": "https://erich-friedman.github.io/packing/squincir/2.gif", "friedman_display_metric_value": 1.118, "id": "friedman-0e4ee169173f3134", "metric_expression": "\u221a5 / 2 = 1.118+", "metric_formula_parsed": "sqrt 5 / 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.118033988749895, "metric_value_source": "exact_expression", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a5 / 2 = 1.118+ | Trivial.", "setup": "squincir", "side": 1.118033988749895, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@3", "external_image_url": "https://erich-friedman.github.io/packing/squincir/3.gif", "friedman_display_metric_value": 1.288, "id": "friedman-b224ef527f65192e", "metric_expression": "5 \u221a17 / 16 = 1.288+", "metric_formula_parsed": "5 sqrt 17 / 16", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.288470508005519, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 5 \u221a17 / 16 = 1.288+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": 1.288470508005519, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@4", "external_image_url": "https://erich-friedman.github.io/packing/squincir/4.gif", "friedman_display_metric_value": 1.414, "id": "friedman-f3807b78d909da78", "metric_expression": "\u221a2 = 1.414+", "metric_formula_parsed": "sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.4142135623730951, "metric_value_source": "exact_expression", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a2 = 1.414+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": 1.4142135623730951, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@5", "external_image_url": "https://erich-friedman.github.io/packing/squincir/5.gif", "friedman_display_metric_value": 1.581, "id": "friedman-88294a7216094c59", "metric_expression": "\u221a10 / 2 = 1.581+", "metric_formula_parsed": "sqrt 10 / 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.5811388300841898, "metric_value_source": "exact_expression", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a10 / 2 = 1.581+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": 1.5811388300841898, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@6", "external_image_url": "https://erich-friedman.github.io/packing/squincir/6.gif", "friedman_display_metric_value": 1.688, "id": "friedman-65e8d793b348932d", "metric_expression": "1.688+ *", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.688, "metric_value_source": "reported_decimal", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.688+ * | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@7", "external_image_url": "https://erich-friedman.github.io/packing/squincir/7.gif", "friedman_display_metric_value": 1.802, "id": "friedman-a59f56f1b2674418", "metric_expression": "\u221a13 / 2 = 1.802+", "metric_formula_parsed": "sqrt 13 / 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.8027756377319946, "metric_value_source": "exact_expression", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a13 / 2 = 1.802+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": 1.8027756377319946, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@8", "external_image_url": "https://erich-friedman.github.io/packing/squincir/8.gif", "friedman_display_metric_value": 1.978, "id": "friedman-43a8cc87dd562e65", "metric_expression": "1.978+ *", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.978, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.978+ * | Found by David W. Cantrell | in March 2002.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@9", "external_image_url": "https://erich-friedman.github.io/packing/squincir/9.gif", "friedman_display_metric_value": 2.077, "id": "friedman-86ca41fcbeeb5e27", "metric_expression": "\u221a1105 / 16 = 2.077+", "metric_formula_parsed": "sqrt 1105 / 16", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.0775962673243327, "metric_value_source": "exact_expression", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a1105 / 16 = 2.077+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": 2.0775962673243327, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@10", "external_image_url": "https://erich-friedman.github.io/packing/squincir/10.gif", "friedman_display_metric_value": 2.121, "id": "friedman-6355730efda78cb7", "metric_expression": "3 \u221a2 / 2 = 2.121+", "metric_formula_parsed": "3 sqrt 2 / 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.1213203435596424, "metric_value_source": "exact_expression", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3 \u221a2 / 2 = 2.121+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": 2.1213203435596424, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@11", "external_image_url": "https://erich-friedman.github.io/packing/squincir/11.gif", "friedman_display_metric_value": 2.214, "id": "friedman-c1b8b1c58054d915", "metric_expression": "2.214+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.214, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.214+ | Found by David W. Cantrell | in March 2002.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@12", "external_image_url": "https://erich-friedman.github.io/packing/squincir/12.gif", "friedman_display_metric_value": 2.236, "id": "friedman-9977a2eaf2805d65", "metric_expression": "\u221a5 = 2.236+", "metric_formula_parsed": "sqrt 5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.23606797749979, "metric_value_source": "exact_expression", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a5 = 2.236+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": 2.23606797749979, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@13", "external_image_url": "https://erich-friedman.github.io/packing/squincir/13.gif", "friedman_display_metric_value": 2.3607, "id": "friedman-cb0c99e6f49a3a7c", "metric_expression": "2.3607+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.3607, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.3607+ | Found by David W. Cantrell | in November 2010.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@14", "external_image_url": "https://erich-friedman.github.io/packing/squincir/14.gif", "friedman_display_metric_value": 2.5, "id": "friedman-9db264d6fbd56f88", "metric_expression": "2.5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.5, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.5 | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "14.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@15", "external_image_url": "https://erich-friedman.github.io/packing/squincir/15.gif", "friedman_display_metric_value": 2.533, "id": "friedman-7a18753406988317", "metric_expression": "2.533+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.533, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.533+ | Found by by David W. Cantrell | in June 2002.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@16", "external_image_url": "https://erich-friedman.github.io/packing/squincir/16.gif", "friedman_display_metric_value": 2.623, "id": "friedman-5ad570c477b4ac2e", "metric_expression": "\u221a11009 / 40 = 2.623+", "metric_formula_parsed": "sqrt 11009 / 40", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.623094546523247, "metric_value_source": "exact_expression", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a11009 / 40 = 2.623+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": 2.623094546523247, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@17", "external_image_url": "https://erich-friedman.github.io/packing/squincir/17.gif", "friedman_display_metric_value": 2.677, "id": "friedman-d4f47c876c439469", "metric_expression": "2.677+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.677, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.677+ | Found by Maurizio Morandi | in December 2010.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@18", "external_image_url": "https://erich-friedman.github.io/packing/squincir/18.gif", "friedman_display_metric_value": 2.741, "id": "friedman-d3d2c90ab2ff01be", "metric_expression": "\u221a481 / 8 = 2.741+", "metric_formula_parsed": "sqrt 481 / 8", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.7414640249326636, "metric_value_source": "exact_expression", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a481 / 8 = 2.741+ | Found by David W. Cantrell | in March 2002.", "setup": "squincir", "side": 2.7414640249326636, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@19", "external_image_url": "https://erich-friedman.github.io/packing/squincir/19.gif", "friedman_display_metric_value": 2.802, "id": "friedman-345374d2edaefdb5", "metric_expression": "2.802+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.802, "metric_value_source": "reported_decimal", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.802+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@20", "external_image_url": "https://erich-friedman.github.io/packing/squincir/20.gif", "friedman_display_metric_value": 2.893, "id": "friedman-9d8656f915990a3a", "metric_expression": "2.893+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.893, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.893+ | Found by David W. Cantrell | in June 2002.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "20.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@21", "external_image_url": "https://erich-friedman.github.io/packing/squincir/21.gif", "friedman_display_metric_value": 2.915, "id": "friedman-9cd3149db57e66f9", "metric_expression": "\u221a34 / 2 = 2.915+", "metric_formula_parsed": "sqrt 34 / 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.9154759474226504, "metric_value_source": "exact_expression", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a34 / 2 = 2.915+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": 2.9154759474226504, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@22", "external_image_url": "https://erich-friedman.github.io/packing/squincir/22.gif", "friedman_display_metric_value": 3.033, "id": "friedman-ebe3742a355dd42c", "metric_expression": "3.033+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.033, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.033+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "22.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@23", "external_image_url": "https://erich-friedman.github.io/packing/squincir/23.gif", "friedman_display_metric_value": 3.073, "id": "friedman-4348f331eb35d40c", "metric_expression": "3.073+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.073, "metric_value_source": "reported_decimal", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.073+ | Found by David W. Cantrell | in June 2002.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "23.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@24", "external_image_url": "https://erich-friedman.github.io/packing/squincir/24.gif", "friedman_display_metric_value": 3.11, "id": "friedman-4d57352fc22cdfc6", "metric_expression": "3.110+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.11, "metric_value_source": "reported_decimal", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.110+ | Found by Maurizio Morandi | in October 2010.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@25", "external_image_url": "https://erich-friedman.github.io/packing/squincir/25.gif", "friedman_display_metric_value": 3.175, "id": "friedman-68b34ad5c97761b2", "metric_expression": "\u221a5809 / 24 = 3.175+", "metric_formula_parsed": "sqrt 5809 / 24", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.175699835381871, "metric_value_source": "exact_expression", "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a5809 / 24 = 3.175+ | Found by David W. Cantrell | in April 2002.", "setup": "squincir", "side": 3.175699835381871, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@26", "external_image_url": "https://erich-friedman.github.io/packing/squincir/26.gif", "friedman_display_metric_value": 3.201, "id": "friedman-b6a112efa3684477", "metric_expression": "\u221a41 / 2 = 3.201+", "metric_formula_parsed": "sqrt 41 / 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.2015621187164243, "metric_value_source": "exact_expression", "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a41 / 2 = 3.201+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": 3.2015621187164243, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@27", "external_image_url": "https://erich-friedman.github.io/packing/squincir/27.gif", "friedman_display_metric_value": 3.261, "id": "friedman-7dcca59d45647799", "metric_expression": "13\u221a145/48 = 3.261+", "metric_formula_parsed": "13 sqrt 145/48", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.2612651984229135, "metric_value_source": "exact_expression", "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 13\u221a145/48 = 3.261+ | Found by Maurizio Morandi | in September 2010.", "setup": "squincir", "side": 3.2612651984229135, "source": "Erich Friedman Packing Center", "source_image": "27.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@28", "external_image_url": "https://erich-friedman.github.io/packing/squincir/28.gif", "friedman_display_metric_value": 3.333, "id": "friedman-76c15924023fc9c9", "metric_expression": "3.333+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.333, "metric_value_source": "reported_decimal", "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.333+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "28.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@29", "external_image_url": "https://erich-friedman.github.io/packing/squincir/29.gif", "friedman_display_metric_value": 3.401, "id": "friedman-1269da4cc3a8081b", "metric_expression": "3.401+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.401, "metric_value_source": "reported_decimal", "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.401+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "29.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@30", "external_image_url": "https://erich-friedman.github.io/packing/squincir/30.gif", "friedman_display_metric_value": 3.472, "id": "friedman-376088620cfc99d9", "metric_expression": "3.472+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.472, "metric_value_source": "reported_decimal", "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.472+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "30.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@31", "external_image_url": "https://erich-friedman.github.io/packing/squincir/31.gif", "friedman_display_metric_value": 3.535, "id": "friedman-14370ff874d2cb2d", "metric_expression": "5 \u221a2 / 2 = 3.535+", "metric_formula_parsed": "5 sqrt 2 / 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.5355339059327378, "metric_value_source": "exact_expression", "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 5 \u221a2 / 2 = 3.535+ | Found by Erich Friedman | in 1997.", "setup": "squincir", "side": 3.5355339059327378, "source": "Erich Friedman Packing Center", "source_image": "31.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@32", "external_image_url": "https://erich-friedman.github.io/packing/squincir/32.gif", "friedman_display_metric_value": 3.584, "id": "friedman-64ecaa354f0fa4c4", "metric_expression": "3.584+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.584, "metric_value_source": "reported_decimal", "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.584+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@33", "external_image_url": "https://erich-friedman.github.io/packing/squincir/33.gif", "friedman_display_metric_value": 3.605, "id": "friedman-d05dcfdf1ac4c4fe", "metric_expression": "\u221a13 = 3.605+", "metric_formula_parsed": "sqrt 13", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.605551275463989, "metric_value_source": "exact_expression", "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in June 2010.", "setup": "squincir", "side": 3.605551275463989, "source": "Erich Friedman Packing Center", "source_image": "33.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@34", "external_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif", "friedman_display_metric_value": 3.629, "id": "friedman-e762304582c78701", "metric_expression": "3.629+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.629, "metric_value_source": "reported_decimal", "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.", "setup": "squincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "34.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Circles", "verified": false}
+{"case": "squincir@35", "external_image_url": "https://erich-friedman.github.io/packing/squincir/35.gif", "friedman_display_metric_value": 3.64, "id": "friedman-2149f75e4bd65fbf", "metric_expression": "\u221a53 / 2 = 3.640+", "metric_formula_parsed": "sqrt 53 / 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.640054944640259, "metric_value_source": "exact_expression", "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a53 / 2 = 3.640+ | Found by David Eppstein | in March 2002.", "setup": "squincir", "side": 3.640054944640259, "source": "Erich Friedman Packing Center", "source_image": "35.gif", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "", "submitted_by": "David Eppstein", "title": "Squares in Circles", "verified": false}
+{"case": "hexincir@1", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/1.png", "friedman_display_metric_value": 1.0, "id": "friedman-f4365a8237f4d536", "metric_expression": "1", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.0, "metric_value_source": "reported_decimal", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1 | Trivial.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "1.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@2", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/2.png", "friedman_display_metric_value": 1.802, "id": "friedman-161cd75eb6ba9ba4", "metric_expression": "\u221a13/2 = 1.802+", "metric_formula_parsed": "sqrt 13/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.8027756377319946, "metric_value_source": "exact_expression", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a13/2 = 1.802+ | Trivial.", "setup": "hexincir", "side": 1.8027756377319946, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@3", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/3.png", "friedman_display_metric_value": 2.0, "id": "friedman-907e870939be554d", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2 | Trivial.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@4", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/4.png", "friedman_display_metric_value": 2.239, "id": "friedman-c1a3d7df20036b35", "metric_expression": "(21\u2013\u221a145)/4 = 2.239+", "metric_formula_parsed": "(21- sqrt 145)/4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.239601355301926, "metric_value_source": "exact_expression", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = (21\u2013\u221a145)/4 = 2.239+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexincir", "side": 2.239601355301926, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@5", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/5.png", "friedman_display_metric_value": 2.471, "id": "friedman-d5d1894268994287", "metric_expression": "2.471+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.471, "metric_value_source": "reported_decimal", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.471+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "5.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@6", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/7.png", "friedman_display_metric_value": 2.645, "id": "friedman-0f6175719a014590", "metric_expression": "\u221a7 = 2.645+", "metric_formula_parsed": "sqrt 7", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.6457513110645907, "metric_value_source": "exact_expression", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a7 = 2.645+ | Trivial. |", "setup": "hexincir", "side": 2.6457513110645907, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@7", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/7.png", "friedman_display_metric_value": 2.645, "id": "friedman-ce7782e664eb3509", "metric_expression": "\u221a7 = 2.645+", "metric_formula_parsed": "sqrt 7", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.6457513110645907, "metric_value_source": "exact_expression", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a7 = 2.645+ | Trivial. |", "setup": "hexincir", "side": 2.6457513110645907, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@8", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/8.png", "friedman_display_metric_value": 2.984, "id": "friedman-8f9fd353f3c39f8f", "metric_expression": "2.984+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.984, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.984+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@9", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/9.png", "friedman_display_metric_value": 3.301, "id": "friedman-ce7d1705ae35759e", "metric_expression": "3.301+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.301, "metric_value_source": "reported_decimal", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.301+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@10", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/10.png", "friedman_display_metric_value": 3.5, "id": "friedman-29b086edb1679805", "metric_expression": "7/2 = 3.5", "metric_formula_parsed": "7/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.5, "metric_value_source": "exact_expression", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 7/2 = 3.5 | Found by Maurizio Morandi | in March 2026.", "setup": "hexincir", "side": 3.5, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@11", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/12.png", "friedman_display_metric_value": 3.605, "id": "friedman-ac95a15bac80aada", "metric_expression": "\u221a13 = 3.605+", "metric_formula_parsed": "sqrt 13", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.605551275463989, "metric_value_source": "exact_expression", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexincir", "side": 3.605551275463989, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@12", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/12.png", "friedman_display_metric_value": 3.605, "id": "friedman-3376d2ccb3372ee0", "metric_expression": "\u221a13 = 3.605+", "metric_formula_parsed": "sqrt 13", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.605551275463989, "metric_value_source": "exact_expression", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexincir", "side": 3.605551275463989, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@13", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/13.png", "friedman_display_metric_value": 3.82298, "id": "friedman-96ae4e9094430c50", "metric_expression": "3.82298+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.82298, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.82298+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@14", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/14.png", "friedman_display_metric_value": 3.877, "id": "friedman-df66c818ec0fcb21", "metric_expression": "\u221a(109\u20139\u221a109) = 3.877+", "metric_formula_parsed": "sqrt (109-9 sqrt 109)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.877788212345415, "metric_value_source": "exact_expression", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a(109\u20139\u221a109) = 3.877+ | Found by Maurizio Morandi | in March 2026.", "setup": "hexincir", "side": 3.877788212345415, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@15", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/15.png", "friedman_display_metric_value": 4.08174, "id": "friedman-1b8f3d32de4efd85", "metric_expression": "4.08174+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.08174, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.08174+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@16", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/16.png", "friedman_display_metric_value": 4.13966, "id": "friedman-984915062df8aaf9", "metric_expression": "4.13966+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.13966, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.13966+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "16.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@17", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/17.png", "friedman_display_metric_value": 4.3017, "id": "friedman-d2e9447ad7d3e656", "metric_expression": "4.30170+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.3017, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.30170+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@18", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "friedman_display_metric_value": 4.35889, "id": "friedman-aaa107cfaf93d0b6", "metric_expression": "\u221a19 = 4.35889+", "metric_formula_parsed": "sqrt 19", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.358898943540673, "metric_value_source": "exact_expression", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "setup": "hexincir", "side": 4.358898943540673, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@19", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "friedman_display_metric_value": 4.35889, "id": "friedman-a90f0ec81a1e11a5", "metric_expression": "\u221a19 = 4.35889+", "metric_formula_parsed": "sqrt 19", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.358898943540673, "metric_value_source": "exact_expression", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "setup": "hexincir", "side": 4.358898943540673, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@20", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/20.png", "friedman_display_metric_value": 4.62598, "id": "friedman-d422aef11edc8b4e", "metric_expression": "4.62598+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.62598, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.62598+ | Found by Jonathan Viquerat | in April 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Circles", "verified": false}
+{"case": "hexincir@21", "external_image_url": "https://erich-friedman.github.io/packing/hexincir/21.png", "friedman_display_metric_value": 4.68339, "id": "friedman-29ad6735609174be", "metric_expression": "4.68339+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.68339, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 4.68339+ | Found by Enea Victor | in April 2026.", "setup": "hexincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "21.png", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "", "submitted_by": "Enea Victor", "title": "Hexagons in Circles", "verified": false}
+{"case": "triinhex@1", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/1.gif", "friedman_display_metric_value": 0.577, "id": "friedman-3da8e7e1948e6736", "metric_expression": "1/\u221a3 = .577+", "metric_formula_parsed": "1/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.5773502691896257, "metric_value_source": "exact_expression", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1/\u221a3 = .577+ | Trivial.", "setup": "triinhex", "side": 0.5773502691896257, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@2", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/2.gif", "friedman_display_metric_value": 0.866, "id": "friedman-6a37d09ba95769ef", "metric_expression": "\u221a3/2 = .866+", "metric_formula_parsed": "sqrt 3/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.8660254037844386, "metric_value_source": "exact_expression", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a3/2 = .866+ | Trivial.", "setup": "triinhex", "side": 0.8660254037844386, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@3", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/3.gif", "friedman_display_metric_value": 0.989, "id": "friedman-2e8c6ffd77fd1caa", "metric_expression": "\u221a((6+\u221a33)/12) = .989+", "metric_formula_parsed": "sqrt ((6+ sqrt 33)/12)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.9892995268765516, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a((6+\u221a33)/12) = .989+ | Found by Erich Friedman | in April 2005.", "setup": "triinhex", "side": 0.9892995268765516, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@4", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/4.gif", "friedman_display_metric_value": 1.0, "id": "friedman-4801232c424f2df0", "metric_expression": "1", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0, "metric_value_source": "reported_decimal", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 | Trivial.", "setup": "triinhex", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@5", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/5.gif", "friedman_display_metric_value": 1.0, "id": "friedman-a98b7b2f0609831c", "metric_expression": "1", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0, "metric_value_source": "reported_decimal", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 | Trivial.", "setup": "triinhex", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@6", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/6.gif", "friedman_display_metric_value": 1.0, "id": "friedman-344dc5b961d22a74", "metric_expression": "1", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0, "metric_value_source": "reported_decimal", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 | Trivial.", "setup": "triinhex", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@7", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/7.gif", "friedman_display_metric_value": 1.277, "id": "friedman-1cfc719fa74e4895", "metric_expression": "1.277+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.277, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.277+ | Found by David W. Cantrell | in May 2005.", "setup": "triinhex", "side": 1.277, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@8", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/8.gif", "friedman_display_metric_value": 1.356, "id": "friedman-1026f883709bd7d3", "metric_expression": "1.356+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.356, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.356+ | Found by David W. Cantrell | in July 2012.", "setup": "triinhex", "side": 1.356, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@9", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/9.gif", "friedman_display_metric_value": 1.434, "id": "friedman-878211b91c2cd25f", "metric_expression": "1.434+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.434, "metric_value_source": "reported_decimal", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.434+ | Found by Erich Friedman | in April 2005.", "setup": "triinhex", "side": 1.434, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@10", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/10.gif", "friedman_display_metric_value": 1.497, "id": "friedman-3f524f23d82a3765", "metric_expression": "1.497+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.497, "metric_value_source": "reported_decimal", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.497+ | Found by Timo Berthold et al | in January 2026.", "setup": "triinhex", "side": 1.497, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@11", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/11.gif", "friedman_display_metric_value": 1.5, "id": "friedman-d8daa892bdde901b", "metric_expression": "3/2 = 1.500", "metric_formula_parsed": "3/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.5, "metric_value_source": "exact_expression", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3/2 = 1.500 | Found by Erich Friedman | in April 2005.", "setup": "triinhex", "side": 1.5, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@12", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/12.gif", "friedman_display_metric_value": 1.623, "id": "friedman-e69ae6a58b2340ae", "metric_expression": "1.623+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.623, "metric_value_source": "reported_decimal", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.623+ | Found by Timo Berthold et al | in January 2026.", "setup": "triinhex", "side": 1.623, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@13", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/13.gif", "friedman_display_metric_value": 1.663829, "id": "friedman-b44ea2e121113705", "metric_expression": "\u221a(587+51\u221a17)/12\u221a2 = 1.663829+", "metric_formula_parsed": "sqrt (587+51 sqrt 17)/(12*sqrt 2)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.663829237726708, "metric_value_source": "exact_expression", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a(587+51\u221a17)/12\u221a2 = 1.663829+ | Found by Ian Watson | in April 2026.", "setup": "triinhex", "side": 1.663829237726708, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@14", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/14.gif", "friedman_display_metric_value": 1.725, "id": "friedman-a3f46ac5df4272b1", "metric_expression": "1.725+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.725, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.725+ | Found by David W. Cantrell | in August 2012.", "setup": "triinhex", "side": 1.725, "source": "Erich Friedman Packing Center", "source_image": "14.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@15", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/15.gif", "friedman_display_metric_value": 1.75, "id": "friedman-f1d60e3a404c89fa", "metric_expression": "7/4 = 1.750", "metric_formula_parsed": "7/4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.75, "metric_value_source": "exact_expression", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7/4 = 1.750 | Found by Erich Friedman | in April 2005.", "setup": "triinhex", "side": 1.75, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@16", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/16.gif", "friedman_display_metric_value": 1.8, "id": "friedman-7fac796b89bce5ba", "metric_expression": "9/5 = 1.800", "metric_formula_parsed": "9/5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.8, "metric_value_source": "exact_expression", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9/5 = 1.800 | Found by Maurizio Morandi | in April 2008.", "setup": "triinhex", "side": 1.8, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@17", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/17.gif", "friedman_display_metric_value": 1.833, "id": "friedman-32b5ba5889634179", "metric_expression": "11/6 = 1.833+", "metric_formula_parsed": "11/6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.8333333333333333, "metric_value_source": "exact_expression", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 11/6 = 1.833+ | Found by Maurizio Morandi | in April 2008.", "setup": "triinhex", "side": 1.8333333333333333, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@18", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/18.gif", "friedman_display_metric_value": 1.888, "id": "friedman-6fe52b2c6562a1a5", "metric_expression": "17/9 = 1.888+", "metric_formula_parsed": "17/9", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.8888888888888888, "metric_value_source": "exact_expression", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 17/9 = 1.888+ | Found by Maurizio Morandi | in April 2008.", "setup": "triinhex", "side": 1.8888888888888888, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@19", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/19.gif", "friedman_display_metric_value": 1.953, "id": "friedman-ae881bae597b1582", "metric_expression": "1.953+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.953, "metric_value_source": "reported_decimal", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.953+ | Found by Alex Adri\u00e1n Nieto | in April 2026.", "setup": "triinhex", "side": 1.953, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Alex Adri\u00e1n Nieto", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@20", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/20.gif", "friedman_display_metric_value": 1.97591, "id": "friedman-e09e2731ede2b818", "metric_expression": "1.97591+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.97591, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.97591+ | Found by Aaden Abraham | in April 2026.", "setup": "triinhex", "side": 1.97591, "source": "Erich Friedman Packing Center", "source_image": "20.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Aaden Abraham", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@21", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/21.gif", "friedman_display_metric_value": 1.99878, "id": "friedman-6a5c03a69b1a0944", "metric_expression": "1.99878+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.99878, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.99878+ | Found by Ian Watson | in April 2026.", "setup": "triinhex", "side": 1.99878, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@22", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "friedman_display_metric_value": 2.0, "id": "friedman-f4b5e7f94a8cb2d9", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial. |", "setup": "triinhex", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@23", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "friedman_display_metric_value": 2.0, "id": "friedman-98ecf39e2c10f60b", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial. |", "setup": "triinhex", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@24", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "friedman_display_metric_value": 2.0, "id": "friedman-848e5e014bbb1c07", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial. |", "setup": "triinhex", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@25", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/25.gif", "friedman_display_metric_value": 2.166, "id": "friedman-0669c70e4fbc9795", "metric_expression": "13/6 = 2.166+", "metric_formula_parsed": "13/6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.1666666666666665, "metric_value_source": "exact_expression", "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 13/6 = 2.166+ | Found by Ignacio Vallejo | in April 2026.", "setup": "triinhex", "side": 2.1666666666666665, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@26", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/26.gif", "friedman_display_metric_value": 2.21991, "id": "friedman-be91cb98d802160b", "metric_expression": "2.21991+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.21991, "metric_value_source": "reported_decimal", "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.21991+ | Found by Ian Watson | in April 2026.", "setup": "triinhex", "side": 2.21991, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@27", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/27.gif", "friedman_display_metric_value": 2.29541, "id": "friedman-de6536d86c63771d", "metric_expression": "2.29541+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.29541, "metric_value_source": "reported_decimal", "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.29541+ | Found by Ian Watson | in April 2026.", "setup": "triinhex", "side": 2.29541, "source": "Erich Friedman Packing Center", "source_image": "27.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@28", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/28.gif", "friedman_display_metric_value": 2.32289, "id": "friedman-84527b93fa221d9a", "metric_expression": "2.32289+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.32289, "metric_value_source": "reported_decimal", "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.32289+ | Found by Ian Watson | in April 2026.", "setup": "triinhex", "side": 2.32289, "source": "Erich Friedman Packing Center", "source_image": "28.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@29", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/29.gif", "friedman_display_metric_value": 2.333, "id": "friedman-760c159820f8d745", "metric_expression": "7/3 = 2.333+", "metric_formula_parsed": "7/3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.3333333333333335, "metric_value_source": "exact_expression", "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7/3 = 2.333+ | Found by Ignacio Vallejo | in April 2026.", "setup": "triinhex", "side": 2.3333333333333335, "source": "Erich Friedman Packing Center", "source_image": "29.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@30", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/30.gif", "friedman_display_metric_value": 2.375, "id": "friedman-b4d9e24006eac400", "metric_expression": "19/8 = 2.375", "metric_formula_parsed": "19/8", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.375, "metric_value_source": "exact_expression", "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 19/8 = 2.375 | Found by Ignacio Vallejo | in April 2026.", "setup": "triinhex", "side": 2.375, "source": "Erich Friedman Packing Center", "source_image": "30.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@31", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/31.gif", "friedman_display_metric_value": 2.4, "id": "friedman-f86fde748b4194e9", "metric_expression": "12/5 = 2.400", "metric_formula_parsed": "12/5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.4, "metric_value_source": "exact_expression", "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 12/5 = 2.400 | Found by Emerson Connelly | in April 2026.", "setup": "triinhex", "side": 2.4, "source": "Erich Friedman Packing Center", "source_image": "31.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@32", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/32.gif", "friedman_display_metric_value": 2.465, "id": "friedman-3dd51f0f97b0b151", "metric_expression": "2.465+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.465, "metric_value_source": "reported_decimal", "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.465+ | Found by Emerson Connelly | in April 2026.", "setup": "triinhex", "side": 2.465, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@33", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/33.gif", "friedman_display_metric_value": 2.498, "id": "friedman-eef0a3d7d3d42660", "metric_expression": "2.498+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.498, "metric_value_source": "reported_decimal", "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.498+ | Found by Emerson Connelly | in April 2026.", "setup": "triinhex", "side": 2.498, "source": "Erich Friedman Packing Center", "source_image": "33.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@34", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "friedman_display_metric_value": 2.5, "id": "friedman-0d6413d764fd130a", "metric_expression": "5/2 = 2.500", "metric_formula_parsed": "5/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.5, "metric_value_source": "exact_expression", "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "setup": "triinhex", "side": 2.5, "source": "Erich Friedman Packing Center", "source_image": "35.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@35", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "friedman_display_metric_value": 2.5, "id": "friedman-3f36e9a7b3ccf62a", "metric_expression": "5/2 = 2.500", "metric_formula_parsed": "5/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.5, "metric_value_source": "exact_expression", "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "setup": "triinhex", "side": 2.5, "source": "Erich Friedman Packing Center", "source_image": "35.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@36", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/36.gif", "friedman_display_metric_value": 2.59123, "id": "friedman-5a3e047914e4c52e", "metric_expression": "2.59123+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.59123, "metric_value_source": "reported_decimal", "n": 36, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.59123+ | Found by Nathan Roll | in April 2026.", "setup": "triinhex", "side": 2.59123, "source": "Erich Friedman Packing Center", "source_image": "36.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@37", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/37.gif", "friedman_display_metric_value": 2.61943, "id": "friedman-88d93da6bb76b1b1", "metric_expression": "2.61943+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.61943, "metric_value_source": "reported_decimal", "n": 37, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.61943+ | Found by Nathan Roll | in April 2026.", "setup": "triinhex", "side": 2.61943, "source": "Erich Friedman Packing Center", "source_image": "37.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@38", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "friedman_display_metric_value": 2.666, "id": "friedman-c5101afcc06aa9b6", "metric_expression": "8/3 = 2.666+", "metric_formula_parsed": "8/3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.6666666666666665, "metric_value_source": "exact_expression", "n": 38, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "setup": "triinhex", "side": 2.6666666666666665, "source": "Erich Friedman Packing Center", "source_image": "39.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@39", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "friedman_display_metric_value": 2.666, "id": "friedman-fe6d3925c241e54c", "metric_expression": "8/3 = 2.666+", "metric_formula_parsed": "8/3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.6666666666666665, "metric_value_source": "exact_expression", "n": 39, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "setup": "triinhex", "side": 2.6666666666666665, "source": "Erich Friedman Packing Center", "source_image": "39.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Hexagons", "verified": false}
+{"case": "triinhex@40", "external_image_url": "https://erich-friedman.github.io/packing/triinhex/40.gif", "friedman_display_metric_value": 2.71622, "id": "friedman-664d8ab6cb5c8368", "metric_expression": "2.71622+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.71622, "metric_value_source": "reported_decimal", "n": 40, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.71622+ | Found by Nathan Roll | in April 2026.", "setup": "triinhex", "side": 2.71622, "source": "Erich Friedman Packing Center", "source_image": "40.gif", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Triangles in Hexagons", "verified": false}
+{"case": "cirinhex@1", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc1.gif", "friedman_display_metric_value": 1.154, "id": "friedman-770d235be87f7626", "metric_expression": "2/\u221a3 = 1.154+", "metric_formula_parsed": "2/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.1547005383792515, "metric_value_source": "exact_expression", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2/\u221a3 = 1.154+ | Trivial.", "setup": "cirinhex", "side": 1.1547005383792515, "source": "Erich Friedman Packing Center", "source_image": "hc1.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@2", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc2.gif", "friedman_display_metric_value": 2.154, "id": "friedman-73fd4a5a73841e9b", "metric_expression": "1 + 2/\u221a3 = 2.154+", "metric_formula_parsed": "1 + 2/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.1547005383792515, "metric_value_source": "exact_expression", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 + 2/\u221a3 = 2.154+ | Trivial.", "setup": "cirinhex", "side": 2.1547005383792515, "source": "Erich Friedman Packing Center", "source_image": "hc2.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@3", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc3.gif", "friedman_display_metric_value": 2.309, "id": "friedman-79ade9f886ed48ae", "metric_expression": "4/\u221a3 = 2.309+", "metric_formula_parsed": "4/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.309401076758503, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4/\u221a3 = 2.309+ | Trivial.", "setup": "cirinhex", "side": 2.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "hc3.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@4", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc4.gif", "friedman_display_metric_value": 2.666, "id": "friedman-bac6d855bac20369", "metric_expression": "2/\u221a3 + 4/\u221a7 = 2.666+", "metric_formula_parsed": "2/ sqrt 3 + 4/ sqrt 7", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.6665584304161603, "metric_value_source": "exact_expression", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2/\u221a3 + 4/\u221a7 = 2.666+ | Found by Shahriar Manzoor | in April 2002.", "setup": "cirinhex", "side": 2.6665584304161603, "source": "Erich Friedman Packing Center", "source_image": "hc4.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Shahriar Manzoor", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@5", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc5.gif", "friedman_display_metric_value": 2.999, "id": "friedman-fd320f8f6c6e941f", "metric_expression": "2.999+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.999, "metric_value_source": "reported_decimal", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.999+ | Found by Erich Friedman | in 1999.", "setup": "cirinhex", "side": 2.999, "source": "Erich Friedman Packing Center", "source_image": "hc5.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@6", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc6.gif", "friedman_display_metric_value": 3.154, "id": "friedman-0fda7696de625f14", "metric_expression": "2 + 2/\u221a3 = 3.154+", "metric_formula_parsed": "2 + 2/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.1547005383792515, "metric_value_source": "exact_expression", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2/\u221a3 = 3.154+ | Trivial. |", "setup": "cirinhex", "side": 3.1547005383792515, "source": "Erich Friedman Packing Center", "source_image": "hc6.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@7", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc7.gif", "friedman_display_metric_value": 3.154, "id": "friedman-ed3a018f5ec225be", "metric_expression": "2 + 2/\u221a3 = 3.154+", "metric_formula_parsed": "2 + 2/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.1547005383792515, "metric_value_source": "exact_expression", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2/\u221a3 = 3.154+ | Trivial. |", "setup": "cirinhex", "side": 3.1547005383792515, "source": "Erich Friedman Packing Center", "source_image": "hc7.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@8", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc8.gif", "friedman_display_metric_value": 3.709, "id": "friedman-993ee06d15d5ed36", "metric_expression": "3.709+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.709, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.709+ | Found by David W. Cantrell | in July 2002.", "setup": "cirinhex", "side": 3.709, "source": "Erich Friedman Packing Center", "source_image": "hc8.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@9", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc9.gif", "friedman_display_metric_value": 4.011, "id": "friedman-c3af9c95b34d4eae", "metric_expression": "20/7 + 2/\u221a3 = 4.011+", "metric_formula_parsed": "20/7 + 2/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.011843395522108, "metric_value_source": "exact_expression", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 20/7 + 2/\u221a3 = 4.011+ | Found by David W. Cantrell | in July 2002.", "setup": "cirinhex", "side": 4.011843395522108, "source": "Erich Friedman Packing Center", "source_image": "hc9.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@10", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc10.gif", "friedman_display_metric_value": 4.119, "id": "friedman-059d42e7a7094200", "metric_expression": "4.119+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.119, "metric_value_source": "reported_decimal", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.119+ | Found by David W. Cantrell | in July 2002.", "setup": "cirinhex", "side": 4.119, "source": "Erich Friedman Packing Center", "source_image": "hc10.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@11", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc11.gif", "friedman_display_metric_value": 4.309, "id": "friedman-d8761b35cf44d4b6", "metric_expression": "2 + 4/\u221a3 = 4.309+", "metric_formula_parsed": "2 + 4/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.309401076758503, "metric_value_source": "exact_expression", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 4/\u221a3 = 4.309+ | Found by Erich Friedman | in 1999.", "setup": "cirinhex", "side": 4.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "hc11.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@12", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc12.gif", "friedman_display_metric_value": 4.309, "id": "friedman-72b7d9ef3a1d1eb3", "metric_expression": "2 + 4/\u221a3 = 4.309+", "metric_formula_parsed": "2 + 4/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.309401076758503, "metric_value_source": "exact_expression", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 4/\u221a3 = 4.309+ | Found by Erich Friedman | in 1999.", "setup": "cirinhex", "side": 4.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "hc12.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@13", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc13.gif", "friedman_display_metric_value": 4.618, "id": "friedman-050ca63d878798db", "metric_expression": "8/\u221a3 = 4.618+", "metric_formula_parsed": "8/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.618802153517006, "metric_value_source": "exact_expression", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8/\u221a3 = 4.618+ | Found by Erich Friedman | in 1999.", "setup": "cirinhex", "side": 4.618802153517006, "source": "Erich Friedman Packing Center", "source_image": "hc13.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@14", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc14.gif", "friedman_display_metric_value": 4.666, "id": "friedman-16d5278528a0de05", "metric_expression": "2 + 2/\u221a3 + 4/\u221a7 = 4.666+", "metric_formula_parsed": "2 + 2/ sqrt 3 + 4/ sqrt 7", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.666558430416161, "metric_value_source": "exact_expression", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 + 2/\u221a3 + 4/\u221a7 = 4.666+ | Found by David W. Cantrell | in July 2002.", "setup": "cirinhex", "side": 4.666558430416161, "source": "Erich Friedman Packing Center", "source_image": "hc14.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@15", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc15.gif", "friedman_display_metric_value": 4.961, "id": "friedman-cbd8c577436a2f32", "metric_expression": "4.961+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.961, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.961+ | Found by David W. Cantrell | in January 2006.", "setup": "cirinhex", "side": 4.961, "source": "Erich Friedman Packing Center", "source_image": "hc15.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@16", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc16.gif", "friedman_display_metric_value": 4.999, "id": "friedman-b904921ad4239ae1", "metric_expression": "4.999+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.999, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.999+ | Found by David W. Cantrell | in July 2002.", "setup": "cirinhex", "side": 4.999, "source": "Erich Friedman Packing Center", "source_image": "hc16.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@17", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc17.gif", "friedman_display_metric_value": 5.133, "id": "friedman-a809c6c673ff63e9", "metric_expression": "5.133+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.133, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.133+ | Found by David W. Cantrell | in January 2006.", "setup": "cirinhex", "side": 5.133, "source": "Erich Friedman Packing Center", "source_image": "hc17.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@18", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc18.gif", "friedman_display_metric_value": 5.154, "id": "friedman-fee81833ed47e1c7", "metric_expression": "4 + 2/\u221a3 = 5.154+", "metric_formula_parsed": "4 + 2/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.1547005383792515, "metric_value_source": "exact_expression", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "setup": "cirinhex", "side": 5.1547005383792515, "source": "Erich Friedman Packing Center", "source_image": "hc18.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@19", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc19.gif", "friedman_display_metric_value": 5.154, "id": "friedman-2008aa727face205", "metric_expression": "4 + 2/\u221a3 = 5.154+", "metric_formula_parsed": "4 + 2/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.1547005383792515, "metric_value_source": "exact_expression", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "setup": "cirinhex", "side": 5.1547005383792515, "source": "Erich Friedman Packing Center", "source_image": "hc19.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@20", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc20.gif", "friedman_display_metric_value": 5.676, "id": "friedman-05e6d5eff9cc57c1", "metric_expression": "5.676+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.676, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.676+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinhex", "side": 5.676, "source": "Erich Friedman Packing Center", "source_image": "hc20.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@21", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc21.gif", "friedman_display_metric_value": 5.709, "id": "friedman-1fbed3d4da59c92b", "metric_expression": "5.709+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.709, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.709+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinhex", "side": 5.709, "source": "Erich Friedman Packing Center", "source_image": "hc21.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@22", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc22.gif", "friedman_display_metric_value": 5.952, "id": "friedman-97ac6750b723bc99", "metric_expression": "5.952+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.952, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.952+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinhex", "side": 5.952, "source": "Erich Friedman Packing Center", "source_image": "hc22.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@23", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc23.gif", "friedman_display_metric_value": 6.011, "id": "friedman-416e07b086cdb41c", "metric_expression": "34/7 + 2/\u221a3 = 6.011+", "metric_formula_parsed": "34/7 + 2/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.011843395522108, "metric_value_source": "exact_expression", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 34/7 + 2/\u221a3 = 6.011+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinhex", "side": 6.011843395522108, "source": "Erich Friedman Packing Center", "source_image": "hc23.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Hexagons", "verified": false}
+{"case": "cirinhex@24", "external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc24.gif", "friedman_display_metric_value": 6.117, "id": "friedman-f836a33ba94ecd25", "metric_expression": "6.117+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.117, "metric_value_source": "reported_decimal", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.117+ | Found by Rob Pratt | in March 2020.", "setup": "cirinhex", "side": 6.117, "source": "Erich Friedman Packing Center", "source_image": "hc24.gif", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "", "submitted_by": "Rob Pratt", "title": "Circles in Hexagons", "verified": false}
+{"case": "squinhex@1", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/1.png", "friedman_display_metric_value": 0.778, "id": "friedman-aa882c20c2730808", "metric_expression": "(3+\u221a3)/6 = 0.778+", "metric_formula_parsed": "(3+ sqrt 3)/6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.7886751345948129, "metric_value_source": "exact_expression", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (3+\u221a3)/6 = 0.778+ | Trivial. |", "setup": "squinhex", "side": 0.7886751345948129, "source": "Erich Friedman Packing Center", "source_image": "1.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@2", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/2.png", "friedman_display_metric_value": 1.154, "id": "friedman-c9575101dedb956d", "metric_expression": "2/\u221a3 = 1.154+", "metric_formula_parsed": "2/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.1547005383792515, "metric_value_source": "exact_expression", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2/\u221a3 = 1.154+ | Trivial. |", "setup": "squinhex", "side": 1.1547005383792515, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@3", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/3.png", "friedman_display_metric_value": 1.366, "id": "friedman-65d767684918c83c", "metric_expression": "(1+\u221a3)/2 = 1.366+", "metric_formula_parsed": "(1+ sqrt 3)/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.3660254037844386, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (1+\u221a3)/2 = 1.366+ | Found by Maurizio Morandi | in March 2026.", "setup": "squinhex", "side": 1.3660254037844386, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@4", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/4.png", "friedman_display_metric_value": 1.519, "id": "friedman-7f3c951c602c858c", "metric_expression": "2/3 1/4 = 1.519+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.519, "metric_value_source": "reported_decimal", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2/3 1/4 = 1.519+ | Found by Maurizio Morandi | in March 2026.", "setup": "squinhex", "side": 1.519, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@5", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/5.png", "friedman_display_metric_value": 1.732, "id": "friedman-059fe44f20dafce7", "metric_expression": "\u221a3 = 1.732+", "metric_formula_parsed": "sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.7320508075688772, "metric_value_source": "exact_expression", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a3 = 1.732+ | Trivial. |", "setup": "squinhex", "side": 1.7320508075688772, "source": "Erich Friedman Packing Center", "source_image": "5.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@6", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/6.png", "friedman_display_metric_value": 1.821, "id": "friedman-e9e76992ebfd0eea", "metric_expression": "1.821+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.821, "metric_value_source": "reported_decimal", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.821+ | Found by Maurizio Morandi | in March 2026.", "setup": "squinhex", "side": 1.821, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@7", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/7.png", "friedman_display_metric_value": 1.861, "id": "friedman-917aa74cad64acc9", "metric_expression": "(\u221a2)3 1/4 = 1.861+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.861, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (\u221a2)3 1/4 = 1.861+ | Found by Maurizio Morandi | in March 2026.", "setup": "squinhex", "side": 1.861, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@8", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/8.png", "friedman_display_metric_value": 2.15378, "id": "friedman-37c209606b5d0be8", "metric_expression": "2.15378+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.15378, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.15378+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 2.15378, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@9", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/9.png", "friedman_display_metric_value": 2.23205, "id": "friedman-6ed5a97a8522fe9f", "metric_expression": "1/2+\u221a3 = 2.23205+", "metric_formula_parsed": "1/2+ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.232050807568877, "metric_value_source": "exact_expression", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1/2+\u221a3 = 2.23205+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squinhex", "side": 2.232050807568877, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@10", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/10.png", "friedman_display_metric_value": 2.309, "id": "friedman-5698b9a145008429", "metric_expression": "4/\u221a3 = 2.309+", "metric_formula_parsed": "4/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.309401076758503, "metric_value_source": "exact_expression", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4/\u221a3 = 2.309+ | Trivial. |", "setup": "squinhex", "side": 2.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@11", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/11.png", "friedman_display_metric_value": 2.40944, "id": "friedman-e4f42dd9bad6e9ae", "metric_expression": "2.40944+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.40944, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.40944+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squinhex", "side": 2.40944, "source": "Erich Friedman Packing Center", "source_image": "11.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@12", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/12.png", "friedman_display_metric_value": 2.443, "id": "friedman-158e465d78189aab", "metric_expression": "1+5\u221a3/6 = 2.443+", "metric_formula_parsed": "1+5 sqrt 3/6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.4433756729740645, "metric_value_source": "exact_expression", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1+5\u221a3/6 = 2.443+ | Found by Maurizio Morandi | in March 2026.", "setup": "squinhex", "side": 2.4433756729740645, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@13", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/13.png", "friedman_display_metric_value": 2.572, "id": "friedman-31834b23bb74454b", "metric_expression": "2.572+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.572, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.572+ | Found by Maurizio Morandi | in April 2026.", "setup": "squinhex", "side": 2.572, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@14", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/14.png", "friedman_display_metric_value": 2.62126, "id": "friedman-7402434f1a7eae36", "metric_expression": "2.62126+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.62126, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.62126+ | Found by Jonathan Viquerat | in April 2026.", "setup": "squinhex", "side": 2.62126, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@15", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/15.png", "friedman_display_metric_value": 2.75365, "id": "friedman-9114dd3f206761d1", "metric_expression": "2.75365+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.75365, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.75365+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 2.75365, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@16", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/16.png", "friedman_display_metric_value": 2.82004, "id": "friedman-a30a52e06c253a1b", "metric_expression": "2.82004+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.82004, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.82004+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 2.82004, "source": "Erich Friedman Packing Center", "source_image": "16.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@17", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/17.png", "friedman_display_metric_value": 2.88675, "id": "friedman-84da5ab39ba704e9", "metric_expression": "5/\u221a3 = 2.88675+", "metric_formula_parsed": "5/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.8867513459481287, "metric_value_source": "exact_expression", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5/\u221a3 = 2.88675+ | Trivial. |", "setup": "squinhex", "side": 2.8867513459481287, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@18", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/18.png", "friedman_display_metric_value": 2.92111, "id": "friedman-35051601e3c9e057", "metric_expression": "2.92111+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.92111, "metric_value_source": "reported_decimal", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.92111+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 2.92111, "source": "Erich Friedman Packing Center", "source_image": "18.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@19", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/19.png", "friedman_display_metric_value": 2.93511, "id": "friedman-231ad19a0b0cd36c", "metric_expression": "2.93511+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.93511, "metric_value_source": "reported_decimal", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.93511+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 2.93511, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@20", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/20.png", "friedman_display_metric_value": 3.16123, "id": "friedman-1cfab8de587ba4c6", "metric_expression": "3.16123+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.16123, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.16123+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.16123, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@21", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png", "friedman_display_metric_value": 3.23496, "id": "friedman-e865847c64403456", "metric_expression": "3.23496+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.23496, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.23496, "source": "Erich Friedman Packing Center", "source_image": "21.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@22", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/22.png", "friedman_display_metric_value": 3.31573, "id": "friedman-66d1403e8b5dee87", "metric_expression": "3.31573+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.31573, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.31573+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.31573, "source": "Erich Friedman Packing Center", "source_image": "22.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@23", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/23.png", "friedman_display_metric_value": 3.36437, "id": "friedman-26ed1439200c2bbc", "metric_expression": "3.36437+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.36437, "metric_value_source": "reported_decimal", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.36437+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.36437, "source": "Erich Friedman Packing Center", "source_image": "23.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@24", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/24.png", "friedman_display_metric_value": 3.41524, "id": "friedman-584ac536e92babf7", "metric_expression": "3.41524+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.41524, "metric_value_source": "reported_decimal", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.41524+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.41524, "source": "Erich Friedman Packing Center", "source_image": "24.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@25", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/25.png", "friedman_display_metric_value": 3.4641, "id": "friedman-65226018eb6187d3", "metric_expression": "2\u221a3 = 3.46410+", "metric_formula_parsed": "2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.4641016151377544, "metric_value_source": "exact_expression", "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2\u221a3 = 3.46410+ | Trivial. |", "setup": "squinhex", "side": 3.4641016151377544, "source": "Erich Friedman Packing Center", "source_image": "25.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@26", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/26.png", "friedman_display_metric_value": 3.4939927, "id": "friedman-f94dfa7915aa6316", "metric_expression": "3.4939927+", "metric_recovery_tolerance_abs": 1e-07, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.4939927, "metric_value_source": "reported_decimal", "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.4939927+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.4939927, "source": "Erich Friedman Packing Center", "source_image": "26.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@27", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/27.png", "friedman_display_metric_value": 3.52072, "id": "friedman-e777b2b5ac8c6ea9", "metric_expression": "(9+7\u221a3)/6 = 3.52072+", "metric_formula_parsed": "(9+7 sqrt 3)/6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.5207259421636903, "metric_value_source": "exact_expression", "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (9+7\u221a3)/6 = 3.52072+ | Found by Erich Friedman | in April 2026.", "setup": "squinhex", "side": 3.5207259421636903, "source": "Erich Friedman Packing Center", "source_image": "27.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@28", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/28.png", "friedman_display_metric_value": 3.62565, "id": "friedman-81a1a54a931ce32e", "metric_expression": "3.62565+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.62565, "metric_value_source": "reported_decimal", "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.62565+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.62565, "source": "Erich Friedman Packing Center", "source_image": "28.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@29", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/29.png", "friedman_display_metric_value": 3.66437, "id": "friedman-2aab609feceb8fed", "metric_expression": "3.66437+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.66437, "metric_value_source": "reported_decimal", "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.66437+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.66437, "source": "Erich Friedman Packing Center", "source_image": "29.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@30", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/30.png", "friedman_display_metric_value": 3.69554, "id": "friedman-04182f5877400446", "metric_expression": "3.69554+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.69554, "metric_value_source": "reported_decimal", "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.69554+ | Found by Ian Watson | in April 2026.", "setup": "squinhex", "side": 3.69554, "source": "Erich Friedman Packing Center", "source_image": "30.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@31", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/31.png", "friedman_display_metric_value": 3.7841, "id": "friedman-c8d8192a6b8559d5", "metric_expression": "3.78410+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.7841, "metric_value_source": "reported_decimal", "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.78410+ | Found by Emerson Connelly | in April 2026.", "setup": "squinhex", "side": 3.7841, "source": "Erich Friedman Packing Center", "source_image": "31.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@32", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/32.png", "friedman_display_metric_value": 3.84795, "id": "friedman-6939c4e529869605", "metric_expression": "3.84795+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.84795, "metric_value_source": "reported_decimal", "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.84795+ | Found by Emerson Connelly | in April 2026.", "setup": "squinhex", "side": 3.84795, "source": "Erich Friedman Packing Center", "source_image": "32.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@33", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/33.png", "friedman_display_metric_value": 3.88897, "id": "friedman-8d87a9abaccdff08", "metric_expression": "3.88897+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.88897, "metric_value_source": "reported_decimal", "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.88897+ | Found by Emerson Connelly | in April 2026.", "setup": "squinhex", "side": 3.88897, "source": "Erich Friedman Packing Center", "source_image": "33.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@34", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/34.png", "friedman_display_metric_value": 3.92704, "id": "friedman-da7dc94b7823a116", "metric_expression": "3.92704+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.92704, "metric_value_source": "reported_decimal", "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.92704+ | Found by Emerson Connelly | in April 2026.", "setup": "squinhex", "side": 3.92704, "source": "Erich Friedman Packing Center", "source_image": "34.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@35", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/35.png", "friedman_display_metric_value": 3.99833, "id": "friedman-7ac34820b3e6a7cb", "metric_expression": "3.99833+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.99833, "metric_value_source": "reported_decimal", "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.99833+ | Found by Emerson Connelly | in April 2026.", "setup": "squinhex", "side": 3.99833, "source": "Erich Friedman Packing Center", "source_image": "35.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@36", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png", "friedman_display_metric_value": 4.02072, "id": "friedman-5c2db381bec4d142", "metric_expression": "2+7\u221a3/6 = 4.02072+", "metric_formula_parsed": "2+7 sqrt 3/6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.02072594216369, "metric_value_source": "exact_expression", "n": 36, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+7\u221a3/6 = 4.02072+ | Found by Maurizio Morandi | in May 2026.", "setup": "squinhex", "side": 4.02072594216369, "source": "Erich Friedman Packing Center", "source_image": "36.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@37", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/37.png", "friedman_display_metric_value": 4.04145, "id": "friedman-581729fe5a584193", "metric_expression": "7/\u221a3 = 4.04145+", "metric_formula_parsed": "7/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.041451884327381, "metric_value_source": "exact_expression", "n": 37, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7/\u221a3 = 4.04145+ | Trivial. |", "setup": "squinhex", "side": 4.041451884327381, "source": "Erich Friedman Packing Center", "source_image": "37.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@38", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/38.png", "friedman_display_metric_value": 4.18476, "id": "friedman-df13cc746b03b8e0", "metric_expression": "4.18476+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.18476, "metric_value_source": "reported_decimal", "n": 38, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.18476+ | Found by Emerson Connelly | in April 2026.", "setup": "squinhex", "side": 4.18476, "source": "Erich Friedman Packing Center", "source_image": "38.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@39", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/39.png", "friedman_display_metric_value": 4.25744, "id": "friedman-1c5ebd8a6ef4b69a", "metric_expression": "4.25744+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.25744, "metric_value_source": "reported_decimal", "n": 39, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.25744+ | Found by Emerson Connelly | in April 2026.", "setup": "squinhex", "side": 4.25744, "source": "Erich Friedman Packing Center", "source_image": "39.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Hexagons", "verified": false}
+{"case": "squinhex@40", "external_image_url": "https://erich-friedman.github.io/packing/squinhex/40.png", "friedman_display_metric_value": 4.31157, "id": "friedman-5c31be5fb74fc454", "metric_expression": "4.31157+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.31157, "metric_value_source": "reported_decimal", "n": 40, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.31157+ | Found by Emerson Connelly | in April 2026.", "setup": "squinhex", "side": 4.31157, "source": "Erich Friedman Packing Center", "source_image": "40.png", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Hexagons", "verified": false}
+{"case": "hexinhex@1", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/1.gif", "friedman_display_metric_value": 1.0, "id": "friedman-7d2fc81f3a8500ae", "metric_expression": "1", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0, "metric_value_source": "reported_decimal", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "1. | | s = 1 | Trivial.", "setup": "hexinhex", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@2", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/2.gif", "friedman_display_metric_value": 2.0, "id": "friedman-f14de263d1f7d57c", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "2. | | s = 2 | Trivial.", "setup": "hexinhex", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@3", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/3.gif", "friedman_display_metric_value": 2.0, "id": "friedman-79e22bfc8102054c", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "3. | | s = 2 | Trivial.", "setup": "hexinhex", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@4", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/4.gif", "friedman_display_metric_value": 2.333, "id": "friedman-ccccf1fc8a7da443", "metric_expression": "7/3 = 2.333+", "metric_formula_parsed": "7/3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.3333333333333335, "metric_value_source": "exact_expression", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "4. | | s = 7/3 = 2.333+ | Trivial.", "setup": "hexinhex", "side": 2.3333333333333335, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@5", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/5.gif", "friedman_display_metric_value": 2.666, "id": "friedman-6ac4c984e4376c53", "metric_expression": "8/3 = 2.666+", "metric_formula_parsed": "8/3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.6666666666666665, "metric_value_source": "exact_expression", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "5. | | s = 8/3 = 2.666+ | Found by Erich Friedman | in March 2015.", "setup": "hexinhex", "side": 2.6666666666666665, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@6", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/7.gif", "friedman_display_metric_value": 2.886, "id": "friedman-588ca2766605f010", "metric_expression": "5/\u221a3 = 2.886+", "metric_formula_parsed": "5/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.8867513459481287, "metric_value_source": "exact_expression", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "6-7. | | s = 5/\u221a3 = 2.886+ | Found by Maurizio Morandi | in April 2015.", "setup": "hexinhex", "side": 2.8867513459481287, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@7", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/7.gif", "friedman_display_metric_value": 2.886, "id": "friedman-db440f9c50e5ab80", "metric_expression": "5/\u221a3 = 2.886+", "metric_formula_parsed": "5/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.8867513459481287, "metric_value_source": "exact_expression", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "6-7. | | s = 5/\u221a3 = 2.886+ | Found by Maurizio Morandi | in April 2015.", "setup": "hexinhex", "side": 2.8867513459481287, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@8", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/8.gif", "friedman_display_metric_value": 3.314, "id": "friedman-20dcb9522b47625e", "metric_expression": "(51+5\u221a3)/18 = 3.314+", "metric_formula_parsed": "(51+5 sqrt 3)/18", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.3144585576580217, "metric_value_source": "exact_expression", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "8. | | s = (51+5\u221a3)/18 = 3.314+ | Found by Maurizio Morandi | in April 2015.", "setup": "hexinhex", "side": 3.3144585576580217, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@9", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/9.gif", "friedman_display_metric_value": 3.628, "id": "friedman-2085529f48890bb9", "metric_expression": "(24+5\u221a3)/9 = 3.628+", "metric_formula_parsed": "(24+5 sqrt 3)/9", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.628917115316043, "metric_value_source": "exact_expression", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "9. | | s = (24+5\u221a3)/9 = 3.628+ | Found by Maurizio Morandi | in April 2015.", "setup": "hexinhex", "side": 3.628917115316043, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@10", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/10.gif", "friedman_display_metric_value": 3.732, "id": "friedman-cc2c8d74be6eabc4", "metric_expression": "2 + \u221a3 = 3.732+", "metric_formula_parsed": "2 + sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.732050807568877, "metric_value_source": "exact_expression", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "10. | | s = 2 + \u221a3 = 3.732+ | Found by Maurizio Morandi | in April 2015.", "setup": "hexinhex", "side": 3.732050807568877, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@11", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/11.gif", "friedman_display_metric_value": 3.9245, "id": "friedman-f57107a4580db9bd", "metric_expression": "2+10/3\u221a3 = 3.92450+", "metric_formula_parsed": "2+10/(3*sqrt 3)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.9245008972987527, "metric_value_source": "exact_expression", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "11. | | s = 2+10/3\u221a3 = 3.92450+ | Found by Johann Schellhorn | in July 2025. | | | |", "setup": "hexinhex", "side": 3.9245008972987527, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Johann Schellhorn", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@12", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/12.gif", "friedman_display_metric_value": 3.94164, "id": "friedman-1d7855153f4426af", "metric_expression": "3.94164+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.94164, "metric_value_source": "reported_decimal", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "12. | | s = 3.94164+ | Found by Alexander Novikov et al | in June 2025. | Improved slightly by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 3.94164, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Alexander Novikov et al", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@13", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/13.gif", "friedman_display_metric_value": 4.0, "id": "friedman-d5e613d60ea5a121", "metric_expression": "4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "13 | | s = 4 | Trivial. | | | | |", "setup": "hexinhex", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@14", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/14.gif", "friedman_display_metric_value": 4.26899, "id": "friedman-7227925526080a56", "metric_expression": "4.26899+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.26899, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14. | | s = 4.26899+ | Found by Dominik Kamp | in April 2026.", "setup": "hexinhex", "side": 4.26899, "source": "Erich Friedman Packing Center", "source_image": "14.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Dominik Kamp", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@15", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/15.gif", "friedman_display_metric_value": 4.44727, "id": "friedman-fd72d6e91face17f", "metric_expression": "4.44727+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.44727, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "15. | | s = 4.44727+ | Found by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 4.44727, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@16", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/16.gif", "friedman_display_metric_value": 4.52746, "id": "friedman-2607d8e05843091b", "metric_expression": "4.52746+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.52746, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "16. | | s = 4.52746+ | Found by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 4.52746, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@17", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/17.gif", "friedman_display_metric_value": 4.6136, "id": "friedman-4a0e3382c2f91341", "metric_expression": "4.6136+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.6136, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "17. | | s = 4.6136+ | Found by Timo Berthold et al | and Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 4.6136, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@18", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "friedman_display_metric_value": 4.618, "id": "friedman-5d106d7a584d2e4a", "metric_expression": "8/\u221a3 = 4.618+", "metric_formula_parsed": "8/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.618802153517006, "metric_value_source": "exact_expression", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "setup": "hexinhex", "side": 4.618802153517006, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@19", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "friedman_display_metric_value": 4.618, "id": "friedman-e8163d17d47f75c5", "metric_expression": "8/\u221a3 = 4.618+", "metric_formula_parsed": "8/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.618802153517006, "metric_value_source": "exact_expression", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "setup": "hexinhex", "side": 4.618802153517006, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@20", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "friedman_display_metric_value": 5.0, "id": "friedman-b9b934450972f3f2", "metric_expression": "5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "20-21. | | s = 5 | Trivial. | |", "setup": "hexinhex", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@21", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "friedman_display_metric_value": 5.0, "id": "friedman-36b066565def6e80", "metric_expression": "5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "20-21. | | s = 5 | Trivial. | |", "setup": "hexinhex", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@22", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/22.gif", "friedman_display_metric_value": 5.285, "id": "friedman-e23498b5cf150f95", "metric_expression": "(39+8\u221a3)/10 = 5.285+", "metric_formula_parsed": "(39+8 sqrt 3)/10", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.285640646055102, "metric_value_source": "exact_expression", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "22. | | s = (39+8\u221a3)/10 = 5.285+ | Found by Maurizio Morandi | in April 2015.", "setup": "hexinhex", "side": 5.285640646055102, "source": "Erich Friedman Packing Center", "source_image": "22.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@23", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/23.gif", "friedman_display_metric_value": 5.4, "id": "friedman-d9dbeab4d45e7737", "metric_expression": "5.400+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.4, "metric_value_source": "reported_decimal", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "23. | | s = 5.400+ | Found by Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 5.4, "source": "Erich Friedman Packing Center", "source_image": "23.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Alex Kravatsky et al", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@24", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/24.gif", "friedman_display_metric_value": 5.484, "id": "friedman-0e3c1a70fd02d7a3", "metric_expression": "19\u221a3/6 = 5.484+", "metric_formula_parsed": "19 sqrt 3/6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.484827557301445, "metric_value_source": "exact_expression", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "24. | | s = 19\u221a3/6 = 5.484+ | Found by Maurizio Morandi | in April 2015.", "setup": "hexinhex", "side": 5.484827557301445, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@25", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/25.gif", "friedman_display_metric_value": 5.6239, "id": "friedman-276cf845aacff93e", "metric_expression": "5.62390+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.6239, "metric_value_source": "reported_decimal", "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "25. | | s = 5.62390+ | Found by Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 5.6239, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Alex Kravatsky et al", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@26", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/26.gif", "friedman_display_metric_value": 5.70972, "id": "friedman-e4991ec3392395d2", "metric_expression": "5.70972+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.70972, "metric_value_source": "reported_decimal", "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "26. | | s = 5.70972+ | Found by Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 5.70972, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Alex Kravatsky et al", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@27", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/27.gif", "friedman_display_metric_value": 5.71415, "id": "friedman-a33e4890e2d48b81", "metric_expression": "5.71415+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.71415, "metric_value_source": "reported_decimal", "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "27. | | s = 5.71415+ | Found by Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 5.71415, "source": "Erich Friedman Packing Center", "source_image": "27.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Alex Kravatsky et al", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@28", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/28.gif", "friedman_display_metric_value": 5.90893, "id": "friedman-746003537392c940", "metric_expression": "5.90893+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.90893, "metric_value_source": "reported_decimal", "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "28. | | s = 5.90893+ | Found by Alex Kravatsky et al | in February 2026.", "setup": "hexinhex", "side": 5.90893, "source": "Erich Friedman Packing Center", "source_image": "28.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Alex Kravatsky et al", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@29", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "friedman_display_metric_value": 6.0, "id": "friedman-0ceba4dddc547424", "metric_expression": "6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.0, "metric_value_source": "reported_decimal", "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "29-31. | | s = 6 | Trivial. |", "setup": "hexinhex", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "31.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@30", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "friedman_display_metric_value": 6.0, "id": "friedman-67ef09edf0264a3d", "metric_expression": "6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.0, "metric_value_source": "reported_decimal", "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "29-31. | | s = 6 | Trivial. |", "setup": "hexinhex", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "31.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "hexinhex@31", "external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "friedman_display_metric_value": 6.0, "id": "friedman-ce339bb897e95790", "metric_expression": "6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.0, "metric_value_source": "reported_decimal", "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "29-31. | | s = 6 | Trivial. |", "setup": "hexinhex", "side": 6.0, "source": "Erich Friedman Packing Center", "source_image": "31.gif", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Hexagons", "verified": false}
+{"case": "triinpen@1", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/1.gif", "friedman_display_metric_value": 0.781, "id": "friedman-96279e2107a71452", "metric_expression": ".781+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.781, "metric_value_source": "reported_decimal", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = cos(42\u00b0) / cos(18\u00b0) | s = .781+ | Trivial. |", "setup": "triinpen", "side": 0.781, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@2", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/2.gif", "friedman_display_metric_value": 1.07, "id": "friedman-bfca58c6417586ac", "metric_expression": "1.070+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.07, "metric_value_source": "reported_decimal", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a(6/(3+\u221a5)) | s = 1.070+ | Trivial. |", "setup": "triinpen", "side": 1.07, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@3", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/3.gif", "friedman_display_metric_value": 1.143, "id": "friedman-c9e48380c0c277f4", "metric_expression": "1.143+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.143, "metric_value_source": "reported_decimal", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.143+ | Found by Maurizio Morandi | in August 2012. |", "setup": "triinpen", "side": 1.143, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@4", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/4.gif", "friedman_display_metric_value": 1.199, "id": "friedman-d9bb9327e072f65a", "metric_expression": "1.199+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.199, "metric_value_source": "reported_decimal", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.199+ | Found by Maurizio Morandi | in July 2012. |", "setup": "triinpen", "side": 1.199, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@5", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/5.gif", "friedman_display_metric_value": 1.24, "id": "friedman-30b99f667d0390f5", "metric_expression": "1.240+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.24, "metric_value_source": "reported_decimal", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 + 2sin(12\u00b0)/\u221a3 | s = 1.240+ | Found by Erich Friedman | in March 2012.", "setup": "triinpen", "side": 1.24, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@6", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/6.gif", "friedman_display_metric_value": 1.393, "id": "friedman-e333c306ac117d09", "metric_expression": "1.393+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.393, "metric_value_source": "reported_decimal", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.393+ | Found by Dominik Kamp | in April 2026.", "setup": "triinpen", "side": 1.393, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Dominik Kamp", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@7", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/7.gif", "friedman_display_metric_value": 1.581, "id": "friedman-06eee10277647397", "metric_expression": "1.581+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.581, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.581+ | Found by David W. Cantrell | in July 2012.", "setup": "triinpen", "side": 1.581, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@8", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/8.gif", "friedman_display_metric_value": 1.659, "id": "friedman-9b9197f5eec0793b", "metric_expression": "1.659+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.659, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.659+ | Found by Maurizio Morandi | in July 2012.", "setup": "triinpen", "side": 1.659, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@9", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/9.gif", "friedman_display_metric_value": 1.767, "id": "friedman-59a5b99b8f4f188b", "metric_expression": "1.767+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.767, "metric_value_source": "reported_decimal", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.767+ | Found by Maurizio Morandi in July 2012. | Improved slightly by David W. Cantrell in August 2012.", "setup": "triinpen", "side": 1.767, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@10", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/10.gif", "friedman_display_metric_value": 1.815, "id": "friedman-bd353f3981693157", "metric_expression": "1.815+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.815, "metric_value_source": "reported_decimal", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.815+ | Found by Timo Berthold et al | in January 2026.", "setup": "triinpen", "side": 1.815, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@11", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/11.gif", "friedman_display_metric_value": 1.871, "id": "friedman-a80f917c602437b6", "metric_expression": "1.871+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.871, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.871+ | Found by Timo Berthold et al | in January 2026.", "setup": "triinpen", "side": 1.871, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@12", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/12.gif", "friedman_display_metric_value": 1.973, "id": "friedman-e9a5008b814199d6", "metric_expression": "1.973+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.973, "metric_value_source": "reported_decimal", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.973+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinpen", "side": 1.973, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@13", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/13.gif", "friedman_display_metric_value": 2.017, "id": "friedman-81819cbb2d23f978", "metric_expression": "2.017+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.017, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.017+ | Found by Timo Berthold et al | in January 2026.", "setup": "triinpen", "side": 2.017, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@14", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/14.gif", "friedman_display_metric_value": 2.088, "id": "friedman-d6a7a899bd38f561", "metric_expression": "2.088+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.088, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.088+ | Found by Ignacio Vallejo | in April 2026.", "setup": "triinpen", "side": 2.088, "source": "Erich Friedman Packing Center", "source_image": "14.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@15", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/15.gif", "friedman_display_metric_value": 2.123, "id": "friedman-f66ac4e6cfdf6828", "metric_expression": "2.123+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.123, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.123+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinpen", "side": 2.123, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@16", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/16.gif", "friedman_display_metric_value": 2.17598, "id": "friedman-64493990df5f4f6e", "metric_expression": "2.17598+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.17598, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.17598+ | Found by Ian Watson | in April 2026.", "setup": "triinpen", "side": 2.17598, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@17", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/17.gif", "friedman_display_metric_value": 2.23658, "id": "friedman-f512cdf042b69a86", "metric_expression": "2.23658+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.23658, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.23658+ | Found by Ian Watson | in April 2026.", "setup": "triinpen", "side": 2.23658, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@18", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/18.gif", "friedman_display_metric_value": 2.29382, "id": "friedman-85070b7792557c87", "metric_expression": "2.29382+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.29382, "metric_value_source": "reported_decimal", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.29382+ | Found by Ian Watson | in April 2026.", "setup": "triinpen", "side": 2.29382, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@19", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "friedman_display_metric_value": 2.344, "id": "friedman-eda74c98590f31cb", "metric_expression": "2.344+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.344, "metric_value_source": "reported_decimal", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinpen", "side": 2.344, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@20", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/20.gif", "friedman_display_metric_value": 2.4335, "id": "friedman-06a2b02781d0120e", "metric_expression": "2.43350+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.4335, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.43350+ | Found by Ian Watson | in April 2026.", "setup": "triinpen", "side": 2.4335, "source": "Erich Friedman Packing Center", "source_image": "20.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@21", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/21.gif", "friedman_display_metric_value": 2.479, "id": "friedman-eb992ca5bc125b67", "metric_expression": "2.479+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.479, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.479+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinpen", "side": 2.479, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@22", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/22.gif", "friedman_display_metric_value": 2.5674, "id": "friedman-6840d8a6ac2c5c99", "metric_expression": "2.56740+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.5674, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.56740+ | Found by Ian Watson | in April 2026.", "setup": "triinpen", "side": 2.5674, "source": "Erich Friedman Packing Center", "source_image": "22.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@23", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/23.gif", "friedman_display_metric_value": 2.61831, "id": "friedman-a4967e0e8babb771", "metric_expression": "2.61831+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.61831, "metric_value_source": "reported_decimal", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.61831+ | Found by Ian Watson | in April 2026.", "setup": "triinpen", "side": 2.61831, "source": "Erich Friedman Packing Center", "source_image": "23.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@24", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/24.gif", "friedman_display_metric_value": 2.66641, "id": "friedman-d47afc4cb7695168", "metric_expression": "2.66641+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.66641, "metric_value_source": "reported_decimal", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.66641+ | Found by Ian Watson | in April 2026.", "setup": "triinpen", "side": 2.66641, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@25", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/25.gif", "friedman_display_metric_value": 2.72, "id": "friedman-2b180c3a0e8120c9", "metric_expression": "2.720+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.72, "metric_value_source": "reported_decimal", "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.720+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinpen", "side": 2.72, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@26", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/26.gif", "friedman_display_metric_value": 2.771, "id": "friedman-79bcdb6fc92c72f5", "metric_expression": "2.771+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.771, "metric_value_source": "reported_decimal", "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.771+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinpen", "side": 2.771, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@27", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/27.gif", "friedman_display_metric_value": 2.81761, "id": "friedman-b9beeccef0536c60", "metric_expression": "2.81761+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.81761, "metric_value_source": "reported_decimal", "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.81761+ | Found by Ian Watson | in April 2026.", "setup": "triinpen", "side": 2.81761, "source": "Erich Friedman Packing Center", "source_image": "27.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@28", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/28.gif", "friedman_display_metric_value": 2.868, "id": "friedman-055b2cf1505d3817", "metric_expression": "2.868+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.868, "metric_value_source": "reported_decimal", "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.868+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinpen", "side": 2.868, "source": "Erich Friedman Packing Center", "source_image": "28.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@29", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/29.gif", "friedman_display_metric_value": 2.903, "id": "friedman-45bc6376621f11ac", "metric_expression": "2.903+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.903, "metric_value_source": "reported_decimal", "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.903+ | Found by Ignacio Vallejo | in April 2026.", "setup": "triinpen", "side": 2.903, "source": "Erich Friedman Packing Center", "source_image": "29.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@30", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/30.gif", "friedman_display_metric_value": 2.952, "id": "friedman-9bbeddaa7856bd2b", "metric_expression": "2.952+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.952, "metric_value_source": "reported_decimal", "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.952+ | Found by Ignacio Vallejo | in April 2026.", "setup": "triinpen", "side": 2.952, "source": "Erich Friedman Packing Center", "source_image": "30.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@31", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/31.gif", "friedman_display_metric_value": 2.992, "id": "friedman-591672036688db40", "metric_expression": "2.992+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.992, "metric_value_source": "reported_decimal", "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.992+ | Found by Emerson Connelly | in April 2026.", "setup": "triinpen", "side": 2.992, "source": "Erich Friedman Packing Center", "source_image": "31.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@32", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/32.gif", "friedman_display_metric_value": 3.029, "id": "friedman-31e29416ce2c1316", "metric_expression": "3.029+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.029, "metric_value_source": "reported_decimal", "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.029+ | Found by Emerson Connelly | in April 2026.", "setup": "triinpen", "side": 3.029, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@33", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/33.gif", "friedman_display_metric_value": 3.078, "id": "friedman-a8c79f30a396724c", "metric_expression": "3.078+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.078, "metric_value_source": "reported_decimal", "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.078+ | Found by Emerson Connelly | in April 2026.", "setup": "triinpen", "side": 3.078, "source": "Erich Friedman Packing Center", "source_image": "33.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@34", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/34.gif", "friedman_display_metric_value": 3.114, "id": "friedman-8b0dda58d5153d92", "metric_expression": "3.114+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.114, "metric_value_source": "reported_decimal", "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.114+ | Found by Emerson Connelly | in April 2026.", "setup": "triinpen", "side": 3.114, "source": "Erich Friedman Packing Center", "source_image": "34.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@35", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/35.gif", "friedman_display_metric_value": 3.15, "id": "friedman-1cb318bc9b8161c4", "metric_expression": "3.150+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.15, "metric_value_source": "reported_decimal", "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.150+ | Found by Emerson Connelly | in April 2026.", "setup": "triinpen", "side": 3.15, "source": "Erich Friedman Packing Center", "source_image": "35.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@36", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/36.gif", "friedman_display_metric_value": 3.177, "id": "friedman-fe8ce057b8d651f6", "metric_expression": "3.177+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.177, "metric_value_source": "reported_decimal", "n": 36, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.177+ | Found by Emerson Connelly | in April 2026.", "setup": "triinpen", "side": 3.177, "source": "Erich Friedman Packing Center", "source_image": "36.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@37", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/37.gif", "friedman_display_metric_value": 3.21529, "id": "friedman-c5eee355e150d7d2", "metric_expression": "3.21529+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.21529, "metric_value_source": "reported_decimal", "n": 37, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.21529+ | Found by Nathan Roll | in April 2026.", "setup": "triinpen", "side": 3.21529, "source": "Erich Friedman Packing Center", "source_image": "37.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@38", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/38.gif", "friedman_display_metric_value": 3.25877, "id": "friedman-be90f7181b1b549b", "metric_expression": "3.25877+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.25877, "metric_value_source": "reported_decimal", "n": 38, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.25877+ | Found by Nathan Roll | in April 2026.", "setup": "triinpen", "side": 3.25877, "source": "Erich Friedman Packing Center", "source_image": "38.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@39", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/39.gif", "friedman_display_metric_value": 3.295, "id": "friedman-7f092aea9b7120aa", "metric_expression": "3.295+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.295, "metric_value_source": "reported_decimal", "n": 39, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.295+ | Found by Emerson Connelly | in April 2026.", "setup": "triinpen", "side": 3.295, "source": "Erich Friedman Packing Center", "source_image": "39.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Triangles in Pentagons", "verified": false}
+{"case": "triinpen@40", "external_image_url": "https://erich-friedman.github.io/packing/triinpen/40.gif", "friedman_display_metric_value": 3.32786, "id": "friedman-a15498f8116a7bcc", "metric_expression": "3.32786+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.32786, "metric_value_source": "reported_decimal", "n": 40, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.32786+ | Found by Nathan Roll | in April 2026.", "setup": "triinpen", "side": 3.32786, "source": "Erich Friedman Packing Center", "source_image": "40.gif", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Triangles in Pentagons", "verified": false}
+{"case": "cirinpen@1", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.1.png", "friedman_display_metric_value": 1.453, "id": "friedman-c9f2bcf3f1dbe7c5", "metric_expression": "1.453+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.453, "metric_value_source": "reported_decimal", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2tan(36\u00b0) | s = 1.453+ | Trivial.", "setup": "cirinpen", "side": 1.453, "source": "Erich Friedman Packing Center", "source_image": "pent.1.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@2", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.2.png", "friedman_display_metric_value": 2.689, "id": "friedman-ed9c0d76bc77ea1a", "metric_expression": "2.689+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.689, "metric_value_source": "reported_decimal", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2tan(36\u00b0) + \u221a5 - 1 | s = 2.689+ | Trivial.", "setup": "cirinpen", "side": 2.689, "source": "Erich Friedman Packing Center", "source_image": "pent.2.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@3", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.3.png", "friedman_display_metric_value": 3.015, "id": "friedman-26644edcfdfec30c", "metric_expression": "3.015+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.015, "metric_value_source": "reported_decimal", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.015+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 3.015, "source": "Erich Friedman Packing Center", "source_image": "pent.3.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@4", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.4.png", "friedman_display_metric_value": 3.314, "id": "friedman-9156e410455106ef", "metric_expression": "3.314+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.314, "metric_value_source": "reported_decimal", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.314+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 3.314, "source": "Erich Friedman Packing Center", "source_image": "pent.4.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@5", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.5.png", "friedman_display_metric_value": 3.453, "id": "friedman-d66ba0c1e7a08c8b", "metric_expression": "3.453+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.453, "metric_value_source": "reported_decimal", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2tan(36\u00b0) + 2 | s = 3.453+ | Trivial.", "setup": "cirinpen", "side": 3.453, "source": "Erich Friedman Packing Center", "source_image": "pent.5.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@6", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.6.png", "friedman_display_metric_value": 3.804, "id": "friedman-4864d7bb2c47dcf5", "metric_expression": "3.804+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.804, "metric_value_source": "reported_decimal", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2tan(36\u00b0) + 4sin(36\u00b0) | s = 3.804+ | Trivial.", "setup": "cirinpen", "side": 3.804, "source": "Erich Friedman Packing Center", "source_image": "pent.6.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@7", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.7.png", "friedman_display_metric_value": 4.236, "id": "friedman-e0d62c06e228a431", "metric_expression": "4.236+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.236, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.236+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 4.236, "source": "Erich Friedman Packing Center", "source_image": "pent.7.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@8", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.8.png", "friedman_display_metric_value": 4.564, "id": "friedman-f94cccc6d82b2ff2", "metric_expression": "4.564+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.564, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.564+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 4.564, "source": "Erich Friedman Packing Center", "source_image": "pent.8.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@9", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.9.png", "friedman_display_metric_value": 4.825, "id": "friedman-0941f9b189caab02", "metric_expression": "4.825+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.825, "metric_value_source": "reported_decimal", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.825+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 4.825, "source": "Erich Friedman Packing Center", "source_image": "pent.9.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@10", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.10.png", "friedman_display_metric_value": 5.095, "id": "friedman-7f3d81e4662c4616", "metric_expression": "5.095+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.095, "metric_value_source": "reported_decimal", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.095+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 5.095, "source": "Erich Friedman Packing Center", "source_image": "pent.10.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@11", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.11.gif", "friedman_display_metric_value": 5.24, "id": "friedman-b4a88a8ece9f21cb", "metric_expression": "5.240+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.24, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.240+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 5.24, "source": "Erich Friedman Packing Center", "source_image": "pent.11.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@12", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.12.png", "friedman_display_metric_value": 5.407, "id": "friedman-734cfcf308e1e9d2", "metric_expression": "5.407+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.407, "metric_value_source": "reported_decimal", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.407+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 5.407, "source": "Erich Friedman Packing Center", "source_image": "pent.12.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@13", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.13.png", "friedman_display_metric_value": 5.651, "id": "friedman-ce3600f54e22eb20", "metric_expression": "5.651+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.651, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.651+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 5.651, "source": "Erich Friedman Packing Center", "source_image": "pent.13.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@14", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.14.png", "friedman_display_metric_value": 5.808, "id": "friedman-158eb3bf8601d310", "metric_expression": "5.808+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.808, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.808+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 5.808, "source": "Erich Friedman Packing Center", "source_image": "pent.14.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@15", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.15.gif", "friedman_display_metric_value": 5.945, "id": "friedman-6a72351047bc84a7", "metric_expression": "5.945+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.945, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.945+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 5.945, "source": "Erich Friedman Packing Center", "source_image": "pent.15.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@16", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.16.png", "friedman_display_metric_value": 6.129, "id": "friedman-208c860fd242dac6", "metric_expression": "6.129+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.129, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.129+ | Found by George Sicherman | in July 2012.", "setup": "cirinpen", "side": 6.129, "source": "Erich Friedman Packing Center", "source_image": "pent.16.png", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "George Sicherman", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@17", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.17.gif", "friedman_display_metric_value": 6.419, "id": "friedman-26afa89c5f7c2ad0", "metric_expression": "6.419+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.419, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.419+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 6.419, "source": "Erich Friedman Packing Center", "source_image": "pent.17.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@18", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.18.gif", "friedman_display_metric_value": 6.586, "id": "friedman-101cf81d62f95e87", "metric_expression": "6.586+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.586, "metric_value_source": "reported_decimal", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.586+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 6.586, "source": "Erich Friedman Packing Center", "source_image": "pent.18.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@19", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.19.gif", "friedman_display_metric_value": 6.777, "id": "friedman-59bf470092f01cbc", "metric_expression": "6.777+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.777, "metric_value_source": "reported_decimal", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.777+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 6.777, "source": "Erich Friedman Packing Center", "source_image": "pent.19.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@20", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.20.gif", "friedman_display_metric_value": 6.944, "id": "friedman-3a1d065c11ca84de", "metric_expression": "6.944+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.944, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.944+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 6.944, "source": "Erich Friedman Packing Center", "source_image": "pent.20.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@21", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.21.gif", "friedman_display_metric_value": 7.107, "id": "friedman-ed29424aa41ad1b1", "metric_expression": "7.107+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.107, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.107+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 7.107, "source": "Erich Friedman Packing Center", "source_image": "pent.21.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@22", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.22.gif", "friedman_display_metric_value": 7.271, "id": "friedman-46ff6d83528fa7a5", "metric_expression": "7.271+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.271, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.271+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 7.271, "source": "Erich Friedman Packing Center", "source_image": "pent.22.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@23", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.23.gif", "friedman_display_metric_value": 7.397, "id": "friedman-84460262a31d0fdc", "metric_expression": "7.397+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.397, "metric_value_source": "reported_decimal", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.397+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 7.397, "source": "Erich Friedman Packing Center", "source_image": "pent.23.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
+{"case": "cirinpen@24", "external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.24.gif", "friedman_display_metric_value": 7.534, "id": "friedman-dbf693fd05289ccf", "metric_expression": "7.534+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.534, "metric_value_source": "reported_decimal", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.534+ | Found by David W. Cantrell | in July 2012.", "setup": "cirinpen", "side": 7.534, "source": "Erich Friedman Packing Center", "source_image": "pent.24.gif", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Circles in Pentagons", "verified": false}
+{"case": "squinpen@1", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/1.gif", "friedman_display_metric_value": 0.936, "id": "friedman-d7ef2119776f0d12", "metric_expression": ".936+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.936, "metric_value_source": "reported_decimal", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = cos(27\u00b0) / cos(18\u00b0) | s = .936+ | Trivial. |", "setup": "squinpen", "side": 0.936, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@2", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/2.gif", "friedman_display_metric_value": 1.535, "id": "friedman-3f4163ac8dcdd1b9", "metric_expression": "1.535+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.535, "metric_value_source": "reported_decimal", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4\u221a(1\u20132/\u221a5)+\u221a5\u20132 | s = 1.535+ | Found by Erich Friedman | in March 2012.", "setup": "squinpen", "side": 1.535, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@3", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/3.gif", "friedman_display_metric_value": 1.695, "id": "friedman-49f61cc055ea2c87", "metric_expression": "1.695+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.695, "metric_value_source": "reported_decimal", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.695+ | Found by David W. Cantrell | in July 2012. |", "setup": "squinpen", "side": 1.695, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@4", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/4.gif", "friedman_display_metric_value": 1.861, "id": "friedman-ef16cdaf2d6a02bd", "metric_expression": "1.861+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.861, "metric_value_source": "reported_decimal", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.861+ | Found by Maurizio Morandi | in July 2012. |", "setup": "squinpen", "side": 1.861, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@5", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/5.gif", "friedman_display_metric_value": 1.951, "id": "friedman-7f70dc3990e182fa", "metric_expression": "1.951+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.951, "metric_value_source": "reported_decimal", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 + cos(18\u00b0) | s = 1.951+ | Found by Erich Friedman | in March 2012.", "setup": "squinpen", "side": 1.951, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@6", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/6.gif", "friedman_display_metric_value": 2.185, "id": "friedman-e7afd9e46316bcc1", "metric_expression": "2.185+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.185, "metric_value_source": "reported_decimal", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6\u221a(1\u20132/\u221a5)+\u221a5\u20132 | s = 2.185+ | Found by Erich Friedman | in March 2012.", "setup": "squinpen", "side": 2.185, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@7", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/7.gif", "friedman_display_metric_value": 2.421, "id": "friedman-2ecddf9cbfa1f173", "metric_expression": "2.421+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.421, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6\u221a(1\u20132/\u221a5)+2\u221a5\u20134 | s = 2.421+ | Found by Erich Friedman | in July 2012.", "setup": "squinpen", "side": 2.421, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@8", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/8.gif", "friedman_display_metric_value": 2.565, "id": "friedman-6a3b223ab63c2947", "metric_expression": "2.565+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.565, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.565+ | Found by David W. Cantrell | in July 2012. |", "setup": "squinpen", "side": 2.565, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@9", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/9.gif", "friedman_display_metric_value": 2.693, "id": "friedman-a6c2b0197783eee5", "metric_expression": "2.693+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.693, "metric_value_source": "reported_decimal", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.693+ | Found by Timo Berthold et al | in January 2026. |", "setup": "squinpen", "side": 2.693, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@10", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/10.gif", "friedman_display_metric_value": 2.793, "id": "friedman-ccbbb98ad3054d40", "metric_expression": "2.793+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.793, "metric_value_source": "reported_decimal", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.793+ | Found by Timo Berthold et al | in January 2026.", "setup": "squinpen", "side": 2.793, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@11", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/11.gif", "friedman_display_metric_value": 2.89, "id": "friedman-12d57458705ce4cb", "metric_expression": "2.890+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.89, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.890+ | Found by Timo Berthold et al | in January 2026.", "setup": "squinpen", "side": 2.89, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@12", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/12.gif", "friedman_display_metric_value": 2.969, "id": "friedman-2be59682b4c2e87c", "metric_expression": "2.969+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.969, "metric_value_source": "reported_decimal", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.969+ | Found by Timo Berthold et al | in January 2026.", "setup": "squinpen", "side": 2.969, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Timo Berthold et al", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@13", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/13.gif", "friedman_display_metric_value": 3.121, "id": "friedman-3d3e0b87fcbe50c3", "metric_expression": "3.121+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.121, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2\u221a(1\u20132/\u221a5)+2\u221a5\u20132 | s = 3.121+ | Found by David W. Cantrell | in July 2012.", "setup": "squinpen", "side": 3.121, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@14", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/14.gif", "friedman_display_metric_value": 3.187, "id": "friedman-02be1bc530651adb", "metric_expression": "3.187+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.187, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.187+ | Found by David W. Cantrell | in July 2012. |", "setup": "squinpen", "side": 3.187, "source": "Erich Friedman Packing Center", "source_image": "14.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@15", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/15.gif", "friedman_display_metric_value": 3.284, "id": "friedman-a43dcbc6943d141b", "metric_expression": "3.284+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.284, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (\u221a(125\u201338\u221a5)+8\u20132\u221a5)/3 | s = 3.284+ | Found by David W. Cantrell | in July 2012.", "setup": "squinpen", "side": 3.284, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@16", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/16.gif", "friedman_display_metric_value": 3.48, "id": "friedman-c6a1e8cb1e0deddf", "metric_expression": "3.480+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.48, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.480+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinpen", "side": 3.48, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@17", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/17.gif", "friedman_display_metric_value": 3.541, "id": "friedman-3456245654cc9b9f", "metric_expression": "3.541+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.541, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.541+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinpen", "side": 3.541, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@18", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/18.gif", "friedman_display_metric_value": 3.626, "id": "friedman-2ffc826ecadac301", "metric_expression": "3.626+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.626, "metric_value_source": "reported_decimal", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.626+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinpen", "side": 3.626, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@19", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/19.gif", "friedman_display_metric_value": 3.71, "id": "friedman-c9abe1676a142edd", "metric_expression": "3.710+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.71, "metric_value_source": "reported_decimal", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.710+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinpen", "side": 3.71, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@20", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/20.gif", "friedman_display_metric_value": 3.802, "id": "friedman-288106ba840a58c8", "metric_expression": "3.802+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.802, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.802+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinpen", "side": 3.802, "source": "Erich Friedman Packing Center", "source_image": "20.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@21", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/21.gif", "friedman_display_metric_value": 3.864, "id": "friedman-2b3be1a404d9d1a5", "metric_expression": "3.864+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.864, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.864+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 3.864, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@22", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/22.gif", "friedman_display_metric_value": 3.937, "id": "friedman-8f8027ed0a740da0", "metric_expression": "3.937+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.937, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.937+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 3.937, "source": "Erich Friedman Packing Center", "source_image": "22.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@23", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/23.gif", "friedman_display_metric_value": 4.002, "id": "friedman-8590a862cf3736dc", "metric_expression": "4.002+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.002, "metric_value_source": "reported_decimal", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.002+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 4.002, "source": "Erich Friedman Packing Center", "source_image": "23.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@24", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/24.gif", "friedman_display_metric_value": 4.107, "id": "friedman-44eadd0b8f885d67", "metric_expression": "4.107+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.107, "metric_value_source": "reported_decimal", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.107+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 4.107, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@25", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/25.gif", "friedman_display_metric_value": 4.169, "id": "friedman-8a9d49a64c978c0f", "metric_expression": "4.169+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.169, "metric_value_source": "reported_decimal", "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.169+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 4.169, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@26", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/26.gif", "friedman_display_metric_value": 4.223, "id": "friedman-b29bdc83b0d065b8", "metric_expression": "4.223+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.223, "metric_value_source": "reported_decimal", "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.223+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 4.223, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@27", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/27.gif", "friedman_display_metric_value": 4.35, "id": "friedman-da78765113e89e22", "metric_expression": "4.350+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.35, "metric_value_source": "reported_decimal", "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.350+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 4.35, "source": "Erich Friedman Packing Center", "source_image": "27.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@28", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/28.gif", "friedman_display_metric_value": 4.421, "id": "friedman-6b34ec50ffe92fbb", "metric_expression": "4.421+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.421, "metric_value_source": "reported_decimal", "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.421+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 4.421, "source": "Erich Friedman Packing Center", "source_image": "28.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@29", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/29.gif", "friedman_display_metric_value": 4.499, "id": "friedman-21c659f8071b2b16", "metric_expression": "4.499+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.499, "metric_value_source": "reported_decimal", "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.499+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 4.499, "source": "Erich Friedman Packing Center", "source_image": "29.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@30", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif", "friedman_display_metric_value": 4.55, "id": "friedman-7173d82201ed6e3c", "metric_expression": "4.550+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.55, "metric_value_source": "reported_decimal", "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.", "setup": "squinpen", "side": 4.55, "source": "Erich Friedman Packing Center", "source_image": "30.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@31", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/31.gif", "friedman_display_metric_value": 4.63041, "id": "friedman-dd2cd3babb384303", "metric_expression": "4.63041+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.63041, "metric_value_source": "reported_decimal", "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.63041+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 4.63041, "source": "Erich Friedman Packing Center", "source_image": "31.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@32", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/32.gif", "friedman_display_metric_value": 4.70774, "id": "friedman-2d92e9603ee41a64", "metric_expression": "4.70774+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.70774, "metric_value_source": "reported_decimal", "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.70774+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 4.70774, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@33", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/33.gif", "friedman_display_metric_value": 4.75774, "id": "friedman-63f93454f18c250d", "metric_expression": "4.75774+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.75774, "metric_value_source": "reported_decimal", "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.75774+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 4.75774, "source": "Erich Friedman Packing Center", "source_image": "33.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@34", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif", "friedman_display_metric_value": 4.81817, "id": "friedman-eeb6149a86c27680", "metric_expression": "4.81817+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.81817, "metric_value_source": "reported_decimal", "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 4.81817, "source": "Erich Friedman Packing Center", "source_image": "34.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@35", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/35.gif", "friedman_display_metric_value": 4.86994, "id": "friedman-e3a828c2c58bf45d", "metric_expression": "4.86994+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.86994, "metric_value_source": "reported_decimal", "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.86994+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 4.86994, "source": "Erich Friedman Packing Center", "source_image": "35.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@36", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/36.gif", "friedman_display_metric_value": 4.93902, "id": "friedman-c86ce8a81dccfffd", "metric_expression": "4.93902+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.93902, "metric_value_source": "reported_decimal", "n": 36, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.93902+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 4.93902, "source": "Erich Friedman Packing Center", "source_image": "36.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@37", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/37.gif", "friedman_display_metric_value": 4.98234, "id": "friedman-8941d727017dcd77", "metric_expression": "4.98234+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.98234, "metric_value_source": "reported_decimal", "n": 37, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.98234+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 4.98234, "source": "Erich Friedman Packing Center", "source_image": "37.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@38", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/38.gif", "friedman_display_metric_value": 5.05233, "id": "friedman-12e2bcc7445aa5de", "metric_expression": "5.05233+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.05233, "metric_value_source": "reported_decimal", "n": 38, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.05233+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 5.05233, "source": "Erich Friedman Packing Center", "source_image": "38.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@39", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/39.gif", "friedman_display_metric_value": 5.13846, "id": "friedman-298c40434327f042", "metric_expression": "5.13846+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.13846, "metric_value_source": "reported_decimal", "n": 39, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.13846+ | Found by Nathan Roll | in April 2026.", "setup": "squinpen", "side": 5.13846, "source": "Erich Friedman Packing Center", "source_image": "39.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Nathan Roll", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinpen@40", "external_image_url": "https://erich-friedman.github.io/packing/squinpen/40.gif", "friedman_display_metric_value": 5.1725, "id": "friedman-4af74e832ea9a0b5", "metric_expression": "5.17250+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.1725, "metric_value_source": "reported_decimal", "n": 40, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.17250+ | Found by Emerson Connelly | in April 2026.", "setup": "squinpen", "side": 5.1725, "source": "Erich Friedman Packing Center", "source_image": "40.gif", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Squares in Pentagons", "verified": false}
+{"case": "squinoct@1", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/1.gif", "friedman_display_metric_value": 0.54119, "id": "friedman-da5933f6713060f4", "metric_expression": "1/\u221a(2+\u221a2) = .54119+", "metric_formula_parsed": "1/ sqrt (2+ sqrt 2)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.541196100146197, "metric_value_source": "exact_expression", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1/\u221a(2+\u221a2) = .54119+ | Trivial. |", "setup": "squinoct", "side": 0.541196100146197, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@2", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/2.gif", "friedman_display_metric_value": 0.87667, "id": "friedman-b25c78ae72aa7537", "metric_expression": ".87667+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.87667, "metric_value_source": "reported_decimal", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = .87667+ | Found by Maurizio Morandi | in December 2013.", "setup": "squinoct", "side": 0.87667, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@3", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/3.gif", "friedman_display_metric_value": 1.0294, "id": "friedman-151639396050713e", "metric_expression": "18 \u2013 12\u221a2 = 1.02940+", "metric_formula_parsed": "18 - 12 sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0294372515228594, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 18 \u2013 12\u221a2 = 1.02940+ | Found by Erich Friedman | in December 2013.", "setup": "squinoct", "side": 1.0294372515228594, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@4", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/4.gif", "friedman_display_metric_value": 1.08239, "id": "friedman-d6bbf9f56c231029", "metric_expression": "\u221a(4\u20132\u221a2) = 1.08239+", "metric_formula_parsed": "sqrt (4-2 sqrt 2)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.082392200292394, "metric_value_source": "exact_expression", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a(4\u20132\u221a2) = 1.08239+ | Trivial. |", "setup": "squinoct", "side": 1.082392200292394, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@5", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/5.gif", "friedman_display_metric_value": 1.24261, "id": "friedman-f0ab9071f835b471", "metric_expression": "3\u221a2 \u2013 3 = 1.24261+", "metric_formula_parsed": "3 sqrt 2 - 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.2426406871192852, "metric_value_source": "exact_expression", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3\u221a2 \u2013 3 = 1.24261+ | Trivial. |", "setup": "squinoct", "side": 1.2426406871192852, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@6", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/6.gif", "friedman_display_metric_value": 1.34314, "id": "friedman-c1e40d7ffb11aded", "metric_expression": "7 \u2013 4\u221a2 = 1.34314+", "metric_formula_parsed": "7 - 4 sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.3431457505076199, "metric_value_source": "exact_expression", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7 \u2013 4\u221a2 = 1.34314+ | Found by Maurizio Morandi | in December 2013.", "setup": "squinoct", "side": 1.3431457505076199, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@7", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/7.gif", "friedman_display_metric_value": 1.43691, "id": "friedman-809d1257bba66448", "metric_expression": "1.43691+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.43691, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.43691+ | Found by Maurizio Morandi | in December 2013.", "setup": "squinoct", "side": 1.43691, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@8", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/8.gif", "friedman_display_metric_value": 1.56967, "id": "friedman-e0291935714d1fb4", "metric_expression": "1.56967+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.56967, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.56967+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 1.56967, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@9", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/9.gif", "friedman_display_metric_value": 1.62358, "id": "friedman-38c5ae1e73ee6676", "metric_expression": "3/\u221a(2+\u221a2) = 1.62358+", "metric_formula_parsed": "3/ sqrt (2+ sqrt 2)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.623588300438591, "metric_value_source": "exact_expression", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3/\u221a(2+\u221a2) = 1.62358+ | Trivial. |", "setup": "squinoct", "side": 1.623588300438591, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@10", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/10.gif", "friedman_display_metric_value": 1.68179, "id": "friedman-427a7450f2d1f4bd", "metric_expression": "2^(3/4) = 1.68179+", "metric_formula_parsed": "2**(3/4)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.681792830507429, "metric_value_source": "exact_expression", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2^(3/4) = 1.68179+ | Found by Maurizio Morandi | in December 2013.", "setup": "squinoct", "side": 1.681792830507429, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@11", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/11.gif", "friedman_display_metric_value": 1.7318, "id": "friedman-f1ab48e521317a08", "metric_expression": "1.73180+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.7318, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.73180+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 1.7318, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@12", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/12.gif", "friedman_display_metric_value": 1.7533, "id": "friedman-9d5e02cc2f15620f", "metric_expression": "1.7533+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.7533, "metric_value_source": "reported_decimal", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.7533+ | Found by Maurizio Morandi | in December 2013.", "setup": "squinoct", "side": 1.7533, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@13", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/13.gif", "friedman_display_metric_value": 1.8976, "id": "friedman-7ea27340e360e857", "metric_expression": "1.89760+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.8976, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.89760+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 1.8976, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@14", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/14.gif", "friedman_display_metric_value": 1.9835, "id": "friedman-06836a0d72a778f5", "metric_expression": "1.98350+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.9835, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.98350+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 1.9835, "source": "Erich Friedman Packing Center", "source_image": "14.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@15", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/15.gif", "friedman_display_metric_value": 2.03259, "id": "friedman-ecf0183547a74f37", "metric_expression": "2.03259+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.03259, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.03259+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.03259, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@16", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/16.gif", "friedman_display_metric_value": 2.07106, "id": "friedman-7b509f9f550de0c6", "metric_expression": "5\u221a2 \u2013 5 = 2.07106+", "metric_formula_parsed": "5 sqrt 2 - 5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.071067811865475, "metric_value_source": "exact_expression", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5\u221a2 \u2013 5 = 2.07106+ | Trivial. |", "setup": "squinoct", "side": 2.071067811865475, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@17", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/17.gif", "friedman_display_metric_value": 2.07106, "id": "friedman-68b2751e38b5b755", "metric_expression": "5\u221a2 \u2013 5 = 2.07106+", "metric_formula_parsed": "5 sqrt 2 - 5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.071067811865475, "metric_value_source": "exact_expression", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5\u221a2 \u2013 5 = 2.07106+ | Trivial. |", "setup": "squinoct", "side": 2.071067811865475, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@18", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/18.gif", "friedman_display_metric_value": 2.16778, "id": "friedman-c94a124453f64dbf", "metric_expression": "2.16778+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.16778, "metric_value_source": "reported_decimal", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.16778+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.16778, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@19", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/19.gif", "friedman_display_metric_value": 2.22823, "id": "friedman-c262f3b0ebec245f", "metric_expression": "2.22823+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.22823, "metric_value_source": "reported_decimal", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.22823+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.22823, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@20", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/20.gif", "friedman_display_metric_value": 2.2873, "id": "friedman-7f4081be3aa060a1", "metric_expression": "2.28730+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.2873, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.28730+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.2873, "source": "Erich Friedman Packing Center", "source_image": "20.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@21", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/21.gif", "friedman_display_metric_value": 2.32167, "id": "friedman-76036df6d6b85434", "metric_expression": "2.32167+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.32167, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.32167+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.32167, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@22", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/22.gif", "friedman_display_metric_value": 2.41811, "id": "friedman-ce6b9a629b4d15aa", "metric_expression": "2.41811+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.41811, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.41811+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.41811, "source": "Erich Friedman Packing Center", "source_image": "22.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@23", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/23.gif", "friedman_display_metric_value": 2.47329, "id": "friedman-c7dfc422fd6ddfcf", "metric_expression": "2.47329+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.47329, "metric_value_source": "reported_decimal", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.47329+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.47329, "source": "Erich Friedman Packing Center", "source_image": "23.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@24", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/24.gif", "friedman_display_metric_value": 2.48528, "id": "friedman-dddbad94b92c6c05", "metric_expression": "6\u221a2 \u2013 6 = 2.48528+", "metric_formula_parsed": "6 sqrt 2 - 6", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.4852813742385704, "metric_value_source": "exact_expression", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6\u221a2 \u2013 6 = 2.48528+ | Trivial.", "setup": "squinoct", "side": 2.4852813742385704, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@25", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/25.gif", "friedman_display_metric_value": 2.49195, "id": "friedman-0ae45c561bb3fc32", "metric_expression": "11/(3+\u221a2) = 2.49195+", "metric_formula_parsed": "11/(3+ sqrt 2)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.491950116270851, "metric_value_source": "exact_expression", "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 11/(3+\u221a2) = 2.49195+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.491950116270851, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@26", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/26.gif", "friedman_display_metric_value": 2.52841, "id": "friedman-36057ce571f3b782", "metric_expression": "2.52841+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.52841, "metric_value_source": "reported_decimal", "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.52841+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.52841, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@27", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/27.gif", "friedman_display_metric_value": 2.58695, "id": "friedman-8164ac63cdc325e5", "metric_expression": "2.58695+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.58695, "metric_value_source": "reported_decimal", "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.58695+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.58695, "source": "Erich Friedman Packing Center", "source_image": "27.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@28", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/28.gif", "friedman_display_metric_value": 2.63116, "id": "friedman-bddf4849ff3a31f0", "metric_expression": "2.63116+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.63116, "metric_value_source": "reported_decimal", "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.63116+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.63116, "source": "Erich Friedman Packing Center", "source_image": "28.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@29", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/29.gif", "friedman_display_metric_value": 2.70811, "id": "friedman-fd024b7869011606", "metric_expression": "2.70811+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.70811, "metric_value_source": "reported_decimal", "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.70811+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.70811, "source": "Erich Friedman Packing Center", "source_image": "29.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
+{"case": "squinoct@30", "external_image_url": "https://erich-friedman.github.io/packing/squinoct/30.gif", "friedman_display_metric_value": 2.7422, "id": "friedman-bc947d974efc5caa", "metric_expression": "2.74220+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.7422, "metric_value_source": "reported_decimal", "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.74220+ | Found by Ignacio Vallejo | in March 2026.", "setup": "squinoct", "side": 2.7422, "source": "Erich Friedman Packing Center", "source_image": "30.gif", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Squares in Octagons", "verified": false}
+{"case": "triinoct@1", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/1.gif", "friedman_display_metric_value": 0.4647, "id": "friedman-c8efc6f47945c67c", "metric_expression": ".46470+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.4647, "metric_value_source": "reported_decimal", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = .46470+ | Trivial. |", "setup": "triinoct", "side": 0.4647, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@2", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/2.gif", "friedman_display_metric_value": 0.66282, "id": "friedman-181b58c3365d23a6", "metric_expression": "\u221a3/\u221a(4+2\u221a2) = .66282+", "metric_formula_parsed": "sqrt 3/ sqrt (4+2 sqrt 2)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.6628271480711836, "metric_value_source": "exact_expression", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a3/\u221a(4+2\u221a2) = .66282+ | Trivial. |", "setup": "triinoct", "side": 0.6628271480711836, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@3", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/3.gif", "friedman_display_metric_value": 0.73651, "id": "friedman-f7af9ac1be8fe735", "metric_expression": ".73651+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.73651, "metric_value_source": "reported_decimal", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = .73651+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 0.73651, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@4", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/4.gif", "friedman_display_metric_value": 0.77733, "id": "friedman-939870266bcc0da1", "metric_expression": ".77733+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.77733, "metric_value_source": "reported_decimal", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = .77733+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 0.77733, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@5", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/5.gif", "friedman_display_metric_value": 0.80367, "id": "friedman-8a3c42dfa07403fd", "metric_expression": ".80367+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.80367, "metric_value_source": "reported_decimal", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = .80367+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 0.80367, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@6", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/6.gif", "friedman_display_metric_value": 0.81574, "id": "friedman-7e71647ac3920a91", "metric_expression": ".81574+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.81574, "metric_value_source": "reported_decimal", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = .81574+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 0.81574, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@7", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/7.gif", "friedman_display_metric_value": 0.92453, "id": "friedman-6e01773283efdfcd", "metric_expression": ".92453+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.92453, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = .92453+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 0.92453, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@8", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/8.gif", "friedman_display_metric_value": 0.98782, "id": "friedman-02c221fe120e674c", "metric_expression": ".98782+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.98782, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = .98782+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 0.98782, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@9", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/9.gif", "friedman_display_metric_value": 1.00875, "id": "friedman-0f68ee9b37f799d1", "metric_expression": "1.00875+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.00875, "metric_value_source": "reported_decimal", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.00875+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.00875, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@10", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/10.gif", "friedman_display_metric_value": 1.07565, "id": "friedman-a31443a9888942ad", "metric_expression": "1.07565+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.07565, "metric_value_source": "reported_decimal", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.07565+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.07565, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@11", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/11.gif", "friedman_display_metric_value": 1.14571, "id": "friedman-e21c3a21adbaaabc", "metric_expression": "1.14571+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.14571, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.14571+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.14571, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@12", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/12.gif", "friedman_display_metric_value": 1.19929, "id": "friedman-a7daf48cc0b7521a", "metric_expression": "1.19929+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.19929, "metric_value_source": "reported_decimal", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.19929+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.19929, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@13", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/13.gif", "friedman_display_metric_value": 1.23759, "id": "friedman-2c82036dc0fc3460", "metric_expression": "1.23759+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.23759, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.23759+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.23759, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@14", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/14.gif", "friedman_display_metric_value": 1.27677, "id": "friedman-82b661560c998f1a", "metric_expression": "1.27677+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.27677, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.27677+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.27677, "source": "Erich Friedman Packing Center", "source_image": "14.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@15", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/15.gif", "friedman_display_metric_value": 1.30275, "id": "friedman-175875dadd122feb", "metric_expression": "1.30275+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.30275, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.30275+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.30275, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@16", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/16.gif", "friedman_display_metric_value": 1.34584, "id": "friedman-4c5ccc91a35d1a01", "metric_expression": "1.34584+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.34584, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.34584+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.34584, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@17", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/17.gif", "friedman_display_metric_value": 1.38964, "id": "friedman-b81f6f653f27ba0a", "metric_expression": "1.38964+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.38964, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.38964+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.38964, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@18", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/18.gif", "friedman_display_metric_value": 1.41836, "id": "friedman-d47d8c67dc8ae82f", "metric_expression": "1.41836+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.41836, "metric_value_source": "reported_decimal", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.41836+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.41836, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@19", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/19.gif", "friedman_display_metric_value": 1.46749, "id": "friedman-8795b2bf292490f1", "metric_expression": "1.46749+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.46749, "metric_value_source": "reported_decimal", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.46749+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.46749, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@20", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/20.gif", "friedman_display_metric_value": 1.49832, "id": "friedman-a30713bb98715f4e", "metric_expression": "1.49832+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.49832, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.49832+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.49832, "source": "Erich Friedman Packing Center", "source_image": "20.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@21", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/21.gif", "friedman_display_metric_value": 1.52615, "id": "friedman-dedc662d5dbfec33", "metric_expression": "1.52615+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.52615, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.52615+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.52615, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@22", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/22.gif", "friedman_display_metric_value": 1.55545, "id": "friedman-818e75465f9d922a", "metric_expression": "1.55545+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.55545, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.55545+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.55545, "source": "Erich Friedman Packing Center", "source_image": "22.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@23", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/23.gif", "friedman_display_metric_value": 1.58458, "id": "friedman-2b90bd6917df7354", "metric_expression": "1.58458+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.58458, "metric_value_source": "reported_decimal", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.58458+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.58458, "source": "Erich Friedman Packing Center", "source_image": "23.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@24", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/24.gif", "friedman_display_metric_value": 1.60261, "id": "friedman-4144217c1c64407b", "metric_expression": "1.60261+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.60261, "metric_value_source": "reported_decimal", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.60261+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.60261, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@25", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/25.gif", "friedman_display_metric_value": 1.63797, "id": "friedman-c4b6e206182f6656", "metric_expression": "1.63797+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.63797, "metric_value_source": "reported_decimal", "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.63797+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.63797, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@26", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/26.gif", "friedman_display_metric_value": 1.67666, "id": "friedman-b5025e53f93dd7df", "metric_expression": "1.67666+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.67666, "metric_value_source": "reported_decimal", "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.67666+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.67666, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@27", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/27.gif", "friedman_display_metric_value": 1.70882, "id": "friedman-6b67435ae7c5d63b", "metric_expression": "1.70882+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.70882, "metric_value_source": "reported_decimal", "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.70882+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.70882, "source": "Erich Friedman Packing Center", "source_image": "27.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@28", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/28.gif", "friedman_display_metric_value": 1.73954, "id": "friedman-480aa33577c942b6", "metric_expression": "1.73954+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.73954, "metric_value_source": "reported_decimal", "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.73954+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.73954, "source": "Erich Friedman Packing Center", "source_image": "28.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@29", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/29.gif", "friedman_display_metric_value": 1.75576, "id": "friedman-98dd78ff4d6f199d", "metric_expression": "1.75576+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.75576, "metric_value_source": "reported_decimal", "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.75576+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.75576, "source": "Erich Friedman Packing Center", "source_image": "29.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "triinoct@30", "external_image_url": "https://erich-friedman.github.io/packing/triinoct/30.gif", "friedman_display_metric_value": 1.78101, "id": "friedman-4e400c77bc6203b7", "metric_expression": "1.78101+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.78101, "metric_value_source": "reported_decimal", "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1.78101+ | Found by Ignacio Vallejo | in March 2026.", "setup": "triinoct", "side": 1.78101, "source": "Erich Friedman Packing Center", "source_image": "30.gif", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Triangles in Octagons", "verified": false}
+{"case": "octinoct@1", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/1.gif", "friedman_display_metric_value": 1.0, "id": "friedman-b24674da59558d1e", "metric_expression": "1", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0, "metric_value_source": "reported_decimal", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 | Trivial. |", "setup": "octinoct", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@2", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/2.gif", "friedman_display_metric_value": 2.0, "id": "friedman-0f39a906713cff4f", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial. |", "setup": "octinoct", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@3", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/3.gif", "friedman_display_metric_value": 2.17157, "id": "friedman-5b836fbc06fd414e", "metric_expression": "5\u20132\u221a2 = 2.17157+", "metric_formula_parsed": "5-2 sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.1715728752538097, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5\u20132\u221a2 = 2.17157+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 2.1715728752538097, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@4", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/4.gif", "friedman_display_metric_value": 2.38895, "id": "friedman-e11eef2c6244ac4b", "metric_expression": "\u221a(5+1/\u221a2) = 2.38895+", "metric_formula_parsed": "sqrt (5+1/ sqrt 2)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.3889551651687704, "metric_value_source": "exact_expression", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a(5+1/\u221a2) = 2.38895+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 2.3889551651687704, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@5", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/5.gif", "friedman_display_metric_value": 2.7071, "id": "friedman-bd10f4529feec332", "metric_expression": "2+1/\u221a2 = 2.70710+", "metric_formula_parsed": "2+1/ sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.7071067811865475, "metric_value_source": "exact_expression", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+1/\u221a2 = 2.70710+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 2.7071067811865475, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@6", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/6.gif", "friedman_display_metric_value": 2.98915, "id": "friedman-f7ac307d81b19162", "metric_expression": "2.98915+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.98915, "metric_value_source": "reported_decimal", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.98915+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 2.98915, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@7", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/7.gif", "friedman_display_metric_value": 3.0, "id": "friedman-0afa616b2a3243c2", "metric_expression": "3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3 | Trivial. |", "setup": "octinoct", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "7.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@8", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/8.gif", "friedman_display_metric_value": 3.27526, "id": "friedman-b639b315fc5e4d08", "metric_expression": "3.27526+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.27526, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.27526+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 3.27526, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@9", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/9.gif", "friedman_display_metric_value": 3.41421, "id": "friedman-f0800ed60969527f", "metric_expression": "2+\u221a2 = 3.41421+", "metric_formula_parsed": "2+ sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.414213562373095, "metric_value_source": "exact_expression", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+\u221a2 = 3.41421+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 3.414213562373095, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@10", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/10.gif", "friedman_display_metric_value": 3.7071, "id": "friedman-98ee7aa5c63524d5", "metric_expression": "3+1/\u221a2 = 3.70710+", "metric_formula_parsed": "3+1/ sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.7071067811865475, "metric_value_source": "exact_expression", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3+1/\u221a2 = 3.70710+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 3.7071067811865475, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@11", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/11.gif", "friedman_display_metric_value": 3.9327, "id": "friedman-0172a8cf71826939", "metric_expression": "3.93270+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.9327, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.93270+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 3.9327, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@12", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/12.gif", "friedman_display_metric_value": 4.0, "id": "friedman-90c1d80bdc44c46d", "metric_expression": "4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "metric_value_source": "reported_decimal", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4 | Trivial. |", "setup": "octinoct", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Trivial", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@13", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/13.gif", "friedman_display_metric_value": 4.17157, "id": "friedman-611052921fc0aead", "metric_expression": "7\u20132\u221a2 = 4.17157+", "metric_formula_parsed": "7-2 sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.17157287525381, "metric_value_source": "exact_expression", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7\u20132\u221a2 = 4.17157+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 4.17157287525381, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@14", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/14.gif", "friedman_display_metric_value": 4.28155, "id": "friedman-9bdc29340ab79bc6", "metric_expression": "4.28155+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.28155, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.28155+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 4.28155, "source": "Erich Friedman Packing Center", "source_image": "14.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@15", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/15.gif", "friedman_display_metric_value": 4.45594, "id": "friedman-6bd941204bb86cc2", "metric_expression": "4.45594+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.45594, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.45594+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 4.45594, "source": "Erich Friedman Packing Center", "source_image": "15.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@16", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/16.gif", "friedman_display_metric_value": 4.59824, "id": "friedman-c1282f4d01a2ddef", "metric_expression": "4.59824+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.59824, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.59824+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 4.59824, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@17", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/17.gif", "friedman_display_metric_value": 4.75741, "id": "friedman-67f790dcd2d7aedf", "metric_expression": "4.75741+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.75741, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.75741+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 4.75741, "source": "Erich Friedman Packing Center", "source_image": "17.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@18", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/18.gif", "friedman_display_metric_value": 4.85717, "id": "friedman-bc52e524d7f1dc6a", "metric_expression": "4.85717+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.85717, "metric_value_source": "reported_decimal", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.85717+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 4.85717, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@19", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/19.gif", "friedman_display_metric_value": 4.93586, "id": "friedman-7f8d435e7e75742a", "metric_expression": "4.93586+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.93586, "metric_value_source": "reported_decimal", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.93586+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 4.93586, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@20", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/20.gif", "friedman_display_metric_value": 5.06781, "id": "friedman-6c5a60f7a5b99e14", "metric_expression": "5.06781+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.06781, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.06781+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.06781, "source": "Erich Friedman Packing Center", "source_image": "20.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@21", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/21.gif", "friedman_display_metric_value": 5.19715, "id": "friedman-62b042a9c4160f76", "metric_expression": "5.19715+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.19715, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.19715+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.19715, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@22", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/22.gif", "friedman_display_metric_value": 5.3575, "id": "friedman-fa85f57ef3ad9e9e", "metric_expression": "5.35750+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.3575, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.35750+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.3575, "source": "Erich Friedman Packing Center", "source_image": "22.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@23", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/23.gif", "friedman_display_metric_value": 5.4144, "id": "friedman-007965e1f7c3b3a8", "metric_expression": "5.41440+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.4144, "metric_value_source": "reported_decimal", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.41440+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.4144, "source": "Erich Friedman Packing Center", "source_image": "23.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@24", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/24.gif", "friedman_display_metric_value": 5.55464, "id": "friedman-c97db9b3738a229d", "metric_expression": "5.55464+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.55464, "metric_value_source": "reported_decimal", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.55464+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.55464, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@25", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/25.gif", "friedman_display_metric_value": 5.65593, "id": "friedman-8c0f88c0b7b2ce6f", "metric_expression": "5.65593+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.65593, "metric_value_source": "reported_decimal", "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.65593+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.65593, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@26", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/26.gif", "friedman_display_metric_value": 5.7394, "id": "friedman-bc05afd85bd1c220", "metric_expression": "5.73940+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.7394, "metric_value_source": "reported_decimal", "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.73940+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.7394, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@27", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/27.gif", "friedman_display_metric_value": 5.81238, "id": "friedman-6eda0588045826bc", "metric_expression": "5.81238+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.81238, "metric_value_source": "reported_decimal", "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.81238+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.81238, "source": "Erich Friedman Packing Center", "source_image": "27.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@28", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/28.gif", "friedman_display_metric_value": 5.82842, "id": "friedman-692f872700d246c9", "metric_expression": "3+2\u221a2 = 5.82842+", "metric_formula_parsed": "3+2 sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.82842712474619, "metric_value_source": "exact_expression", "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3+2\u221a2 = 5.82842+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 5.82842712474619, "source": "Erich Friedman Packing Center", "source_image": "28.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@29", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/29.gif", "friedman_display_metric_value": 6.05746, "id": "friedman-9d7906d7782ebbc1", "metric_expression": "6.05746+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.05746, "metric_value_source": "reported_decimal", "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.05746+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 6.05746, "source": "Erich Friedman Packing Center", "source_image": "29.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "octinoct@30", "external_image_url": "https://erich-friedman.github.io/packing/octinoct/30.gif", "friedman_display_metric_value": 6.15432, "id": "friedman-99e7b695be48aeea", "metric_expression": "6.15432+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.15432, "metric_value_source": "reported_decimal", "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.15432+ | Found by Ignacio Vallejo | in March 2026.", "setup": "octinoct", "side": 6.15432, "source": "Erich Friedman Packing Center", "source_image": "30.gif", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Octagons in Octagons", "verified": false}
+{"case": "domintri@1", "external_image_url": "https://erich-friedman.github.io/packing/domintri/1.png", "friedman_display_metric_value": 3.1547, "id": "friedman-0c092c16e65ef91c", "metric_expression": "2+2/\u221a3 = 3.15470+", "metric_formula_parsed": "2+2/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.1547005383792515, "metric_value_source": "exact_expression", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+2/\u221a3 = 3.15470+ | Trivial.", "setup": "domintri", "side": 3.1547005383792515, "source": "Erich Friedman Packing Center", "source_image": "1.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@2", "external_image_url": "https://erich-friedman.github.io/packing/domintri/2.png", "friedman_display_metric_value": 4.3094, "id": "friedman-a15bc7dfac6ef1a7", "metric_expression": "2+4/\u221a3 = 4.30940+", "metric_formula_parsed": "2+4/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.309401076758503, "metric_value_source": "exact_expression", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+4/\u221a3 = 4.30940+ | Trivial.", "setup": "domintri", "side": 4.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@3", "external_image_url": "https://erich-friedman.github.io/packing/domintri/3.png", "friedman_display_metric_value": 4.30934, "id": "friedman-70e897d9bfc25e33", "metric_expression": "2+4/\u221a3 = 4.30934+", "metric_formula_parsed": "2+4/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.309401076758503, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+4/\u221a3 = 4.30934+ | Trivial.", "setup": "domintri", "side": 4.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@4", "external_image_url": "https://erich-friedman.github.io/packing/domintri/4.png", "friedman_display_metric_value": 5.38188, "id": "friedman-d81827e82f0d5304", "metric_expression": "5.38188+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.38188, "metric_value_source": "reported_decimal", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.38188+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 5.38188, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@5", "external_image_url": "https://erich-friedman.github.io/packing/domintri/5.png", "friedman_display_metric_value": 5.4641, "id": "friedman-fdda6ecdc3a976e8", "metric_expression": "2+2\u221a3 = 5.46410+", "metric_formula_parsed": "2+2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.464101615137754, "metric_value_source": "exact_expression", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+2\u221a3 = 5.46410+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 5.464101615137754, "source": "Erich Friedman Packing Center", "source_image": "5.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@6", "external_image_url": "https://erich-friedman.github.io/packing/domintri/6.png", "friedman_display_metric_value": 6.3094, "id": "friedman-98b3407b42e56d92", "metric_expression": "4+4/\u221a3 = 6.30940+", "metric_formula_parsed": "4+4/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.309401076758503, "metric_value_source": "exact_expression", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4+4/\u221a3 = 6.30940+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 6.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@7", "external_image_url": "https://erich-friedman.github.io/packing/domintri/7.png", "friedman_display_metric_value": 6.61409, "id": "friedman-95970e29a4251c10", "metric_expression": "6.61409+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.61409, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.61409+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 6.61409, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@8", "external_image_url": "https://erich-friedman.github.io/packing/domintri/8.png", "friedman_display_metric_value": 7.1547, "id": "friedman-1a13d6a472aa7bee", "metric_expression": "6+2/\u221a3 = 7.15470+", "metric_formula_parsed": "6+2/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.1547005383792515, "metric_value_source": "exact_expression", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6+2/\u221a3 = 7.15470+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 7.1547005383792515, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@9", "external_image_url": "https://erich-friedman.github.io/packing/domintri/9.png", "friedman_display_metric_value": 7.3094, "id": "friedman-0e81766811a88057", "metric_expression": "5+4/\u221a3 = 7.30940+", "metric_formula_parsed": "5+4/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.309401076758503, "metric_value_source": "exact_expression", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5+4/\u221a3 = 7.30940+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 7.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@10", "external_image_url": "https://erich-friedman.github.io/packing/domintri/10.png", "friedman_display_metric_value": 7.61885, "id": "friedman-6e457e60eeab7f0c", "metric_expression": "3+8/\u221a3 = 7.61885+", "metric_formula_parsed": "3+8/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.618802153517006, "metric_value_source": "exact_expression", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3+8/\u221a3 = 7.61885+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 7.618802153517006, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@11", "external_image_url": "https://erich-friedman.github.io/packing/domintri/11.png", "friedman_display_metric_value": 8.1547, "id": "friedman-52e1b51216b50748", "metric_expression": "7+2/\u221a3 = 8.15470+", "metric_formula_parsed": "7+2/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.154700538379252, "metric_value_source": "exact_expression", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7+2/\u221a3 = 8.15470+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 8.154700538379252, "source": "Erich Friedman Packing Center", "source_image": "11.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@12", "external_image_url": "https://erich-friedman.github.io/packing/domintri/12.png", "friedman_display_metric_value": 8.3094, "id": "friedman-844f628390e4c5f4", "metric_expression": "6+4/\u221a3 = 8.30940+", "metric_formula_parsed": "6+4/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.309401076758503, "metric_value_source": "exact_expression", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6+4/\u221a3 = 8.30940+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 8.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@13", "external_image_url": "https://erich-friedman.github.io/packing/domintri/13.png", "friedman_display_metric_value": 8.61885, "id": "friedman-922f258e8787be46", "metric_expression": "4+8/\u221a3 = 8.61885+", "metric_formula_parsed": "4+8/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.618802153517006, "metric_value_source": "exact_expression", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4+8/\u221a3 = 8.61885+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 8.618802153517006, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@14", "external_image_url": "https://erich-friedman.github.io/packing/domintri/14.png", "friedman_display_metric_value": 8.7735, "id": "friedman-3b37cfa994994ce2", "metric_expression": "3+10/\u221a3 = 8.77350+", "metric_formula_parsed": "3+10/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.773502691896258, "metric_value_source": "exact_expression", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3+10/\u221a3 = 8.77350+ | Found by Maurizio Morandi | in April 2026.", "setup": "domintri", "side": 8.773502691896258, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@15", "external_image_url": "https://erich-friedman.github.io/packing/domintri/15.png", "friedman_display_metric_value": 9.3094, "id": "friedman-5353651e0a25321c", "metric_expression": "7+4/\u221a3 = 9.30940+", "metric_formula_parsed": "7+4/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.309401076758503, "metric_value_source": "exact_expression", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7+4/\u221a3 = 9.30940+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 9.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@16", "external_image_url": "https://erich-friedman.github.io/packing/domintri/16.png", "friedman_display_metric_value": 9.4641, "id": "friedman-fb928d23da3debe6", "metric_expression": "6+2\u221a3 = 9.46410+", "metric_formula_parsed": "6+2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.464101615137755, "metric_value_source": "exact_expression", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6+2\u221a3 = 9.46410+ | Found by Maurizio Morandi | in April 2026.", "setup": "domintri", "side": 9.464101615137755, "source": "Erich Friedman Packing Center", "source_image": "16.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@17", "external_image_url": "https://erich-friedman.github.io/packing/domintri/17.png", "friedman_display_metric_value": 9.7735, "id": "friedman-032a49fde439e321", "metric_expression": "4+10/\u221a3 = 9.77350+", "metric_formula_parsed": "4+10/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.773502691896258, "metric_value_source": "exact_expression", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4+10/\u221a3 = 9.77350+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 9.773502691896258, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@18", "external_image_url": "https://erich-friedman.github.io/packing/domintri/18.png", "friedman_display_metric_value": 9.9282, "id": "friedman-5cecc605aaf6b720", "metric_expression": "3+4\u221a3 = 9.92820+", "metric_formula_parsed": "3+4 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.928203230275509, "metric_value_source": "exact_expression", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3+4\u221a3 = 9.92820+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 9.928203230275509, "source": "Erich Friedman Packing Center", "source_image": "18.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@19", "external_image_url": "https://erich-friedman.github.io/packing/domintri/19.png", "friedman_display_metric_value": 10.3094, "id": "friedman-4f9c928d94b3ffd2", "metric_expression": "8+4/\u221a3 = 10.30940+", "metric_formula_parsed": "8+4/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.309401076758503, "metric_value_source": "exact_expression", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 8+4/\u221a3 = 10.30940+ | Found by Jonathan Viquerat | in April 2026.", "setup": "domintri", "side": 10.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@20", "external_image_url": "https://erich-friedman.github.io/packing/domintri/20.png", "friedman_display_metric_value": 10.4641, "id": "friedman-babeccb1f91a5e4e", "metric_expression": "7+2\u221a3 = 10.46410+", "metric_formula_parsed": "7+2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.464101615137755, "metric_value_source": "exact_expression", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7+2\u221a3 = 10.46410+ | Found by Maurizio Morandi | in April 2026.", "setup": "domintri", "side": 10.464101615137755, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@21", "external_image_url": "https://erich-friedman.github.io/packing/domintri/21.png", "friedman_display_metric_value": 10.66025, "id": "friedman-d3880ffccb6fbbf0", "metric_expression": "2+5\u221a3 = 10.66025+", "metric_formula_parsed": "2+5 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.660254037844387, "metric_value_source": "exact_expression", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+5\u221a3 = 10.66025+ | Found by Maurizio Morandi | in April 2026.", "setup": "domintri", "side": 10.660254037844387, "source": "Erich Friedman Packing Center", "source_image": "21.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@22", "external_image_url": "https://erich-friedman.github.io/packing/domintri/22.png", "friedman_display_metric_value": 10.9282, "id": "friedman-ffa257a36540a61e", "metric_expression": "4(1+\u221a3) = 10.92820+", "metric_formula_parsed": "4(1+ sqrt 3)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.928203230275509, "metric_value_source": "exact_expression", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4(1+\u221a3) = 10.92820+ | Found by Maurizio Morandi | in April 2026.", "setup": "domintri", "side": 10.928203230275509, "source": "Erich Friedman Packing Center", "source_image": "22.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@23", "external_image_url": "https://erich-friedman.github.io/packing/domintri/23.png", "friedman_display_metric_value": 11.1547, "id": "friedman-454e14ef9a5ce734", "metric_expression": "10+2/\u221a3 = 11.15470+", "metric_formula_parsed": "10+2/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 11.154700538379252, "metric_value_source": "exact_expression", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 10+2/\u221a3 = 11.15470+ | Found by Maurizio Morandi | in April 2026.", "setup": "domintri", "side": 11.154700538379252, "source": "Erich Friedman Packing Center", "source_image": "23.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Triangles", "verified": false}
+{"case": "domintri@24", "external_image_url": "https://erich-friedman.github.io/packing/domintri/24.png", "friedman_display_metric_value": 11.3094, "id": "friedman-29114dd835ba2559", "metric_expression": "9+4/\u221a3 = 11.30940+", "metric_formula_parsed": "9+4/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 11.309401076758503, "metric_value_source": "exact_expression", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 9+4/\u221a3 = 11.30940+ | Found by Maurizio Morandi | in April 2026.", "setup": "domintri", "side": 11.309401076758503, "source": "Erich Friedman Packing Center", "source_image": "24.png", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Triangles", "verified": false}
+{"case": "squindom@1", "external_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "friedman_display_metric_value": 1.0, "id": "friedman-5014797fdaddc695", "metric_expression": "1", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0, "metric_value_source": "reported_decimal", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "1-2. | | s = 1 | Trivial. |", "setup": "squindom", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@2", "external_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "friedman_display_metric_value": 1.0, "id": "friedman-757770ad1f8b5cc0", "metric_expression": "1", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0, "metric_value_source": "reported_decimal", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "1-2. | | s = 1 | Trivial. |", "setup": "squindom", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@3", "external_image_url": "https://erich-friedman.github.io/packing/squindom/3.gif", "friedman_display_metric_value": 1.5, "id": "friedman-a44d8b6d6f0e9f52", "metric_expression": "3/2 = 1.5", "metric_formula_parsed": "3/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.5, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "3. | | s = 3/2 = 1.5 | Trivial. |", "setup": "squindom", "side": 1.5, "source": "Erich Friedman Packing Center", "source_image": "3.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@4", "external_image_url": "https://erich-friedman.github.io/packing/squindom/4.gif", "friedman_display_metric_value": 1.93, "id": "friedman-d5b324bb4da5564f", "metric_expression": "1.930+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.93, "metric_value_source": "reported_decimal", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "4. | | s = 1.930+ | Found by Evert Stenlund | in June 2010.", "setup": "squindom", "side": 1.93, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Evert Stenlund", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@5", "external_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "friedman_display_metric_value": 2.0, "id": "friedman-eb7f1f6a68787eb8", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "5-8. | | s = 2 | Trivial. |", "setup": "squindom", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@6", "external_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "friedman_display_metric_value": 2.0, "id": "friedman-26d4d607db286852", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "5-8. | | s = 2 | Trivial. |", "setup": "squindom", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@7", "external_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "friedman_display_metric_value": 2.0, "id": "friedman-26d2174cf47693e2", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "5-8. | | s = 2 | Trivial. |", "setup": "squindom", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@8", "external_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "friedman_display_metric_value": 2.0, "id": "friedman-770447a5fa93bcce", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "5-8. | | s = 2 | Trivial. |", "setup": "squindom", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "8.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@9", "external_image_url": "https://erich-friedman.github.io/packing/squindom/9.gif", "friedman_display_metric_value": 2.471, "id": "friedman-911b5ee29fe3308b", "metric_expression": "2 + \u221a2/3 = 2.471+", "metric_formula_parsed": "2 + sqrt 2/3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.471404520791032, "metric_value_source": "exact_expression", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "9. | | s = 2 + \u221a2/3 = 2.471+ | Found by Evert Stenlund | in June 2010.", "setup": "squindom", "side": 2.471404520791032, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Evert Stenlund", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@10", "external_image_url": "https://erich-friedman.github.io/packing/squindom/10.gif", "friedman_display_metric_value": 2.5, "id": "friedman-ec07df79d37cfd19", "metric_expression": "5/2 = 2.5", "metric_formula_parsed": "5/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.5, "metric_value_source": "exact_expression", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "10. | | s = 5/2 = 2.5 | Trivial. |", "setup": "squindom", "side": 2.5, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@11", "external_image_url": "https://erich-friedman.github.io/packing/squindom/11.gif", "friedman_display_metric_value": 2.779, "id": "friedman-f84588ec5a02cbec", "metric_expression": "2.779+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.779, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "11. | | s = 2.779+ | Found by Evert Stenlund | in June 2010. |", "setup": "squindom", "side": 2.779, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Evert Stenlund", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@12", "external_image_url": "https://erich-friedman.github.io/packing/squindom/12.gif", "friedman_display_metric_value": 2.897, "id": "friedman-15eb4c3098fcb692", "metric_expression": "6 (1 + \u221a2) / 5 = 2.897+", "metric_formula_parsed": "6 (1 + sqrt 2) / 5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.897056274847714, "metric_value_source": "exact_expression", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "12. | | s = 6 (1 + \u221a2) / 5 = 2.897+ | Found by Maurizio Morandi | in June 2010. |", "setup": "squindom", "side": 2.897056274847714, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@13", "external_image_url": "https://erich-friedman.github.io/packing/squindom/13.gif", "friedman_display_metric_value": 2.976, "id": "friedman-24cddd09aa88a137", "metric_expression": "2.976+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.976, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "13. | | s = 2.976+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)", "setup": "squindom", "side": 2.976, "source": "Erich Friedman Packing Center", "source_image": "13.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@14", "external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "friedman_display_metric_value": 3.0, "id": "friedman-31da3a9cc8386278", "metric_expression": "3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14-18. | | s = 3 | Trivial. |", "setup": "squindom", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@15", "external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "friedman_display_metric_value": 3.0, "id": "friedman-2d2c7495b99e6c10", "metric_expression": "3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14-18. | | s = 3 | Trivial. |", "setup": "squindom", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@16", "external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "friedman_display_metric_value": 3.0, "id": "friedman-4e8a4fa1e52bd953", "metric_expression": "3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14-18. | | s = 3 | Trivial. |", "setup": "squindom", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@17", "external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "friedman_display_metric_value": 3.0, "id": "friedman-c77c38f2962c132b", "metric_expression": "3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14-18. | | s = 3 | Trivial. |", "setup": "squindom", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@18", "external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "friedman_display_metric_value": 3.0, "id": "friedman-abc916e48c35716f", "metric_expression": "3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0, "metric_value_source": "reported_decimal", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14-18. | | s = 3 | Trivial. |", "setup": "squindom", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@19", "external_image_url": "https://erich-friedman.github.io/packing/squindom/19.gif", "friedman_display_metric_value": 3.447, "id": "friedman-67d27c6311c73bae", "metric_expression": "3 + 1/\u221a5 = 3.447+", "metric_formula_parsed": "3 + 1/ sqrt 5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.447213595499958, "metric_value_source": "exact_expression", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "19. | | s = 3 + 1/\u221a5 = 3.447+ | Found by Maurizio Morandi | in June 2010.", "setup": "squindom", "side": 3.447213595499958, "source": "Erich Friedman Packing Center", "source_image": "19.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@20", "external_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "friedman_display_metric_value": 3.5, "id": "friedman-b1853e9c65016dd9", "metric_expression": "7/2 = 3.5", "metric_formula_parsed": "7/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.5, "metric_value_source": "exact_expression", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "setup": "squindom", "side": 3.5, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@21", "external_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "friedman_display_metric_value": 3.5, "id": "friedman-2e90bf9b358b7411", "metric_expression": "7/2 = 3.5", "metric_formula_parsed": "7/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.5, "metric_value_source": "exact_expression", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "setup": "squindom", "side": 3.5, "source": "Erich Friedman Packing Center", "source_image": "21.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@22", "external_image_url": "https://erich-friedman.github.io/packing/squindom/22.gif", "friedman_display_metric_value": 3.745, "id": "friedman-c7cdc02320008438", "metric_expression": "3.745+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.745, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "22. | | s = 3.745+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)", "setup": "squindom", "side": 3.745, "source": "Erich Friedman Packing Center", "source_image": "22.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@23", "external_image_url": "https://erich-friedman.github.io/packing/squindom/23.gif", "friedman_display_metric_value": 3.849, "id": "friedman-ec1ade482aa1a7fd", "metric_expression": "3.849+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.849, "metric_value_source": "reported_decimal", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "23. | | s = 3.849+ | Found by Maurizio Morandi | in June 2010. |", "setup": "squindom", "side": 3.849, "source": "Erich Friedman Packing Center", "source_image": "23.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@24", "external_image_url": "https://erich-friedman.github.io/packing/squindom/24.gif", "friedman_display_metric_value": 3.882, "id": "friedman-44afa839c5d4e499", "metric_expression": "3.882+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.882, "metric_value_source": "reported_decimal", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "24. | | s = 3.882+ | Found by DC after MM | in August 2012. |", "setup": "squindom", "side": 3.882, "source": "Erich Friedman Packing Center", "source_image": "24.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "David W. Cantrell after Maurizio Morandi", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@25", "external_image_url": "https://erich-friedman.github.io/packing/squindom/25.gif", "friedman_display_metric_value": 3.939, "id": "friedman-f4a086f1320dfc36", "metric_expression": "3.939+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.939, "metric_value_source": "reported_decimal", "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "25. | | s = 3.939+ | Found by DC after MM | in August 2012. |", "setup": "squindom", "side": 3.939, "source": "Erich Friedman Packing Center", "source_image": "25.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "David W. Cantrell after Maurizio Morandi", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@26", "external_image_url": "https://erich-friedman.github.io/packing/squindom/26.gif", "friedman_display_metric_value": 3.981, "id": "friedman-50a558ebf9de8bab", "metric_expression": "3.981+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.981, "metric_value_source": "reported_decimal", "n": 26, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "26. | | s = 3.981+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in July 2012.)", "setup": "squindom", "side": 3.981, "source": "Erich Friedman Packing Center", "source_image": "26.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@27", "external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_display_metric_value": 4.0, "id": "friedman-16ff90552c02c33d", "metric_expression": "4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "metric_value_source": "reported_decimal", "n": 27, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "27-32. | | s = 4 | Trivial. | |", "setup": "squindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@28", "external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_display_metric_value": 4.0, "id": "friedman-2b582527ece8934e", "metric_expression": "4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "metric_value_source": "reported_decimal", "n": 28, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "27-32. | | s = 4 | Trivial. | |", "setup": "squindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@29", "external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_display_metric_value": 4.0, "id": "friedman-46309bc7457b0cfe", "metric_expression": "4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "metric_value_source": "reported_decimal", "n": 29, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "27-32. | | s = 4 | Trivial. | |", "setup": "squindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@30", "external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_display_metric_value": 4.0, "id": "friedman-88ebdc8d7b60ef88", "metric_expression": "4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "metric_value_source": "reported_decimal", "n": 30, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "27-32. | | s = 4 | Trivial. | |", "setup": "squindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@31", "external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_display_metric_value": 4.0, "id": "friedman-65ea5574d4dd0878", "metric_expression": "4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "metric_value_source": "reported_decimal", "n": 31, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "27-32. | | s = 4 | Trivial. | |", "setup": "squindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@32", "external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_display_metric_value": 4.0, "id": "friedman-020cc762b911b6b6", "metric_expression": "4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "metric_value_source": "reported_decimal", "n": 32, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "27-32. | | s = 4 | Trivial. | |", "setup": "squindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "32.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@33", "external_image_url": "https://erich-friedman.github.io/packing/squindom/33.gif", "friedman_display_metric_value": 4.414, "id": "friedman-f71ebd16ddf3d624", "metric_expression": "3 + \u221a2 = 4.414+", "metric_formula_parsed": "3 + sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.414213562373095, "metric_value_source": "exact_expression", "n": 33, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "33. | | s = 3 + \u221a2 = 4.414+ | Found by Maurizio Morandi | in July 2012.", "setup": "squindom", "side": 4.414213562373095, "source": "Erich Friedman Packing Center", "source_image": "33.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@34", "external_image_url": "https://erich-friedman.github.io/packing/squindom/34.gif", "friedman_display_metric_value": 4.471, "id": "friedman-9278a960daf8d32f", "metric_expression": "4 + \u221a2/3 = 4.471+", "metric_formula_parsed": "4 + sqrt 2/3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.471404520791031, "metric_value_source": "exact_expression", "n": 34, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "34. | | s = 4 + \u221a2/3 = 4.471+ | Found by David W. Cantrell | in July 2012.", "setup": "squindom", "side": 4.471404520791031, "source": "Erich Friedman Packing Center", "source_image": "34.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@35", "external_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "friedman_display_metric_value": 4.5, "id": "friedman-f71f478216853ec9", "metric_expression": "9/2 = 4.5", "metric_formula_parsed": "9/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.5, "metric_value_source": "exact_expression", "n": 35, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "setup": "squindom", "side": 4.5, "source": "Erich Friedman Packing Center", "source_image": "36.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@36", "external_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "friedman_display_metric_value": 4.5, "id": "friedman-0816f27e30f718f7", "metric_expression": "9/2 = 4.5", "metric_formula_parsed": "9/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.5, "metric_value_source": "exact_expression", "n": 36, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "setup": "squindom", "side": 4.5, "source": "Erich Friedman Packing Center", "source_image": "36.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@37", "external_image_url": "https://erich-friedman.github.io/packing/squindom/37.gif", "friedman_display_metric_value": 4.747, "id": "friedman-de32dfcf3ec55123", "metric_expression": "10 / 3 + \u221a2 = 4.747+", "metric_formula_parsed": "10 / 3 + sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.747546895706428, "metric_value_source": "exact_expression", "n": 37, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "37. | | s = 10 / 3 + \u221a2 = 4.747+ | Found by Maurizio Morandi | in August 2012.", "setup": "squindom", "side": 4.747546895706428, "source": "Erich Friedman Packing Center", "source_image": "37.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@38", "external_image_url": "https://erich-friedman.github.io/packing/squindom/38.gif", "friedman_display_metric_value": 4.804, "id": "friedman-72a9e74eacdae400", "metric_expression": "(13 + \u221a2) / 3 = 4.804+", "metric_formula_parsed": "(13 + sqrt 2) / 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.804737854124365, "metric_value_source": "exact_expression", "n": 38, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "38. | | s = (13 + \u221a2) / 3 = 4.804+ | Found by Maurizio Morandi | in August 2012.", "setup": "squindom", "side": 4.804737854124365, "source": "Erich Friedman Packing Center", "source_image": "38.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@39", "external_image_url": "https://erich-friedman.github.io/packing/squindom/39.gif", "friedman_display_metric_value": 4.839, "id": "friedman-e3ba16dca355ea1e", "metric_expression": "4.839+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.839, "metric_value_source": "reported_decimal", "n": 39, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "39. | | s = 4.839+ | Found by David W. Cantrell | in August 2012.", "setup": "squindom", "side": 4.839, "source": "Erich Friedman Packing Center", "source_image": "39.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@40", "external_image_url": "https://erich-friedman.github.io/packing/squindom/40.gif", "friedman_display_metric_value": 4.895, "id": "friedman-ca00577d0d0551b5", "metric_expression": "4.895+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.895, "metric_value_source": "reported_decimal", "n": 40, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "40. | | s = 4.895+ | Found by Sigvart Brendberg | in June 2023.", "setup": "squindom", "side": 4.895, "source": "Erich Friedman Packing Center", "source_image": "40.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Sigvart Brendberg", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@41", "external_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif", "friedman_display_metric_value": 4.927, "id": "friedman-e8c33cfe5bb26c8e", "metric_expression": "4.927+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.927, "metric_value_source": "reported_decimal", "n": 41, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.", "setup": "squindom", "side": 4.927, "source": "Erich Friedman Packing Center", "source_image": "41.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Sigvart Brendberg", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@42", "external_image_url": "https://erich-friedman.github.io/packing/squindom/42.gif", "friedman_display_metric_value": 4.989, "id": "friedman-f0e1ef88792ca2f0", "metric_expression": "4.989+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.989, "metric_value_source": "reported_decimal", "n": 42, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "42. | | s = 4.989+ | Found by David W. Cantrell | in August 2012.", "setup": "squindom", "side": 4.989, "source": "Erich Friedman Packing Center", "source_image": "42.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "David W. Cantrell", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@43", "external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_display_metric_value": 5.0, "id": "friedman-dc3910f178baa82e", "metric_expression": "5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "metric_value_source": "reported_decimal", "n": 43, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "43-50. | | s = 5 | Trivial. |", "setup": "squindom", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "50.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@44", "external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_display_metric_value": 5.0, "id": "friedman-dc0442edd8b13f81", "metric_expression": "5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "metric_value_source": "reported_decimal", "n": 44, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "43-50. | | s = 5 | Trivial. |", "setup": "squindom", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "50.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@45", "external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_display_metric_value": 5.0, "id": "friedman-92203de7a78a89e0", "metric_expression": "5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "metric_value_source": "reported_decimal", "n": 45, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "43-50. | | s = 5 | Trivial. |", "setup": "squindom", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "50.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@46", "external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_display_metric_value": 5.0, "id": "friedman-8bc8251fb17bd0a4", "metric_expression": "5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "metric_value_source": "reported_decimal", "n": 46, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "43-50. | | s = 5 | Trivial. |", "setup": "squindom", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "50.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@47", "external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_display_metric_value": 5.0, "id": "friedman-6f799588ad84ce0f", "metric_expression": "5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "metric_value_source": "reported_decimal", "n": 47, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "43-50. | | s = 5 | Trivial. |", "setup": "squindom", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "50.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@48", "external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_display_metric_value": 5.0, "id": "friedman-ac8b979d645373c3", "metric_expression": "5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "metric_value_source": "reported_decimal", "n": 48, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "43-50. | | s = 5 | Trivial. |", "setup": "squindom", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "50.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@49", "external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_display_metric_value": 5.0, "id": "friedman-f8b2f277dc699002", "metric_expression": "5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "metric_value_source": "reported_decimal", "n": 49, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "43-50. | | s = 5 | Trivial. |", "setup": "squindom", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "50.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "squindom@50", "external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_display_metric_value": 5.0, "id": "friedman-0655ad47f55fec32", "metric_expression": "5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "metric_value_source": "reported_decimal", "n": 50, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "43-50. | | s = 5 | Trivial. |", "setup": "squindom", "side": 5.0, "source": "Erich Friedman Packing Center", "source_image": "50.gif", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Squares in Dominoes", "verified": false}
+{"case": "domindom@1", "external_image_url": "https://erich-friedman.github.io/packing/domindom/1.gif", "friedman_display_metric_value": 1.0, "id": "friedman-fe5074fb42926405", "metric_expression": "1", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0, "metric_value_source": "reported_decimal", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "1. | | s = 1 | Trivial.", "setup": "domindom", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "1.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
+{"case": "domindom@2", "external_image_url": "https://erich-friedman.github.io/packing/domindom/2.gif", "friedman_display_metric_value": 1.971, "id": "friedman-c285aa9cd5d12a71", "metric_expression": "(2+\u221a2)/\u221a3 = 1.971+", "metric_formula_parsed": "(2+ sqrt 2)/ sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.9711971193069775, "metric_value_source": "exact_expression", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "2. | | s = (2+\u221a2)/\u221a3 = 1.971+ | Found by Erich Friedman in April 2026.", "setup": "domindom", "side": 1.9711971193069775, "source": "Erich Friedman Packing Center", "source_image": "2.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Dominoes in Dominoes", "verified": false}
+{"case": "domindom@3", "external_image_url": "https://erich-friedman.github.io/packing/domindom/4.gif", "friedman_display_metric_value": 2.0, "id": "friedman-a40b473968b13df2", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "3.-4. | | s = 2 | Trivial.", "setup": "domindom", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
+{"case": "domindom@4", "external_image_url": "https://erich-friedman.github.io/packing/domindom/4.gif", "friedman_display_metric_value": 2.0, "id": "friedman-35c8c1dcb75aaa80", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "3.-4. | | s = 2 | Trivial.", "setup": "domindom", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "4.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
+{"case": "domindom@5", "external_image_url": "https://erich-friedman.github.io/packing/domindom/5.gif", "friedman_display_metric_value": 2.5, "id": "friedman-8fe8d537307854a7", "metric_expression": "5/2 = 2.5", "metric_formula_parsed": "5/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.5, "metric_value_source": "exact_expression", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "5. | | s = 5/2 = 2.5 | Trivial.", "setup": "domindom", "side": 2.5, "source": "Erich Friedman Packing Center", "source_image": "5.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
+{"case": "domindom@6", "external_image_url": "https://erich-friedman.github.io/packing/domindom/6.gif", "friedman_display_metric_value": 2.916, "id": "friedman-82b5ac658d668d43", "metric_expression": "2.916+", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.916, "metric_value_source": "reported_decimal", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "6. | | s = 2.916+ | Found by Erich Friedman in April 2026.", "setup": "domindom", "side": 2.916, "source": "Erich Friedman Packing Center", "source_image": "6.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Erich Friedman", "title": "Dominoes in Dominoes", "verified": false}
+{"case": "domindom@7", "external_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "friedman_display_metric_value": 3.0, "id": "friedman-b6ff64c8ec34d9e5", "metric_expression": "3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "7.-9. | | s = 3 | Trivial.", "setup": "domindom", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
+{"case": "domindom@8", "external_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "friedman_display_metric_value": 3.0, "id": "friedman-f7a6ac29d49b90a3", "metric_expression": "3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "7.-9. | | s = 3 | Trivial.", "setup": "domindom", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
+{"case": "domindom@9", "external_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "friedman_display_metric_value": 3.0, "id": "friedman-c66f72045cce92b7", "metric_expression": "3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0, "metric_value_source": "reported_decimal", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "7.-9. | | s = 3 | Trivial.", "setup": "domindom", "side": 3.0, "source": "Erich Friedman Packing Center", "source_image": "9.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
+{"case": "domindom@10", "external_image_url": "https://erich-friedman.github.io/packing/domindom/10.gif", "friedman_display_metric_value": 3.5, "id": "friedman-7632a523c5e58279", "metric_expression": "7/2 = 3.5", "metric_formula_parsed": "7/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.5, "metric_value_source": "exact_expression", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "10. | | s = 7/2 = 3.5 | Trivial.", "setup": "domindom", "side": 3.5, "source": "Erich Friedman Packing Center", "source_image": "10.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
+{"case": "domindom@11", "external_image_url": "https://erich-friedman.github.io/packing/domindom/11.gif", "friedman_display_metric_value": 3.801, "id": "friedman-3428de772f6a382f", "metric_expression": "(5+\u221a41)/3 = 3.801+", "metric_formula_parsed": "(5+ sqrt 41)/3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.801041412477616, "metric_value_source": "exact_expression", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "11. | | s = (5+\u221a41)/3 = 3.801+ | Found by Maurizio Morandi in April 2026.", "setup": "domindom", "side": 3.801041412477616, "source": "Erich Friedman Packing Center", "source_image": "11.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Dominoes", "verified": false}
+{"case": "domindom@12", "external_image_url": "https://erich-friedman.github.io/packing/domindom/12.gif", "friedman_display_metric_value": 3.914, "id": "friedman-f23035aabd01a5b7", "metric_expression": "5/2+\u221a2 = 3.914+", "metric_formula_parsed": "5/2+ sqrt 2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.914213562373095, "metric_value_source": "exact_expression", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "12. | | s = 5/2+\u221a2 = 3.914+ | Found by Maurizio Morandi in April 2026.", "setup": "domindom", "side": 3.914213562373095, "source": "Erich Friedman Packing Center", "source_image": "12.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Maurizio Morandi", "title": "Dominoes in Dominoes", "verified": false}
+{"case": "domindom@14", "external_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "friedman_display_metric_value": 4.0, "id": "friedman-b1aa68da6c91ef71", "metric_expression": "4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14.-16 | | s = 4 | Trivial.", "setup": "domindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
+{"case": "domindom@15", "external_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "friedman_display_metric_value": 4.0, "id": "friedman-a6466cde31e289b0", "metric_expression": "4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14.-16 | | s = 4 | Trivial.", "setup": "domindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
+{"case": "domindom@16", "external_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "friedman_display_metric_value": 4.0, "id": "friedman-63618f5cbe16b7ba", "metric_expression": "4", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14.-16 | | s = 4 | Trivial.", "setup": "domindom", "side": 4.0, "source": "Erich Friedman Packing Center", "source_image": "16.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
+{"case": "domindom@17", "external_image_url": "https://erich-friedman.github.io/packing/domindom/18.gif", "friedman_display_metric_value": 4.5, "id": "friedman-88637958ab2f0bd2", "metric_expression": "9/2 = 4.5", "metric_formula_parsed": "9/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.5, "metric_value_source": "exact_expression", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "17.-18 | | s = 9/2 = 4.5 | Trivial.", "setup": "domindom", "side": 4.5, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
+{"case": "domindom@18", "external_image_url": "https://erich-friedman.github.io/packing/domindom/18.gif", "friedman_display_metric_value": 4.5, "id": "friedman-d53361ac7a36e5b8", "metric_expression": "9/2 = 4.5", "metric_formula_parsed": "9/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.5, "metric_value_source": "exact_expression", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "17.-18 | | s = 9/2 = 4.5 | Trivial.", "setup": "domindom", "side": 4.5, "source": "Erich Friedman Packing Center", "source_image": "18.gif", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Dominoes in Dominoes", "verified": false}
+{"case": "triindom@1", "external_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "friedman_display_metric_value": 0.8660254037844386, "id": "friedman-6b448902241352f2", "metric_expression": "\u221a3/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.8660254037844386, "metric_value_source": "reported_decimal", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "setup": "triindom", "side": 0.8660254037844386, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@2", "external_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "friedman_display_metric_value": 0.8660254037844386, "id": "friedman-3631b27632253615", "metric_expression": "\u221a3/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.8660254037844386, "metric_value_source": "reported_decimal", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "setup": "triindom", "side": 0.8660254037844386, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@3", "external_image_url": "https://erich-friedman.github.io/packing/triindom/3.png", "friedman_display_metric_value": 0.96796, "id": "friedman-1455255ba68cde92", "metric_expression": ".96796+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.96796, "metric_value_source": "reported_decimal", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "3. | | s = .96796+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 0.96796, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@4", "external_image_url": "https://erich-friedman.github.io/packing/triindom/4.png", "friedman_display_metric_value": 1.12036, "id": "friedman-0417703b28057480", "metric_expression": "1.12036+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.12036, "metric_value_source": "reported_decimal", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "4. | | s = 1.12036+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.12036, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@5", "external_image_url": "https://erich-friedman.github.io/packing/triindom/5.png", "friedman_display_metric_value": 1.26315, "id": "friedman-debd0a7c19c484e1", "metric_expression": "1.26315+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.26315, "metric_value_source": "reported_decimal", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "5. | | s = 1.26315+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.26315, "source": "Erich Friedman Packing Center", "source_image": "5.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@6", "external_image_url": "https://erich-friedman.github.io/packing/triindom/6.png", "friedman_display_metric_value": 1.37629, "id": "friedman-34403ff3ad786191", "metric_expression": "1.37629+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.37629, "metric_value_source": "reported_decimal", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "6. | | s = 1.37629+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.37629, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@7", "external_image_url": "https://erich-friedman.github.io/packing/triindom/7.png", "friedman_display_metric_value": 1.49076, "id": "friedman-945df93d80c9c3d2", "metric_expression": "1.49076+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.49076, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "7. | | s = 1.49076+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.49076, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@8", "external_image_url": "https://erich-friedman.github.io/packing/triindom/8.png", "friedman_display_metric_value": 1.56293, "id": "friedman-dfa7a589fe07b565", "metric_expression": "1.56293+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.56293, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "8. | | s = 1.56293+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.56293, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@9", "external_image_url": "https://erich-friedman.github.io/packing/triindom/9.png", "friedman_display_metric_value": 1.64908, "id": "friedman-c53aecbe04dfab59", "metric_expression": "1.64908+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.64908, "metric_value_source": "reported_decimal", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "9. | | s = 1.64908+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.64908, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@10", "external_image_url": "https://erich-friedman.github.io/packing/triindom/10.png", "friedman_display_metric_value": 1.68303, "id": "friedman-c9503bfc16e9a2ba", "metric_expression": "1.68303+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.68303, "metric_value_source": "reported_decimal", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "10. | | s = 1.68303+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.68303, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@11", "external_image_url": "https://erich-friedman.github.io/packing/triindom/11.png", "friedman_display_metric_value": 1.73127, "id": "friedman-c915dc3af9332ca3", "metric_expression": "1.73127+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.73127, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "11. | | s = 1.73127+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.73127, "source": "Erich Friedman Packing Center", "source_image": "11.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@12", "external_image_url": "https://erich-friedman.github.io/packing/triindom/12.png", "friedman_display_metric_value": 1.7404, "id": "friedman-eea7c6944997f18c", "metric_expression": "1.74040+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.7404, "metric_value_source": "reported_decimal", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "12. | | s = 1.74040+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.7404, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@13", "external_image_url": "https://erich-friedman.github.io/packing/triindom/13.png", "friedman_display_metric_value": 1.85319, "id": "friedman-d3e1a59ca736eabf", "metric_expression": "1.85319+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.85319, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "13. | | s = 1.85319+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.85319, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@14", "external_image_url": "https://erich-friedman.github.io/packing/triindom/14.png", "friedman_display_metric_value": 1.90192, "id": "friedman-ce118ec85cf41825", "metric_expression": "3(3\u2013\u221a3)/2 = 1.90192+", "metric_formula_parsed": "3(3- sqrt 3)/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.901923788646684, "metric_value_source": "exact_expression", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14. | | s = 3(3\u2013\u221a3)/2 = 1.90192+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.901923788646684, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@15", "external_image_url": "https://erich-friedman.github.io/packing/triindom/15.png", "friedman_display_metric_value": 1.9795, "id": "friedman-08d901dffb40a794", "metric_expression": "1.97950+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.9795, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "15. | | s = 1.97950+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 1.9795, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@16", "external_image_url": "https://erich-friedman.github.io/packing/triindom/16.png", "friedman_display_metric_value": 2.0, "id": "friedman-1f6e1fe57c5f2442", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "16. | | s = 2 | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "16.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@17", "external_image_url": "https://erich-friedman.github.io/packing/triindom/17.png", "friedman_display_metric_value": 2.10306, "id": "friedman-5d31f2162dd84c17", "metric_expression": "2.10306+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.10306, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "17. | | s = 2.10306+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 2.10306, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@18", "external_image_url": "https://erich-friedman.github.io/packing/triindom/18.png", "friedman_display_metric_value": 2.14913, "id": "friedman-02be21094cf7b39a", "metric_expression": "2.14913.+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.14913, "metric_value_source": "reported_decimal", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "18. | | s = 2.14913.+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 2.14913, "source": "Erich Friedman Packing Center", "source_image": "18.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@19", "external_image_url": "https://erich-friedman.github.io/packing/triindom/19.png", "friedman_display_metric_value": 2.24848, "id": "friedman-b2d8895e526d7303", "metric_expression": "2.24848+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.24848, "metric_value_source": "reported_decimal", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "19. | | s = 2.24848+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 2.24848, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "triindom@20", "external_image_url": "https://erich-friedman.github.io/packing/triindom/20.png", "friedman_display_metric_value": 2.2973, "id": "friedman-6398e99b9a2f63fa", "metric_expression": "2.29730+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.2973, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "20. | | s = 2.29730+ | Found by Jonathan Viquerat | in April 2026", "setup": "triindom", "side": 2.2973, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Triangles in Dominoes", "verified": false}
+{"case": "hexindom@1", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/1.png", "friedman_display_metric_value": 1.73205, "id": "friedman-1461f42fd98f7a6a", "metric_expression": "\u221a3 = 1.73205+", "metric_formula_parsed": "sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.7320508075688772, "metric_value_source": "exact_expression", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "1. | | s = \u221a3 = 1.73205+ | Trivial.", "setup": "hexindom", "side": 1.7320508075688772, "source": "Erich Friedman Packing Center", "source_image": "1.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@2", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/2.png", "friedman_display_metric_value": 1.8946, "id": "friedman-7d5e1327de198c15", "metric_expression": "1.8946+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.8946, "metric_value_source": "reported_decimal", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "2. | | s = 1.8946+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 1.8946, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@3", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/3.png", "friedman_display_metric_value": 2.53589, "id": "friedman-d90bd8f82b040166", "metric_expression": "6\u20132\u221a3 = 2.53589+", "metric_formula_parsed": "6-2 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.5358983848622456, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "3. | | s = 6\u20132\u221a3 = 2.53589+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 2.5358983848622456, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@4", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/4.png", "friedman_display_metric_value": 2.94744, "id": "friedman-28ca5ddf4b39fa00", "metric_expression": "22\u201311\u221a3 = 2.94744+", "metric_formula_parsed": "22-11 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.9474411167423495, "metric_value_source": "exact_expression", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "4. | | s = 22\u201311\u221a3 = 2.94744+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 2.9474411167423495, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@5", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/5.png", "friedman_display_metric_value": 3.24871, "id": "friedman-cf482f91d8c8bce5", "metric_expression": "7(2\u221a3\u20133) = 3.24871+", "metric_formula_parsed": "7(2 sqrt 3-3)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.248711305964282, "metric_value_source": "exact_expression", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "5. | | s = 7(2\u221a3\u20133) = 3.24871+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 3.248711305964282, "source": "Erich Friedman Packing Center", "source_image": "5.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@6", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/6.png", "friedman_display_metric_value": 3.41202, "id": "friedman-5aeee784110012c1", "metric_expression": "21(15\u20132\u221a3)/71 = 3.41202+", "metric_formula_parsed": "21(15-2 sqrt 3)/71", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.4120262828465795, "metric_value_source": "exact_expression", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "6. | | s = 21(15\u20132\u221a3)/71 = 3.41202+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 3.4120262828465795, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@7", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/7.png", "friedman_display_metric_value": 3.4873, "id": "friedman-2a9436ef5fcff759", "metric_expression": "3.4873+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.4873, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "7. | | s = 3.4873+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 3.4873, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@8", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/8.png", "friedman_display_metric_value": 3.6906, "id": "friedman-ed40f04ec723e8e5", "metric_expression": "3.6906+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.6906, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "8. | | s = 3.6906+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 3.6906, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@9", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/9.png", "friedman_display_metric_value": 4.06002, "id": "friedman-dea7c54e25c3fa0a", "metric_expression": "(36+5\u221a3)/11 = 4.06002+", "metric_formula_parsed": "(36+5 sqrt 3)/11", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.060023094349489, "metric_value_source": "exact_expression", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "9. | | s = (36+5\u221a3)/11 = 4.06002+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 4.060023094349489, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@10", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/10.png", "friedman_display_metric_value": 4.17691, "id": "friedman-7a8236d7b304056d", "metric_expression": "9(2\u221a3\u20133) = 4.17691+", "metric_formula_parsed": "9(2 sqrt 3-3)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.176914536239791, "metric_value_source": "exact_expression", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "10. | | s = 9(2\u221a3\u20133) = 4.17691+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 4.176914536239791, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@11", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/11.png", "friedman_display_metric_value": 4.5036, "id": "friedman-23dad7daa2ff8934", "metric_expression": "4.5036+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.5036, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "11. | | s = 4.5036+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 4.5036, "source": "Erich Friedman Packing Center", "source_image": "11.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@12", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/12.png", "friedman_display_metric_value": 4.6136, "id": "friedman-5a47dfb6b80a6234", "metric_expression": "41(18\u20135\u221a3)/83 = 4.6136+", "metric_formula_parsed": "41(18-5 sqrt 3)/83", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.613609451185303, "metric_value_source": "exact_expression", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "12. | | s = 41(18\u20135\u221a3)/83 = 4.6136+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 4.613609451185303, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@13", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/13.png", "friedman_display_metric_value": 4.8137, "id": "friedman-bb2ef399bf9176f5", "metric_expression": "4.8137+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.8137, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "13. | | s = 4.8137+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 4.8137, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@14", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/14.png", "friedman_display_metric_value": 4.84994, "id": "friedman-62cc49b91435c7ec", "metric_expression": "25(6\u2013\u221a3)/22 = 4.84994+", "metric_formula_parsed": "25(6- sqrt 3)/22", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.849942264126276, "metric_value_source": "exact_expression", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "14. | | s = 25(6\u2013\u221a3)/22 = 4.84994+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 4.849942264126276, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@15", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/15.png", "friedman_display_metric_value": 4.95163, "id": "friedman-d667d7fb283e5388", "metric_expression": "56(27\u20134\u221a3)/227 = 4.95163+", "metric_formula_parsed": "56(27-4 sqrt 3)/227", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.95163268328005, "metric_value_source": "exact_expression", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "15. | | s = 56(27\u20134\u221a3)/227 = 4.95163+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 4.95163268328005, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@16", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/17.png", "friedman_display_metric_value": 5.19615, "id": "friedman-dca43056adc15966", "metric_expression": "3\u221a3 = 5.19615+", "metric_formula_parsed": "3 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.196152422706632, "metric_value_source": "exact_expression", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "16.-17. | | s = 3\u221a3 = 5.19615+ | Trivial.", "setup": "hexindom", "side": 5.196152422706632, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@17", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/17.png", "friedman_display_metric_value": 5.19615, "id": "friedman-db297820cc5a8688", "metric_expression": "3\u221a3 = 5.19615+", "metric_formula_parsed": "3 sqrt 3", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.196152422706632, "metric_value_source": "exact_expression", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "16.-17. | | s = 3\u221a3 = 5.19615+ | Trivial.", "setup": "hexindom", "side": 5.196152422706632, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Trivial", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@18", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/18.png", "friedman_display_metric_value": 5.40818, "id": "friedman-7800a531b4789b9f", "metric_expression": "31(4\u2013\u221a3)/13 = 5.40818+", "metric_formula_parsed": "31(4- sqrt 3)/13", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.4081865357972925, "metric_value_source": "exact_expression", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "18. | | s = 31(4\u2013\u221a3)/13 = 5.40818+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 5.4081865357972925, "source": "Erich Friedman Packing Center", "source_image": "18.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@19", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/19.png", "friedman_display_metric_value": 5.653, "id": "friedman-b7d670339a43ec6b", "metric_expression": "5.6530+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.653, "metric_value_source": "reported_decimal", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "19. | | s = 5.6530+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 5.653, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "hexindom@20", "external_image_url": "https://erich-friedman.github.io/packing/hexindom/20.png", "friedman_display_metric_value": 5.8012, "id": "friedman-f39e5484db44fdfe", "metric_expression": "5.8012+", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.8012, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "20. | | s = 5.8012+ | Found by Jonathan Viquerat in April 2026.", "setup": "hexindom", "side": 5.8012, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Hexagons in Dominoes", "verified": false}
+{"case": "peninsqu@1", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/1.png", "friedman_display_metric_value": 1.59811, "id": "friedman-7e15ce644e4f9c5a", "metric_expression": "(3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+", "metric_formula_parsed": "(3 sqrt 2+ sqrt 10+2 sqrt (5+ sqrt 5))/8", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.5981133053749155, "metric_value_source": "exact_expression", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+ | Trivial. |", "setup": "peninsqu", "side": 1.5981133053749155, "source": "Erich Friedman Packing Center", "source_image": "1.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@2", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/2.png", "friedman_display_metric_value": 2.46345, "id": "friedman-24eb94771b341380", "metric_expression": "2.46345+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.46345, "metric_value_source": "reported_decimal", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.46345+ | Trivial. |", "setup": "peninsqu", "side": 2.46345, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@3", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/3.png", "friedman_display_metric_value": 2.90812, "id": "friedman-99cdebf50cc70a7b", "metric_expression": "2.90812+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.90812, "metric_value_source": "reported_decimal", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.90812+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 2.90812, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@4", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/4.png", "friedman_display_metric_value": 3.10252, "id": "friedman-3b6b6b416d6a90ab", "metric_expression": "3.10252+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.10252, "metric_value_source": "reported_decimal", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.10252+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 3.10252, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@5", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/5.png", "friedman_display_metric_value": 3.54903, "id": "friedman-b7d5a744e282c95a", "metric_expression": "3.54903+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.54903, "metric_value_source": "reported_decimal", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.54903+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 3.54903, "source": "Erich Friedman Packing Center", "source_image": "5.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@6", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/6.png", "friedman_display_metric_value": 3.883, "id": "friedman-68649f95f43f5c9b", "metric_expression": "3.88300+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.883, "metric_value_source": "reported_decimal", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.88300+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 3.883, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@7", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/7.png", "friedman_display_metric_value": 4.18038, "id": "friedman-cc971af6673d00d8", "metric_expression": "4.18038+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.18038, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.18038+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 4.18038, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@8", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/8.png", "friedman_display_metric_value": 4.38191, "id": "friedman-59e36ba91686eefb", "metric_expression": "4.38191+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.38191, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.38191+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 4.38191, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@9", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/9.png", "friedman_display_metric_value": 4.60033, "id": "friedman-2ce3a5fe408a3dfd", "metric_expression": "4.60033+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.60033, "metric_value_source": "reported_decimal", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.60033+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 4.60033, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@10", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/10.png", "friedman_display_metric_value": 4.90584, "id": "friedman-5182d89ad3c76f97", "metric_expression": "4.90584+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.90584, "metric_value_source": "reported_decimal", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.90584+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 4.90584, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@11", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/11.png", "friedman_display_metric_value": 5.11557, "id": "friedman-81b654bc5e2cbb88", "metric_expression": "5.11557+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.11557, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.11557+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 5.11557, "source": "Erich Friedman Packing Center", "source_image": "11.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@12", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/12.png", "friedman_display_metric_value": 5.2325, "id": "friedman-277b0b7ca884a6e6", "metric_expression": "5.23250+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.2325, "metric_value_source": "reported_decimal", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.23250+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 5.2325, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@13", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/13.png", "friedman_display_metric_value": 5.52183, "id": "friedman-2188f40153726aa1", "metric_expression": "5.52183+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.52183, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.52183+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 5.52183, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@14", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/14.png", "friedman_display_metric_value": 5.69775, "id": "friedman-50a67ef59b0e0b84", "metric_expression": "5.69775+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.69775, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.69775+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 5.69775, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@15", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/15.png", "friedman_display_metric_value": 5.91106, "id": "friedman-cc27ef00c2ecb2cd", "metric_expression": "5.91106+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.91106, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.91106+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 5.91106, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@16", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/16.png", "friedman_display_metric_value": 6.11021, "id": "friedman-bd78c96c0c713b24", "metric_expression": "6.11021+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.11021, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.11021+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 6.11021, "source": "Erich Friedman Packing Center", "source_image": "16.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@17", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/17.png", "friedman_display_metric_value": 6.26466, "id": "friedman-46003f0493f05d4c", "metric_expression": "6.26466+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.26466, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.26466+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 6.26466, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@18", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/18.png", "friedman_display_metric_value": 6.33632, "id": "friedman-ea74d2b6fe45f281", "metric_expression": "6.33632+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.33632, "metric_value_source": "reported_decimal", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.33632+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 6.33632, "source": "Erich Friedman Packing Center", "source_image": "18.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@19", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/19.png", "friedman_display_metric_value": 6.55939, "id": "friedman-315fd8b234cd54b2", "metric_expression": "6.55939+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.55939, "metric_value_source": "reported_decimal", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.55939+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 6.55939, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@20", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/20.png", "friedman_display_metric_value": 6.69588, "id": "friedman-b4ebac20ab7a97c2", "metric_expression": "6.69588+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.69588, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.69588+ | Found by Jonathan Viquerat | in April 2026.", "setup": "peninsqu", "side": 6.69588, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@21", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/21.png", "friedman_display_metric_value": 6.8554, "id": "friedman-471bdfdb778fab95", "metric_expression": "6.85540+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.8554, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 6.85540+ | Found by Emerson Connelly | in April 2026.", "setup": "peninsqu", "side": 6.8554, "source": "Erich Friedman Packing Center", "source_image": "21.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@22", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/22.png", "friedman_display_metric_value": 7.04532, "id": "friedman-d63a5d0588c65ab3", "metric_expression": "7.04532+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.04532, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.04532+ | Found by Teodors Smith | in April 2026.", "setup": "peninsqu", "side": 7.04532, "source": "Erich Friedman Packing Center", "source_image": "22.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Teodors Smith", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@23", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/23.png", "friedman_display_metric_value": 7.20731, "id": "friedman-04176d404ee2c823", "metric_expression": "7.20731+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.20731, "metric_value_source": "reported_decimal", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.20731+ | Found by Emerson Connelly | in April 2026.", "setup": "peninsqu", "side": 7.20731, "source": "Erich Friedman Packing Center", "source_image": "23.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Pentagons in Squares", "verified": false}
+{"case": "peninsqu@24", "external_image_url": "https://erich-friedman.github.io/packing/peninsqu/24.png", "friedman_display_metric_value": 7.33823, "id": "friedman-605e0d56f6df289f", "metric_expression": "7.33823+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.33823, "metric_value_source": "reported_decimal", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 7.33823+ | Found by Emerson Connelly | in April 2026.", "setup": "peninsqu", "side": 7.33823, "source": "Erich Friedman Packing Center", "source_image": "24.png", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "", "submitted_by": "Emerson Connelly", "title": "Pentagons in Squares", "verified": false}
+{"case": "penincir@1", "external_image_url": "https://erich-friedman.github.io/packing/penincir/1.png", "friedman_display_metric_value": 0.86065, "id": "friedman-d406bb60cb04bec8", "metric_expression": "\u221a((5+\u221a5)/10) = .86065+", "metric_formula_parsed": "sqrt ((5+ sqrt 5)/10)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 0.8506508083520399, "metric_value_source": "exact_expression", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a((5+\u221a5)/10) = .86065+ | Trivial.", "setup": "penincir", "side": 0.8506508083520399, "source": "Erich Friedman Packing Center", "source_image": "1.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@2", "external_image_url": "https://erich-friedman.github.io/packing/penincir/2.png", "friedman_display_metric_value": 1.53884, "id": "friedman-c1d311342820e254", "metric_expression": "\u221a(5+2\u221a5)/2 = 1.53884+", "metric_formula_parsed": "sqrt (5+2 sqrt 5)/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.5388417685876268, "metric_value_source": "exact_expression", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a(5+2\u221a5)/2 = 1.53884+ | Trivial.", "setup": "penincir", "side": 1.5388417685876268, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@3", "external_image_url": "https://erich-friedman.github.io/packing/penincir/3.png", "friedman_display_metric_value": 1.61803, "id": "friedman-584001d603a8d226", "metric_expression": "(1+\u221a5)/2 = 1.61803+", "metric_formula_parsed": "(1+ sqrt 5)/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.618033988749895, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = (1+\u221a5)/2 = 1.61803+ | Trivial.", "setup": "penincir", "side": 1.618033988749895, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@4", "external_image_url": "https://erich-friedman.github.io/packing/penincir/4.png", "friedman_display_metric_value": 1.82971, "id": "friedman-afcd1b3f0d4b1f0d", "metric_expression": "1.82971+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.82971, "metric_value_source": "reported_decimal", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 1.82971+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@5", "external_image_url": "https://erich-friedman.github.io/packing/penincir/5.png", "friedman_display_metric_value": 2.03271, "id": "friedman-1ad57916719a9a56", "metric_expression": "2.03271+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.03271, "metric_value_source": "reported_decimal", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.03271+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "5.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@6", "external_image_url": "https://erich-friedman.github.io/packing/penincir/6.png", "friedman_display_metric_value": 2.22703, "id": "friedman-12822fdb89455dab", "metric_expression": "\u221a((25+11\u221a5)/10) = 2.22703+", "metric_formula_parsed": "sqrt ((25+11 sqrt 5)/10)", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.2270327288232137, "metric_value_source": "exact_expression", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a((25+11\u221a5)/10) = 2.22703+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": 2.2270327288232137, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@7", "external_image_url": "https://erich-friedman.github.io/packing/penincir/7.png", "friedman_display_metric_value": 2.29474, "id": "friedman-162c0670b694ad7e", "metric_expression": "2.29474+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.29474, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.29474+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@8", "external_image_url": "https://erich-friedman.github.io/packing/penincir/8.png", "friedman_display_metric_value": 2.48128, "id": "friedman-fe0a52f918bd5917", "metric_expression": "2.48128+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.48128, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.48128+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@9", "external_image_url": "https://erich-friedman.github.io/packing/penincir/9.png", "friedman_display_metric_value": 2.70171, "id": "friedman-437b0288e72edf4b", "metric_expression": "2.70171+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.70171, "metric_value_source": "reported_decimal", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.70171+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@10", "external_image_url": "https://erich-friedman.github.io/packing/penincir/10.png", "friedman_display_metric_value": 2.79768, "id": "friedman-dd5f3170e3194179", "metric_expression": "2.79768+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.79768, "metric_value_source": "reported_decimal", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.79768+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@11", "external_image_url": "https://erich-friedman.github.io/packing/penincir/11.png", "friedman_display_metric_value": 2.9018, "id": "friedman-8f226f7fca76de25", "metric_expression": "2.90180+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.9018, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 2.90180+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "11.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@12", "external_image_url": "https://erich-friedman.github.io/packing/penincir/12.png", "friedman_display_metric_value": 3.01826, "id": "friedman-1cb1d1196a113e11", "metric_expression": "3.01826+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.01826, "metric_value_source": "reported_decimal", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.01826+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@13", "external_image_url": "https://erich-friedman.github.io/packing/penincir/13.png", "friedman_display_metric_value": 3.07769, "id": "friedman-e2b856e3113c6a69", "metric_expression": "\u221a(5+2\u221a5)/2 =3.07769+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.07769, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = \u221a(5+2\u221a5)/2 =3.07769+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@14", "external_image_url": "https://erich-friedman.github.io/packing/penincir/14.png", "friedman_display_metric_value": 3.23385, "id": "friedman-3616fa5406506d9f", "metric_expression": "3.23385+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.23385, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.23385+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@15", "external_image_url": "https://erich-friedman.github.io/packing/penincir/15.png", "friedman_display_metric_value": 3.33911, "id": "friedman-6ea0be20a21123dc", "metric_expression": "3.33911+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.33911, "metric_value_source": "reported_decimal", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.33911+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@16", "external_image_url": "https://erich-friedman.github.io/packing/penincir/16.png", "friedman_display_metric_value": 3.43657, "id": "friedman-3d2f175a3fc14f29", "metric_expression": "3.43657+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.43657, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.43657+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "16.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@17", "external_image_url": "https://erich-friedman.github.io/packing/penincir/17.png", "friedman_display_metric_value": 3.50958, "id": "friedman-b012044b6051ffc2", "metric_expression": "3.50958+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.50958, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.50958+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@18", "external_image_url": "https://erich-friedman.github.io/packing/penincir/18.png", "friedman_display_metric_value": 3.6208, "id": "friedman-dd71777879a485ed", "metric_expression": "3.62080+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.6208, "metric_value_source": "reported_decimal", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.62080+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "18.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@19", "external_image_url": "https://erich-friedman.github.io/packing/penincir/19.png", "friedman_display_metric_value": 3.67287, "id": "friedman-17041aab438560fc", "metric_expression": "3.67287+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.67287, "metric_value_source": "reported_decimal", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.67287+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@20", "external_image_url": "https://erich-friedman.github.io/packing/penincir/20.png", "friedman_display_metric_value": 3.80415, "id": "friedman-12e982d92f646f18", "metric_expression": "3.80415+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.80415, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.80415+ | Found by Jonathan Viquerat | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Circles", "verified": false}
+{"case": "penincir@21", "external_image_url": "https://erich-friedman.github.io/packing/penincir/21.png", "friedman_display_metric_value": 3.90735, "id": "friedman-201ad4373d160900", "metric_expression": "3.90735+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.90735, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "r = 3.90735+ | Found by Cyril Summerfield | in April 2026.", "setup": "penincir", "side": null, "source": "Erich Friedman Packing Center", "source_image": "21.png", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "", "submitted_by": "Cyril Summerfield", "title": "Pentagons in Circles", "verified": false}
+{"case": "peninpen@1", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/1.png", "friedman_display_metric_value": 1.0, "id": "friedman-f9f52c1e8d515658", "metric_expression": "1", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0, "metric_value_source": "reported_decimal", "n": 1, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 1 | Trivial.", "setup": "peninpen", "side": 1.0, "source": "Erich Friedman Packing Center", "source_image": "1.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@2", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/2.png", "friedman_display_metric_value": 2.0, "id": "friedman-a4081ac98088edfc", "metric_expression": "2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "metric_value_source": "reported_decimal", "n": 2, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2 | Trivial.", "setup": "peninpen", "side": 2.0, "source": "Erich Friedman Packing Center", "source_image": "2.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@3", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/3.png", "friedman_display_metric_value": 2.23606, "id": "friedman-5046d857d2856fcc", "metric_expression": "\u221a5 = 2.23606+", "metric_formula_parsed": "sqrt 5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.23606797749979, "metric_value_source": "exact_expression", "n": 3, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = \u221a5 = 2.23606+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 2.23606797749979, "source": "Erich Friedman Packing Center", "source_image": "3.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@4", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/4.png", "friedman_display_metric_value": 2.44719, "id": "friedman-4db0f711f785c6c8", "metric_expression": "2.44719+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.44719, "metric_value_source": "reported_decimal", "n": 4, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2.44719+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 2.44719, "source": "Erich Friedman Packing Center", "source_image": "4.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@5", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/6.png", "friedman_display_metric_value": 2.61803, "id": "friedman-07b4275bce72d2f8", "metric_expression": "(3+\u221a5)/2 = 2.61803+", "metric_formula_parsed": "(3+ sqrt 5)/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.618033988749895, "metric_value_source": "exact_expression", "n": 5, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (3+\u221a5)/2 = 2.61803+ | Trivial.", "setup": "peninpen", "side": 2.618033988749895, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@6", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/6.png", "friedman_display_metric_value": 2.61803, "id": "friedman-05e9eb87f4d4588a", "metric_expression": "(3+\u221a5)/2 = 2.61803+", "metric_formula_parsed": "(3+ sqrt 5)/2", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.618033988749895, "metric_value_source": "exact_expression", "n": 6, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = (3+\u221a5)/2 = 2.61803+ | Trivial.", "setup": "peninpen", "side": 2.618033988749895, "source": "Erich Friedman Packing Center", "source_image": "6.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@7", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/7.png", "friedman_display_metric_value": 3.07866, "id": "friedman-070578b8cff8b55e", "metric_expression": "3.07866+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.07866, "metric_value_source": "reported_decimal", "n": 7, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.07866+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 3.07866, "source": "Erich Friedman Packing Center", "source_image": "7.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@8", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/8.png", "friedman_display_metric_value": 3.33514, "id": "friedman-dcc9fda4fbc43032", "metric_expression": "3.33514+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.33514, "metric_value_source": "reported_decimal", "n": 8, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.33514+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 3.33514, "source": "Erich Friedman Packing Center", "source_image": "8.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@9", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/9.png", "friedman_display_metric_value": 3.44956, "id": "friedman-bcb280dc7cd22f84", "metric_expression": "3.44956+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.44956, "metric_value_source": "reported_decimal", "n": 9, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.44956+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 3.44956, "source": "Erich Friedman Packing Center", "source_image": "9.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@10", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/10.png", "friedman_display_metric_value": 3.68324, "id": "friedman-d80c616dfa0aaa49", "metric_expression": "3.68324+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.68324, "metric_value_source": "reported_decimal", "n": 10, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.68324+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 3.68324, "source": "Erich Friedman Packing Center", "source_image": "10.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@11", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/11.png", "friedman_display_metric_value": 3.79704, "id": "friedman-1282da0f3edc0bd9", "metric_expression": "3.79704+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.79704, "metric_value_source": "reported_decimal", "n": 11, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.79704+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 3.79704, "source": "Erich Friedman Packing Center", "source_image": "11.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@12", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/12.png", "friedman_display_metric_value": 3.96926, "id": "friedman-8b914755a9f1e439", "metric_expression": "3.96926+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.96926, "metric_value_source": "reported_decimal", "n": 12, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 3.96926+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 3.96926, "source": "Erich Friedman Packing Center", "source_image": "12.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@13", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/13.png", "friedman_display_metric_value": 4.06523, "id": "friedman-5e9a9ce0bec89084", "metric_expression": "4.06523+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.06523, "metric_value_source": "reported_decimal", "n": 13, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.06523+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 4.06523, "source": "Erich Friedman Packing Center", "source_image": "13.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@14", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/14.png", "friedman_display_metric_value": 4.2112, "id": "friedman-3afcc3dd8f832d7e", "metric_expression": "4.21120+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.2112, "metric_value_source": "reported_decimal", "n": 14, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.21120+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 4.2112, "source": "Erich Friedman Packing Center", "source_image": "14.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@15", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/15.png", "friedman_display_metric_value": 4.23606, "id": "friedman-939f351e8fd006a2", "metric_expression": "2+\u221a5 = 4.23606+", "metric_formula_parsed": "2+ sqrt 5", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.23606797749979, "metric_value_source": "exact_expression", "n": 15, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 2+\u221a5 = 4.23606+ | Trivial.", "setup": "peninpen", "side": 4.23606797749979, "source": "Erich Friedman Packing Center", "source_image": "15.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Trivial", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@16", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/16.png", "friedman_display_metric_value": 4.41636, "id": "friedman-01bc819429ff8629", "metric_expression": "4.41636+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.41636, "metric_value_source": "reported_decimal", "n": 16, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.41636+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 4.41636, "source": "Erich Friedman Packing Center", "source_image": "16.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@17", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/17.png", "friedman_display_metric_value": 4.65561, "id": "friedman-76f0cb13a9a97cb4", "metric_expression": "4.65561+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.65561, "metric_value_source": "reported_decimal", "n": 17, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.65561+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 4.65561, "source": "Erich Friedman Packing Center", "source_image": "17.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@18", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/18.png", "friedman_display_metric_value": 4.77541, "id": "friedman-4c9b35e62cec039a", "metric_expression": "4.77541+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.77541, "metric_value_source": "reported_decimal", "n": 18, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.77541+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 4.77541, "source": "Erich Friedman Packing Center", "source_image": "18.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@19", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/19.png", "friedman_display_metric_value": 4.95269, "id": "friedman-f86fad763d9b64f5", "metric_expression": "4.95269+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.95269, "metric_value_source": "reported_decimal", "n": 19, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 4.95269+ | Found by Ian Watson in April 2026.", "setup": "peninpen", "side": 4.95269, "source": "Erich Friedman Packing Center", "source_image": "19.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Ian Watson", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@20", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/20.png", "friedman_display_metric_value": 5.04154, "id": "friedman-2f420c79190960f4", "metric_expression": "5.04154+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.04154, "metric_value_source": "reported_decimal", "n": 20, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.04154+ | Found by Jonathan Viquerat in April 2026.", "setup": "peninpen", "side": 5.04154, "source": "Erich Friedman Packing Center", "source_image": "20.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Jonathan Viquerat", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@21", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/21.png", "friedman_display_metric_value": 5.15948, "id": "friedman-8db20f7456e53f2c", "metric_expression": "5.15948+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.15948, "metric_value_source": "reported_decimal", "n": 21, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.15948+ | Found by Ignacio Vallejo in April 2026.", "setup": "peninpen", "side": 5.15948, "source": "Erich Friedman Packing Center", "source_image": "21.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@22", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/22.png", "friedman_display_metric_value": 5.2674, "id": "friedman-26aaee8ebea05fc0", "metric_expression": "5.26740+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.2674, "metric_value_source": "reported_decimal", "n": 22, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.26740+ | Found by Ignacio Vallejo in April 2026.", "setup": "peninpen", "side": 5.2674, "source": "Erich Friedman Packing Center", "source_image": "22.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@23", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/23.png", "friedman_display_metric_value": 5.34794, "id": "friedman-cdba463397eebb91", "metric_expression": "5.34794+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.34794, "metric_value_source": "reported_decimal", "n": 23, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.34794+ | Found by Ignacio Vallejo in April 2026.", "setup": "peninpen", "side": 5.34794, "source": "Erich Friedman Packing Center", "source_image": "23.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@24", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/24.png", "friedman_display_metric_value": 5.49241, "id": "friedman-7f618eb1ea83663a", "metric_expression": "5.49241+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.49241, "metric_value_source": "reported_decimal", "n": 24, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.49241+ | Found by Ignacio Vallejo in April 2026.", "setup": "peninpen", "side": 5.49241, "source": "Erich Friedman Packing Center", "source_image": "24.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Pentagons in Pentagons", "verified": false}
+{"case": "peninpen@25", "external_image_url": "https://erich-friedman.github.io/packing/peninpen/25.png", "friedman_display_metric_value": 5.5837, "id": "friedman-811ff41caea519c7", "metric_expression": "5.58370+", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.5837, "metric_value_source": "reported_decimal", "n": 25, "notes": "Scraped from displayed Friedman Packing Center reference page; not coordinate-verified.", "record_type": "reference", "reference_text": "s = 5.58370+ | Found by Ignacio Vallejo in April 2026.", "setup": "peninpen", "side": 5.5837, "source": "Erich Friedman Packing Center", "source_image": "25.png", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "", "submitted_by": "Ignacio Vallejo", "title": "Pentagons in Pentagons", "verified": false}
diff --git a/data/records.jsonl b/data/records.jsonl
index 14b1fd5a009884b174cb7b355ea4d949eaa28b82..42b4161df83396de65a3a039fbb41aa3ecbf3ffe 100644
--- a/data/records.jsonl
+++ b/data/records.jsonl
@@ -1,842 +1,866 @@
-{"case": "cirincir@1", "density": 0.9999989965161072, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc1.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "1", "friedman_metric_symbol": "r", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "r", "metric_value": 1.0, "reference_text": "r = 1 | Trivial.", "source_image": "ccc1.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc1.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 1 | Trivial.", "friedman_source_image": "ccc1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "d8dddd0385fd067c", "improvement": -5.017423239106478e-07, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1979053238242443e-07, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00000", "metric_symbol": "r", "metric_value": 1.000000501742324, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.0, "setup": "cirincir", "side": 2.000001003484648, "solution_path": "data/solutions/generated/cirincir_001_d8dddd0385fd067c.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d8dddd0385fd067c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@2", "density": 0.4999800974887553, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc2.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "2", "friedman_metric_symbol": "r", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "r", "metric_value": 2.0, "reference_text": "r = 2 | Trivial.", "source_image": "ccc2.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc2.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 2 | Trivial.", "friedman_source_image": "ccc2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "ab9a33067266df01", "improvement": -3.9806210858639446e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.204627911923552e-06, "max_pair_overlap_depth": -5.010172176866945e-05, "metric_expression": "2.00004", "metric_symbol": "r", "metric_value": 2.0000398062108586, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "cirincir", "side": 4.000079612421717, "solution_path": "data/solutions/generated/cirincir_002_ab9a33067266df01.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/ab9a33067266df01.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@3", "density": 0.646133359064875, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc3.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "1 + 2 / \u221a3 = 2.154+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.154, "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1 + 2 / \u221a3 = 2.154+", "metric_symbol": "r", "metric_value": 2.154, "reference_text": "r = 1 + 2 / \u221a3 = 2.154+ | Trivial.", "source_image": "ccc3.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc3.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 1 + 2 / \u221a3 = 2.154+ | Trivial.", "friedman_source_image": "ccc3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "fe973ff9a23dc34c", "improvement": -0.000763178385080554, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.918381111833185e-06, "max_pair_overlap_depth": -9.100356622360195e-05, "metric_expression": "2.15476", "metric_symbol": "r", "metric_value": 2.1547631783850805, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.154, "setup": "cirincir", "side": 4.309526356770161, "solution_path": "data/solutions/generated/cirincir_003_fe973ff9a23dc34c.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/fe973ff9a23dc34c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@4", "density": 0.6862704996379871, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc4.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "1 + \u221a2 = 2.414+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.414, "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@4", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1 + \u221a2 = 2.414+", "metric_symbol": "r", "metric_value": 2.414, "reference_text": "r = 1 + \u221a2 = 2.414+ | Trivial.", "source_image": "ccc4.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc4.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 1 + \u221a2 = 2.414+ | Trivial.", "friedman_source_image": "ccc4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "9d3e9e7ea6ba298b", "improvement": -0.00025050219633326876, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.985176337373275e-06, "max_pair_overlap_depth": -4.660490859054178e-05, "metric_expression": "2.41425", "metric_symbol": "r", "metric_value": 2.4142505021963334, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.414, "setup": "cirincir", "side": 4.828501004392667, "solution_path": "data/solutions/generated/cirincir_004_9d3e9e7ea6ba298b.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/9d3e9e7ea6ba298b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@5", "density": 0.6851849889863537, "friedman_analytical_or_proved": true, "friedman_credit": "Graham", "friedman_date": "1968", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc5.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "2.701+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.701, "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@5", "credit": "Graham", "date": "1968", "family_updated": "", "metric_expression": "2.701+", "metric_symbol": "r", "metric_value": 2.701, "reference_text": "r = 2.701+ | Proved by Graham in 1968.", "source_image": "ccc5.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc5.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 2.701+ | Proved by Graham in 1968.", "friedman_source_image": "ccc5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "9c2ab1f687c06eec", "improvement": -0.0003514001027240532, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.911145805306603e-06, "max_pair_overlap_depth": -4.497481208476373e-05, "metric_expression": "2.70135", "metric_symbol": "r", "metric_value": 2.701351400102724, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.701, "setup": "cirincir", "side": 5.402702800205448, "solution_path": "data/solutions/generated/cirincir_005_9c2ab1f687c06eec.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Graham", "svg_path": "data/svg/9c2ab1f687c06eec.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@6", "density": 0.6666416612940322, "friedman_analytical_or_proved": true, "friedman_credit": "Graham", "friedman_date": "1968", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc6.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "3", "friedman_metric_symbol": "r", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@6", "credit": "Graham", "date": "1968", "family_updated": "", "metric_expression": "3", "metric_symbol": "r", "metric_value": 3.0, "reference_text": "r = 3 | Proved by Graham in 1968.", "source_image": "ccc6.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc6.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 3 | Proved by Graham in 1968.", "friedman_source_image": "ccc6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "5d3d5beee3c5f33c", "improvement": -5.626367118827247e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.011848064282674e-06, "max_pair_overlap_depth": -4.5345095143201064e-05, "metric_expression": "3.00006", "metric_symbol": "r", "metric_value": 3.0000562636711883, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.0, "setup": "cirincir", "side": 6.0001125273423765, "solution_path": "data/solutions/generated/cirincir_006_5d3d5beee3c5f33c.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Graham", "svg_path": "data/svg/5d3d5beee3c5f33c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@7", "density": 0.77774147574625, "friedman_analytical_or_proved": true, "friedman_credit": "Graham", "friedman_date": "1968", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc7.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "3", "friedman_metric_symbol": "r", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@7", "credit": "Graham", "date": "1968", "family_updated": "", "metric_expression": "3", "metric_symbol": "r", "metric_value": 3.0, "reference_text": "r = 3 | Proved by Graham in 1968.", "source_image": "ccc7.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc7.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 3 | Proved by Graham in 1968.", "friedman_source_image": "ccc7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "2b1985e4094e6893", "improvement": -7.001351167312819e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.2947164267690425e-06, "max_pair_overlap_depth": -6.231680049051391e-05, "metric_expression": "3.00007", "metric_symbol": "r", "metric_value": 3.000070013511673, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.0, "setup": "cirincir", "side": 6.000140027023346, "solution_path": "data/solutions/generated/cirincir_007_2b1985e4094e6893.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Graham", "svg_path": "data/svg/2b1985e4094e6893.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@8", "density": 0.7324681263291527, "friedman_analytical_or_proved": true, "friedman_credit": "Braaksma", "friedman_date": "1963", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc8.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "3.304+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.304, "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@8", "credit": "Braaksma", "date": "1963", "family_updated": "", "metric_expression": "3.304+", "metric_symbol": "r", "metric_value": 3.304, "reference_text": "r = 3.304+ | Proved by Braaksma in 1963.", "source_image": "ccc8.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc8.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 3.304+ | Proved by Braaksma in 1963.", "friedman_source_image": "ccc8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "0193661647fd3854", "improvement": -0.0008414425517750956, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.96872891495326e-06, "max_pair_overlap_depth": -4.3191348294779885e-05, "metric_expression": "3.30484", "metric_symbol": "r", "metric_value": 3.304841442551775, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.304, "setup": "cirincir", "side": 6.60968288510355, "solution_path": "data/solutions/generated/cirincir_008_0193661647fd3854.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Braaksma", "svg_path": "data/svg/0193661647fd3854.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@9", "density": 0.6893878045655164, "friedman_analytical_or_proved": true, "friedman_credit": "Pirl", "friedman_date": "1969", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc9.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "3.613+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.613, "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@9", "credit": "Pirl", "date": "1969", "family_updated": "", "metric_expression": "3.613+", "metric_symbol": "r", "metric_value": 3.613, "reference_text": "r = 3.613+ | Proved by Pirl in 1969.", "source_image": "ccc9.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc9.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 3.613+ | Proved by Pirl in 1969.", "friedman_source_image": "ccc9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "b51df67181f6833b", "improvement": -0.00017882622267562098, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.656082665643879e-06, "max_pair_overlap_depth": -2.396342999144707e-05, "metric_expression": "3.61318", "metric_symbol": "r", "metric_value": 3.6131788262226756, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.613, "setup": "cirincir", "side": 7.226357652445351, "solution_path": "data/solutions/generated/cirincir_009_b51df67181f6833b.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Pirl", "svg_path": "data/svg/b51df67181f6833b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@10", "density": 0.6877649990272218, "friedman_analytical_or_proved": true, "friedman_credit": "Pirl", "friedman_date": "1969", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc10.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "3.813+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.813, "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@10", "credit": "Pirl", "date": "1969", "family_updated": "", "metric_expression": "3.813+", "metric_symbol": "r", "metric_value": 3.813, "reference_text": "r = 3.813+ | Proved by Pirl in 1969.", "source_image": "ccc10.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc10.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 3.813+ | Proved by Pirl in 1969.", "friedman_source_image": "ccc10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "be14c55679a54b28", "improvement": -0.00011553912424266954, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.081326946625552e-06, "max_pair_overlap_depth": -3.967607896537828e-05, "metric_expression": "3.81312", "metric_symbol": "r", "metric_value": 3.813115539124243, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.813, "setup": "cirincir", "side": 7.626231078248486, "solution_path": "data/solutions/generated/cirincir_10_be14c55679a54b28.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Pirl", "svg_path": "data/svg/be14c55679a54b28.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@11", "density": 0.714418364520267, "friedman_analytical_or_proved": true, "friedman_credit": "Melissen", "friedman_date": "1994", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc11.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "3.923+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.923, "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@11", "credit": "Melissen", "date": "1994", "family_updated": "", "metric_expression": "3.923+", "metric_symbol": "r", "metric_value": 3.923, "reference_text": "r = 3.923+ | Proved by Melissen in 1994.", "source_image": "ccc11.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc11.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 3.923+ | Proved by Melissen in 1994.", "friedman_source_image": "ccc11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "e624f391927921fb", "improvement": -0.0009190348380849755, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.92009600810772e-06, "max_pair_overlap_depth": -4.346382940223492e-05, "metric_expression": "3.92392", "metric_symbol": "r", "metric_value": 3.923919034838085, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.923, "setup": "cirincir", "side": 7.84783806967617, "solution_path": "data/solutions/generated/cirincir_011_e624f391927921fb.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Melissen", "svg_path": "data/svg/e624f391927921fb.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@12", "density": 0.7389828254275508, "friedman_analytical_or_proved": false, "friedman_credit": "Kravitz", "friedman_date": "1967", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc12.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "4.029+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.029, "friedman_reference": {"analytical_or_proved": false, "case": "cirincir@12", "credit": "Kravitz", "date": "1967", "family_updated": "", "metric_expression": "4.029+", "metric_symbol": "r", "metric_value": 4.029, "reference_text": "r = 4.029+ | Found by Kravitz in 1967.", "source_image": "ccc12.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc12.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 4.029+ | Found by Kravitz in 1967.", "friedman_source_image": "ccc12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "0d7fc8a14b1c4e0e", "improvement": -0.0007068210362959348, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.338373973515445e-06, "max_pair_overlap_depth": -5.019209633871924e-05, "metric_expression": "4.02971", "metric_symbol": "r", "metric_value": 4.029706821036296, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.029, "setup": "cirincir", "side": 8.059413642072592, "solution_path": "data/solutions/generated/cirincir_012_0d7fc8a14b1c4e0e.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Kravitz", "svg_path": "data/svg/0d7fc8a14b1c4e0e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@13", "density": 0.7244255598642273, "friedman_analytical_or_proved": true, "friedman_credit": "F. Fodor", "friedman_date": "2003", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc13.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "2 + \u221a5 = 4.236+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.236, "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@13", "credit": "F. Fodor", "date": "2003", "family_updated": "", "metric_expression": "2 + \u221a5 = 4.236+", "metric_symbol": "r", "metric_value": 4.236, "reference_text": "r = 2 + \u221a5 = 4.236+ | Proved by F. Fodor in 2003.", "source_image": "ccc13.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc13.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 2 + \u221a5 = 4.236+ | Proved by F. Fodor in 2003.", "friedman_source_image": "ccc13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "a118f33872e0cb30", "improvement": -0.00018378579659206196, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.324667153277062e-06, "max_pair_overlap_depth": -4.7467215169572086e-05, "metric_expression": "4.23618", "metric_symbol": "r", "metric_value": 4.236183785796592, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.236, "setup": "cirincir", "side": 8.472367571593184, "solution_path": "data/solutions/generated/cirincir_013_a118f33872e0cb30.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "F. Fodor", "svg_path": "data/svg/a118f33872e0cb30.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@14", "density": 0.7472109217319929, "friedman_analytical_or_proved": false, "friedman_credit": "Goldberg", "friedman_date": "1971", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc14.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "4.328+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.328, "friedman_reference": {"analytical_or_proved": false, "case": "cirincir@14", "credit": "Goldberg", "date": "1971", "family_updated": "", "metric_expression": "4.328+", "metric_symbol": "r", "metric_value": 4.328, "reference_text": "r = 4.328+ | Found by Goldberg in 1971.", "source_image": "ccc14.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc14.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 4.328+ | Found by Goldberg in 1971.", "friedman_source_image": "ccc14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "b2ec44e582e5ab93", "improvement": -0.000549738133919675, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.732062089120916e-06, "max_pair_overlap_depth": -4.9839299053555663e-05, "metric_expression": "4.32855", "metric_symbol": "r", "metric_value": 4.32854973813392, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.328, "setup": "cirincir", "side": 8.65709947626784, "solution_path": "data/solutions/generated/cirincir_014_b2ec44e582e5ab93.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Goldberg", "svg_path": "data/svg/b2ec44e582e5ab93.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@15", "density": 0.7334069336541974, "friedman_analytical_or_proved": false, "friedman_credit": "Kravitz", "friedman_date": "1967", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc15.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "4.521+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.521, "friedman_reference": {"analytical_or_proved": false, "case": "cirincir@15", "credit": "Kravitz", "date": "1967", "family_updated": "", "metric_expression": "4.521+", "metric_symbol": "r", "metric_value": 4.521, "reference_text": "r = 4.521+ | Found by Kravitz in 1967.", "source_image": "ccc15.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc15.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 4.521+ | Found by Kravitz in 1967.", "friedman_source_image": "ccc15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "eeff7b918e6d6618", "improvement": -0.00144322894722837, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.2291583220711573e-06, "max_pair_overlap_depth": -2.9276985216153406e-05, "metric_expression": "4.52244", "metric_symbol": "r", "metric_value": 4.522443228947228, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.521, "setup": "cirincir", "side": 9.044886457894457, "solution_path": "data/solutions/generated/cirincir_015_eeff7b918e6d6618.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Kravitz", "svg_path": "data/svg/eeff7b918e6d6618.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@16", "density": 0.7510554296860762, "friedman_analytical_or_proved": false, "friedman_credit": "Goldberg", "friedman_date": "1971", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc16.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "4.615+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.615, "friedman_reference": {"analytical_or_proved": false, "case": "cirincir@16", "credit": "Goldberg", "date": "1971", "family_updated": "", "metric_expression": "4.615+", "metric_symbol": "r", "metric_value": 4.615, "reference_text": "r = 4.615+ | Found by Goldberg in 1971.", "source_image": "ccc16.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc16.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 4.615+ | Found by Goldberg in 1971.", "friedman_source_image": "ccc16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "7824261a02b5ed90", "improvement": -0.0005556989154120728, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.219226596077988e-06, "max_pair_overlap_depth": -4.8324434488655754e-05, "metric_expression": "4.61556", "metric_symbol": "r", "metric_value": 4.615555698915412, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.615, "setup": "cirincir", "side": 9.231111397830825, "solution_path": "data/solutions/generated/cirincir_016_7824261a02b5ed90.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Goldberg", "svg_path": "data/svg/7824261a02b5ed90.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@17", "density": 0.7402604737017356, "friedman_analytical_or_proved": false, "friedman_credit": "Reis", "friedman_date": "1975", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc17.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "4.792+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.792, "friedman_reference": {"analytical_or_proved": false, "case": "cirincir@17", "credit": "Reis", "date": "1975", "family_updated": "", "metric_expression": "4.792+", "metric_symbol": "r", "metric_value": 4.792, "reference_text": "r = 4.792+ | Found by Reis in 1975.", "source_image": "ccc17.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc17.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 4.792+ | Found by Reis in 1975.", "friedman_source_image": "ccc17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "68c41c427924b99a", "improvement": -0.00016960544150546042, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.357123401303568e-06, "max_pair_overlap_depth": -5.05938755308577e-05, "metric_expression": "4.79217", "metric_symbol": "r", "metric_value": 4.792169605441505, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.792, "setup": "cirincir", "side": 9.58433921088301, "solution_path": "data/solutions/generated/cirincir_017_68c41c427924b99a.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Reis", "svg_path": "data/svg/68c41c427924b99a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@18", "density": 0.7608872603215449, "friedman_analytical_or_proved": true, "friedman_credit": "Kravitz", "friedman_date": "1967", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc18.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "1 + \u221a2 + \u221a6 = 4.863+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.863, "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@18", "credit": "Kravitz", "date": "1967", "family_updated": "", "metric_expression": "1 + \u221a2 + \u221a6 = 4.863+", "metric_symbol": "r", "metric_value": 4.863, "reference_text": "r = 1 + \u221a2 + \u221a6 = 4.863+ | Found by Kravitz in 1967.", "source_image": "ccc18.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc18.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 1 + \u221a2 + \u221a6 = 4.863+ | Found by Kravitz in 1967.", "friedman_source_image": "ccc18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "6acc78721c0b4ca1", "improvement": -0.000804343250861983, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.509170524220508e-07, "max_pair_overlap_depth": -3.6364882113559815e-05, "metric_expression": "4.86380", "metric_symbol": "r", "metric_value": 4.863804343250862, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.863, "setup": "cirincir", "side": 9.727608686501725, "solution_path": "data/solutions/generated/cirincir_018_6acc78721c0b4ca1.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Kravitz", "svg_path": "data/svg/6acc78721c0b4ca1.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@19", "density": 0.8031578398507155, "friedman_analytical_or_proved": true, "friedman_credit": "F. Fodor", "friedman_date": "1999", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc19.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "1 + \u221a2 + \u221a6 = 4.863+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.863, "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@19", "credit": "F. Fodor", "date": "1999", "family_updated": "", "metric_expression": "1 + \u221a2 + \u221a6 = 4.863+", "metric_symbol": "r", "metric_value": 4.863, "reference_text": "r = 1 + \u221a2 + \u221a6 = 4.863+ | Proved by F. Fodor in 1999.", "source_image": "ccc19.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc19.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 1 + \u221a2 + \u221a6 = 4.863+ | Proved by F. Fodor in 1999.", "friedman_source_image": "ccc19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "8325b5bff319f74f", "improvement": -0.0008071741580044645, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.170379222960378e-06, "max_pair_overlap_depth": -3.89864445309307e-05, "metric_expression": "4.86381", "metric_symbol": "r", "metric_value": 4.863807174158005, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.863, "setup": "cirincir", "side": 9.72761434831601, "solution_path": "data/solutions/generated/cirincir_019_8325b5bff319f74f.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "F. Fodor", "svg_path": "data/svg/8325b5bff319f74f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirincir@20", "density": 0.7622179661920169, "friedman_analytical_or_proved": false, "friedman_credit": "Goldberg", "friedman_date": "1971", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc20.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "5.122+", "friedman_metric_symbol": "r", "friedman_metric_value": 5.122, "friedman_reference": {"analytical_or_proved": false, "case": "cirincir@20", "credit": "Goldberg", "date": "1971", "family_updated": "", "metric_expression": "5.122+", "metric_symbol": "r", "metric_value": 5.122, "reference_text": "r = 5.122+ | Found by Goldberg in 1971.", "source_image": "ccc20.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc20.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 5.122+ | Found by Goldberg in 1971.", "friedman_source_image": "ccc20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "f0718319f5a05220", "improvement": -0.0004226268079490225, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.474954062416714e-06, "max_pair_overlap_depth": -3.4642111702343215e-05, "metric_expression": "5.12242", "metric_symbol": "r", "metric_value": 5.122422626807949, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.122, "setup": "cirincir", "side": 10.244845253615898, "solution_path": "data/solutions/generated/cirincir_020_f0718319f5a05220.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Goldberg", "svg_path": "data/svg/f0718319f5a05220.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@1", "density": 0.9068802327278791, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc1.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "2/\u221a3 = 1.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.154, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2/\u221a3 = 1.154+", "metric_symbol": "s", "metric_value": 1.154, "reference_text": "s = 2/\u221a3 = 1.154+ | Trivial.", "source_image": "hc1.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc1.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 2/\u221a3 = 1.154+ | Trivial.", "friedman_source_image": "hc1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "37d86bed2252b572", "improvement": -0.0007129204441553849, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.894559686663413e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.15471", "metric_symbol": "s", "metric_value": 1.1547129204441553, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.154, "setup": "cirinhex", "side": 1.1547129204441553, "solution_path": "data/solutions/generated/cirinhex_001_37d86bed2252b572.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/37d86bed2252b572.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@2", "density": 0.5208916187605724, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc2.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "1 + 2/\u221a3 = 2.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.154, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1 + 2/\u221a3 = 2.154+", "metric_symbol": "s", "metric_value": 2.154, "reference_text": "s = 1 + 2/\u221a3 = 2.154+ | Trivial.", "source_image": "hc2.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc2.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 1 + 2/\u221a3 = 2.154+ | Trivial.", "friedman_source_image": "hc2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "4ba45a45587fd527", "improvement": -0.0007173376388385222, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.535667492477913e-06, "max_pair_overlap_depth": -1.2900139699567603e-05, "metric_expression": "2.15472", "metric_symbol": "s", "metric_value": 2.1547173376388384, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.154, "setup": "cirinhex", "side": 2.1547173376388384, "solution_path": "data/solutions/generated/cirinhex_002_4ba45a45587fd527.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4ba45a45587fd527.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@3", "density": 0.6801656739683151, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc3.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "4/\u221a3 = 2.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.309, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4/\u221a3 = 2.309+", "metric_symbol": "s", "metric_value": 2.309, "reference_text": "s = 4/\u221a3 = 2.309+ | Trivial.", "source_image": "hc3.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc3.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 4/\u221a3 = 2.309+ | Trivial.", "friedman_source_image": "hc3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "fa4a26f729d80904", "improvement": -0.00041650453514563424, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3364075199806535e-06, "max_pair_overlap_depth": -1.818559246702378e-05, "metric_expression": "2.30942", "metric_symbol": "s", "metric_value": 2.309416504535146, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.309, "setup": "cirinhex", "side": 2.309416504535146, "solution_path": "data/solutions/generated/cirinhex_003_fa4a26f729d80904.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/fa4a26f729d80904.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@4", "density": 0.6802066538449848, "friedman_analytical_or_proved": true, "friedman_credit": "Shahriar Manzoor", "friedman_date": "April 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc4.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "2/\u221a3 + 4/\u221a7 = 2.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.666, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@4", "credit": "Shahriar Manzoor", "date": "April 2002", "family_updated": "", "metric_expression": "2/\u221a3 + 4/\u221a7 = 2.666+", "metric_symbol": "s", "metric_value": 2.666, "reference_text": "s = 2/\u221a3 + 4/\u221a7 = 2.666+ | Found by Shahriar Manzoor | in April 2002.", "source_image": "hc4.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc4.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 2/\u221a3 + 4/\u221a7 = 2.666+ | Found by Shahriar Manzoor | in April 2002.", "friedman_source_image": "hc4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "4ea68db180a8d4c4", "improvement": -0.0006041510947536466, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3940250920849735e-07, "max_pair_overlap_depth": -4.6158989302380604e-05, "metric_expression": "2.66660", "metric_symbol": "s", "metric_value": 2.6666041510947536, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.666, "setup": "cirinhex", "side": 2.6666041510947536, "solution_path": "data/solutions/generated/cirinhex_004_4ea68db180a8d4c4.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Shahriar Manzoor", "svg_path": "data/svg/4ea68db180a8d4c4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@5", "density": 0.672041103262025, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1999", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc5.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "2.999+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.999, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@5", "credit": "Erich Friedman", "date": "1999", "family_updated": "", "metric_expression": "2.999+", "metric_symbol": "s", "metric_value": 2.999, "reference_text": "s = 2.999+ | Found by Erich Friedman | in 1999.", "source_image": "hc5.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc5.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 2.999+ | Found by Erich Friedman | in 1999.", "friedman_source_image": "hc5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "eb88c54ef20a6355", "improvement": -0.00041167259487728813, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6369105032841844e-07, "max_pair_overlap_depth": -3.862655436481788e-05, "metric_expression": "2.99941", "metric_symbol": "s", "metric_value": 2.9994116725948774, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.999, "setup": "cirinhex", "side": 2.9994116725948774, "solution_path": "data/solutions/generated/cirinhex_005_eb88c54ef20a6355.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/eb88c54ef20a6355.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@6", "density": 0.7289750468062609, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc6.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "2 + 2/\u221a3 = 3.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.154, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@6", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2 + 2/\u221a3 = 3.154+", "metric_symbol": "s", "metric_value": 3.154, "reference_text": "s = 2 + 2/\u221a3 = 3.154+ | Trivial. |", "source_image": "hc6.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc6.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 2 + 2/\u221a3 = 3.154+ | Trivial. |", "friedman_source_image": "hc6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "9b7724fab73c49c1", "improvement": -0.0007742481949115643, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.7088474341983044e-06, "max_pair_overlap_depth": -4.5158069021944414e-05, "metric_expression": "3.15477", "metric_symbol": "s", "metric_value": 3.1547742481949115, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.154, "setup": "cirinhex", "side": 3.1547742481949115, "solution_path": "data/solutions/generated/cirinhex_006_9b7724fab73c49c1.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/9b7724fab73c49c1.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@7", "density": 0.8504825176668179, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc7.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "2 + 2/\u221a3 = 3.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.154, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@7", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2 + 2/\u221a3 = 3.154+", "metric_symbol": "s", "metric_value": 3.154, "reference_text": "s = 2 + 2/\u221a3 = 3.154+ | Trivial. |", "source_image": "hc7.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc7.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 2 + 2/\u221a3 = 3.154+ | Trivial. |", "friedman_source_image": "hc7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "7368090471750227", "improvement": -0.0007526785063349806, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.857578518338343e-06, "max_pair_overlap_depth": -3.893260533160969e-05, "metric_expression": "3.15475", "metric_symbol": "s", "metric_value": 3.154752678506335, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.154, "setup": "cirinhex", "side": 3.154752678506335, "solution_path": "data/solutions/generated/cirinhex_007_7368090471750227.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/7368090471750227.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@8", "density": 0.7030218969047355, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc8.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "3.709+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.709, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@8", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "3.709+", "metric_symbol": "s", "metric_value": 3.709, "reference_text": "s = 3.709+ | Found by David W. Cantrell | in July 2002.", "source_image": "hc8.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc8.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 3.709+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "hc8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "afebd04e4720460b", "improvement": -0.0004503331818734857, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.1028444985304873e-08, "max_pair_overlap_depth": -2.2199913737530608e-05, "metric_expression": "3.70945", "metric_symbol": "s", "metric_value": 3.7094503331818736, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.709, "setup": "cirinhex", "side": 3.7094503331818736, "solution_path": "data/solutions/generated/cirinhex_008_afebd04e4720460b.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/afebd04e4720460b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@9", "density": 0.6761453195206264, "friedman_analytical_or_proved": true, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc9.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "20/7 + 2/\u221a3 = 4.011+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.011, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@9", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "20/7 + 2/\u221a3 = 4.011+", "metric_symbol": "s", "metric_value": 4.011, "reference_text": "s = 20/7 + 2/\u221a3 = 4.011+ | Found by David W. Cantrell | in July 2002.", "source_image": "hc9.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc9.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 20/7 + 2/\u221a3 = 4.011+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "hc9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "64b59a5605599f8e", "improvement": -0.0009011593404411045, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.491846259144452e-06, "max_pair_overlap_depth": -2.6999063512000987e-05, "metric_expression": "4.01190", "metric_symbol": "s", "metric_value": 4.011901159340441, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.011, "setup": "cirinhex", "side": 4.011901159340441, "solution_path": "data/solutions/generated/cirinhex_009_64b59a5605599f8e.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/64b59a5605599f8e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@10", "density": 0.7125686135385136, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc10.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "4.119+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.119, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@10", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "4.119+", "metric_symbol": "s", "metric_value": 4.119, "reference_text": "s = 4.119+ | Found by David W. Cantrell | in July 2002.", "source_image": "hc10.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc10.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 4.119+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "hc10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "cd79fdfeb9e3f24b", "improvement": -0.00041597258721015606, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.240617525155585e-06, "max_pair_overlap_depth": -1.610926851469685e-05, "metric_expression": "4.11942", "metric_symbol": "s", "metric_value": 4.11941597258721, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.119, "setup": "cirinhex", "side": 4.11941597258721, "solution_path": "data/solutions/generated/cirinhex_010_cd79fdfeb9e3f24b.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/cd79fdfeb9e3f24b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@11", "density": 0.7162109607848701, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1999", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc11.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "2 + 4/\u221a3 = 4.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.309, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@11", "credit": "Erich Friedman", "date": "1999", "family_updated": "", "metric_expression": "2 + 4/\u221a3 = 4.309+", "metric_symbol": "s", "metric_value": 4.309, "reference_text": "s = 2 + 4/\u221a3 = 4.309+ | Found by Erich Friedman | in 1999.", "source_image": "hc11.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc11.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 2 + 4/\u221a3 = 4.309+ | Found by Erich Friedman | in 1999.", "friedman_source_image": "hc11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "cda2ccbbf4de67aa", "improvement": -0.00047984763128994246, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.3670191174924895e-06, "max_pair_overlap_depth": -2.2677850788799248e-05, "metric_expression": "4.30948", "metric_symbol": "s", "metric_value": 4.30947984763129, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.309, "setup": "cirinhex", "side": 4.30947984763129, "solution_path": "data/solutions/generated/cirinhex_011_cda2ccbbf4de67aa.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/cda2ccbbf4de67aa.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@12", "density": 0.7813203208949625, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1999", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc12.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "2 + 4/\u221a3 = 4.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.309, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@12", "credit": "Erich Friedman", "date": "1999", "family_updated": "", "metric_expression": "2 + 4/\u221a3 = 4.309+", "metric_symbol": "s", "metric_value": 4.309, "reference_text": "s = 2 + 4/\u221a3 = 4.309+ | Found by Erich Friedman | in 1999.", "source_image": "hc12.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc12.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 2 + 4/\u221a3 = 4.309+ | Found by Erich Friedman | in 1999.", "friedman_source_image": "hc12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "c3d795864cfeb74c", "improvement": -0.0004818532104344797, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.009897945360223e-06, "max_pair_overlap_depth": -3.7913329796079864e-05, "metric_expression": "4.30948", "metric_symbol": "s", "metric_value": 4.309481853210435, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.309, "setup": "cirinhex", "side": 4.309481853210435, "solution_path": "data/solutions/generated/cirinhex_012_c3d795864cfeb74c.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/c3d795864cfeb74c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@13", "density": 0.7368031353920613, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1999", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc13.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "8/\u221a3 = 4.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.618, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@13", "credit": "Erich Friedman", "date": "1999", "family_updated": "", "metric_expression": "8/\u221a3 = 4.618+", "metric_symbol": "s", "metric_value": 4.618, "reference_text": "s = 8/\u221a3 = 4.618+ | Found by Erich Friedman | in 1999.", "source_image": "hc13.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc13.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 8/\u221a3 = 4.618+ | Found by Erich Friedman | in 1999.", "friedman_source_image": "hc13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "62c003d981fbe524", "improvement": -0.0009678209334929022, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.589858579651107e-06, "max_pair_overlap_depth": -5.483667702588235e-05, "metric_expression": "4.61897", "metric_symbol": "s", "metric_value": 4.618967820933493, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.618, "setup": "cirinhex", "side": 4.618967820933493, "solution_path": "data/solutions/generated/cirinhex_013_62c003d981fbe524.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/62c003d981fbe524.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@14", "density": 0.7773468150841377, "friedman_analytical_or_proved": true, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc14.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "2 + 2/\u221a3 + 4/\u221a7 = 4.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.666, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@14", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "2 + 2/\u221a3 + 4/\u221a7 = 4.666+", "metric_symbol": "s", "metric_value": 4.666, "reference_text": "s = 2 + 2/\u221a3 + 4/\u221a7 = 4.666+ | Found by David W. Cantrell | in July 2002.", "source_image": "hc14.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc14.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 2 + 2/\u221a3 + 4/\u221a7 = 4.666+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "hc14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "d3d8d6f246feeaad", "improvement": -0.0006539683763504556, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4490171600378687e-06, "max_pair_overlap_depth": -3.940553381864831e-05, "metric_expression": "4.66665", "metric_symbol": "s", "metric_value": 4.666653968376351, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.666, "setup": "cirinhex", "side": 4.666653968376351, "solution_path": "data/solutions/generated/cirinhex_014_d3d8d6f246feeaad.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d3d8d6f246feeaad.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@15", "density": 0.7368006709671345, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "January 2006", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc15.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "4.961+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.961, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@15", "credit": "David W. Cantrell", "date": "January 2006", "family_updated": "", "metric_expression": "4.961+", "metric_symbol": "s", "metric_value": 4.961, "reference_text": "s = 4.961+ | Found by David W. Cantrell | in January 2006.", "source_image": "hc15.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc15.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 4.961+ | Found by David W. Cantrell | in January 2006.", "friedman_source_image": "hc15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "d923ba7fbcb56e93", "improvement": -0.0005756365508533534, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.177000685334775e-07, "max_pair_overlap_depth": -3.4253106946380285e-05, "metric_expression": "4.96158", "metric_symbol": "s", "metric_value": 4.961575636550854, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.961, "setup": "cirinhex", "side": 4.961575636550854, "solution_path": "data/solutions/generated/cirinhex_015_d923ba7fbcb56e93.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d923ba7fbcb56e93.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@16", "density": 0.774039756730763, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc16.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "4.999+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.999, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@16", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "4.999+", "metric_symbol": "s", "metric_value": 4.999, "reference_text": "s = 4.999+ | Found by David W. Cantrell | in July 2002.", "source_image": "hc16.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc16.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 4.999+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "hc16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "b6a042d1d6eee5a4", "improvement": -0.0005089546268814971, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.665337648678829e-06, "max_pair_overlap_depth": -4.998313684900779e-05, "metric_expression": "4.99951", "metric_symbol": "s", "metric_value": 4.999508954626881, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.999, "setup": "cirinhex", "side": 4.999508954626881, "solution_path": "data/solutions/generated/cirinhex_016_b6a042d1d6eee5a4.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/b6a042d1d6eee5a4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@17", "density": 0.7801137203230791, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "January 2006", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc17.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "5.133+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.133, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@17", "credit": "David W. Cantrell", "date": "January 2006", "family_updated": "", "metric_expression": "5.133+", "metric_symbol": "s", "metric_value": 5.133, "reference_text": "s = 5.133+ | Found by David W. Cantrell | in January 2006.", "source_image": "hc17.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc17.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 5.133+ | Found by David W. Cantrell | in January 2006.", "friedman_source_image": "hc17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "4927714d5d50ab2b", "improvement": -0.00027458420964432406, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.495950815863736e-06, "max_pair_overlap_depth": -5.684433644859155e-05, "metric_expression": "5.13327", "metric_symbol": "s", "metric_value": 5.133274584209644, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.133, "setup": "cirinhex", "side": 5.133274584209644, "solution_path": "data/solutions/generated/cirinhex_017_4927714d5d50ab2b.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/4927714d5d50ab2b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@18", "density": 0.81913146509039, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc18.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "4 + 2/\u221a3 = 5.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.154, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@18", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4 + 2/\u221a3 = 5.154+", "metric_symbol": "s", "metric_value": 5.154, "reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "source_image": "hc18.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc18.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "friedman_source_image": "hc18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "223b1a3f7b7d0e67", "improvement": -0.000759899456760138, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.33856736717064e-06, "max_pair_overlap_depth": -1.657857602177515e-05, "metric_expression": "5.15476", "metric_symbol": "s", "metric_value": 5.15475989945676, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.154, "setup": "cirinhex", "side": 5.15475989945676, "solution_path": "data/solutions/generated/cirinhex_018_223b1a3f7b7d0e67.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/223b1a3f7b7d0e67.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@19", "density": 0.8646358262071194, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc19.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "4 + 2/\u221a3 = 5.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.154, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@19", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4 + 2/\u221a3 = 5.154+", "metric_symbol": "s", "metric_value": 5.154, "reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "source_image": "hc19.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc19.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "friedman_source_image": "hc19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "78f9327e80d8ab20", "improvement": -0.0007686707015803762, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.035946609195264e-07, "max_pair_overlap_depth": -1.6136694912294303e-05, "metric_expression": "5.15477", "metric_symbol": "s", "metric_value": 5.15476867070158, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.154, "setup": "cirinhex", "side": 5.15476867070158, "solution_path": "data/solutions/generated/cirinhex_019_78f9327e80d8ab20.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/78f9327e80d8ab20.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@20", "density": 0.7503080962551325, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc20.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "5.676+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.676, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@20", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "5.676+", "metric_symbol": "s", "metric_value": 5.676, "reference_text": "s = 5.676+ | Found by David W. Cantrell | in July 2012.", "source_image": "hc20.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc20.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 5.676+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "hc20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "247c6c06779a7d8b", "improvement": -0.0013304688728235092, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.66649728101143e-06, "max_pair_overlap_depth": -2.983410910761819e-05, "metric_expression": "5.67733", "metric_symbol": "s", "metric_value": 5.677330468872824, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.676, "setup": "cirinhex", "side": 5.677330468872824, "solution_path": "data/solutions/generated/cirinhex_020_247c6c06779a7d8b.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/247c6c06779a7d8b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@21", "density": 0.7789652581067265, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc21.gif", "friedman_metric_expression": "5.709+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.709, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@21", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "5.709+", "metric_symbol": "s", "metric_value": 5.709, "reference_text": "s = 5.709+ | Found by David W. Cantrell | in July 2012.", "source_image": "hc21.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc21.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 5.709+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "hc21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "38040eceeb63c1e3", "improvement": -0.0005199689632231497, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.315374129847953e-06, "max_pair_overlap_depth": -3.751451804223649e-05, "metric_expression": "5.70952", "metric_symbol": "s", "metric_value": 5.709519968963223, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.709, "setup": "cirinhex", "side": 5.709519968963223, "solution_path": "data/solutions/generated/cirinhex_021_38040eceeb63c1e3.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/38040eceeb63c1e3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@22", "density": 0.7509530082141859, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc22.gif", "friedman_metric_expression": "5.952+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.952, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@22", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "5.952+", "metric_symbol": "s", "metric_value": 5.952, "reference_text": "s = 5.952+ | Found by David W. Cantrell | in July 2012.", "source_image": "hc22.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc22.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 5.952+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "hc22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "cd7262f9f7d0d279", "improvement": 0.0001229278734493633, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.663138574891647e-06, "max_pair_overlap_depth": -3.268885699680979e-05, "metric_expression": "5.95188", "metric_symbol": "s", "metric_value": 5.951877072126551, "n": 22, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 5.952, "setup": "cirinhex", "side": 5.951877072126551, "solution_path": "data/solutions/generated/cirinhex_022_cd7262f9f7d0d279.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/cd7262f9f7d0d279.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@23", "density": 0.7694641578789073, "friedman_analytical_or_proved": true, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc23.gif", "friedman_metric_expression": "34/7 + 2/\u221a3 = 6.011+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.011, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@23", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "34/7 + 2/\u221a3 = 6.011+", "metric_symbol": "s", "metric_value": 6.011, "reference_text": "s = 34/7 + 2/\u221a3 = 6.011+ | Found by David W. Cantrell | in July 2012.", "source_image": "hc23.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc23.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 34/7 + 2/\u221a3 = 6.011+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "hc23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "de2d2aabdc650ad2", "improvement": -0.0009964252593954726, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.1931154748950945e-06, "max_pair_overlap_depth": -3.920500316656472e-05, "metric_expression": "6.01200", "metric_symbol": "s", "metric_value": 6.011996425259396, "n": 23, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.011, "setup": "cirinhex", "side": 6.011996425259396, "solution_path": "data/solutions/generated/cirinhex_023_de2d2aabdc650ad2.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/de2d2aabdc650ad2.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinhex@24", "density": 0.7747882438352293, "friedman_analytical_or_proved": false, "friedman_credit": "Rob Pratt", "friedman_date": "March 2020", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc24.gif", "friedman_metric_expression": "6.117+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.117, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@24", "credit": "Rob Pratt", "date": "March 2020", "family_updated": "", "metric_expression": "6.117+", "metric_symbol": "s", "metric_value": 6.117, "reference_text": "s = 6.117+ | Found by Rob Pratt | in March 2020.", "source_image": "hc24.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc24.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 6.117+ | Found by Rob Pratt | in March 2020.", "friedman_source_image": "hc24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "61a86ae12328c1ca", "improvement": -0.003164603994216364, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4542492504119338e-06, "max_pair_overlap_depth": -2.04098607499148e-05, "metric_expression": "6.12016", "metric_symbol": "s", "metric_value": 6.120164603994216, "n": 24, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.117, "setup": "cirinhex", "side": 6.120164603994216, "solution_path": "data/solutions/generated/cirinhex_024_61a86ae12328c1ca.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Rob Pratt", "svg_path": "data/svg/61a86ae12328c1ca.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@1", "density": 0.8647965566225578, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.1.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "1.453+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.453, "friedman_reference": {"analytical_or_proved": true, "case": "cirinpen@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1.453+", "metric_symbol": "s", "metric_value": 1.453, "reference_text": "s = 2tan(36\u00b0) | s = 1.453+ | Trivial.", "source_image": "pent.1.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.1.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 2tan(36\u00b0) | s = 1.453+ | Trivial.", "friedman_source_image": "pent.1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "2249439da521383e", "improvement": -9.321311914245456e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.798939718275719e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.45309", "metric_symbol": "s", "metric_value": 1.4530932131191425, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.453, "setup": "cirinpen", "side": 1.4530932131191425, "solution_path": "data/solutions/generated/cirinpen_001_2249439da521383e.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/2249439da521383e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@2", "density": 0.5049856179230741, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.2.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "2.689+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.689, "friedman_reference": {"analytical_or_proved": true, "case": "cirinpen@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2.689+", "metric_symbol": "s", "metric_value": 2.689, "reference_text": "s = 2tan(36\u00b0) + \u221a5 - 1 | s = 2.689+ | Trivial.", "source_image": "pent.2.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.2.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 2tan(36\u00b0) + \u221a5 - 1 | s = 2.689+ | Trivial.", "friedman_source_image": "pent.2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "042df6c460b769f5", "improvement": -0.00021758992828191381, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.904067621218203e-06, "max_pair_overlap_depth": -5.9422400474407056e-05, "metric_expression": "2.68922", "metric_symbol": "s", "metric_value": 2.689217589928282, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.689, "setup": "cirinpen", "side": 2.689217589928282, "solution_path": "data/solutions/generated/cirinpen_002_042df6c460b769f5.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/042df6c460b769f5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@3", "density": 0.6022625992350803, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.3.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "3.015+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.015, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@3", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "3.015+", "metric_symbol": "s", "metric_value": 3.015, "reference_text": "s = 3.015+ | Found by George Sicherman | in July 2012.", "source_image": "pent.3.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.3.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 3.015+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "7afe63c4f78d1c3c", "improvement": -0.0009082861357154748, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.348511423333477e-06, "max_pair_overlap_depth": -3.760319804513301e-05, "metric_expression": "3.01591", "metric_symbol": "s", "metric_value": 3.0159082861357156, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.015, "setup": "cirinpen", "side": 3.0159082861357156, "solution_path": "data/solutions/generated/cirinpen_003_7afe63c4f78d1c3c.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/7afe63c4f78d1c3c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@4", "density": 0.6648380416307991, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.4.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "3.314+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.314, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@4", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "3.314+", "metric_symbol": "s", "metric_value": 3.314, "reference_text": "s = 3.314+ | Found by George Sicherman | in July 2012.", "source_image": "pent.4.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.4.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 3.314+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "3b6f81450d56967c", "improvement": -0.0005342806983965609, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4291241632899983e-06, "max_pair_overlap_depth": -5.729132607923404e-05, "metric_expression": "3.31453", "metric_symbol": "s", "metric_value": 3.3145342806983966, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.314, "setup": "cirinpen", "side": 3.3145342806983966, "solution_path": "data/solutions/generated/cirinpen_004_3b6f81450d56967c.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/3b6f81450d56967c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@5", "density": 0.7656755676390014, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.5.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "3.453+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.453, "friedman_reference": {"analytical_or_proved": true, "case": "cirinpen@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3.453+", "metric_symbol": "s", "metric_value": 3.453, "reference_text": "s = 2tan(36\u00b0) + 2 | s = 3.453+ | Trivial.", "source_image": "pent.5.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.5.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 2tan(36\u00b0) + 2 | s = 3.453+ | Trivial.", "friedman_source_image": "pent.5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "6a788c9a1ab05f1f", "improvement": -0.00013102756244531832, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4842628671150067e-07, "max_pair_overlap_depth": -2.3617760550376232e-05, "metric_expression": "3.45313", "metric_symbol": "s", "metric_value": 3.453131027562445, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.453, "setup": "cirinpen", "side": 3.453131027562445, "solution_path": "data/solutions/generated/cirinpen_005_6a788c9a1ab05f1f.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/6a788c9a1ab05f1f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@6", "density": 0.7570230558933833, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.6.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "3.804+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.804, "friedman_reference": {"analytical_or_proved": true, "case": "cirinpen@6", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3.804+", "metric_symbol": "s", "metric_value": 3.804, "reference_text": "s = 2tan(36\u00b0) + 4sin(36\u00b0) | s = 3.804+ | Trivial.", "source_image": "pent.6.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.6.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 2tan(36\u00b0) + 4sin(36\u00b0) | s = 3.804+ | Trivial.", "friedman_source_image": "pent.6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "a73fe466a153c6dc", "improvement": -0.0002716609440795992, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.235659036235575e-06, "max_pair_overlap_depth": -1.860019961119619e-05, "metric_expression": "3.80427", "metric_symbol": "s", "metric_value": 3.8042716609440794, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.804, "setup": "cirinpen", "side": 3.8042716609440794, "solution_path": "data/solutions/generated/cirinpen_006_a73fe466a153c6dc.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/a73fe466a153c6dc.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@7", "density": 0.7122554139396908, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.7.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "4.236+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.236, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@7", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "4.236+", "metric_symbol": "s", "metric_value": 4.236, "reference_text": "s = 4.236+ | Found by George Sicherman | in July 2012.", "source_image": "pent.7.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.7.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 4.236+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "f2fb4964063d721f", "improvement": -0.0002500861768837126, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.256168874145928e-06, "max_pair_overlap_depth": -7.389596920859276e-05, "metric_expression": "4.23625", "metric_symbol": "s", "metric_value": 4.2362500861768835, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.236, "setup": "cirinpen", "side": 4.2362500861768835, "solution_path": "data/solutions/generated/cirinpen_007_f2fb4964063d721f.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/f2fb4964063d721f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@8", "density": 0.7010960627351681, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.8.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "4.564+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.564, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@8", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "4.564+", "metric_symbol": "s", "metric_value": 4.564, "reference_text": "s = 4.564+ | Found by George Sicherman | in July 2012.", "source_image": "pent.8.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.8.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 4.564+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "7550c7a4a15ba971", "improvement": -0.0006415548993858877, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.759741664666194e-07, "max_pair_overlap_depth": -2.5138721591932978e-05, "metric_expression": "4.56464", "metric_symbol": "s", "metric_value": 4.564641554899386, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.564, "setup": "cirinpen", "side": 4.564641554899386, "solution_path": "data/solutions/generated/cirinpen_008_7550c7a4a15ba971.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/7550c7a4a15ba971.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@9", "density": 0.7058543729480167, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.9.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "4.825+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.825, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@9", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "4.825+", "metric_symbol": "s", "metric_value": 4.825, "reference_text": "s = 4.825+ | Found by George Sicherman | in July 2012.", "source_image": "pent.9.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.9.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 4.825+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "44a9c06211e4a669", "improvement": -0.0001870114230673181, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.33965970525874e-06, "max_pair_overlap_depth": -6.87249875483964e-05, "metric_expression": "4.82519", "metric_symbol": "s", "metric_value": 4.8251870114230675, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.825, "setup": "cirinpen", "side": 4.8251870114230675, "solution_path": "data/solutions/generated/cirinpen_009_44a9c06211e4a669.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/44a9c06211e4a669.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@10", "density": 0.7033183837462447, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.10.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "5.095+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.095, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@10", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "5.095+", "metric_symbol": "s", "metric_value": 5.095, "reference_text": "s = 5.095+ | Found by George Sicherman | in July 2012.", "source_image": "pent.10.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.10.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 5.095+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "38c046e395ee0204", "improvement": -0.0003552139806179966, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.918153382491795e-06, "max_pair_overlap_depth": -5.2545257565039805e-05, "metric_expression": "5.09536", "metric_symbol": "s", "metric_value": 5.095355213980618, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.095, "setup": "cirinpen", "side": 5.095355213980618, "solution_path": "data/solutions/generated/cirinpen_010_38c046e395ee0204.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/38c046e395ee0204.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@11", "density": 0.7314145264425335, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.11.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "5.240+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.24, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@11", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "5.240+", "metric_symbol": "s", "metric_value": 5.24, "reference_text": "s = 5.240+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.11.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.11.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 5.240+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "3c4a20ceb03b166b", "improvement": -0.0004068061718305316, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.25538255039082e-06, "max_pair_overlap_depth": -4.98370515433777e-05, "metric_expression": "5.24041", "metric_symbol": "s", "metric_value": 5.240406806171831, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.24, "setup": "cirinpen", "side": 5.240406806171831, "solution_path": "data/solutions/generated/cirinpen_011_3c4a20ceb03b166b.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/3c4a20ceb03b166b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@12", "density": 0.7492511392398852, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.12.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "5.407+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.407, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@12", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "5.407+", "metric_symbol": "s", "metric_value": 5.407, "reference_text": "s = 5.407+ | Found by George Sicherman | in July 2012.", "source_image": "pent.12.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.12.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 5.407+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "1156bc3b50d815fe", "improvement": -0.0008839986719992865, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7054584944851143e-06, "max_pair_overlap_depth": -3.0020938044383882e-05, "metric_expression": "5.40788", "metric_symbol": "s", "metric_value": 5.407883998671999, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.407, "setup": "cirinpen", "side": 5.407883998671999, "solution_path": "data/solutions/generated/cirinpen_012_1156bc3b50d815fe.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/1156bc3b50d815fe.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@13", "density": 0.7430341365754948, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.13.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "5.651+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.651, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@13", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "5.651+", "metric_symbol": "s", "metric_value": 5.651, "reference_text": "s = 5.651+ | Found by George Sicherman | in July 2012.", "source_image": "pent.13.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.13.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 5.651+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "213cdbfbbdb494b1", "improvement": -0.0012028933276413412, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.063538795673338e-06, "max_pair_overlap_depth": -3.936589445130423e-05, "metric_expression": "5.65220", "metric_symbol": "s", "metric_value": 5.652202893327641, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.651, "setup": "cirinpen", "side": 5.652202893327641, "solution_path": "data/solutions/generated/cirinpen_013_213cdbfbbdb494b1.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/213cdbfbbdb494b1.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@14", "density": 0.7576628256268029, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.14.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "5.808+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.808, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@14", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "5.808+", "metric_symbol": "s", "metric_value": 5.808, "reference_text": "s = 5.808+ | Found by George Sicherman | in July 2012.", "source_image": "pent.14.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.14.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 5.808+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "44805be876ac7787", "improvement": -0.0006669796446772125, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.282572655998294e-06, "max_pair_overlap_depth": -2.37953924338008e-05, "metric_expression": "5.80867", "metric_symbol": "s", "metric_value": 5.808666979644677, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.808, "setup": "cirinpen", "side": 5.808666979644677, "solution_path": "data/solutions/generated/cirinpen_014_44805be876ac7787.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/44805be876ac7787.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@15", "density": 0.7748926471130506, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.15.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "5.945+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.945, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@15", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "5.945+", "metric_symbol": "s", "metric_value": 5.945, "reference_text": "s = 5.945+ | Found by George Sicherman | in July 2012.", "source_image": "pent.15.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.15.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 5.945+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "36fcf02cb6fd9f92", "improvement": -0.0003210236521935528, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.123112133491702e-06, "max_pair_overlap_depth": -5.711461050461608e-05, "metric_expression": "5.94532", "metric_symbol": "s", "metric_value": 5.945321023652194, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.945, "setup": "cirinpen", "side": 5.945321023652194, "solution_path": "data/solutions/generated/cirinpen_015_36fcf02cb6fd9f92.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/36fcf02cb6fd9f92.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@16", "density": 0.7775664873268765, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.16.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "6.129+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.129, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@16", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "6.129+", "metric_symbol": "s", "metric_value": 6.129, "reference_text": "s = 6.129+ | Found by George Sicherman | in July 2012.", "source_image": "pent.16.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.16.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 6.129+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "39b6519b6fb7eef4", "improvement": -0.0007346433642512196, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.515317749508867e-06, "max_pair_overlap_depth": -2.965957000666819e-05, "metric_expression": "6.12973", "metric_symbol": "s", "metric_value": 6.129734643364251, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.129, "setup": "cirinpen", "side": 6.129734643364251, "solution_path": "data/solutions/generated/cirinpen_016_39b6519b6fb7eef4.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/39b6519b6fb7eef4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@17", "density": 0.7527556084558986, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.17.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "6.419+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.419, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@17", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "6.419+", "metric_symbol": "s", "metric_value": 6.419, "reference_text": "s = 6.419+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.17.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.17.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 6.419+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "5e677c639e143e85", "improvement": -0.0026689184768269314, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.2234530213948176e-06, "max_pair_overlap_depth": -4.317787105012627e-05, "metric_expression": "6.42167", "metric_symbol": "s", "metric_value": 6.4216689184768265, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.419, "setup": "cirinpen", "side": 6.4216689184768265, "solution_path": "data/solutions/generated/cirinpen_017_5e677c639e143e85.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/5e677c639e143e85.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@18", "density": 0.7574722105185439, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.18.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "6.586+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.586, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@18", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "6.586+", "metric_symbol": "s", "metric_value": 6.586, "reference_text": "s = 6.586+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.18.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.18.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 6.586+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "34fda06736bbaaf7", "improvement": -0.0012379322999080955, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.803338162222119e-06, "max_pair_overlap_depth": -4.5158559001112764e-05, "metric_expression": "6.58724", "metric_symbol": "s", "metric_value": 6.587237932299908, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.586, "setup": "cirinpen", "side": 6.587237932299908, "solution_path": "data/solutions/generated/cirinpen_018_34fda06736bbaaf7.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/34fda06736bbaaf7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@19", "density": 0.7551620068495595, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.19.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "6.777+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.777, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@19", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "6.777+", "metric_symbol": "s", "metric_value": 6.777, "reference_text": "s = 6.777+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.19.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.19.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 6.777+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "dfaba7cef14e53f5", "improvement": -0.0010877146457399789, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.911905938958071e-06, "max_pair_overlap_depth": -5.528697090007029e-05, "metric_expression": "6.77809", "metric_symbol": "s", "metric_value": 6.77808771464574, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.777, "setup": "cirinpen", "side": 6.77808771464574, "solution_path": "data/solutions/generated/cirinpen_019_dfaba7cef14e53f5.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/dfaba7cef14e53f5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@20", "density": 0.7572204985441312, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.20.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "6.944+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.944, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@20", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "6.944+", "metric_symbol": "s", "metric_value": 6.944, "reference_text": "s = 6.944+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.20.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.20.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 6.944+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "d513055d785b23f7", "improvement": -0.0007124298362715109, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4085836122521584e-06, "max_pair_overlap_depth": -2.3984136221066876e-05, "metric_expression": "6.94471", "metric_symbol": "s", "metric_value": 6.9447124298362715, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.944, "setup": "cirinpen", "side": 6.9447124298362715, "solution_path": "data/solutions/generated/cirinpen_020_d513055d785b23f7.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d513055d785b23f7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@21", "density": 0.7590915818467144, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.21.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "7.107+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.107, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@21", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "7.107+", "metric_symbol": "s", "metric_value": 7.107, "reference_text": "s = 7.107+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.21.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.21.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 7.107+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "71add6eacc6c4fb9", "improvement": -0.0004368549852129533, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.952484924405695e-06, "max_pair_overlap_depth": -3.840822292655588e-05, "metric_expression": "7.10744", "metric_symbol": "s", "metric_value": 7.107436854985213, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.107, "setup": "cirinpen", "side": 7.107436854985213, "solution_path": "data/solutions/generated/cirinpen_021_71add6eacc6c4fb9.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/71add6eacc6c4fb9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@22", "density": 0.7595290345154431, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.22.gif", "friedman_metric_expression": "7.271+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.271, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@22", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "7.271+", "metric_symbol": "s", "metric_value": 7.271, "reference_text": "s = 7.271+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.22.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.22.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 7.271+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "ebdb05232e56526e", "improvement": -0.0015983061562394596, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.413438632810411e-06, "max_pair_overlap_depth": -6.856237147889743e-05, "metric_expression": "7.27260", "metric_symbol": "s", "metric_value": 7.272598306156239, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.271, "setup": "cirinpen", "side": 7.272598306156239, "solution_path": "data/solutions/generated/cirinpen_022_ebdb05232e56526e.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/ebdb05232e56526e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@23", "density": 0.7675010590620791, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.23.gif", "friedman_metric_expression": "7.397+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.397, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@23", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "7.397+", "metric_symbol": "s", "metric_value": 7.397, "reference_text": "s = 7.397+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.23.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.23.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 7.397+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "0115bd21477c01e6", "improvement": -0.0003280102549396702, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.583943801847681e-07, "max_pair_overlap_depth": -3.4243400256706025e-05, "metric_expression": "7.39733", "metric_symbol": "s", "metric_value": 7.39732801025494, "n": 23, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.397, "setup": "cirinpen", "side": 7.39732801025494, "solution_path": "data/solutions/generated/cirinpen_023_0115bd21477c01e6.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/0115bd21477c01e6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinpen@24", "density": 0.7719374015643087, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.24.gif", "friedman_metric_expression": "7.534+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.534, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@24", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "7.534+", "metric_symbol": "s", "metric_value": 7.534, "reference_text": "s = 7.534+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.24.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.24.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 7.534+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "9eb26a95274f1d1d", "improvement": -0.0006837609794780874, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.468927518428643e-06, "max_pair_overlap_depth": -2.3713548386705696e-05, "metric_expression": "7.53468", "metric_symbol": "s", "metric_value": 7.534683760979478, "n": 24, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.534, "setup": "cirinpen", "side": 7.534683760979478, "solution_path": "data/solutions/generated/cirinpen_024_9eb26a95274f1d1d.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/9eb26a95274f1d1d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@1", "density": 0.7853971453379307, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs1.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "cs1.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs1.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "cs1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "329c377d412c468f", "improvement": -1.2962348967526793e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0795596527835016e-07, "max_pair_overlap_depth": 0.0, "metric_expression": "2.00000", "metric_symbol": "s", "metric_value": 2.0000012962348968, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "cirinsqu", "side": 2.0000012962348968, "solution_path": "data/solutions/generated/cirinsqu_001_329c377d412c468f.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/329c377d412c468f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@2", "density": 0.5390070210000131, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs2.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + \u221a2 = 3.414+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.414, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2 + \u221a2 = 3.414+", "metric_symbol": "s", "metric_value": 3.414, "reference_text": "s = 2 + \u221a2 = 3.414+ | Trivial.", "source_image": "cs2.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs2.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + \u221a2 = 3.414+ | Trivial.", "friedman_source_image": "cs2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "e3bab8445b304ebe", "improvement": -0.00022959896202801033, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.1788679802625666e-06, "max_pair_overlap_depth": -1.6252235923275293e-05, "metric_expression": "3.41423", "metric_symbol": "s", "metric_value": 3.414229598962028, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.414, "setup": "cirinsqu", "side": 3.414229598962028, "solution_path": "data/solutions/generated/cirinsqu_002_e3bab8445b304ebe.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/e3bab8445b304ebe.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@3", "density": 0.6096071430698954, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs3.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + 1/\u221a2 + \u221a6/2 = 3.931+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.931, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2 + 1/\u221a2 + \u221a6/2 = 3.931+", "metric_symbol": "s", "metric_value": 3.931, "reference_text": "s = 2 + 1/\u221a2 + \u221a6/2 = 3.931+ | Trivial.", "source_image": "cs3.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs3.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + 1/\u221a2 + \u221a6/2 = 3.931+ | Trivial.", "friedman_source_image": "cs3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "63c314af1da3741c", "improvement": -0.0009731189575252763, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.540614135605807e-06, "max_pair_overlap_depth": -7.777950709542125e-05, "metric_expression": "3.93197", "metric_symbol": "s", "metric_value": 3.9319731189575253, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.931, "setup": "cirinsqu", "side": 3.9319731189575253, "solution_path": "data/solutions/generated/cirinsqu_003_63c314af1da3741c.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/63c314af1da3741c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@4", "density": 0.7853846601471004, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs4.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@4", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "s = 4 | Trivial.", "source_image": "cs4.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs4.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 4 | Trivial.", "friedman_source_image": "cs4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "9917d423eeeb95cb", "improvement": -3.438618804896265e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3561316251363706e-06, "max_pair_overlap_depth": -2.9461600919766795e-05, "metric_expression": "4.00003", "metric_symbol": "s", "metric_value": 4.000034386188049, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.0, "setup": "cirinsqu", "side": 4.000034386188049, "solution_path": "data/solutions/generated/cirinsqu_004_9917d423eeeb95cb.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/9917d423eeeb95cb.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@5", "density": 0.6737513675455145, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs5.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + 2\u221a2 = 4.828+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.828, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2 + 2\u221a2 = 4.828+", "metric_symbol": "s", "metric_value": 4.828, "reference_text": "s = 2 + 2\u221a2 = 4.828+ | Trivial.", "source_image": "cs5.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs5.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + 2\u221a2 = 4.828+ | Trivial.", "friedman_source_image": "cs5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "f91bd37c36f9320b", "improvement": -0.000476351133615438, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.7157366511154635e-07, "max_pair_overlap_depth": -2.294469225416762e-05, "metric_expression": "4.82848", "metric_symbol": "s", "metric_value": 4.828476351133616, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.828, "setup": "cirinsqu", "side": 4.828476351133616, "solution_path": "data/solutions/generated/cirinsqu_005_f91bd37c36f9320b.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/f91bd37c36f9320b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@6", "density": 0.6639170340529372, "friedman_analytical_or_proved": true, "friedman_credit": "Graham", "friedman_date": "1963", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs6.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + 12/\u221a13 = 5.328+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.328, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@6", "credit": "Graham", "date": "1963", "family_updated": "", "metric_expression": "2 + 12/\u221a13 = 5.328+", "metric_symbol": "s", "metric_value": 5.328, "reference_text": "s = 2 + 12/\u221a13 = 5.328+ | Proved by Graham in 1963.", "source_image": "cs6.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs6.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + 12/\u221a13 = 5.328+ | Proved by Graham in 1963.", "friedman_source_image": "cs6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "96dda57e28868925", "improvement": -0.0003611830538092775, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.928735258591388e-06, "max_pair_overlap_depth": -7.200734794432506e-05, "metric_expression": "5.32836", "metric_symbol": "s", "metric_value": 5.32836118305381, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.328, "setup": "cirinsqu", "side": 5.32836118305381, "solution_path": "data/solutions/generated/cirinsqu_006_96dda57e28868925.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Graham", "svg_path": "data/svg/96dda57e28868925.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@7", "density": 0.669268877528072, "friedman_analytical_or_proved": true, "friedman_credit": "Schaer", "friedman_date": "1964", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs7.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "4 + \u221a3 = 5.732+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.732, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@7", "credit": "Schaer", "date": "1964", "family_updated": "", "metric_expression": "4 + \u221a3 = 5.732+", "metric_symbol": "s", "metric_value": 5.732, "reference_text": "s = 4 + \u221a3 = 5.732+ | Proved by Schaer in 1964.", "source_image": "cs7.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs7.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 4 + \u221a3 = 5.732+ | Proved by Schaer in 1964.", "friedman_source_image": "cs7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "7e4d3361af467e5d", "improvement": -0.0002304452542292168, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.33238067148811e-06, "max_pair_overlap_depth": -6.633595249638802e-05, "metric_expression": "5.73223", "metric_symbol": "s", "metric_value": 5.732230445254229, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.732, "setup": "cirinsqu", "side": 5.732230445254229, "solution_path": "data/solutions/generated/cirinsqu_007_7e4d3361af467e5d.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Schaer", "svg_path": "data/svg/7e4d3361af467e5d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@8", "density": 0.7309263604724501, "friedman_analytical_or_proved": true, "friedman_credit": "Schaer/Meir", "friedman_date": "1964", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs8.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + \u221a2 + \u221a6 = 5.863+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.863, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@8", "credit": "Schaer/Meir", "date": "1964", "family_updated": "", "metric_expression": "2 + \u221a2 + \u221a6 = 5.863+", "metric_symbol": "s", "metric_value": 5.863, "reference_text": "s = 2 + \u221a2 + \u221a6 = 5.863+ | Proved by Schaer/Meir in 1964.", "source_image": "cs8.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs8.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + \u221a2 + \u221a6 = 5.863+ | Proved by Schaer/Meir in 1964.", "friedman_source_image": "cs8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "67f6750a9af94d2c", "improvement": -0.0008535799033406732, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.247320970871769e-06, "max_pair_overlap_depth": -5.202375940349668e-05, "metric_expression": "5.86385", "metric_symbol": "s", "metric_value": 5.863853579903341, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.863, "setup": "cirinsqu", "side": 5.863853579903341, "solution_path": "data/solutions/generated/cirinsqu_008_67f6750a9af94d2c.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Schaer/Meir", "svg_path": "data/svg/67f6750a9af94d2c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@9", "density": 0.7853720614609764, "friedman_analytical_or_proved": true, "friedman_credit": "Schaer", "friedman_date": "1964", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs9.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@9", "credit": "Schaer", "date": "1964", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Proved by Schaer in 1964.", "source_image": "cs9.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs9.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 6 | Proved by Schaer in 1964.", "friedman_source_image": "cs9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "a35561fa5a518c8b", "improvement": -9.970453832330861e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.26657331825875e-06, "max_pair_overlap_depth": -3.06706256441025e-05, "metric_expression": "6.00010", "metric_symbol": "s", "metric_value": 6.000099704538323, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.0, "setup": "cirinsqu", "side": 6.000099704538323, "solution_path": "data/solutions/generated/cirinsqu_009_a35561fa5a518c8b.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Schaer", "svg_path": "data/svg/a35561fa5a518c8b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@10", "density": 0.6900075339157021, "friedman_analytical_or_proved": true, "friedman_credit": "De Groot", "friedman_date": "1990", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs10.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "6.747+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.747, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@10", "credit": "De Groot", "date": "1990", "family_updated": "", "metric_expression": "6.747+", "metric_symbol": "s", "metric_value": 6.747, "reference_text": "s = 6.747+ | Proved by De Groot in 1990.", "source_image": "cs10.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs10.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 6.747+ | Proved by De Groot in 1990.", "friedman_source_image": "cs10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "522948d614943781", "improvement": -0.0005796538825402209, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.6772848518975536e-06, "max_pair_overlap_depth": -4.0928067794876455e-05, "metric_expression": "6.74758", "metric_symbol": "s", "metric_value": 6.74757965388254, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.747, "setup": "cirinsqu", "side": 6.74757965388254, "solution_path": "data/solutions/generated/cirinsqu_10_522948d614943781.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "De Groot", "svg_path": "data/svg/522948d614943781.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@11", "density": 0.7006956988559802, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs11.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "7.022+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.022, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@11", "credit": "Peikert", "date": "1991", "family_updated": "", "metric_expression": "7.022+", "metric_symbol": "s", "metric_value": 7.022, "reference_text": "s = 7.022+ | Proved by Peikert in 1991.", "source_image": "cs11.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs11.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 7.022+ | Proved by Peikert in 1991.", "friedman_source_image": "cs11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "b0ae38086de8cdf9", "improvement": -0.0007394033277021705, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.667419736983149e-06, "max_pair_overlap_depth": -2.585792898823769e-05, "metric_expression": "7.02274", "metric_symbol": "s", "metric_value": 7.022739403327702, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.022, "setup": "cirinsqu", "side": 7.022739403327702, "solution_path": "data/solutions/generated/cirinsqu_011_b0ae38086de8cdf9.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Peikert", "svg_path": "data/svg/b0ae38086de8cdf9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@12", "density": 0.7384288108172983, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs12.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + 15\u221a(2/17) = 7.144+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.144, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@12", "credit": "Peikert", "date": "1991", "family_updated": "", "metric_expression": "2 + 15\u221a(2/17) = 7.144+", "metric_symbol": "s", "metric_value": 7.144, "reference_text": "s = 2 + 15\u221a(2/17) = 7.144+ | Proved by Peikert in 1991.", "source_image": "cs12.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs12.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + 15\u221a(2/17) = 7.144+ | Proved by Peikert in 1991.", "friedman_source_image": "cs12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "e58733a8646795ab", "improvement": -0.0011482300231175913, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.939770909988098e-06, "max_pair_overlap_depth": -5.93949466169974e-05, "metric_expression": "7.14515", "metric_symbol": "s", "metric_value": 7.145148230023118, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.144, "setup": "cirinsqu", "side": 7.145148230023118, "solution_path": "data/solutions/generated/cirinsqu_012_e58733a8646795ab.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Peikert", "svg_path": "data/svg/e58733a8646795ab.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@13", "density": 0.7332320892098975, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs13.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "7.463+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.463, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@13", "credit": "Peikert", "date": "1991", "family_updated": "", "metric_expression": "7.463+", "metric_symbol": "s", "metric_value": 7.463, "reference_text": "s = 7.463+ | Proved by Peikert in 1991.", "source_image": "cs13.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs13.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 7.463+ | Proved by Peikert in 1991.", "friedman_source_image": "cs13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "60997371c312edb4", "improvement": -0.0002137620977080701, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.323292483705444e-06, "max_pair_overlap_depth": -3.8715255959331785e-05, "metric_expression": "7.46321", "metric_symbol": "s", "metric_value": 7.463213762097708, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.463, "setup": "cirinsqu", "side": 7.463213762097708, "solution_path": "data/solutions/generated/cirinsqu_013_60997371c312edb4.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Peikert", "svg_path": "data/svg/60997371c312edb4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@14", "density": 0.7356508336971848, "friedman_analytical_or_proved": true, "friedman_credit": "Wengerodt", "friedman_date": "1987", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs14.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "6 + \u221a3 = 7.732+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.732, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@14", "credit": "Wengerodt", "date": "1987", "family_updated": "", "metric_expression": "6 + \u221a3 = 7.732+", "metric_symbol": "s", "metric_value": 7.732, "reference_text": "s = 6 + \u221a3 = 7.732+ | Proved by Wengerodt in 1987.", "source_image": "cs14.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs14.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 6 + \u221a3 = 7.732+ | Proved by Wengerodt in 1987.", "friedman_source_image": "cs14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "2ccdf5f3d4bee77b", "improvement": -0.000200169889159163, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.480532338595026e-07, "max_pair_overlap_depth": -3.0206326999682176e-05, "metric_expression": "7.73220", "metric_symbol": "s", "metric_value": 7.732200169889159, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.732, "setup": "cirinsqu", "side": 7.732200169889159, "solution_path": "data/solutions/generated/cirinsqu_014_2ccdf5f3d4bee77b.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Wengerodt", "svg_path": "data/svg/2ccdf5f3d4bee77b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@15", "density": 0.7620259985870776, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs15.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "4 + \u221a2 + \u221a6 = 7.863+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.863, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@15", "credit": "Peikert", "date": "1991", "family_updated": "", "metric_expression": "4 + \u221a2 + \u221a6 = 7.863+", "metric_symbol": "s", "metric_value": 7.863, "reference_text": "s = 4 + \u221a2 + \u221a6 = 7.863+ | Proved by Peikert in 1991.", "source_image": "cs15.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs15.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 4 + \u221a2 + \u221a6 = 7.863+ | Proved by Peikert in 1991.", "friedman_source_image": "cs15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "edc16b42d64e4d82", "improvement": -0.0008581593284961997, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.610873706565542e-06, "max_pair_overlap_depth": -3.564256081922679e-05, "metric_expression": "7.86386", "metric_symbol": "s", "metric_value": 7.863858159328497, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.863, "setup": "cirinsqu", "side": 7.863858159328497, "solution_path": "data/solutions/generated/cirinsqu_015_edc16b42d64e4d82.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Peikert", "svg_path": "data/svg/edc16b42d64e4d82.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@16", "density": 0.7853654831135446, "friedman_analytical_or_proved": true, "friedman_credit": "Wengerodt", "friedman_date": "1983", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs16.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "8", "friedman_metric_symbol": "s", "friedman_metric_value": 8.0, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@16", "credit": "Wengerodt", "date": "1983", "family_updated": "", "metric_expression": "8", "metric_symbol": "s", "metric_value": 8.0, "reference_text": "s = 8 | Proved by Wengerodt in 1983.", "source_image": "cs16.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs16.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 8 | Proved by Wengerodt in 1983.", "friedman_source_image": "cs16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "6ef91613d0db44e8", "improvement": -0.00016644451351055523, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.383802090528576e-06, "max_pair_overlap_depth": -3.451016213729119e-05, "metric_expression": "8.00017", "metric_symbol": "s", "metric_value": 8.00016644451351, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.0, "setup": "cirinsqu", "side": 8.00016644451351, "solution_path": "data/solutions/generated/cirinsqu_016_6ef91613d0db44e8.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Wengerodt", "svg_path": "data/svg/6ef91613d0db44e8.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@17", "density": 0.7333955245290497, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs17.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "8.532+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.532, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@17", "credit": "Peikert", "date": "1991", "family_updated": "", "metric_expression": "8.532+", "metric_symbol": "s", "metric_value": 8.532, "reference_text": "s = 8.532+ | Proved by Peikert in 1991.", "source_image": "cs17.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs17.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 8.532+ | Proved by Peikert in 1991.", "friedman_source_image": "cs17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "9211255584acb7a4", "improvement": -0.001560450998908891, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6768059695481128e-06, "max_pair_overlap_depth": -3.5588125128604986e-05, "metric_expression": "8.53356", "metric_symbol": "s", "metric_value": 8.533560450998909, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.532, "setup": "cirinsqu", "side": 8.533560450998909, "solution_path": "data/solutions/generated/cirinsqu_017_9211255584acb7a4.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Peikert", "svg_path": "data/svg/9211255584acb7a4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@18", "density": 0.7546080214690231, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs18.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + 24/\u221a13 = 8.656+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.656, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@18", "credit": "Peikert", "date": "1991", "family_updated": "", "metric_expression": "2 + 24/\u221a13 = 8.656+", "metric_symbol": "s", "metric_value": 8.656, "reference_text": "s = 2 + 24/\u221a13 = 8.656+ | Proved by Peikert in 1991.", "source_image": "cs18.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs18.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + 24/\u221a13 = 8.656+ | Proved by Peikert in 1991.", "friedman_source_image": "cs18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "4872462eca76de82", "improvement": -0.0006623865813519814, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.585640835636951e-06, "max_pair_overlap_depth": -5.7251545610981225e-05, "metric_expression": "8.65666", "metric_symbol": "s", "metric_value": 8.656662386581353, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.656, "setup": "cirinsqu", "side": 8.656662386581353, "solution_path": "data/solutions/generated/cirinsqu_018_4872462eca76de82.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Peikert", "svg_path": "data/svg/4872462eca76de82.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@19", "density": 0.752224113091453, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs19.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "8.907+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.907, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@19", "credit": "Peikert", "date": "1991", "family_updated": "", "metric_expression": "8.907+", "metric_symbol": "s", "metric_value": 8.907, "reference_text": "s = 8.907+ | Proved by Peikert in 1991.", "source_image": "cs19.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs19.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 8.907+ | Proved by Peikert in 1991.", "friedman_source_image": "cs19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "72fa8cf8e074fd32", "improvement": -0.0009569875134012307, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.019564082723974e-06, "max_pair_overlap_depth": -6.564483433546542e-05, "metric_expression": "8.90796", "metric_symbol": "s", "metric_value": 8.907956987513401, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.907, "setup": "cirinsqu", "side": 8.907956987513401, "solution_path": "data/solutions/generated/cirinsqu_019_72fa8cf8e074fd32.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Peikert", "svg_path": "data/svg/72fa8cf8e074fd32.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@20", "density": 0.7794478091956536, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs20.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "130/17 + 16/17\u221a2 = 8.978+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.978, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@20", "credit": "Peikert", "date": "1991", "family_updated": "", "metric_expression": "130/17 + 16/17\u221a2 = 8.978+", "metric_symbol": "s", "metric_value": 8.978, "reference_text": "s = 130/17 + 16/17\u221a2 = 8.978+ | Proved by Peikert in 1991.", "source_image": "cs20.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs20.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 130/17 + 16/17\u221a2 = 8.978+ | Proved by Peikert in 1991.", "friedman_source_image": "cs20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "ed16784370181dab", "improvement": -0.0003475703211961445, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3975782322539487e-06, "max_pair_overlap_depth": -5.140241392753708e-05, "metric_expression": "8.97835", "metric_symbol": "s", "metric_value": 8.978347570321196, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.978, "setup": "cirinsqu", "side": 8.978347570321196, "solution_path": "data/solutions/generated/cirinsqu_020_ed16784370181dab.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Peikert", "svg_path": "data/svg/ed16784370181dab.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@21", "density": 0.7531827030031223, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman Packing Center", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs21.gif", "friedman_metric_expression": "9.358+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.358, "friedman_reference": {"analytical_or_proved": false, "case": "cirinsqu@21", "credit": "Erich Friedman Packing Center", "date": "", "family_updated": "", "metric_expression": "9.358+", "metric_symbol": "s", "metric_value": 9.358, "reference_text": "s = 9.358+", "source_image": "cs21.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs21.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 9.358+", "friedman_source_image": "cs21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "65afc927a4d3cb10", "improvement": -0.0011070505635846217, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.857662265602471e-06, "max_pair_overlap_depth": -3.291297220409106e-05, "metric_expression": "9.35911", "metric_symbol": "s", "metric_value": 9.359107050563585, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.358, "setup": "cirinsqu", "side": 9.359107050563585, "solution_path": "data/solutions/generated/cirinsqu_021_65afc927a4d3cb10.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman Packing Center", "svg_path": "data/svg/65afc927a4d3cb10.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@22", "density": 0.7716499915329439, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman Packing Center", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs22.gif", "friedman_metric_expression": "9.463+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.463, "friedman_reference": {"analytical_or_proved": false, "case": "cirinsqu@22", "credit": "Erich Friedman Packing Center", "date": "", "family_updated": "", "metric_expression": "9.463+", "metric_symbol": "s", "metric_value": 9.463, "reference_text": "s = 9.463+", "source_image": "cs22.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs22.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 9.463+", "friedman_source_image": "cs22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "27d48d864449f174", "improvement": -0.0010297949122062278, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1647620365984324e-06, "max_pair_overlap_depth": -2.796224374757017e-05, "metric_expression": "9.46403", "metric_symbol": "s", "metric_value": 9.464029794912205, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.463, "setup": "cirinsqu", "side": 9.464029794912205, "solution_path": "data/solutions/generated/cirinsqu_022_27d48d864449f174.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman Packing Center", "svg_path": "data/svg/27d48d864449f174.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@23", "density": 0.7628623175184639, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman Packing Center", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs23.gif", "friedman_metric_expression": "2 + 2\u221a2 + 2\u221a6 = 9.727+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.727, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@23", "credit": "Erich Friedman Packing Center", "date": "", "family_updated": "", "metric_expression": "2 + 2\u221a2 + 2\u221a6 = 9.727+", "metric_symbol": "s", "metric_value": 9.727, "reference_text": "s = 2 + 2\u221a2 + 2\u221a6 = 9.727+", "source_image": "cs23.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs23.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + 2\u221a2 + 2\u221a6 = 9.727+", "friedman_source_image": "cs23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "cfa99060ee2203a1", "improvement": -0.005306391434194424, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8298221013957061e-06, "max_pair_overlap_depth": -2.6081243190478887e-05, "metric_expression": "9.73231", "metric_symbol": "s", "metric_value": 9.732306391434195, "n": 23, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.727, "setup": "cirinsqu", "side": 9.732306391434195, "solution_path": "data/solutions/generated/cirinsqu_023_cfa99060ee2203a1.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman Packing Center", "svg_path": "data/svg/cfa99060ee2203a1.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirinsqu@24", "density": 0.7749295071503051, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman Packing Center", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs24.gif", "friedman_metric_expression": "6 + \u221a2 + \u221a6 = 9.863+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.863, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@24", "credit": "Erich Friedman Packing Center", "date": "", "family_updated": "", "metric_expression": "6 + \u221a2 + \u221a6 = 9.863+", "metric_symbol": "s", "metric_value": 9.863, "reference_text": "s = 6 + \u221a2 + \u221a6 = 9.863+", "source_image": "cs24.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs24.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 6 + \u221a2 + \u221a6 = 9.863+", "friedman_source_image": "cs24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "e2eca298edbdb88c", "improvement": -0.0009181131343805049, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.506144878683841e-06, "max_pair_overlap_depth": -4.0021533562306644e-05, "metric_expression": "9.86392", "metric_symbol": "s", "metric_value": 9.86391811313438, "n": 24, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.863, "setup": "cirinsqu", "side": 9.86391811313438, "solution_path": "data/solutions/generated/cirinsqu_024_e2eca298edbdb88c.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman Packing Center", "svg_path": "data/svg/e2eca298edbdb88c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirintri@1", "density": 0.6045962978262086, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct1.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "2\u221a3 = 3.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.464, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2\u221a3 = 3.464+", "metric_symbol": "s", "metric_value": 3.464, "reference_text": "s = 2\u221a3 = 3.464+ | Trivial.", "source_image": "ct1.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct1.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 2\u221a3 = 3.464+ | Trivial.", "friedman_source_image": "ct1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "10a7a380c7f5376a", "improvement": -0.00011161401610815247, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7091087705090047e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "3.46411", "metric_symbol": "s", "metric_value": 3.464111614016108, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.464, "setup": "cirintri", "side": 3.464111614016108, "solution_path": "data/solutions/generated/cirintri_001_10a7a380c7f5376a.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/10a7a380c7f5376a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirintri@2", "density": 0.48598475821399, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct2.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "2 + 2\u221a3 = 5.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.464, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2 + 2\u221a3 = 5.464+", "metric_symbol": "s", "metric_value": 5.464, "reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "source_image": "ct2.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct2.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "friedman_source_image": "ct2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "f5cde1b8295da3ad", "improvement": -0.00022144929157175142, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7587277048611867e-06, "max_pair_overlap_depth": -7.068795172848752e-05, "metric_expression": "5.46422", "metric_symbol": "s", "metric_value": 5.464221449291572, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.464, "setup": "cirintri", "side": 5.464221449291572, "solution_path": "data/solutions/generated/cirintri_002_f5cde1b8295da3ad.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/f5cde1b8295da3ad.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirintri@3", "density": 0.7289907317557431, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct3.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "2 + 2\u221a3 = 5.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.464, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2 + 2\u221a3 = 5.464+", "metric_symbol": "s", "metric_value": 5.464, "reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "source_image": "ct3.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct3.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "friedman_source_image": "ct3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "fcee9d6e8b7c5ce0", "improvement": -0.000170499845251193, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0755666179917966e-07, "max_pair_overlap_depth": -5.0474041760395494e-05, "metric_expression": "5.46417", "metric_symbol": "s", "metric_value": 5.464170499845252, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.464, "setup": "cirintri", "side": 5.464170499845252, "solution_path": "data/solutions/generated/cirintri_003_fcee9d6e8b7c5ce0.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/fcee9d6e8b7c5ce0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirintri@4", "density": 0.6045810458812538, "friedman_analytical_or_proved": true, "friedman_credit": "Milano", "friedman_date": "1987", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct4.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "4\u221a3 = 6.928+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.928, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@4", "credit": "Milano", "date": "1987", "family_updated": "", "metric_expression": "4\u221a3 = 6.928+", "metric_symbol": "s", "metric_value": 6.928, "reference_text": "s = 4\u221a3 = 6.928+ | Proved by Milano in 1987.", "source_image": "ct4.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct4.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 4\u221a3 = 6.928+ | Proved by Milano in 1987.", "friedman_source_image": "ct4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "9e0c39beb3cc8aa7", "improvement": -0.0003106176498706148, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7330840119143005e-06, "max_pair_overlap_depth": -4.49553106092182e-05, "metric_expression": "6.92831", "metric_symbol": "s", "metric_value": 6.9283106176498706, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.928, "setup": "cirintri", "side": 6.9283106176498706, "solution_path": "data/solutions/generated/cirintri_004_9e0c39beb3cc8aa7.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Milano", "svg_path": "data/svg/9e0c39beb3cc8aa7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirintri@5", "density": 0.6510985676665063, "friedman_analytical_or_proved": true, "friedman_credit": "Milano", "friedman_date": "1987", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct5.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "4 + 2\u221a3 = 7.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.464, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@5", "credit": "Milano", "date": "1987", "family_updated": "", "metric_expression": "4 + 2\u221a3 = 7.464+", "metric_symbol": "s", "metric_value": 7.464, "reference_text": "s = 4 + 2\u221a3 = 7.464+ | Proved by Milano in 1987.", "source_image": "ct5.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct5.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 4 + 2\u221a3 = 7.464+ | Proved by Milano in 1987.", "friedman_source_image": "ct5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "ad32c3b8e4c714b5", "improvement": -0.00025126705611278055, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.12146637612598e-06, "max_pair_overlap_depth": -3.650753517803196e-05, "metric_expression": "7.46425", "metric_symbol": "s", "metric_value": 7.464251267056113, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.464, "setup": "cirintri", "side": 7.464251267056113, "solution_path": "data/solutions/generated/cirintri_005_ad32c3b8e4c714b5.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Milano", "svg_path": "data/svg/ad32c3b8e4c714b5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirintri@6", "density": 0.7813295579764934, "friedman_analytical_or_proved": true, "friedman_credit": "Oler/Groemer", "friedman_date": "1961", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct6.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "4 + 2\u221a3 = 7.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.464, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@6", "credit": "Oler/Groemer", "date": "1961", "family_updated": "", "metric_expression": "4 + 2\u221a3 = 7.464+", "metric_symbol": "s", "metric_value": 7.464, "reference_text": "s = 4 + 2\u221a3 = 7.464+ | Proved by Oler/Groemer in 1961.", "source_image": "ct6.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct6.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 4 + 2\u221a3 = 7.464+ | Proved by Oler/Groemer in 1961.", "friedman_source_image": "ct6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "09bddcb97a85d368", "improvement": -0.00019740182247307558, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.6105130511423482e-06, "max_pair_overlap_depth": -3.3410124574029254e-05, "metric_expression": "7.46420", "metric_symbol": "s", "metric_value": 7.4641974018224735, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.464, "setup": "cirintri", "side": 7.4641974018224735, "solution_path": "data/solutions/generated/cirintri_006_09bddcb97a85d368.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Oler/Groemer", "svg_path": "data/svg/09bddcb97a85d368.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirintri@7", "density": 0.6370913423934993, "friedman_analytical_or_proved": true, "friedman_credit": "Melissen", "friedman_date": "1993", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct7.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "2 + 4\u221a3 = 8.928+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.928, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@7", "credit": "Melissen", "date": "1993", "family_updated": "", "metric_expression": "2 + 4\u221a3 = 8.928+", "metric_symbol": "s", "metric_value": 8.928, "reference_text": "s = 2 + 4\u221a3 = 8.928+ | Proved by Melissen in 1993.", "source_image": "ct7.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct7.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 2 + 4\u221a3 = 8.928+ | Proved by Melissen in 1993.", "friedman_source_image": "ct7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "1d479488f6f25560", "improvement": -0.0003824812590771387, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.6242968528307244e-06, "max_pair_overlap_depth": -4.768068922000879e-05, "metric_expression": "8.92838", "metric_symbol": "s", "metric_value": 8.928382481259078, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.928, "setup": "cirintri", "side": 8.928382481259078, "solution_path": "data/solutions/generated/cirintri_007_1d479488f6f25560.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Melissen", "svg_path": "data/svg/1d479488f6f25560.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirintri@8", "density": 0.6718185539703104, "friedman_analytical_or_proved": true, "friedman_credit": "Melissen", "friedman_date": "1993", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct8.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "2 + 2\u221a3 + 2\u221a33/3 = 9.293+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.293, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@8", "credit": "Melissen", "date": "1993", "family_updated": "", "metric_expression": "2 + 2\u221a3 + 2\u221a33/3 = 9.293+", "metric_symbol": "s", "metric_value": 9.293, "reference_text": "s = 2 + 2\u221a3 + 2\u221a33/3 = 9.293+ | Proved by Melissen in 1993.", "source_image": "ct8.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct8.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 2 + 2\u221a3 + 2\u221a33/3 = 9.293+ | Proved by Melissen in 1993.", "friedman_source_image": "ct8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "ad6e4ca149e6364f", "improvement": -0.0018763116025901638, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.090428418316975e-06, "max_pair_overlap_depth": -4.461887232398709e-05, "metric_expression": "9.29488", "metric_symbol": "s", "metric_value": 9.29487631160259, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.293, "setup": "cirintri", "side": 9.29487631160259, "solution_path": "data/solutions/generated/cirintri_008_ad6e4ca149e6364f.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Melissen", "svg_path": "data/svg/ad6e4ca149e6364f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirintri@9", "density": 0.728985395977573, "friedman_analytical_or_proved": true, "friedman_credit": "Melissen", "friedman_date": "1993", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct9.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "6 + 2\u221a3 = 9.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.464, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@9", "credit": "Melissen", "date": "1993", "family_updated": "", "metric_expression": "6 + 2\u221a3 = 9.464+", "metric_symbol": "s", "metric_value": 9.464, "reference_text": "s = 6 + 2\u221a3 = 9.464+ | Proved by Melissen in 1993.", "source_image": "ct9.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct9.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 6 + 2\u221a3 = 9.464+ | Proved by Melissen in 1993.", "friedman_source_image": "ct9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "108d2156f1819ef5", "improvement": -0.0002555633725904727, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.43897889048894e-06, "max_pair_overlap_depth": -2.63301951002326e-05, "metric_expression": "9.46426", "metric_symbol": "s", "metric_value": 9.46425556337259, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.464, "setup": "cirintri", "side": 9.46425556337259, "solution_path": "data/solutions/generated/cirintri_009_108d2156f1819ef5.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Melissen", "svg_path": "data/svg/108d2156f1819ef5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirintri@10", "density": 0.8099824382101458, "friedman_analytical_or_proved": true, "friedman_credit": "Oler/Groemer", "friedman_date": "1961", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct10.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "6 + 2\u221a3 = 9.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.464, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@10", "credit": "Oler/Groemer", "date": "1961", "family_updated": "", "metric_expression": "6 + 2\u221a3 = 9.464+", "metric_symbol": "s", "metric_value": 9.464, "reference_text": "s = 6 + 2\u221a3 = 9.464+ | Proved by Oler/Groemer in 1961.", "source_image": "ct10.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct10.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 6 + 2\u221a3 = 9.464+ | Proved by Oler/Groemer in 1961.", "friedman_source_image": "ct10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "abf88e494059d012", "improvement": -0.0002633633602293628, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.885918628489861e-06, "max_pair_overlap_depth": -4.501428401626484e-05, "metric_expression": "9.46426", "metric_symbol": "s", "metric_value": 9.46426336336023, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.464, "setup": "cirintri", "side": 9.46426336336023, "solution_path": "data/solutions/generated/cirintri_010_abf88e494059d012.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Oler/Groemer", "svg_path": "data/svg/abf88e494059d012.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirintri@11", "density": 0.693141460882906, "friedman_analytical_or_proved": true, "friedman_credit": "Melissen", "friedman_date": "1993", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct11.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "4 + 2\u221a3 + 4\u221a6/3 = 10.730+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.73, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@11", "credit": "Melissen", "date": "1993", "family_updated": "", "metric_expression": "4 + 2\u221a3 + 4\u221a6/3 = 10.730+", "metric_symbol": "s", "metric_value": 10.73, "reference_text": "s = 4 + 2\u221a3 + 4\u221a6/3 = 10.730+ | Proved by Melissen in 1993.", "source_image": "ct11.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct11.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 4 + 2\u221a3 + 4\u221a6/3 = 10.730+ | Proved by Melissen in 1993.", "friedman_source_image": "ct11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "64f835afcfaa2245", "improvement": -0.00025448918442982915, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7228747402064926e-06, "max_pair_overlap_depth": -3.113241300978231e-05, "metric_expression": "10.73025", "metric_symbol": "s", "metric_value": 10.73025448918443, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 10.73, "setup": "cirintri", "side": 10.73025448918443, "solution_path": "data/solutions/generated/cirintri_011_64f835afcfaa2245.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Melissen", "svg_path": "data/svg/64f835afcfaa2245.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirintri@12", "density": 0.7289832647467578, "friedman_analytical_or_proved": true, "friedman_credit": "Melissen", "friedman_date": "1994", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct12.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "4 + 4\u221a3 = 10.928+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.928, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@12", "credit": "Melissen", "date": "1994", "family_updated": "", "metric_expression": "4 + 4\u221a3 = 10.928+", "metric_symbol": "s", "metric_value": 10.928, "reference_text": "s = 4 + 4\u221a3 = 10.928+ | Proved by Melissen in 1994.", "source_image": "ct12.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct12.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 4 + 4\u221a3 = 10.928+ | Proved by Melissen in 1994.", "friedman_source_image": "ct12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "c94cd40d17cad41e", "improvement": -0.00039696929599308817, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.790000236816084e-06, "max_pair_overlap_depth": -3.824380327710486e-05, "metric_expression": "10.92840", "metric_symbol": "s", "metric_value": 10.928396969295994, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 10.928, "setup": "cirintri", "side": 10.928396969295994, "solution_path": "data/solutions/generated/cirintri_012_c94cd40d17cad41e.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Melissen", "svg_path": "data/svg/c94cd40d17cad41e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirintri@13", "density": 0.7248761583522253, "friedman_analytical_or_proved": true, "friedman_credit": "Melissen", "friedman_date": "1993", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct13.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "4 + 2\u221a6/3 + 10\u221a3/3 = 11.406+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.406, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@13", "credit": "Melissen", "date": "1993", "family_updated": "", "metric_expression": "4 + 2\u221a6/3 + 10\u221a3/3 = 11.406+", "metric_symbol": "s", "metric_value": 11.406, "reference_text": "s = 4 + 2\u221a6/3 + 10\u221a3/3 = 11.406+ | Found by Melissen in 1993.", "source_image": "ct13.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct13.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 4 + 2\u221a6/3 + 10\u221a3/3 = 11.406+ | Found by Melissen in 1993.", "friedman_source_image": "ct13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "4ca74ad9707b79ad", "improvement": -0.0008146992920448071, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.27136224545599e-06, "max_pair_overlap_depth": -4.371332125208127e-05, "metric_expression": "11.40681", "metric_symbol": "s", "metric_value": 11.406814699292045, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 11.406, "setup": "cirintri", "side": 11.406814699292045, "solution_path": "data/solutions/generated/cirintri_013_4ca74ad9707b79ad.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Melissen", "svg_path": "data/svg/4ca74ad9707b79ad.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirintri@14", "density": 0.7728234005113342, "friedman_analytical_or_proved": true, "friedman_credit": "Erd\u0151s/Oler", "friedman_date": "1961", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct14.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "8 + 2\u221a3 = 11.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.464, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@14", "credit": "Erd\u0151s/Oler", "date": "1961", "family_updated": "", "metric_expression": "8 + 2\u221a3 = 11.464+", "metric_symbol": "s", "metric_value": 11.464, "reference_text": "s = 8 + 2\u221a3 = 11.464+ | Found by Erd\u0151s/Oler in 1961.", "source_image": "ct14.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct14.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 8 + 2\u221a3 = 11.464+ | Found by Erd\u0151s/Oler in 1961.", "friedman_source_image": "ct14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "67743153538612b8", "improvement": -0.00032539636501560665, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.0042126467086945e-06, "max_pair_overlap_depth": -3.7763457817252544e-05, "metric_expression": "11.46433", "metric_symbol": "s", "metric_value": 11.464325396365016, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 11.464, "setup": "cirintri", "side": 11.464325396365016, "solution_path": "data/solutions/generated/cirintri_014_67743153538612b8.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erd\u0151s/Oler", "svg_path": "data/svg/67743153538612b8.svg", "tolerance": 1e-08, "verified": true}
-{"case": "cirintri@15", "density": 0.82802371463932, "friedman_analytical_or_proved": true, "friedman_credit": "Erd\u0151s/Groemer", "friedman_date": "1961", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct15.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "8 + 2\u221a3 = 11.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.464, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@15", "credit": "Erd\u0151s/Groemer", "date": "1961", "family_updated": "", "metric_expression": "8 + 2\u221a3 = 11.464+", "metric_symbol": "s", "metric_value": 11.464, "reference_text": "s = 8 + 2\u221a3 = 11.464+ | Proved by Erd\u0151s/Groemer in 1961.", "source_image": "ct15.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct15.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 8 + 2\u221a3 = 11.464+ | Proved by Erd\u0151s/Groemer in 1961.", "friedman_source_image": "ct15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "2a26f9d337f635e0", "improvement": -0.00033479280357262553, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.377565219179871e-06, "max_pair_overlap_depth": -4.0761680023315705e-05, "metric_expression": "11.46433", "metric_symbol": "s", "metric_value": 11.464334792803573, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 11.464, "setup": "cirintri", "side": 11.464334792803573, "solution_path": "data/solutions/generated/cirintri_015_2a26f9d337f635e0.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erd\u0151s/Groemer", "svg_path": "data/svg/2a26f9d337f635e0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domindom@1", "density": 0.9999892980292665, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/1.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "domindom@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "1. | | s = 1 | Trivial.", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/1.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "1. | | s = 1 | Trivial.", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "6b50d5741feee5dc", "improvement": -5.351028316669115e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6755141583345576e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_symbol": "s", "metric_value": 1.0000053510283167, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.0, "setup": "domindom", "side": 2.0000107020566333, "solution_path": "data/solutions/generated/domindom_001_6b50d5741feee5dc.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/6b50d5741feee5dc.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domindom@2", "density": 0.5146978614404703, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/2.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "(2+\u221a2)/\u221a3 = 1.971+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.971, "friedman_reference": {"analytical_or_proved": true, "case": "domindom@2", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "", "metric_expression": "(2+\u221a2)/\u221a3 = 1.971+", "metric_symbol": "s", "metric_value": 1.971, "reference_text": "2. | | s = (2+\u221a2)/\u221a3 = 1.971+ | Found by Erich Friedman in April 2026.", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/2.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "2. | | s = (2+\u221a2)/\u221a3 = 1.971+ | Found by Erich Friedman in April 2026.", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "e1760976ec64bd64", "improvement": -0.000236880650400062, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9155926735958673e-06, "max_pair_overlap_depth": -6.0125633082330765e-06, "metric_expression": "1.97124", "metric_symbol": "s", "metric_value": 1.9712368806504001, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.971, "setup": "domindom", "side": 3.9424737613008003, "solution_path": "data/solutions/generated/domindom_002_e1760976ec64bd64.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/e1760976ec64bd64.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domindom@3", "density": 0.7499858951262421, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/4.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "domindom@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "3.-4. | | s = 2 | Trivial.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/4.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "3.-4. | | s = 2 | Trivial.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "5194ab3dddc343bb", "improvement": -1.8806763611323163e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3349574317089719e-06, "max_pair_overlap_depth": -6.50598393479697e-06, "metric_expression": "2.00002", "metric_symbol": "s", "metric_value": 2.0000188067636113, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "domindom", "side": 4.000037613527223, "solution_path": "data/solutions/generated/domindom_003_5194ab3dddc343bb.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/5194ab3dddc343bb.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domindom@4", "density": 0.9999632147512098, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/4.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "domindom@4", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "3.-4. | | s = 2 | Trivial.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/4.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "3.-4. | | s = 2 | Trivial.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "14a703d2c83d5b43", "improvement": -3.6786263687194065e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.672168442576563e-06, "max_pair_overlap_depth": -2.5740489017265176e-05, "metric_expression": "2.00004", "metric_symbol": "s", "metric_value": 2.000036786263687, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "domindom", "side": 4.000073572527374, "solution_path": "data/solutions/generated/domindom_004_14a703d2c83d5b43.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/14a703d2c83d5b43.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domindom@5", "density": 0.7999239260919105, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/5.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "5/2 = 2.5", "friedman_metric_symbol": "s", "friedman_metric_value": 2.5, "friedman_reference": {"analytical_or_proved": true, "case": "domindom@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5/2 = 2.5", "metric_symbol": "s", "metric_value": 2.5, "reference_text": "5. | | s = 5/2 = 2.5 | Trivial.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/5.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "5. | | s = 5/2 = 2.5 | Trivial.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "af0995e19f0dc8ce", "improvement": -0.00011887395946308388, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.6075584103633105e-07, "max_pair_overlap_depth": -2.297221660940707e-05, "metric_expression": "2.50012", "metric_symbol": "s", "metric_value": 2.500118873959463, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.5, "setup": "domindom", "side": 5.000237747918926, "solution_path": "data/solutions/generated/domindom_005_af0995e19f0dc8ce.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/af0995e19f0dc8ce.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domindom@6", "density": 0.7051360525077088, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/6.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "2.916+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.916, "friedman_reference": {"analytical_or_proved": false, "case": "domindom@6", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "", "metric_expression": "2.916+", "metric_symbol": "s", "metric_value": 2.916, "reference_text": "6. | | s = 2.916+ | Found by Erich Friedman in April 2026.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/6.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "6. | | s = 2.916+ | Found by Erich Friedman in April 2026.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "0f3d5defa1e042a8", "improvement": -0.001018377106842383, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.01302900812739e-06, "max_pair_overlap_depth": -7.57681649177222e-06, "metric_expression": "2.91702", "metric_symbol": "s", "metric_value": 2.9170183771068423, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.916, "setup": "domindom", "side": 5.834036754213685, "solution_path": "data/solutions/generated/domindom_006_0f3d5defa1e042a8.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/0f3d5defa1e042a8.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domindom@7", "density": 0.777726224180711, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "domindom@7", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "7.-9. | | s = 3 | Trivial.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "7.-9. | | s = 3 | Trivial.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "7b5335d8b8c4a5db", "improvement": -9.942973726095872e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3331344280185253e-06, "max_pair_overlap_depth": -2.1961883454491016e-05, "metric_expression": "3.00010", "metric_symbol": "s", "metric_value": 3.000099429737261, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.0, "setup": "domindom", "side": 6.000198859474522, "solution_path": "data/solutions/generated/domindom_007_7b5335d8b8c4a5db.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/7b5335d8b8c4a5db.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domindom@8", "density": 0.8888442639489805, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "domindom@8", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "7.-9. | | s = 3 | Trivial.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "7.-9. | | s = 3 | Trivial.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "953d10b3e926402a", "improvement": -7.530742160444248e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.80012014980602e-06, "max_pair_overlap_depth": -1.8965164302886528e-05, "metric_expression": "3.00008", "metric_symbol": "s", "metric_value": 3.0000753074216044, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.0, "setup": "domindom", "side": 6.000150614843209, "solution_path": "data/solutions/generated/domindom_008_953d10b3e926402a.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/953d10b3e926402a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domindom@9", "density": 0.9999668695349745, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "domindom@9", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "7.-9. | | s = 3 | Trivial.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "7.-9. | | s = 3 | Trivial.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "43b9630822b40990", "improvement": -4.9696932403531235e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7542337882889854e-07, "max_pair_overlap_depth": -3.0527855267026283e-06, "metric_expression": "3.00005", "metric_symbol": "s", "metric_value": 3.0000496969324035, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.0, "setup": "domindom", "side": 6.000099393864807, "solution_path": "data/solutions/generated/domindom_009_43b9630822b40990.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/43b9630822b40990.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domindom@10", "density": 0.8162099861183555, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/10.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "7/2 = 3.5", "friedman_metric_symbol": "s", "friedman_metric_value": 3.5, "friedman_reference": {"analytical_or_proved": true, "case": "domindom@10", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "7/2 = 3.5", "metric_symbol": "s", "metric_value": 3.5, "reference_text": "10. | | s = 7/2 = 3.5 | Trivial.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/10.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "10. | | s = 7/2 = 3.5 | Trivial.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "d7508c45c3f18a7c", "improvement": -0.0002498690138819093, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5739397918324016e-07, "max_pair_overlap_depth": -9.291197802940854e-05, "metric_expression": "3.50025", "metric_symbol": "s", "metric_value": 3.500249869013882, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.5, "setup": "domindom", "side": 7.000499738027764, "solution_path": "data/solutions/generated/domindom_010_d7508c45c3f18a7c.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d7508c45c3f18a7c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domindom@11", "density": 0.7611589259525644, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/11.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "(5+\u221a41)/3 = 3.801+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.801, "friedman_reference": {"analytical_or_proved": true, "case": "domindom@11", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "(5+\u221a41)/3 = 3.801+", "metric_symbol": "s", "metric_value": 3.801, "reference_text": "11. | | s = (5+\u221a41)/3 = 3.801+ | Found by Maurizio Morandi in April 2026.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/11.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "11. | | s = (5+\u221a41)/3 = 3.801+ | Found by Maurizio Morandi in April 2026.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "0fa9d3de612fbf03", "improvement": -0.0005321723096423092, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0757791549262947e-06, "max_pair_overlap_depth": -0.0001019023981195799, "metric_expression": "3.80153", "metric_symbol": "s", "metric_value": 3.8015321723096425, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.801, "setup": "domindom", "side": 7.603064344619285, "solution_path": "data/solutions/generated/domindom_011_0fa9d3de612fbf03.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/0fa9d3de612fbf03.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domindom@12", "density": 0.7822558234911755, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/12.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "5/2+\u221a2 = 3.914+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.914, "friedman_reference": {"analytical_or_proved": true, "case": "domindom@12", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "5/2+\u221a2 = 3.914+", "metric_symbol": "s", "metric_value": 3.914, "reference_text": "12. | | s = 5/2+\u221a2 = 3.914+ | Found by Maurizio Morandi in April 2026.", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/12.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "12. | | s = 5/2+\u221a2 = 3.914+ | Found by Maurizio Morandi in April 2026.", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "3a75d33bd56228b0", "improvement": -0.002663137487304734, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.0673284962267076e-07, "max_pair_overlap_depth": -1.4217486933421064e-05, "metric_expression": "3.91666", "metric_symbol": "s", "metric_value": 3.916663137487305, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.914, "setup": "domindom", "side": 7.83332627497461, "solution_path": "data/solutions/generated/domindom_012_3a75d33bd56228b0.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T03:07:58+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/3a75d33bd56228b0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domindom@14", "density": 0.8749484114386541, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "domindom@14", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "14.-16 | | s = 4 | Trivial.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "14.-16 | | s = 4 | Trivial.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "8be6cbfdbea40909", "improvement": -0.00011792192603543583, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.966859551203129e-06, "max_pair_overlap_depth": -1.688780940467538e-05, "metric_expression": "4.00012", "metric_symbol": "s", "metric_value": 4.000117921926035, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.0, "setup": "domindom", "side": 8.00023584385207, "solution_path": "data/solutions/generated/domindom_014_8be6cbfdbea40909.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/8be6cbfdbea40909.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domindom@15", "density": 0.9374471956142247, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "domindom@15", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "14.-16 | | s = 4 | Trivial.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "14.-16 | | s = 4 | Trivial.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "d2b8e4757dde349c", "improvement": -0.00011265411524785662, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.415030228686277e-06, "max_pair_overlap_depth": -1.0456826571081379e-05, "metric_expression": "4.00011", "metric_symbol": "s", "metric_value": 4.000112654115248, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.0, "setup": "domindom", "side": 8.000225308230496, "solution_path": "data/solutions/generated/domindom_015_d2b8e4757dde349c.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d2b8e4757dde349c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domindom@16", "density": 0.9999595560012681, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "domindom@16", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "14.-16 | | s = 4 | Trivial.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "14.-16 | | s = 4 | Trivial.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "5102d8436800a7ff", "improvement": -8.08904511222508e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.23688533190969e-06, "max_pair_overlap_depth": -4.621969549978289e-06, "metric_expression": "4.00008", "metric_symbol": "s", "metric_value": 4.000080890451122, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.0, "setup": "domindom", "side": 8.000161780902245, "solution_path": "data/solutions/generated/domindom_016_5102d8436800a7ff.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/5102d8436800a7ff.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domindom@17", "density": 0.8394293686085971, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/18.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "9/2 = 4.5", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5, "friedman_reference": {"analytical_or_proved": true, "case": "domindom@17", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "9/2 = 4.5", "metric_symbol": "s", "metric_value": 4.5, "reference_text": "17.-18 | | s = 9/2 = 4.5 | Trivial.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/18.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "17.-18 | | s = 9/2 = 4.5 | Trivial.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "3b388ddd068a843f", "improvement": -0.00020586075893191946, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.953267209728551e-07, "max_pair_overlap_depth": -5.000451830872166e-05, "metric_expression": "4.50021", "metric_symbol": "s", "metric_value": 4.500205860758932, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.5, "setup": "domindom", "side": 9.000411721517864, "solution_path": "data/solutions/generated/domindom_017_3b388ddd068a843f.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/3b388ddd068a843f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domindom@18", "density": 0.887184224626392, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/18.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "9/2 = 4.5", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5, "friedman_reference": {"analytical_or_proved": true, "case": "domindom@18", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "9/2 = 4.5", "metric_symbol": "s", "metric_value": 4.5, "reference_text": "17.-18 | | s = 9/2 = 4.5 | Trivial.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/18.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "17.-18 | | s = 9/2 = 4.5 | Trivial.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "6a5fcb6ec4e55187", "improvement": -0.004321147560441219, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4781434060372476e-06, "max_pair_overlap_depth": -4.894490537976637e-05, "metric_expression": "4.50432", "metric_symbol": "s", "metric_value": 4.504321147560441, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.5, "setup": "domindom", "side": 9.008642295120882, "solution_path": "data/solutions/generated/domindom_018_6a5fcb6ec4e55187.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/6a5fcb6ec4e55187.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@1", "density": 0.46408935997723705, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/1.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "2+2/\u221a3 = 3.15470+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.1547, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2+2/\u221a3 = 3.15470+", "metric_symbol": "s", "metric_value": 3.1547, "reference_text": "s = 2+2/\u221a3 = 3.15470+ | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/1.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 2+2/\u221a3 = 3.15470+ | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "6121ec989c6c813b", "improvement": -4.219103236957622e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.613940413552034e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "3.15474", "metric_symbol": "s", "metric_value": 3.1547421910323696, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.1547, "setup": "domintri", "side": 3.1547421910323696, "solution_path": "data/solutions/generated/domintri_001_6121ec989c6c813b.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/6121ec989c6c813b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@2", "density": 0.4973974214603669, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/2.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "2+4/\u221a3 = 4.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.3094, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2+4/\u221a3 = 4.30940+", "metric_symbol": "s", "metric_value": 4.3094, "reference_text": "s = 2+4/\u221a3 = 4.30940+ | Trivial.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/2.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 2+4/\u221a3 = 4.30940+ | Trivial.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "75b0ecc0320e01de", "improvement": -0.00011019921439459068, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.546312299587745e-06, "max_pair_overlap_depth": -2.318487220109855e-05, "metric_expression": "4.30951", "metric_symbol": "s", "metric_value": 4.309510199214395, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.3094, "setup": "domintri", "side": 4.309510199214395, "solution_path": "data/solutions/generated/domintri_002_75b0ecc0320e01de.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/75b0ecc0320e01de.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@3", "density": 0.746073641317824, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/3.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "2+4/\u221a3 = 4.30934+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.30934, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2+4/\u221a3 = 4.30934+", "metric_symbol": "s", "metric_value": 4.30934, "reference_text": "s = 2+4/\u221a3 = 4.30934+ | Trivial.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/3.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 2+4/\u221a3 = 4.30934+ | Trivial.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "ecf54a038a2d7184", "improvement": -0.00023515521175365706, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2511235262659097e-06, "max_pair_overlap_depth": -8.934604283755698e-05, "metric_expression": "4.30958", "metric_symbol": "s", "metric_value": 4.309575155211753, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.30934, "setup": "domintri", "side": 4.309575155211753, "solution_path": "data/solutions/generated/domintri_003_ecf54a038a2d7184.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/ecf54a038a2d7184.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@4", "density": 0.6377999539199563, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/4.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "5.38188+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.38188, "friedman_reference": {"analytical_or_proved": false, "case": "domintri@4", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.38188+", "metric_symbol": "s", "metric_value": 5.38188, "reference_text": "s = 5.38188+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/4.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 5.38188+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "6f3730492b03ce4f", "improvement": -0.0002283152146249634, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.401205447247945e-07, "max_pair_overlap_depth": -4.238554796887062e-05, "metric_expression": "5.38211", "metric_symbol": "s", "metric_value": 5.382108315214625, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.38188, "setup": "domintri", "side": 5.382108315214625, "solution_path": "data/solutions/generated/domintri_004_6f3730492b03ce4f.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/6f3730492b03ce4f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@5", "density": 0.7734497127773695, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/5.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "2+2\u221a3 = 5.46410+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.4641, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@5", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2+2\u221a3 = 5.46410+", "metric_symbol": "s", "metric_value": 5.4641, "reference_text": "s = 2+2\u221a3 = 5.46410+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "5.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/5.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 2+2\u221a3 = 5.46410+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "272a5ede0aa9a415", "improvement": -0.00018874969044357925, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.315600305266359e-07, "max_pair_overlap_depth": -2.2346020378205544e-05, "metric_expression": "5.46429", "metric_symbol": "s", "metric_value": 5.464288749690444, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.4641, "setup": "domintri", "side": 5.464288749690444, "solution_path": "data/solutions/generated/domintri_005_272a5ede0aa9a415.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/272a5ede0aa9a415.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@6", "density": 0.6961017329945272, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/6.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "4+4/\u221a3 = 6.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.3094, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@6", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4+4/\u221a3 = 6.30940+", "metric_symbol": "s", "metric_value": 6.3094, "reference_text": "s = 4+4/\u221a3 = 6.30940+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/6.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 4+4/\u221a3 = 6.30940+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "5709487003259292", "improvement": -0.0002307959840699425, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1058985619703807e-06, "max_pair_overlap_depth": -5.695799924376743e-05, "metric_expression": "6.30963", "metric_symbol": "s", "metric_value": 6.30963079598407, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.3094, "setup": "domintri", "side": 6.30963079598407, "solution_path": "data/solutions/generated/domintri_006_5709487003259292.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/5709487003259292.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@7", "density": 0.7379982685276676, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/7.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "6.61409+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.61409, "friedman_reference": {"analytical_or_proved": false, "case": "domintri@7", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6.61409+", "metric_symbol": "s", "metric_value": 6.61409, "reference_text": "s = 6.61409+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/7.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 6.61409+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "4f3a41ae14776742", "improvement": -0.004813180227946745, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.155481361422797e-07, "max_pair_overlap_depth": -2.185552101252597e-05, "metric_expression": "6.61890", "metric_symbol": "s", "metric_value": 6.618903180227947, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.61409, "setup": "domintri", "side": 6.618903180227947, "solution_path": "data/solutions/generated/domintri_007_4f3a41ae14776742.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/4f3a41ae14776742.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@8", "density": 0.7218039663224785, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/8.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "6+2/\u221a3 = 7.15470+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.1547, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@8", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6+2/\u221a3 = 7.15470+", "metric_symbol": "s", "metric_value": 7.1547, "reference_text": "s = 6+2/\u221a3 = 7.15470+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/8.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 6+2/\u221a3 = 7.15470+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "6c005b2a9a930ec2", "improvement": -0.00014189325334523772, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4194624753243232e-06, "max_pair_overlap_depth": -3.0722639065561275e-05, "metric_expression": "7.15484", "metric_symbol": "s", "metric_value": 7.154841893253345, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.1547, "setup": "domintri", "side": 7.154841893253345, "solution_path": "data/solutions/generated/domintri_008_6c005b2a9a930ec2.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/6c005b2a9a930ec2.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@9", "density": 0.7778159590517906, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/9.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "5+4/\u221a3 = 7.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.3094, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@9", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5+4/\u221a3 = 7.30940+", "metric_symbol": "s", "metric_value": 7.3094, "reference_text": "s = 5+4/\u221a3 = 7.30940+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/9.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 5+4/\u221a3 = 7.30940+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "efd3c01a911fbe39", "improvement": -0.0011072089155117482, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4249809133477843e-06, "max_pair_overlap_depth": -9.12510211048545e-05, "metric_expression": "7.31051", "metric_symbol": "s", "metric_value": 7.310507208915512, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.3094, "setup": "domintri", "side": 7.310507208915512, "solution_path": "data/solutions/generated/domintri_009_efd3c01a911fbe39.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/efd3c01a911fbe39.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@10", "density": 0.7955429934788115, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/10.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "3+8/\u221a3 = 7.61885+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.61885, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@10", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3+8/\u221a3 = 7.61885+", "metric_symbol": "s", "metric_value": 7.61885, "reference_text": "s = 3+8/\u221a3 = 7.61885+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/10.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 3+8/\u221a3 = 7.61885+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "0ce8e56f538c019b", "improvement": -0.000761914714127343, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.832683484389887e-07, "max_pair_overlap_depth": -3.7959726496283874e-06, "metric_expression": "7.61961", "metric_symbol": "s", "metric_value": 7.6196119147141275, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.61885, "setup": "domintri", "side": 7.6196119147141275, "solution_path": "data/solutions/generated/domintri_010_0ce8e56f538c019b.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/0ce8e56f538c019b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@11", "density": 0.7639001254938724, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/11.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "7+2/\u221a3 = 8.15470+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.1547, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@11", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "7+2/\u221a3 = 8.15470+", "metric_symbol": "s", "metric_value": 8.1547, "reference_text": "s = 7+2/\u221a3 = 8.15470+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "11.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/11.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 7+2/\u221a3 = 8.15470+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "11.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "9dea260c7a23e4ab", "improvement": -0.0006523939405695955, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.1114403341932665e-06, "max_pair_overlap_depth": -5.305705658820159e-06, "metric_expression": "8.15535", "metric_symbol": "s", "metric_value": 8.15535239394057, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.1547, "setup": "domintri", "side": 8.15535239394057, "solution_path": "data/solutions/generated/domintri_011_9dea260c7a23e4ab.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/9dea260c7a23e4ab.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@12", "density": 0.8025727620592626, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/12.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "6+4/\u221a3 = 8.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.3094, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@12", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6+4/\u221a3 = 8.30940+", "metric_symbol": "s", "metric_value": 8.3094, "reference_text": "s = 6+4/\u221a3 = 8.30940+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/12.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 6+4/\u221a3 = 8.30940+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "c7b6e34fcb0ca6b3", "improvement": -0.0008309724073285452, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.6999836404354686e-06, "max_pair_overlap_depth": -5.386448125865861e-06, "metric_expression": "8.31023", "metric_symbol": "s", "metric_value": 8.310230972407329, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.3094, "setup": "domintri", "side": 8.310230972407329, "solution_path": "data/solutions/generated/domintri_012_c7b6e34fcb0ca6b3.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/c7b6e34fcb0ca6b3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@13", "density": 0.8080926405411509, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/13.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "4+8/\u221a3 = 8.61885+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.61885, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@13", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4+8/\u221a3 = 8.61885+", "metric_symbol": "s", "metric_value": 8.61885, "reference_text": "s = 4+8/\u221a3 = 8.61885+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/13.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 4+8/\u221a3 = 8.61885+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "9f9d19c6f117401b", "improvement": -0.0011205125576889685, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.5415762652602807e-06, "max_pair_overlap_depth": -3.765847597092531e-05, "metric_expression": "8.61997", "metric_symbol": "s", "metric_value": 8.619970512557689, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.61885, "setup": "domintri", "side": 8.619970512557689, "solution_path": "data/solutions/generated/domintri_013_9f9d19c6f117401b.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/9f9d19c6f117401b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@14", "density": 0.8398945758370188, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/14.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "3+10/\u221a3 = 8.77350+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.7735, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@14", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "3+10/\u221a3 = 8.77350+", "metric_symbol": "s", "metric_value": 8.7735, "reference_text": "s = 3+10/\u221a3 = 8.77350+ | Found by Maurizio Morandi | in April 2026.", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/14.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 3+10/\u221a3 = 8.77350+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "333566d5c4b3657c", "improvement": -0.0008773842173539492, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 2.796172321890858e-09, "max_pair_overlap_depth": -3.2457310312317134e-05, "metric_expression": "8.77438", "metric_symbol": "s", "metric_value": 8.774377384217354, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.7735, "setup": "domintri", "side": 8.774377384217354, "solution_path": "data/solutions/generated/domintri_014_333566d5c4b3657c.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/333566d5c4b3657c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@15", "density": 0.7991843102868493, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/15.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "7+4/\u221a3 = 9.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.3094, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@15", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "7+4/\u221a3 = 9.30940+", "metric_symbol": "s", "metric_value": 9.3094, "reference_text": "s = 7+4/\u221a3 = 9.30940+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/15.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 7+4/\u221a3 = 9.30940+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "2da1308626a02461", "improvement": -0.0013965021666475508, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.5011317742776256e-06, "max_pair_overlap_depth": -8.262234862044249e-05, "metric_expression": "9.31080", "metric_symbol": "s", "metric_value": 9.310796502166648, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.3094, "setup": "domintri", "side": 9.310796502166648, "solution_path": "data/solutions/generated/domintri_015_2da1308626a02461.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/2da1308626a02461.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@16", "density": 0.8249213221645568, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/16.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "6+2\u221a3 = 9.46410+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.4641, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@16", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "6+2\u221a3 = 9.46410+", "metric_symbol": "s", "metric_value": 9.4641, "reference_text": "s = 6+2\u221a3 = 9.46410+ | Found by Maurizio Morandi | in April 2026.", "source_image": "16.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/16.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 6+2\u221a3 = 9.46410+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "cc2a76b6a75c7120", "improvement": -0.000851797392776632, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.428695004104409e-06, "max_pair_overlap_depth": -2.0153462060745753e-05, "metric_expression": "9.46495", "metric_symbol": "s", "metric_value": 9.464951797392777, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.4641, "setup": "domintri", "side": 9.464951797392777, "solution_path": "data/solutions/generated/domintri_016_cc2a76b6a75c7120.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/cc2a76b6a75c7120.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@17", "density": 0.8218638425440753, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/17.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "4+10/\u221a3 = 9.77350+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.7735, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@17", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4+10/\u221a3 = 9.77350+", "metric_symbol": "s", "metric_value": 9.7735, "reference_text": "s = 4+10/\u221a3 = 9.77350+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/17.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 4+10/\u221a3 = 9.77350+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "842ace76b15a5c6d", "improvement": -0.0008796443209906357, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.8870325675374086e-06, "max_pair_overlap_depth": -2.297706007370337e-05, "metric_expression": "9.77438", "metric_symbol": "s", "metric_value": 9.774379644320991, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.7735, "setup": "domintri", "side": 9.774379644320991, "solution_path": "data/solutions/generated/domintri_017_842ace76b15a5c6d.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/842ace76b15a5c6d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@18", "density": 0.8433917909368376, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/18.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "3+4\u221a3 = 9.92820+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.9282, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3+4\u221a3 = 9.92820+", "metric_symbol": "s", "metric_value": 9.9282, "reference_text": "s = 3+4\u221a3 = 9.92820+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/18.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 3+4\u221a3 = 9.92820+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "286272298adf99a4", "improvement": -0.00035960973454685075, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.814371048432239e-06, "max_pair_overlap_depth": -1.8972863250255045e-05, "metric_expression": "9.92856", "metric_symbol": "s", "metric_value": 9.928559609734547, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.9282, "setup": "domintri", "side": 9.928559609734547, "solution_path": "data/solutions/generated/domintri_018_286272298adf99a4.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/286272298adf99a4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@19", "density": 0.8255562955017095, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/19.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "8+4/\u221a3 = 10.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.3094, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "8+4/\u221a3 = 10.30940+", "metric_symbol": "s", "metric_value": 10.3094, "reference_text": "s = 8+4/\u221a3 = 10.30940+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/19.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 8+4/\u221a3 = 10.30940+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "77c1eb98f0e7fed4", "improvement": -0.0008247746809697531, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.73171847830086e-06, "max_pair_overlap_depth": -2.8002623395084747e-06, "metric_expression": "10.31022", "metric_symbol": "s", "metric_value": 10.31022477468097, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 10.3094, "setup": "domintri", "side": 10.31022477468097, "solution_path": "data/solutions/generated/domintri_019_77c1eb98f0e7fed4.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/77c1eb98f0e7fed4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@20", "density": 0.843501980040664, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/20.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "7+2\u221a3 = 10.46410+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.4641, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@20", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "7+2\u221a3 = 10.46410+", "metric_symbol": "s", "metric_value": 10.4641, "reference_text": "s = 7+2\u221a3 = 10.46410+ | Found by Maurizio Morandi | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/20.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 7+2\u221a3 = 10.46410+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "19214c32485a435f", "improvement": -0.0008371510213134314, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8019716271983103e-06, "max_pair_overlap_depth": -2.85508650477162e-06, "metric_expression": "10.46494", "metric_symbol": "s", "metric_value": 10.464937151021314, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 10.4641, "setup": "domintri", "side": 10.464937151021314, "solution_path": "data/solutions/generated/domintri_020_19214c32485a435f.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/19214c32485a435f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@21", "density": 0.8533496545178485, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/21.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "2+5\u221a3 = 10.66025+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.66025, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@21", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "2+5\u221a3 = 10.66025+", "metric_symbol": "s", "metric_value": 10.66025, "reference_text": "s = 2+5\u221a3 = 10.66025+ | Found by Maurizio Morandi | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/21.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 2+5\u221a3 = 10.66025+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "797030ebf0f8c4e4", "improvement": -0.0010660665758290833, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.564559491289197e-06, "max_pair_overlap_depth": -2.4360684990565318e-05, "metric_expression": "10.66132", "metric_symbol": "s", "metric_value": 10.661316066575829, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 10.66025, "setup": "domintri", "side": 10.661316066575829, "solution_path": "data/solutions/generated/domintri_021_797030ebf0f8c4e4.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/797030ebf0f8c4e4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@22", "density": 0.8506833122891716, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/22.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "4(1+\u221a3) = 10.92820+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.9282, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@22", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "4(1+\u221a3) = 10.92820+", "metric_symbol": "s", "metric_value": 10.9282, "reference_text": "s = 4(1+\u221a3) = 10.92820+ | Found by Maurizio Morandi | in April 2026.", "source_image": "22.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/22.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 4(1+\u221a3) = 10.92820+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "90061b49654f08af", "improvement": -0.001092862620856394, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.631830815268069e-06, "max_pair_overlap_depth": -1.6046632975275088e-05, "metric_expression": "10.92929", "metric_symbol": "s", "metric_value": 10.929292862620857, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 10.9282, "setup": "domintri", "side": 10.929292862620857, "solution_path": "data/solutions/generated/domintri_022_90061b49654f08af.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/90061b49654f08af.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@23", "density": 0.8536884993646849, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/23.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "10+2/\u221a3 = 11.15470+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.1547, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@23", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "10+2/\u221a3 = 11.15470+", "metric_symbol": "s", "metric_value": 11.1547, "reference_text": "s = 10+2/\u221a3 = 11.15470+ | Found by Maurizio Morandi | in April 2026.", "source_image": "23.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/23.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 10+2/\u221a3 = 11.15470+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "8ca8e97a5947c876", "improvement": -0.0005390769738546908, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.068904299595512e-06, "max_pair_overlap_depth": -1.1497281311445562e-05, "metric_expression": "11.15524", "metric_symbol": "s", "metric_value": 11.155239076973855, "n": 23, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 11.1547, "setup": "domintri", "side": 11.155239076973855, "solution_path": "data/solutions/generated/domintri_023_8ca8e97a5947c876.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/8ca8e97a5947c876.svg", "tolerance": 1e-08, "verified": true}
-{"case": "domintri@24", "density": 0.8664947344465272, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/24.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "9+4/\u221a3 = 11.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.3094, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@24", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "9+4/\u221a3 = 11.30940+", "metric_symbol": "s", "metric_value": 11.3094, "reference_text": "s = 9+4/\u221a3 = 11.30940+ | Found by Maurizio Morandi | in April 2026.", "source_image": "24.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/24.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 9+4/\u221a3 = 11.30940+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "f8436aa831ae57e5", "improvement": -0.0012440894174083894, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.95572835399557e-06, "max_pair_overlap_depth": -5.492290923159171e-05, "metric_expression": "11.31064", "metric_symbol": "s", "metric_value": 11.310644089417409, "n": 24, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 11.3094, "setup": "domintri", "side": 11.310644089417409, "solution_path": "data/solutions/generated/domintri_024_f8436aa831ae57e5.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/f8436aa831ae57e5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@1", "density": 0.826977987261634, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/1.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "r", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "r", "metric_value": 1.0, "reference_text": "r = 1 | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/1.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 1 | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "48f5aa37c90550c8", "improvement": -9.284285680699611e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.547655283739573e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_symbol": "r", "metric_value": 1.0000092842856807, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.0, "setup": "hexincir", "side": 2.0000185685713614, "solution_path": "data/solutions/generated/hexincir_001_48f5aa37c90550c8.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/48f5aa37c90550c8.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@2", "density": 0.508894613048892, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/2.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a13/2 = 1.802+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.802, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a13/2 = 1.802+", "metric_symbol": "r", "metric_value": 1.802, "reference_text": "r = \u221a13/2 = 1.802+ | Trivial.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/2.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a13/2 = 1.802+ | Trivial.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "3b6bd2554e997adc", "improvement": -0.0008187982614582534, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4989872811899119e-06, "max_pair_overlap_depth": -3.954921521903687e-05, "metric_expression": "1.80282", "metric_symbol": "r", "metric_value": 1.8028187982614583, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.802, "setup": "hexincir", "side": 3.6056375965229166, "solution_path": "data/solutions/generated/hexincir_002_3b6bd2554e997adc.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/3b6bd2554e997adc.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@3", "density": 0.6202101203168955, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/3.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "r", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "r", "metric_value": 2.0, "reference_text": "r = 2 | Trivial.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/3.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 2 | Trivial.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "194e619a74e29452", "improvement": -5.624955299809997e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.970405754344824e-06, "max_pair_overlap_depth": -7.230141190991447e-05, "metric_expression": "2.00006", "metric_symbol": "r", "metric_value": 2.000056249552998, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "hexincir", "side": 4.000112499105996, "solution_path": "data/solutions/generated/hexincir_003_194e619a74e29452.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/194e619a74e29452.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@4", "density": 0.6594633839026793, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/4.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(21\u2013\u221a145)/4 = 2.239+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.239, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@4", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "(21\u2013\u221a145)/4 = 2.239+", "metric_symbol": "r", "metric_value": 2.239, "reference_text": "r = (21\u2013\u221a145)/4 = 2.239+ | Found by Maurizio Morandi | in March 2026.", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/4.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = (21\u2013\u221a145)/4 = 2.239+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "355b11dfc363f5ba", "improvement": -0.0006783874729134887, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.544625404889757e-07, "max_pair_overlap_depth": -5.057462804924917e-05, "metric_expression": "2.23968", "metric_symbol": "r", "metric_value": 2.2396783874729134, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.239, "setup": "hexincir", "side": 4.479356774945827, "solution_path": "data/solutions/generated/hexincir_004_355b11dfc363f5ba.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/355b11dfc363f5ba.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@5", "density": 0.6766813833384198, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/5.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2.471+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.471, "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@5", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "2.471+", "metric_symbol": "r", "metric_value": 2.471, "reference_text": "r = 2.471+ | Found by Maurizio Morandi | in March 2026.", "source_image": "5.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/5.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 2.471+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "9427b00c077aafc3", "improvement": -0.0009739785189006867, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.673907177263573e-06, "max_pair_overlap_depth": -5.983134966366932e-05, "metric_expression": "2.47197", "metric_symbol": "r", "metric_value": 2.4719739785189008, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.471, "setup": "hexincir", "side": 4.9439479570378015, "solution_path": "data/solutions/generated/hexincir_005_9427b00c077aafc3.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/9427b00c077aafc3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@6", "density": 0.7087991567669789, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/7.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a7 = 2.645+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.645, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@6", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a7 = 2.645+", "metric_symbol": "r", "metric_value": 2.645, "reference_text": "r = \u221a7 = 2.645+ | Trivial. |", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/7.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a7 = 2.645+ | Trivial. |", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "d7d900dd0bba32a3", "improvement": -0.0008488830398025726, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.0221671226394733e-07, "max_pair_overlap_depth": -3.6674166167594e-05, "metric_expression": "2.64585", "metric_symbol": "r", "metric_value": 2.6458488830398026, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.645, "setup": "hexincir", "side": 5.291697766079605, "solution_path": "data/solutions/generated/hexincir_006_d7d900dd0bba32a3.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d7d900dd0bba32a3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@7", "density": 0.8269668154291873, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/7.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a7 = 2.645+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.645, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@7", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a7 = 2.645+", "metric_symbol": "r", "metric_value": 2.645, "reference_text": "r = \u221a7 = 2.645+ | Trivial. |", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/7.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a7 = 2.645+ | Trivial. |", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "5cd27a740cc9b2a5", "improvement": -0.0007937463486662466, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.370930279076532e-06, "max_pair_overlap_depth": -2.6143388138111234e-05, "metric_expression": "2.64579", "metric_symbol": "r", "metric_value": 2.6457937463486663, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.645, "setup": "hexincir", "side": 5.2915874926973325, "solution_path": "data/solutions/generated/hexincir_007_5cd27a740cc9b2a5.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/5cd27a740cc9b2a5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@8", "density": 0.7426247287224678, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/8.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2.984+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.984, "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@8", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "2.984+", "metric_symbol": "r", "metric_value": 2.984, "reference_text": "r = 2.984+ | Found by Maurizio Morandi | in March 2026.", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/8.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 2.984+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "7d27528d78a05a43", "improvement": -0.0007729280237529501, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.6889173538057207e-06, "max_pair_overlap_depth": -1.732806256671271e-05, "metric_expression": "2.98477", "metric_symbol": "r", "metric_value": 2.984772928023753, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.984, "setup": "hexincir", "side": 5.969545856047506, "solution_path": "data/solutions/generated/hexincir_008_7d27528d78a05a43.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/7d27528d78a05a43.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@9", "density": 0.682777017123973, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/9.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3.301+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.301, "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@9", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "3.301+", "metric_symbol": "r", "metric_value": 3.301, "reference_text": "r = 3.301+ | Found by Maurizio Morandi | in March 2026.", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/9.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 3.301+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "5f9496662ac0b661", "improvement": -0.000663545504778984, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.641836701819614e-06, "max_pair_overlap_depth": -2.219136600895011e-05, "metric_expression": "3.30166", "metric_symbol": "r", "metric_value": 3.301663545504779, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.301, "setup": "hexincir", "side": 6.603327091009558, "solution_path": "data/solutions/generated/hexincir_009_5f9496662ac0b661.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/5f9496662ac0b661.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@10", "density": 0.6804997422869841, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/10.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "7/2 = 3.5", "friedman_metric_symbol": "r", "friedman_metric_value": 3.5, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@10", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "7/2 = 3.5", "metric_symbol": "r", "metric_value": 3.5, "reference_text": "r = 7/2 = 3.5 | Found by Maurizio Morandi | in March 2026.", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/10.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 7/2 = 3.5 | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": false, "id": "8fccd3008565aabb", "improvement": 0.013922608209857135, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.016042661651568e-06, "max_pair_overlap_depth": -3.440098626628085e-05, "metric_expression": "3.48608", "metric_symbol": "r", "metric_value": 3.486077391790143, "n": 10, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.", "record_type": "verified", "reference_side": 3.5, "setup": "hexincir", "side": 6.972154783580286, "solution_path": "data/solutions/generated/hexincir_010_8fccd3008565aabb.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/8fccd3008565aabb.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@11", "density": 0.7038726397318542, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/12.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a13 = 3.605+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.605, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@11", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "\u221a13 = 3.605+", "metric_symbol": "r", "metric_value": 3.605, "reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in March 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/12.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": false, "id": "2d2e76ec34c49fb5", "improvement": 0.009988305972369105, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.0630450586220945e-06, "max_pair_overlap_depth": -3.6222629933746475e-05, "metric_expression": "3.59501", "metric_symbol": "r", "metric_value": 3.595011694027631, "n": 11, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.", "record_type": "verified", "reference_side": 3.605, "setup": "hexincir", "side": 7.190023388055262, "solution_path": "data/solutions/generated/hexincir_011_2d2e76ec34c49fb5.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/2d2e76ec34c49fb5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@12", "density": 0.7629156641677376, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/12.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a13 = 3.605+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.605, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@12", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "\u221a13 = 3.605+", "metric_symbol": "r", "metric_value": 3.605, "reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in March 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/12.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "5515c10818a71365", "improvement": -0.001644724814655607, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.2444141653265035e-06, "max_pair_overlap_depth": -3.49998284549164e-05, "metric_expression": "3.60664", "metric_symbol": "r", "metric_value": 3.6066447248146556, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.605, "setup": "hexincir", "side": 7.213289449629311, "solution_path": "data/solutions/generated/hexincir_012_5515c10818a71365.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/5515c10818a71365.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@13", "density": 0.7347845850822048, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/13.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3.82298+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.82298, "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@13", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.82298+", "metric_symbol": "r", "metric_value": 3.82298, "reference_text": "r = 3.82298+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/13.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 3.82298+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "defdebc1228b1d63", "improvement": -0.002118865563556671, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3642191814564626e-06, "max_pair_overlap_depth": -3.899276946051078e-05, "metric_expression": "3.82510", "metric_symbol": "r", "metric_value": 3.8250988655635565, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.82298, "setup": "hexincir", "side": 7.650197731127113, "solution_path": "data/solutions/generated/hexincir_013_defdebc1228b1d63.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/defdebc1228b1d63.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@14", "density": 0.7696929179154312, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/14.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a(109\u20139\u221a109) = 3.877+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.877, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@14", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "\u221a(109\u20139\u221a109) = 3.877+", "metric_symbol": "r", "metric_value": 3.877, "reference_text": "r = \u221a(109\u20139\u221a109) = 3.877+ | Found by Maurizio Morandi | in March 2026.", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/14.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a(109\u20139\u221a109) = 3.877+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "cf6592c7009ff83d", "improvement": -0.0014328751718628574, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.009541618976158e-06, "max_pair_overlap_depth": -5.416099891136783e-05, "metric_expression": "3.87843", "metric_symbol": "r", "metric_value": 3.8784328751718626, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.877, "setup": "hexincir", "side": 7.756865750343725, "solution_path": "data/solutions/generated/hexincir_014_cf6592c7009ff83d.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/cf6592c7009ff83d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@15", "density": 0.7439908773476231, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/15.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.08174+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.08174, "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@15", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.08174+", "metric_symbol": "r", "metric_value": 4.08174, "reference_text": "r = 4.08174+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/15.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 4.08174+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "ea523b99f3bf81fb", "improvement": -0.001574502888137097, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.330196611616714e-06, "max_pair_overlap_depth": -5.918641434021765e-05, "metric_expression": "4.08331", "metric_symbol": "r", "metric_value": 4.083314502888137, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.08174, "setup": "hexincir", "side": 8.166629005776274, "solution_path": "data/solutions/generated/hexincir_015_ea523b99f3bf81fb.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/ea523b99f3bf81fb.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@16", "density": 0.7714178714001686, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/16.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.13966+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.13966, "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@16", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.13966+", "metric_symbol": "r", "metric_value": 4.13966, "reference_text": "r = 4.13966+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "16.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/16.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 4.13966+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "928ee7a851bce6e5", "improvement": -0.0019209106018989175, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.8109720468001456e-06, "max_pair_overlap_depth": -4.18854370716204e-05, "metric_expression": "4.14158", "metric_symbol": "r", "metric_value": 4.141580910601899, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.13966, "setup": "hexincir", "side": 8.283161821203798, "solution_path": "data/solutions/generated/hexincir_016_928ee7a851bce6e5.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/928ee7a851bce6e5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@17", "density": 0.7591563034967428, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/17.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.30170+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.3017, "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@17", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.30170+", "metric_symbol": "r", "metric_value": 4.3017, "reference_text": "r = 4.30170+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/17.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 4.30170+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "e582b760dc061cd3", "improvement": -0.001681676380650643, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.855951803468429e-06, "max_pair_overlap_depth": -4.543663468803416e-05, "metric_expression": "4.30338", "metric_symbol": "r", "metric_value": 4.303381676380651, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.3017, "setup": "hexincir", "side": 8.606763352761302, "solution_path": "data/solutions/generated/hexincir_017_e582b760dc061cd3.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T03:07:58+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/e582b760dc061cd3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@18", "density": 0.7834006630179079, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a19 = 4.35889+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.35889, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@18", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a19 = 4.35889+", "metric_symbol": "r", "metric_value": 4.35889, "reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "12eaac899664a007", "improvement": -0.0001945423028058002, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.696366953105269e-06, "max_pair_overlap_depth": -1.0490734119961154e-05, "metric_expression": "4.35908", "metric_symbol": "r", "metric_value": 4.3590845423028055, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.35889, "setup": "hexincir", "side": 8.718169084605611, "solution_path": "data/solutions/generated/hexincir_018_12eaac899664a007.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/12eaac899664a007.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@19", "density": 0.8269599994475847, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a19 = 4.35889+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.35889, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@19", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a19 = 4.35889+", "metric_symbol": "r", "metric_value": 4.35889, "reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "b4bf200670caf09c", "improvement": -9.681979153608467e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.636539265552187e-06, "max_pair_overlap_depth": -6.973398227638761e-06, "metric_expression": "4.35899", "metric_symbol": "r", "metric_value": 4.358986819791536, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.35889, "setup": "hexincir", "side": 8.717973639583072, "solution_path": "data/solutions/generated/hexincir_019_b4bf200670caf09c.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/b4bf200670caf09c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@20", "density": 0.7723857667872704, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/20.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.62598+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.62598, "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.62598+", "metric_symbol": "r", "metric_value": 4.62598, "reference_text": "r = 4.62598+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/20.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 4.62598+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "30108dc5d1ea9a14", "improvement": -0.0015460646281777457, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8288872105642895e-06, "max_pair_overlap_depth": -4.792351042670617e-06, "metric_expression": "4.62753", "metric_symbol": "r", "metric_value": 4.627526064628178, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.62598, "setup": "hexincir", "side": 9.255052129256356, "solution_path": "data/solutions/generated/hexincir_020_30108dc5d1ea9a14.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/30108dc5d1ea9a14.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexincir@21", "density": 0.7917677222663352, "friedman_analytical_or_proved": false, "friedman_credit": "Enea Victor", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/21.png", "friedman_metric_expression": "4.68339+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.68339, "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@21", "credit": "Enea Victor", "date": "April 2026", "family_updated": "", "metric_expression": "4.68339+", "metric_symbol": "r", "metric_value": 4.68339, "reference_text": "r = 4.68339+ | Found by Enea Victor | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/21.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 4.68339+ | Found by Enea Victor | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "49a047c29bb184c3", "improvement": -1.5457789629635954e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.498160996568856e-06, "max_pair_overlap_depth": -3.8704072840012316e-06, "metric_expression": "4.68341", "metric_symbol": "r", "metric_value": 4.68340545778963, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.68339, "setup": "hexincir", "side": 9.36681091557926, "solution_path": "data/solutions/generated/hexincir_021_49a047c29bb184c3.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Enea Victor", "svg_path": "data/svg/49a047c29bb184c3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@1", "density": 0.433010701548144, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/1.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "\u221a3 = 1.73205+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.73205, "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a3 = 1.73205+", "metric_symbol": "s", "metric_value": 1.73205, "reference_text": "1. | | s = \u221a3 = 1.73205+ | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/1.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "1. | | s = \u221a3 = 1.73205+ | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "899222ca3c83cd8e", "improvement": -4.8082708896668436e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0003297862271054e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.73205", "metric_symbol": "s", "metric_value": 1.7320548082708898, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.73205, "setup": "hexindom", "side": 3.4641096165417795, "solution_path": "data/solutions/generated/hexindom_001_899222ca3c83cd8e.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/899222ca3c83cd8e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@2", "density": 0.7237057542591544, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/2.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "1.8946+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.8946, "friedman_reference": {"analytical_or_proved": false, "case": "hexindom@2", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.8946+", "metric_symbol": "s", "metric_value": 1.8946, "reference_text": "2. | | s = 1.8946+ | Found by Jonathan Viquerat in April 2026.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/2.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "2. | | s = 1.8946+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "419ae881803808e0", "improvement": -0.00011952413629479075, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.154031481298006e-06, "max_pair_overlap_depth": -4.420983116036614e-05, "metric_expression": "1.89472", "metric_symbol": "s", "metric_value": 1.8947195241362949, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.8946, "setup": "hexindom", "side": 3.7894390482725897, "solution_path": "data/solutions/generated/hexindom_002_419ae881803808e0.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/419ae881803808e0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@3", "density": 0.6059845041872388, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/3.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "6\u20132\u221a3 = 2.53589+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.53589, "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@3", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6\u20132\u221a3 = 2.53589+", "metric_symbol": "s", "metric_value": 2.53589, "reference_text": "3. | | s = 6\u20132\u221a3 = 2.53589+ | Found by Jonathan Viquerat in April 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/3.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "3. | | s = 6\u20132\u221a3 = 2.53589+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "b8984cccc8c8714d", "improvement": -6.074031198854968e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3815485928603266e-06, "max_pair_overlap_depth": -3.5690372763075295e-05, "metric_expression": "2.53595", "metric_symbol": "s", "metric_value": 2.5359507403119887, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.53589, "setup": "hexindom", "side": 5.0719014806239775, "solution_path": "data/solutions/generated/hexindom_003_b8984cccc8c8714d.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/b8984cccc8c8714d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@4", "density": 0.5981044188175139, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/4.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "22\u201311\u221a3 = 2.94744+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.94744, "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@4", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "22\u201311\u221a3 = 2.94744+", "metric_symbol": "s", "metric_value": 2.94744, "reference_text": "4. | | s = 22\u201311\u221a3 = 2.94744+ | Found by Jonathan Viquerat in April 2026.", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/4.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "4. | | s = 22\u201311\u221a3 = 2.94744+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "de86d3aed3d6a439", "improvement": -5.064613954619546e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.326043343385379e-06, "max_pair_overlap_depth": -1.3607159264461544e-05, "metric_expression": "2.94749", "metric_symbol": "s", "metric_value": 2.947490646139546, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.94744, "setup": "hexindom", "side": 5.894981292279092, "solution_path": "data/solutions/generated/hexindom_004_de86d3aed3d6a439.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/de86d3aed3d6a439.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@5", "density": 0.6153950410217744, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/5.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "7(2\u221a3\u20133) = 3.24871+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.24871, "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@5", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "7(2\u221a3\u20133) = 3.24871+", "metric_symbol": "s", "metric_value": 3.24871, "reference_text": "5. | | s = 7(2\u221a3\u20133) = 3.24871+ | Found by Jonathan Viquerat in April 2026.", "source_image": "5.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/5.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "5. | | s = 7(2\u221a3\u20133) = 3.24871+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "6c9e9b8c4daf8e17", "improvement": -5.988993836103518e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.879985772620616e-06, "max_pair_overlap_depth": -1.7392941288552066e-05, "metric_expression": "3.24877", "metric_symbol": "s", "metric_value": 3.248769889938361, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.24871, "setup": "hexindom", "side": 6.497539779876722, "solution_path": "data/solutions/generated/hexindom_005_6c9e9b8c4daf8e17.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/6c9e9b8c4daf8e17.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@6", "density": 0.669460522582725, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/6.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "21(15\u20132\u221a3)/71 = 3.41202+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.41202, "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@6", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "21(15\u20132\u221a3)/71 = 3.41202+", "metric_symbol": "s", "metric_value": 3.41202, "reference_text": "6. | | s = 21(15\u20132\u221a3)/71 = 3.41202+ | Found by Jonathan Viquerat in April 2026.", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/6.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "6. | | s = 21(15\u20132\u221a3)/71 = 3.41202+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "3331b621360b9c32", "improvement": -9.83352674857052e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.54326023255247e-06, "max_pair_overlap_depth": -5.983710998713754e-05, "metric_expression": "3.41212", "metric_symbol": "s", "metric_value": 3.4121183352674858, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.41202, "setup": "hexindom", "side": 6.8242366705349715, "solution_path": "data/solutions/generated/hexindom_006_3331b621360b9c32.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/3331b621360b9c32.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@7", "density": 0.74772405053785, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/7.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "3.4873+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.4873, "friedman_reference": {"analytical_or_proved": false, "case": "hexindom@7", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.4873+", "metric_symbol": "s", "metric_value": 3.4873, "reference_text": "7. | | s = 3.4873+ | Found by Jonathan Viquerat in April 2026.", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/7.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "7. | | s = 3.4873+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "1cf3d5c48cc9bce3", "improvement": 1.5563940758411832e-07, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.731889618803109e-06, "max_pair_overlap_depth": -2.9943125185782904e-05, "metric_expression": "3.48730", "metric_symbol": "s", "metric_value": 3.4872998443605923, "n": 7, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.4873, "setup": "hexindom", "side": 6.9745996887211845, "solution_path": "data/solutions/generated/hexindom_007_1cf3d5c48cc9bce3.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/1cf3d5c48cc9bce3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@8", "density": 0.7629201456996986, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/8.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "3.6906+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.6906, "friedman_reference": {"analytical_or_proved": false, "case": "hexindom@8", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.6906+", "metric_symbol": "s", "metric_value": 3.6906, "reference_text": "8. | | s = 3.6906+ | Found by Jonathan Viquerat in April 2026.", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/8.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "8. | | s = 3.6906+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "645a3046b41a06e7", "improvement": -0.00016503281621149668, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.30145200672294e-06, "max_pair_overlap_depth": -4.406733776018967e-05, "metric_expression": "3.69077", "metric_symbol": "s", "metric_value": 3.6907650328162114, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.6906, "setup": "hexindom", "side": 7.381530065632423, "solution_path": "data/solutions/generated/hexindom_008_645a3046b41a06e7.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/645a3046b41a06e7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@9", "density": 0.7092437911682054, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/9.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "(36+5\u221a3)/11 = 4.06002+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.06002, "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@9", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "(36+5\u221a3)/11 = 4.06002+", "metric_symbol": "s", "metric_value": 4.06002, "reference_text": "9. | | s = (36+5\u221a3)/11 = 4.06002+ | Found by Jonathan Viquerat in April 2026.", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/9.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "9. | | s = (36+5\u221a3)/11 = 4.06002+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "412a5c4dab2378db", "improvement": -5.848340764558202e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.8730699123165095e-06, "max_pair_overlap_depth": -8.397966625661724e-06, "metric_expression": "4.06008", "metric_symbol": "s", "metric_value": 4.060078483407645, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.06002, "setup": "hexindom", "side": 8.12015696681529, "solution_path": "data/solutions/generated/hexindom_009_412a5c4dab2378db.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/412a5c4dab2378db.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@10", "density": 0.7445544573306387, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/10.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "9(2\u221a3\u20133) = 4.17691+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.17691, "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@10", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "9(2\u221a3\u20133) = 4.17691+", "metric_symbol": "s", "metric_value": 4.17691, "reference_text": "10. | | s = 9(2\u221a3\u20133) = 4.17691+ | Found by Jonathan Viquerat in April 2026.", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/10.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "10. | | s = 9(2\u221a3\u20133) = 4.17691+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "b404bfce93e4b698", "improvement": -7.303556637161535e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.152317509946272e-07, "max_pair_overlap_depth": -2.262161166943777e-05, "metric_expression": "4.17698", "metric_symbol": "s", "metric_value": 4.176983035566372, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.17691, "setup": "hexindom", "side": 8.353966071132744, "solution_path": "data/solutions/generated/hexindom_010_b404bfce93e4b698.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/b404bfce93e4b698.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@11", "density": 0.7041255860017571, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/11.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "4.5036+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5036, "friedman_reference": {"analytical_or_proved": false, "case": "hexindom@11", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.5036+", "metric_symbol": "s", "metric_value": 4.5036, "reference_text": "11. | | s = 4.5036+ | Found by Jonathan Viquerat in April 2026.", "source_image": "11.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/11.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "11. | | s = 4.5036+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "11.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "de36b527dfa03258", "improvement": -0.0012696093619926074, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.31456043970391e-06, "max_pair_overlap_depth": -1.8725366454197534e-05, "metric_expression": "4.50487", "metric_symbol": "s", "metric_value": 4.504869609361992, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.5036, "setup": "hexindom", "side": 9.009739218723984, "solution_path": "data/solutions/generated/hexindom_011_de36b527dfa03258.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/de36b527dfa03258.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@12", "density": 0.7322405469378734, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/12.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "41(18\u20135\u221a3)/83 = 4.6136+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.6136, "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@12", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "41(18\u20135\u221a3)/83 = 4.6136+", "metric_symbol": "s", "metric_value": 4.6136, "reference_text": "12. | | s = 41(18\u20135\u221a3)/83 = 4.6136+ | Found by Jonathan Viquerat in April 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/12.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "12. | | s = 41(18\u20135\u221a3)/83 = 4.6136+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "32dafbf1407bbd72", "improvement": -0.0003690981500499291, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.932113721409451e-07, "max_pair_overlap_depth": -3.449528945953517e-05, "metric_expression": "4.61397", "metric_symbol": "s", "metric_value": 4.61396909815005, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.6136, "setup": "hexindom", "side": 9.2279381963001, "solution_path": "data/solutions/generated/hexindom_012_32dafbf1407bbd72.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/32dafbf1407bbd72.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@13", "density": 0.7287142254379715, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/13.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "4.8137+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.8137, "friedman_reference": {"analytical_or_proved": false, "case": "hexindom@13", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.8137+", "metric_symbol": "s", "metric_value": 4.8137, "reference_text": "13. | | s = 4.8137+ | Found by Jonathan Viquerat in April 2026.", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/13.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "13. | | s = 4.8137+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "4d59f64640558812", "improvement": -0.000276853025948931, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.288235630449776e-07, "max_pair_overlap_depth": -5.701790221179781e-05, "metric_expression": "4.81398", "metric_symbol": "s", "metric_value": 4.813976853025949, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.8137, "setup": "hexindom", "side": 9.627953706051898, "solution_path": "data/solutions/generated/hexindom_013_4d59f64640558812.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/4d59f64640558812.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@14", "density": 0.7731048613358414, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/14.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "25(6\u2013\u221a3)/22 = 4.84994+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.84994, "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@14", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "25(6\u2013\u221a3)/22 = 4.84994+", "metric_symbol": "s", "metric_value": 4.84994, "reference_text": "14. | | s = 25(6\u2013\u221a3)/22 = 4.84994+ | Found by Jonathan Viquerat in April 2026.", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/14.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "14. | | s = 25(6\u2013\u221a3)/22 = 4.84994+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "1f0ed34d05c35380", "improvement": -0.00021659973266263677, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.312817282834061e-06, "max_pair_overlap_depth": -5.706330400911952e-05, "metric_expression": "4.85016", "metric_symbol": "s", "metric_value": 4.850156599732663, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.84994, "setup": "hexindom", "side": 9.700313199465326, "solution_path": "data/solutions/generated/hexindom_014_1f0ed34d05c35380.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/1f0ed34d05c35380.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@15", "density": 0.7946102881582437, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/15.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "56(27\u20134\u221a3)/227 = 4.95163+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.95163, "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@15", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "56(27\u20134\u221a3)/227 = 4.95163+", "metric_symbol": "s", "metric_value": 4.95163, "reference_text": "15. | | s = 56(27\u20134\u221a3)/227 = 4.95163+ | Found by Jonathan Viquerat in April 2026.", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/15.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "15. | | s = 56(27\u20134\u221a3)/227 = 4.95163+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "1b00a25adb5cc2e4", "improvement": -0.0003568532282001158, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.185835293301636e-06, "max_pair_overlap_depth": -6.286085527285046e-05, "metric_expression": "4.95199", "metric_symbol": "s", "metric_value": 4.9519868532282, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.95163, "setup": "hexindom", "side": 9.9039737064564, "solution_path": "data/solutions/generated/hexindom_015_1b00a25adb5cc2e4.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/1b00a25adb5cc2e4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@16", "density": 0.7697888241254879, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/17.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "3\u221a3 = 5.19615+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.19615, "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@16", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3\u221a3 = 5.19615+", "metric_symbol": "s", "metric_value": 5.19615, "reference_text": "16.-17. | | s = 3\u221a3 = 5.19615+ | Trivial.", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/17.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "16.-17. | | s = 3\u221a3 = 5.19615+ | Trivial.", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "f690e0f9c2986401", "improvement": -4.135307393138277e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.00251676779817e-06, "max_pair_overlap_depth": -1.257294679668508e-05, "metric_expression": "5.19619", "metric_symbol": "s", "metric_value": 5.196191353073932, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.19615, "setup": "hexindom", "side": 10.392382706147863, "solution_path": "data/solutions/generated/hexindom_016_f690e0f9c2986401.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/f690e0f9c2986401.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@17", "density": 0.8178722029268405, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/17.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "3\u221a3 = 5.19615+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.19615, "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@17", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3\u221a3 = 5.19615+", "metric_symbol": "s", "metric_value": 5.19615, "reference_text": "16.-17. | | s = 3\u221a3 = 5.19615+ | Trivial.", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/17.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "16.-17. | | s = 3\u221a3 = 5.19615+ | Trivial.", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "fe395a0426baa674", "improvement": -0.00013164134761289858, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.712543075160227e-06, "max_pair_overlap_depth": -2.5961203853341885e-08, "metric_expression": "5.19628", "metric_symbol": "s", "metric_value": 5.196281641347613, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.19615, "setup": "hexindom", "side": 10.392563282695226, "solution_path": "data/solutions/generated/hexindom_017_fe395a0426baa674.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/fe395a0426baa674.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@18", "density": 0.7993930048940154, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/18.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "31(4\u2013\u221a3)/13 = 5.40818+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.40818, "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "31(4\u2013\u221a3)/13 = 5.40818+", "metric_symbol": "s", "metric_value": 5.40818, "reference_text": "18. | | s = 31(4\u2013\u221a3)/13 = 5.40818+ | Found by Jonathan Viquerat in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/18.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "18. | | s = 31(4\u2013\u221a3)/13 = 5.40818+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "24be62ab2c11bd5c", "improvement": -0.0001978579530232949, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.006386418315856e-06, "max_pair_overlap_depth": -4.2927090152522496e-05, "metric_expression": "5.40838", "metric_symbol": "s", "metric_value": 5.408377857953023, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.40818, "setup": "hexindom", "side": 10.816755715906046, "solution_path": "data/solutions/generated/hexindom_018_24be62ab2c11bd5c.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/24be62ab2c11bd5c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@19", "density": 0.7722825822258855, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/19.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "5.6530+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.653, "friedman_reference": {"analytical_or_proved": false, "case": "hexindom@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.6530+", "metric_symbol": "s", "metric_value": 5.653, "reference_text": "19. | | s = 5.6530+ | Found by Jonathan Viquerat in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/19.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "19. | | s = 5.6530+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "ca10088586ed125c", "improvement": -0.0002686721147275861, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.885998928396475e-06, "max_pair_overlap_depth": -2.764579666703071e-05, "metric_expression": "5.65327", "metric_symbol": "s", "metric_value": 5.653268672114727, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.653, "setup": "hexindom", "side": 11.306537344229454, "solution_path": "data/solutions/generated/hexindom_019_ca10088586ed125c.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/ca10088586ed125c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexindom@20", "density": 0.7718745532343245, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/20.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "5.8012+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.8012, "friedman_reference": {"analytical_or_proved": false, "case": "hexindom@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.8012+", "metric_symbol": "s", "metric_value": 5.8012, "reference_text": "20. | | s = 5.8012+ | Found by Jonathan Viquerat in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/20.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "20. | | s = 5.8012+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "49ce661db444ec25", "improvement": -0.0004641087628032281, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.575652109486185e-06, "max_pair_overlap_depth": -1.0063478294242145e-05, "metric_expression": "5.80166", "metric_symbol": "s", "metric_value": 5.801664108762803, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.8012, "setup": "hexindom", "side": 11.603328217525606, "solution_path": "data/solutions/generated/hexindom_020_49ce661db444ec25.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/49ce661db444ec25.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@1", "density": 0.9999864500659439, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/1.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "1. | | s = 1 | Trivial.", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/1.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "1. | | s = 1 | Trivial.", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "fd6c6df7b6a9fd4f", "improvement": -6.7750358792029175e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.374323059598708e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_symbol": "s", "metric_value": 1.0000067750358792, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.0, "setup": "hexinhex", "side": 1.0000067750358792, "solution_path": "data/solutions/generated/hexinhex_001_fd6c6df7b6a9fd4f.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/fd6c6df7b6a9fd4f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@2", "density": 0.49998387949392886, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/2.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "2. | | s = 2 | Trivial.", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/2.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "2. | | s = 2 | Trivial.", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4c0cc36e970c84b1", "improvement": -3.2241791775522444e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.177681809212628e-06, "max_pair_overlap_depth": -3.6384174144801684e-05, "metric_expression": "2.00003", "metric_symbol": "s", "metric_value": 2.0000322417917755, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "hexinhex", "side": 2.0000322417917755, "solution_path": "data/solutions/generated/hexinhex_002_4c0cc36e970c84b1.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4c0cc36e970c84b1.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@3", "density": 0.7499882422262695, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/3.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "3. | | s = 2 | Trivial.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/3.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "3. | | s = 2 | Trivial.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "2e22e12b6d11de4d", "improvement": -1.5677215970288927e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.457810528986454e-06, "max_pair_overlap_depth": -9.916736621090457e-06, "metric_expression": "2.00002", "metric_symbol": "s", "metric_value": 2.0000156772159703, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "hexinhex", "side": 2.0000156772159703, "solution_path": "data/solutions/generated/hexinhex_003_2e22e12b6d11de4d.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/2e22e12b6d11de4d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@4", "density": 0.7346808358825446, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/4.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "7/3 = 2.333+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.333, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@4", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "7/3 = 2.333+", "metric_symbol": "s", "metric_value": 2.333, "reference_text": "4. | | s = 7/3 = 2.333+ | Trivial.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/4.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "4. | | s = 7/3 = 2.333+ | Trivial.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "73ddab3f27a95ffe", "improvement": -0.00035404329556776304, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.969618748468479e-06, "max_pair_overlap_depth": -1.5832978702556844e-05, "metric_expression": "2.33335", "metric_symbol": "s", "metric_value": 2.333354043295568, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.333, "setup": "hexinhex", "side": 2.333354043295568, "solution_path": "data/solutions/generated/hexinhex_004_73ddab3f27a95ffe.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/73ddab3f27a95ffe.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@5", "density": 0.7031111089487749, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "March 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/5.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "8/3 = 2.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.666, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@5", "credit": "Erich Friedman", "date": "March 2015", "family_updated": "", "metric_expression": "8/3 = 2.666+", "metric_symbol": "s", "metric_value": 2.666, "reference_text": "5. | | s = 8/3 = 2.666+ | Found by Erich Friedman | in March 2015.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/5.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "5. | | s = 8/3 = 2.666+ | Found by Erich Friedman | in March 2015.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "f45300c86d046ee7", "improvement": -0.0006930086059693252, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5309295562371306e-06, "max_pair_overlap_depth": -6.88869177611906e-06, "metric_expression": "2.66669", "metric_symbol": "s", "metric_value": 2.6666930086059693, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.666, "setup": "hexinhex", "side": 2.6666930086059693, "solution_path": "data/solutions/generated/hexinhex_005_f45300c86d046ee7.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/f45300c86d046ee7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@6", "density": 0.7199337426480286, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/7.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "5/\u221a3 = 2.886+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.886, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@6", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "5/\u221a3 = 2.886+", "metric_symbol": "s", "metric_value": 2.886, "reference_text": "6-7. | | s = 5/\u221a3 = 2.886+ | Found by Maurizio Morandi | in April 2015.", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/7.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "6-7. | | s = 5/\u221a3 = 2.886+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "06b9c79146f8c119", "improvement": -0.0008841804633918926, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.09670685382364e-06, "max_pair_overlap_depth": -5.069396536394599e-05, "metric_expression": "2.88688", "metric_symbol": "s", "metric_value": 2.886884180463392, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.886, "setup": "hexinhex", "side": 2.886884180463392, "solution_path": "data/solutions/generated/hexinhex_006_06b9c79146f8c119.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/06b9c79146f8c119.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@7", "density": 0.8399730426517898, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/7.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "5/\u221a3 = 2.886+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.886, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@7", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "5/\u221a3 = 2.886+", "metric_symbol": "s", "metric_value": 2.886, "reference_text": "6-7. | | s = 5/\u221a3 = 2.886+ | Found by Maurizio Morandi | in April 2015.", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/7.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "6-7. | | s = 5/\u221a3 = 2.886+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "d2a43d4ca2836467", "improvement": -0.0007976679923635821, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.6806989039887556e-06, "max_pair_overlap_depth": -2.9189085207215193e-05, "metric_expression": "2.88680", "metric_symbol": "s", "metric_value": 2.8867976679923637, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.886, "setup": "hexinhex", "side": 2.8867976679923637, "solution_path": "data/solutions/generated/hexinhex_007_d2a43d4ca2836467.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/d2a43d4ca2836467.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@8", "density": 0.728171041468435, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/8.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "(51+5\u221a3)/18 = 3.314+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.314, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@8", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "(51+5\u221a3)/18 = 3.314+", "metric_symbol": "s", "metric_value": 3.314, "reference_text": "8. | | s = (51+5\u221a3)/18 = 3.314+ | Found by Maurizio Morandi | in April 2015.", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/8.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "8. | | s = (51+5\u221a3)/18 = 3.314+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "8d9e02005a596470", "improvement": -0.0005783682856219663, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.71875974277703e-06, "max_pair_overlap_depth": -2.9528072121864923e-05, "metric_expression": "3.31458", "metric_symbol": "s", "metric_value": 3.314578368285622, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.314, "setup": "hexinhex", "side": 3.314578368285622, "solution_path": "data/solutions/generated/hexinhex_008_8d9e02005a596470.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/8d9e02005a596470.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@9", "density": 0.683335999337671, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/9.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "(24+5\u221a3)/9 = 3.628+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.628, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@9", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "(24+5\u221a3)/9 = 3.628+", "metric_symbol": "s", "metric_value": 3.628, "reference_text": "9. | | s = (24+5\u221a3)/9 = 3.628+ | Found by Maurizio Morandi | in April 2015.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/9.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "9. | | s = (24+5\u221a3)/9 = 3.628+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "21c530fbe612f27c", "improvement": -0.0011431939654920065, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.454488069704802e-06, "max_pair_overlap_depth": -2.836888994439679e-05, "metric_expression": "3.62914", "metric_symbol": "s", "metric_value": 3.629143193965492, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.628, "setup": "hexinhex", "side": 3.629143193965492, "solution_path": "data/solutions/generated/hexinhex_009_21c530fbe612f27c.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/21c530fbe612f27c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@10", "density": 0.7179574622038186, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/10.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "2 + \u221a3 = 3.732+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.732, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@10", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "2 + \u221a3 = 3.732+", "metric_symbol": "s", "metric_value": 3.732, "reference_text": "10. | | s = 2 + \u221a3 = 3.732+ | Found by Maurizio Morandi | in April 2015.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/10.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "10. | | s = 2 + \u221a3 = 3.732+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "fd5a10d8a6354174", "improvement": -7.740911509834802e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.847623197892974e-06, "max_pair_overlap_depth": -2.6880918478910942e-06, "metric_expression": "3.73208", "metric_symbol": "s", "metric_value": 3.7320774091150986, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.732, "setup": "hexinhex", "side": 3.7320774091150986, "solution_path": "data/solutions/generated/hexinhex_010_fd5a10d8a6354174.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/fd5a10d8a6354174.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@11", "density": 0.7131589068275569, "friedman_analytical_or_proved": true, "friedman_credit": "Johann Schellhorn", "friedman_date": "July 2025", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/11.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "2+10/3\u221a3 = 3.92450+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.9245, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@11", "credit": "Johann Schellhorn", "date": "July 2025", "family_updated": "", "metric_expression": "2+10/3\u221a3 = 3.92450+", "metric_symbol": "s", "metric_value": 3.9245, "reference_text": "11. | | s = 2+10/3\u221a3 = 3.92450+ | Found by Johann Schellhorn | in July 2025. | | | |", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/11.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "11. | | s = 2+10/3\u221a3 = 3.92450+ | Found by Johann Schellhorn | in July 2025. | | | |", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "cf10a9116bb04a72", "improvement": -0.0028823793751930893, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3732870796469545e-06, "max_pair_overlap_depth": -1.938912890975253e-05, "metric_expression": "3.92738", "metric_symbol": "s", "metric_value": 3.927382379375193, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.9245, "setup": "hexinhex", "side": 3.927382379375193, "solution_path": "data/solutions/generated/hexinhex_011_cf10a9116bb04a72.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Johann Schellhorn", "svg_path": "data/svg/cf10a9116bb04a72.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@12", "density": 0.7723090107470407, "friedman_analytical_or_proved": true, "friedman_credit": "Alexander Novikov et al", "friedman_date": "June 2025", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/12.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "3.94164+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.94164, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@12", "credit": "Alexander Novikov et al", "date": "June 2025", "family_updated": "", "metric_expression": "3.94164+", "metric_symbol": "s", "metric_value": 3.94164, "reference_text": "12. | | s = 3.94164+ | Found by Alexander Novikov et al | in June 2025. | Improved slightly by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/12.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "12. | | s = 3.94164+ | Found by Alexander Novikov et al | in June 2025. | Improved slightly by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "bdc671b076ad0ffe", "improvement": -0.0001644193364005453, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.69077332163481e-06, "max_pair_overlap_depth": -4.133319357890741e-07, "metric_expression": "3.94180", "metric_symbol": "s", "metric_value": 3.9418044193364006, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.94164, "setup": "hexinhex", "side": 3.9418044193364006, "solution_path": "data/solutions/generated/hexinhex_012_bdc671b076ad0ffe.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Alexander Novikov et al", "svg_path": "data/svg/bdc671b076ad0ffe.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@13", "density": 0.8124849152838151, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/13.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@13", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "13 | | s = 4 | Trivial. | | | | |", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/13.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "13 | | s = 4 | Trivial. | | | | |", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "1ac594ff5f07e3d9", "improvement": -3.7132126112560115e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.027960154271181e-06, "max_pair_overlap_depth": -5.440029557712833e-06, "metric_expression": "4.00004", "metric_symbol": "s", "metric_value": 4.000037132126113, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.0, "setup": "hexinhex", "side": 4.000037132126113, "solution_path": "data/solutions/generated/hexinhex_013_1ac594ff5f07e3d9.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/1ac594ff5f07e3d9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@14", "density": 0.7678833113230449, "friedman_analytical_or_proved": false, "friedman_credit": "Dominik Kamp", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/14.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "4.26899+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.26899, "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@14", "credit": "Dominik Kamp", "date": "April 2026", "family_updated": "", "metric_expression": "4.26899+", "metric_symbol": "s", "metric_value": 4.26899, "reference_text": "14. | | s = 4.26899+ | Found by Dominik Kamp | in April 2026.", "source_image": "14.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/14.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "14. | | s = 4.26899+ | Found by Dominik Kamp | in April 2026.", "friedman_source_image": "14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "f86af09d863723a2", "improvement": -0.0008972113481453547, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.52825412539728e-06, "max_pair_overlap_depth": -2.1736642138669993e-05, "metric_expression": "4.26989", "metric_symbol": "s", "metric_value": 4.269887211348145, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.26899, "setup": "hexinhex", "side": 4.269887211348145, "solution_path": "data/solutions/generated/hexinhex_014_f86af09d863723a2.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Dominik Kamp", "svg_path": "data/svg/f86af09d863723a2.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@15", "density": 0.7579263950656321, "friedman_analytical_or_proved": true, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/15.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "4.44727+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.44727, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@15", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "4.44727+", "metric_symbol": "s", "metric_value": 4.44727, "reference_text": "15. | | s = 4.44727+ | Found by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/15.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "15. | | s = 4.44727+ | Found by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "536c412ab623afbc", "improvement": -0.0014196922804980971, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.564398033090082e-06, "max_pair_overlap_depth": -2.5468766324809877e-06, "metric_expression": "4.44869", "metric_symbol": "s", "metric_value": 4.448689692280498, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.44727, "setup": "hexinhex", "side": 4.448689692280498, "solution_path": "data/solutions/generated/hexinhex_015_536c412ab623afbc.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/536c412ab623afbc.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@16", "density": 0.7803167098453238, "friedman_analytical_or_proved": true, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/16.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "4.52746+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.52746, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@16", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "4.52746+", "metric_symbol": "s", "metric_value": 4.52746, "reference_text": "16. | | s = 4.52746+ | Found by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/16.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "16. | | s = 4.52746+ | Found by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "17cb432379a18c18", "improvement": -0.0007289208955771898, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.541715273786282e-06, "max_pair_overlap_depth": -2.3206185233659582e-05, "metric_expression": "4.52819", "metric_symbol": "s", "metric_value": 4.528188920895577, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.52746, "setup": "hexinhex", "side": 4.528188920895577, "solution_path": "data/solutions/generated/hexinhex_016_17cb432379a18c18.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/17cb432379a18c18.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@17", "density": 0.7985097849440846, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "February 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/17.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "4.6136+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.6136, "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@17", "credit": "Timo Berthold et al", "date": "February 2026", "family_updated": "", "metric_expression": "4.6136+", "metric_symbol": "s", "metric_value": 4.6136, "reference_text": "17. | | s = 4.6136+ | Found by Timo Berthold et al | and Alex Kravatsky et al | in February 2026.", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/17.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "17. | | s = 4.6136+ | Found by Timo Berthold et al | and Alex Kravatsky et al | in February 2026.", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "df809b176b000a6d", "improvement": -0.0004717062665458016, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.290243996089003e-06, "max_pair_overlap_depth": -4.642493336670661e-05, "metric_expression": "4.61407", "metric_symbol": "s", "metric_value": 4.614071706266546, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.6136, "setup": "hexinhex", "side": 4.614071706266546, "solution_path": "data/solutions/generated/hexinhex_017_df809b176b000a6d.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/df809b176b000a6d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@18", "density": 0.8437116836701195, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "8/\u221a3 = 4.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.618, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@18", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "8/\u221a3 = 4.618+", "metric_symbol": "s", "metric_value": 4.618, "reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "e320d39029a817c1", "improvement": -0.0009070314872570151, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 1.0443685916789865e-09, "max_pair_overlap_depth": -3.080790913889686e-05, "metric_expression": "4.61891", "metric_symbol": "s", "metric_value": 4.618907031487257, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.618, "setup": "hexinhex", "side": 4.618907031487257, "solution_path": "data/solutions/generated/hexinhex_018_e320d39029a817c1.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/e320d39029a817c1.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@19", "density": 0.8905854861904853, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "8/\u221a3 = 4.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.618, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@19", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "8/\u221a3 = 4.618+", "metric_symbol": "s", "metric_value": 4.618, "reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4b11a1a09f2a5b70", "improvement": -0.0009046166982376036, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.772589960788204e-06, "max_pair_overlap_depth": -3.612300978728111e-05, "metric_expression": "4.61890", "metric_symbol": "s", "metric_value": 4.618904616698238, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.618, "setup": "hexinhex", "side": 4.618904616698238, "solution_path": "data/solutions/generated/hexinhex_019_4b11a1a09f2a5b70.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/4b11a1a09f2a5b70.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@20", "density": 0.7999496824068819, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@20", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "20-21. | | s = 5 | Trivial. | |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "20-21. | | s = 5 | Trivial. | |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "2830e2dec38749ef", "improvement": -0.00015724989644283482, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.445035556179186e-06, "max_pair_overlap_depth": -1.6551811964360397e-06, "metric_expression": "5.00016", "metric_symbol": "s", "metric_value": 5.000157249896443, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.0, "setup": "hexinhex", "side": 5.000157249896443, "solution_path": "data/solutions/generated/hexinhex_020_2830e2dec38749ef.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/2830e2dec38749ef.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@21", "density": 0.8399773177134815, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@21", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "20-21. | | s = 5 | Trivial. | |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "20-21. | | s = 5 | Trivial. | |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4a431b677be571c9", "improvement": -6.750817229672634e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5389132812752791e-06, "max_pair_overlap_depth": -3.519050301936666e-06, "metric_expression": "5.00007", "metric_symbol": "s", "metric_value": 5.000067508172297, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.0, "setup": "hexinhex", "side": 5.000067508172297, "solution_path": "data/solutions/generated/hexinhex_021_4a431b677be571c9.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4a431b677be571c9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@22", "density": 0.7873804951730353, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/22.gif", "friedman_metric_expression": "(39+8\u221a3)/10 = 5.285+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.285, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@22", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "(39+8\u221a3)/10 = 5.285+", "metric_symbol": "s", "metric_value": 5.285, "reference_text": "22. | | s = (39+8\u221a3)/10 = 5.285+ | Found by Maurizio Morandi | in April 2015.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/22.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "22. | | s = (39+8\u221a3)/10 = 5.285+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "003a713177cb171c", "improvement": -0.0009008698048820207, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.575542655386671e-06, "max_pair_overlap_depth": -1.0001604064946434e-05, "metric_expression": "5.28590", "metric_symbol": "s", "metric_value": 5.285900869804882, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.285, "setup": "hexinhex", "side": 5.285900869804882, "solution_path": "data/solutions/generated/hexinhex_022_003a713177cb171c.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/003a713177cb171c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@23", "density": 0.7886255260759908, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/23.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "5.400+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.4, "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@23", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "", "metric_expression": "5.400+", "metric_symbol": "s", "metric_value": 5.4, "reference_text": "23. | | s = 5.400+ | Found by Alex Kravatsky et al | in February 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/23.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "23. | | s = 5.400+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "e0a82406671652d2", "improvement": -0.00043201188015196124, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4507055603926188e-06, "max_pair_overlap_depth": -1.2502329530761358e-05, "metric_expression": "5.40043", "metric_symbol": "s", "metric_value": 5.400432011880152, "n": 23, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.4, "setup": "hexinhex", "side": 5.400432011880152, "solution_path": "data/solutions/generated/hexinhex_023_e0a82406671652d2.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Alex Kravatsky et al", "svg_path": "data/svg/e0a82406671652d2.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@24", "density": 0.797738483588153, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/24.gif", "friedman_metric_expression": "19\u221a3/6 = 5.484+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.484, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@24", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "19\u221a3/6 = 5.484+", "metric_symbol": "s", "metric_value": 5.484, "reference_text": "24. | | s = 19\u221a3/6 = 5.484+ | Found by Maurizio Morandi | in April 2015.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/24.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "24. | | s = 19\u221a3/6 = 5.484+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "c96649ff013a9455", "improvement": -0.00098379990619879, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.588312731744032e-06, "max_pair_overlap_depth": -4.485524381903083e-05, "metric_expression": "5.48498", "metric_symbol": "s", "metric_value": 5.484983799906199, "n": 24, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.484, "setup": "hexinhex", "side": 5.484983799906199, "solution_path": "data/solutions/generated/hexinhex_024_c96649ff013a9455.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/c96649ff013a9455.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@25", "density": 0.7898226009433017, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/25.gif", "friedman_metric_expression": "5.62390+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.6239, "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@25", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "", "metric_expression": "5.62390+", "metric_symbol": "s", "metric_value": 5.6239, "reference_text": "25. | | s = 5.62390+ | Found by Alex Kravatsky et al | in February 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/25.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "25. | | s = 5.62390+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4ac680367830872b", "improvement": -0.002171223468265815, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8833146044517865e-07, "max_pair_overlap_depth": -2.7316686140865798e-05, "metric_expression": "5.62607", "metric_symbol": "s", "metric_value": 5.626071223468266, "n": 25, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.6239, "setup": "hexinhex", "side": 5.626071223468266, "solution_path": "data/solutions/generated/hexinhex_025_4ac680367830872b.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Alex Kravatsky et al", "svg_path": "data/svg/4ac680367830872b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@26", "density": 0.7965297187067493, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/26.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "5.70972+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.70972, "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@26", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "", "metric_expression": "5.70972+", "metric_symbol": "s", "metric_value": 5.70972, "reference_text": "26. | | s = 5.70972+ | Found by Alex Kravatsky et al | in February 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/26.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "26. | | s = 5.70972+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "8ed8c9fb94f18119", "improvement": -0.0035622784284790043, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9624619447323227e-06, "max_pair_overlap_depth": -1.2105377510118753e-05, "metric_expression": "5.71328", "metric_symbol": "s", "metric_value": 5.713282278428479, "n": 26, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.70972, "setup": "hexinhex", "side": 5.713282278428479, "solution_path": "data/solutions/generated/hexinhex_026_8ed8c9fb94f18119.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Alex Kravatsky et al", "svg_path": "data/svg/8ed8c9fb94f18119.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@27", "density": 0.82621496088318, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/27.gif", "friedman_metric_expression": "5.71415+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.71415, "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@27", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "", "metric_expression": "5.71415+", "metric_symbol": "s", "metric_value": 5.71415, "reference_text": "27. | | s = 5.71415+ | Found by Alex Kravatsky et al | in February 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/27.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "27. | | s = 5.71415+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4e9628a9f49def85", "improvement": -0.0024177469948583052, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.56387472302006e-06, "max_pair_overlap_depth": -5.6693937127594296e-05, "metric_expression": "5.71657", "metric_symbol": "s", "metric_value": 5.716567746994858, "n": 27, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.71415, "setup": "hexinhex", "side": 5.716567746994858, "solution_path": "data/solutions/generated/hexinhex_027_4e9628a9f49def85.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Alex Kravatsky et al", "svg_path": "data/svg/4e9628a9f49def85.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@28", "density": 0.8011452289129106, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/28.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "5.90893+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.90893, "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@28", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "", "metric_expression": "5.90893+", "metric_symbol": "s", "metric_value": 5.90893, "reference_text": "28. | | s = 5.90893+ | Found by Alex Kravatsky et al | in February 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/28.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "28. | | s = 5.90893+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "ba522f97744aed1a", "improvement": -0.002919783094952777, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.424277796084301e-06, "max_pair_overlap_depth": -3.209757705180394e-05, "metric_expression": "5.91185", "metric_symbol": "s", "metric_value": 5.911849783094953, "n": 28, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.90893, "setup": "hexinhex", "side": 5.911849783094953, "solution_path": "data/solutions/generated/hexinhex_028_ba522f97744aed1a.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T02:51:36+00:00", "submitted_by": "Alex Kravatsky et al", "svg_path": "data/svg/ba522f97744aed1a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@29", "density": 0.8055194808067645, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@29", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "29-31. | | s = 6 | Trivial. |", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "29-31. | | s = 6 | Trivial. |", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "dba25a591b8992bc", "improvement": -0.00013435185279675466, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.231638156342025e-06, "max_pair_overlap_depth": -6.307567709251671e-06, "metric_expression": "6.00013", "metric_symbol": "s", "metric_value": 6.000134351852797, "n": 29, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.0, "setup": "hexinhex", "side": 6.000134351852797, "solution_path": "data/solutions/generated/hexinhex_029_dba25a591b8992bc.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/dba25a591b8992bc.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@30", "density": 0.8333115277207207, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@30", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "29-31. | | s = 6 | Trivial. |", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "29-31. | | s = 6 | Trivial. |", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "100db5f9f28894cc", "improvement": -7.850174601031767e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7272811687230685e-07, "max_pair_overlap_depth": -4.232627726974414e-06, "metric_expression": "6.00008", "metric_symbol": "s", "metric_value": 6.00007850174601, "n": 30, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.0, "setup": "hexinhex", "side": 6.00007850174601, "solution_path": "data/solutions/generated/hexinhex_030_100db5f9f28894cc.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/100db5f9f28894cc.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinhex@31", "density": 0.8610814974425702, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@31", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "29-31. | | s = 6 | Trivial. |", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "29-31. | | s = 6 | Trivial. |", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "d503e2b08764a35e", "improvement": -0.0001031728611780025, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0312532034243658e-06, "max_pair_overlap_depth": -8.80446118189937e-06, "metric_expression": "6.00010", "metric_symbol": "s", "metric_value": 6.000103172861178, "n": 31, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.0, "setup": "hexinhex", "side": 6.000103172861178, "solution_path": "data/solutions/generated/hexinhex_031_d503e2b08764a35e.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d503e2b08764a35e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@1", "density": 0.6961402306608654, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/1.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(1+\u221a3)/\u221a2 = 1.931+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.931, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "(1+\u221a3)/\u221a2 = 1.931+", "metric_symbol": "s", "metric_value": 1.931, "reference_text": "s = (1+\u221a3)/\u221a2 = 1.931+ | Trivial. |", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/1.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = (1+\u221a3)/\u221a2 = 1.931+ | Trivial. |", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "1cfff36edc20de72", "improvement": -0.000868569514983486, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8875760125229138e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.93187", "metric_symbol": "s", "metric_value": 1.9318685695149835, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.931, "setup": "hexinsqu", "side": 1.9318685695149835, "solution_path": "data/solutions/generated/hexinsqu_001_1cfff36edc20de72.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/1cfff36edc20de72.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@2", "density": 0.5214616218348717, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/2.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(1+2\u221a3)/\u221a2 = 3.156+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.156, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "(1+2\u221a3)/\u221a2 = 3.156+", "metric_symbol": "s", "metric_value": 3.156, "reference_text": "s = (1+2\u221a3)/\u221a2 = 3.156+ | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/2.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = (1+2\u221a3)/\u221a2 = 3.156+ | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "ff43d04cda84c856", "improvement": -0.0006742348964126066, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2405599436706566e-05, "max_pair_overlap_depth": -1.629836664562411e-05, "metric_expression": "3.15667", "metric_symbol": "s", "metric_value": 3.1566742348964127, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.156, "setup": "hexinsqu", "side": 3.1566742348964127, "solution_path": "data/solutions/generated/hexinsqu_002_ff43d04cda84c856.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/ff43d04cda84c856.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@3", "density": 0.6391474518535116, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/3.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "9(6\u2013\u221a3)/11 = 3.491+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.491, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@3", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "9(6\u2013\u221a3)/11 = 3.491+", "metric_symbol": "s", "metric_value": 3.491, "reference_text": "s = 9(6\u2013\u221a3)/11 = 3.491+ | Found by Maurizio Morandi | in March 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/3.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 9(6\u2013\u221a3)/11 = 3.491+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "9525d376eafe3c9c", "improvement": -0.0010949178753740796, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.084317521962771e-06, "max_pair_overlap_depth": -8.912711465047796e-05, "metric_expression": "3.49209", "metric_symbol": "s", "metric_value": 3.492094917875374, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.491, "setup": "hexinsqu", "side": 3.492094917875374, "solution_path": "data/solutions/generated/hexinsqu_003_9525d376eafe3c9c.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/9525d376eafe3c9c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@4", "density": 0.748920266367969, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/4.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(7\u2013\u221a3)/\u221a2 = 3.725+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.725, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@4", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "(7\u2013\u221a3)/\u221a2 = 3.725+", "metric_symbol": "s", "metric_value": 3.725, "reference_text": "s = (7\u2013\u221a3)/\u221a2 = 3.725+ | Found by Maurizio Morandi | in March 2026.", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/4.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = (7\u2013\u221a3)/\u221a2 = 3.725+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "33ddf042dd02d191", "improvement": -0.00010181398140396425, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.577436704193743e-06, "max_pair_overlap_depth": -5.3695636117151446e-05, "metric_expression": "3.72510", "metric_symbol": "s", "metric_value": 3.725101813981404, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.725, "setup": "hexinsqu", "side": 3.725101813981404, "solution_path": "data/solutions/generated/hexinsqu_004_33ddf042dd02d191.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/33ddf042dd02d191.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@5", "density": 0.6595778437263831, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/5.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "7(3\u2013\u221a3)/2 = 4.437+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.437, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@5", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "7(3\u2013\u221a3)/2 = 4.437+", "metric_symbol": "s", "metric_value": 4.437, "reference_text": "s = 7(3\u2013\u221a3)/2 = 4.437+ | Found by Maurizio Morandi | in March 2026.", "source_image": "5.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/5.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 7(3\u2013\u221a3)/2 = 4.437+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "38f2dc66ba941978", "improvement": -0.0009041295527705273, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.5429089870357805e-06, "max_pair_overlap_depth": -1.5874388830661168e-05, "metric_expression": "4.43790", "metric_symbol": "s", "metric_value": 4.437904129552771, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.437, "setup": "hexinsqu", "side": 4.437904129552771, "solution_path": "data/solutions/generated/hexinsqu_005_38f2dc66ba941978.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/38f2dc66ba941978.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@6", "density": 0.6726426228424899, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/6.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "20(9\u20132\u221a3)/23 = 4.813+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.813, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@6", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "20(9\u20132\u221a3)/23 = 4.813+", "metric_symbol": "s", "metric_value": 4.813, "reference_text": "s = 20(9\u20132\u221a3)/23 = 4.813+ | Found by Maurizio Morandi | in March 2026.", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/6.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 20(9\u20132\u221a3)/23 = 4.813+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "31291850c6887128", "improvement": -0.0010364766922137392, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6841191118288626e-06, "max_pair_overlap_depth": -6.696342223433405e-05, "metric_expression": "4.81404", "metric_symbol": "s", "metric_value": 4.8140364766922135, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.813, "setup": "hexinsqu", "side": 4.8140364766922135, "solution_path": "data/solutions/generated/hexinsqu_006_31291850c6887128.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/31291850c6887128.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@7", "density": 0.6735519886722757, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/8.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3\u221a3 = 5.196+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.196, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@7", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3\u221a3 = 5.196+", "metric_symbol": "s", "metric_value": 5.196, "reference_text": "s = 3\u221a3 = 5.196+ | Trivial. |", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/8.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 3\u221a3 = 5.196+ | Trivial. |", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "a4c696c014daab3c", "improvement": -0.00024239437505713113, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.667089398456013e-06, "max_pair_overlap_depth": -2.5433886154724306e-05, "metric_expression": "5.19624", "metric_symbol": "s", "metric_value": 5.196242394375057, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.196, "setup": "hexinsqu", "side": 5.196242394375057, "solution_path": "data/solutions/generated/hexinsqu_007_a4c696c014daab3c.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/a4c696c014daab3c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@8", "density": 0.7697897324076285, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/8.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3\u221a3 = 5.196+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.196, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@8", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3\u221a3 = 5.196+", "metric_symbol": "s", "metric_value": 5.196, "reference_text": "s = 3\u221a3 = 5.196+ | Trivial. |", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/8.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 3\u221a3 = 5.196+ | Trivial. |", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "b1252a56565d2ec0", "improvement": -0.00018828755551858478, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.033193436423119e-06, "max_pair_overlap_depth": -1.0846799477937097e-05, "metric_expression": "5.19619", "metric_symbol": "s", "metric_value": 5.196188287555518, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.196, "setup": "hexinsqu", "side": 5.196188287555518, "solution_path": "data/solutions/generated/hexinsqu_008_b1252a56565d2ec0.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/b1252a56565d2ec0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@9", "density": 0.7678652278206223, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/9.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(13\u20133\u221a3)/\u221a2 = 5.518+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.518, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@9", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "(13\u20133\u221a3)/\u221a2 = 5.518+", "metric_symbol": "s", "metric_value": 5.518, "reference_text": "s = (13\u20133\u221a3)/\u221a2 = 5.518+ | Found by Maurizio Morandi | in March 2026.", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/9.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = (13\u20133\u221a3)/\u221a2 = 5.518+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "5b4ef4c36dcfba05", "improvement": -0.0002922521392276778, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.874395903155008e-06, "max_pair_overlap_depth": -4.408050364324012e-05, "metric_expression": "5.51829", "metric_symbol": "s", "metric_value": 5.5182922521392275, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.518, "setup": "hexinsqu", "side": 5.5182922521392275, "solution_path": "data/solutions/generated/hexinsqu_009_5b4ef4c36dcfba05.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/5b4ef4c36dcfba05.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@10", "density": 0.6970336920701942, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/10.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.10469+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.10469, "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@10", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6.10469+", "metric_symbol": "s", "metric_value": 6.10469, "reference_text": "s = 6.10469+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/10.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 6.10469+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "031f63d864cce10c", "improvement": -0.0004982231227232958, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.5872663706407347e-08, "max_pair_overlap_depth": -2.0702587337384504e-05, "metric_expression": "6.10519", "metric_symbol": "s", "metric_value": 6.105188223122723, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.10469, "setup": "hexinsqu", "side": 6.105188223122723, "solution_path": "data/solutions/generated/hexinsqu_010_031f63d864cce10c.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/031f63d864cce10c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@11", "density": 0.7126826634184014, "friedman_analytical_or_proved": false, "friedman_credit": "Maksymilian Jankowski", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/11.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.33218+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.33218, "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@11", "credit": "Maksymilian Jankowski", "date": "April 2026", "family_updated": "", "metric_expression": "6.33218+", "metric_symbol": "s", "metric_value": 6.33218, "reference_text": "s = 6.33218+ | Found by Maksymilian Jankowski | in April 2026.", "source_image": "11.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/11.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 6.33218+ | Found by Maksymilian Jankowski | in April 2026.", "friedman_source_image": "11.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "f0fe574f6ed3708e", "improvement": -0.0003052751802421483, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.734623780299186e-06, "max_pair_overlap_depth": -4.342994577477555e-05, "metric_expression": "6.33249", "metric_symbol": "s", "metric_value": 6.332485275180242, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.33218, "setup": "hexinsqu", "side": 6.332485275180242, "solution_path": "data/solutions/generated/hexinsqu_011_f0fe574f6ed3708e.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maksymilian Jankowski", "svg_path": "data/svg/f0fe574f6ed3708e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@12", "density": 0.7640646951117188, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/12.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "43(5\u2013\u221a3)/22 = 6.387+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.387, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@12", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "43(5\u2013\u221a3)/22 = 6.387+", "metric_symbol": "s", "metric_value": 6.387, "reference_text": "s = 43(5\u2013\u221a3)/22 = 6.387+ | Found by Maurizio Morandi | in March 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/12.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 43(5\u2013\u221a3)/22 = 6.387+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "70f372d7c2d3b859", "improvement": -0.0008027909827861279, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.6841159701879252e-07, "max_pair_overlap_depth": -5.12694605685482e-05, "metric_expression": "6.38780", "metric_symbol": "s", "metric_value": 6.387802790982786, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.387, "setup": "hexinsqu", "side": 6.387802790982786, "solution_path": "data/solutions/generated/hexinsqu_012_70f372d7c2d3b859.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/70f372d7c2d3b859.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@13", "density": 0.7399851108638961, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/13.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.75558+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.75558, "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@13", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6.75558+", "metric_symbol": "s", "metric_value": 6.75558, "reference_text": "s = 6.75558+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/13.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 6.75558+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "96118c364cb8b05d", "improvement": -0.0003653626017898759, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.852098428599495e-06, "max_pair_overlap_depth": -2.731772979069902e-05, "metric_expression": "6.75595", "metric_symbol": "s", "metric_value": 6.75594536260179, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.75558, "setup": "hexinsqu", "side": 6.75594536260179, "solution_path": "data/solutions/generated/hexinsqu_013_96118c364cb8b05d.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/96118c364cb8b05d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@14", "density": 0.7577523835410583, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/14.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4\u221a3 = 6.928+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.928, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@14", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4\u221a3 = 6.928+", "metric_symbol": "s", "metric_value": 6.928, "reference_text": "s = 4\u221a3 = 6.928+ | Trivial. |", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/14.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 4\u221a3 = 6.928+ | Trivial. |", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "8b7d0912d343dc8b", "improvement": -0.00029395100744089575, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.277327734003356e-06, "max_pair_overlap_depth": -1.698575172759398e-05, "metric_expression": "6.92829", "metric_symbol": "s", "metric_value": 6.928293951007441, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.928, "setup": "hexinsqu", "side": 6.928293951007441, "solution_path": "data/solutions/generated/hexinsqu_014_8b7d0912d343dc8b.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/8b7d0912d343dc8b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@15", "density": 0.8035851614122442, "friedman_analytical_or_proved": false, "friedman_credit": "Maksymilian Jankowski", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/15.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.96367+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.96367, "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@15", "credit": "Maksymilian Jankowski", "date": "April 2026", "family_updated": "", "metric_expression": "6.96367+", "metric_symbol": "s", "metric_value": 6.96367, "reference_text": "s = 6.96367+ | Found by Maksymilian Jankowski | in April 2026.", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/15.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 6.96367+ | Found by Maksymilian Jankowski | in April 2026.", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "0691341c684bd112", "improvement": -0.00027958460374311045, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.156990403080692e-07, "max_pair_overlap_depth": -5.813914172492218e-05, "metric_expression": "6.96395", "metric_symbol": "s", "metric_value": 6.963949584603743, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.96367, "setup": "hexinsqu", "side": 6.963949584603743, "solution_path": "data/solutions/generated/hexinsqu_015_0691341c684bd112.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maksymilian Jankowski", "svg_path": "data/svg/0691341c684bd112.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@16", "density": 0.7776171365327941, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/16.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(19\u20135\u221a3)/\u221a2 = 7.311+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.311, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@16", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "(19\u20135\u221a3)/\u221a2 = 7.311+", "metric_symbol": "s", "metric_value": 7.311, "reference_text": "s = (19\u20135\u221a3)/\u221a2 = 7.311+ | Found by Maurizio Morandi | in April 2026.", "source_image": "16.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/16.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = (19\u20135\u221a3)/\u221a2 = 7.311+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "03465bdf660197b5", "improvement": -0.000441730863443901, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8577837974051795e-06, "max_pair_overlap_depth": -3.069264188360066e-05, "metric_expression": "7.31144", "metric_symbol": "s", "metric_value": 7.311441730863444, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.311, "setup": "hexinsqu", "side": 7.311441730863444, "solution_path": "data/solutions/generated/hexinsqu_016_03465bdf660197b5.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/03465bdf660197b5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@17", "density": 0.7624212140097384, "friedman_analytical_or_proved": true, "friedman_credit": "Maksymilian Jankowski", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/17.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6(3\u2013\u221a3) = 7.60383+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.60383, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@17", "credit": "Maksymilian Jankowski", "date": "April 2026", "family_updated": "", "metric_expression": "6(3\u2013\u221a3) = 7.60383+", "metric_symbol": "s", "metric_value": 7.60383, "reference_text": "s = 6(3\u2013\u221a3) = 7.60383+ | Found by Maksymilian Jankowski | in April 2026.", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/17.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 6(3\u2013\u221a3) = 7.60383+ | Found by Maksymilian Jankowski | in April 2026.", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "080714e7afd39346", "improvement": -0.007366212799500005, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.378937853940429e-07, "max_pair_overlap_depth": -2.071443269358042e-05, "metric_expression": "7.61120", "metric_symbol": "s", "metric_value": 7.6111962127995, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.60383, "setup": "hexinsqu", "side": 7.6111962127995, "solution_path": "data/solutions/generated/hexinsqu_017_080714e7afd39346.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maksymilian Jankowski", "svg_path": "data/svg/080714e7afd39346.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@18", "density": 0.7882207738949305, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/18.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "32(9\u20132\u221a3)/23 = 7.702+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.702, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@18", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "32(9\u20132\u221a3)/23 = 7.702+", "metric_symbol": "s", "metric_value": 7.702, "reference_text": "s = 32(9\u20132\u221a3)/23 = 7.702+ | Found by Maurizio Morandi | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/18.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 32(9\u20132\u221a3)/23 = 7.702+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "39a9a99a50ac7cba", "improvement": -0.0006161769446162424, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5800172874233264e-06, "max_pair_overlap_depth": -3.4078889656230515e-05, "metric_expression": "7.70262", "metric_symbol": "s", "metric_value": 7.702616176944616, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.702, "setup": "hexinsqu", "side": 7.702616176944616, "solution_path": "data/solutions/generated/hexinsqu_018_39a9a99a50ac7cba.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/39a9a99a50ac7cba.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@19", "density": 0.7859807737367643, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/19.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "25(3\u2013\u221a3)/4 = 7.924+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.924, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@19", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "25(3\u2013\u221a3)/4 = 7.924+", "metric_symbol": "s", "metric_value": 7.924, "reference_text": "s = 25(3\u2013\u221a3)/4 = 7.924+ | Found by Maurizio Morandi | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/19.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 25(3\u2013\u221a3)/4 = 7.924+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "10d9f5dde53d25ba", "improvement": -0.0009545892016307178, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.893895229540556e-06, "max_pair_overlap_depth": -3.6221248433054853e-05, "metric_expression": "7.92495", "metric_symbol": "s", "metric_value": 7.924954589201631, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.924, "setup": "hexinsqu", "side": 7.924954589201631, "solution_path": "data/solutions/generated/hexinsqu_019_10d9f5dde53d25ba.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/10d9f5dde53d25ba.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@20", "density": 0.8222377903171622, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/20.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "74(21\u20134\u221a3)/131 = 7.948+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.948, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@20", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "74(21\u20134\u221a3)/131 = 7.948+", "metric_symbol": "s", "metric_value": 7.948, "reference_text": "s = 74(21\u20134\u221a3)/131 = 7.948+ | Found by Maurizio Morandi | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/20.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 74(21\u20134\u221a3)/131 = 7.948+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "3d530c0ac6e7e3b1", "improvement": -0.0015441274741458955, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.121785608292394e-06, "max_pair_overlap_depth": -4.480534023287852e-05, "metric_expression": "7.94954", "metric_symbol": "s", "metric_value": 7.949544127474146, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.948, "setup": "hexinsqu", "side": 7.949544127474146, "solution_path": "data/solutions/generated/hexinsqu_020_3d530c0ac6e7e3b1.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/3d530c0ac6e7e3b1.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@21", "density": 0.7762795555424945, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/21.png", "friedman_metric_expression": "8.381+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.381, "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@21", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "8.381+", "metric_symbol": "s", "metric_value": 8.381, "reference_text": "s = 8.381+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/21.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 8.381+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "5d369a2740fde606", "improvement": -0.002522153681731254, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.85221561134309e-06, "max_pair_overlap_depth": -3.989714052887727e-05, "metric_expression": "8.38352", "metric_symbol": "s", "metric_value": 8.383522153681731, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.381, "setup": "hexinsqu", "side": 8.383522153681731, "solution_path": "data/solutions/generated/hexinsqu_021_5d369a2740fde606.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/5d369a2740fde606.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@22", "density": 0.7770815845496467, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/22.png", "friedman_metric_expression": "8.568+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.568, "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@22", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "8.568+", "metric_symbol": "s", "metric_value": 8.568, "reference_text": "s = 8.568+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "22.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/22.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 8.568+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "2f0b0033f0c66708", "improvement": -0.008379204155273712, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.913077650512531e-06, "max_pair_overlap_depth": -1.9097490104869053e-05, "metric_expression": "8.57638", "metric_symbol": "s", "metric_value": 8.576379204155273, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.568, "setup": "hexinsqu", "side": 8.576379204155273, "solution_path": "data/solutions/generated/hexinsqu_022_2f0b0033f0c66708.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/2f0b0033f0c66708.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@23", "density": 0.7967168154089415, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/23.png", "friedman_metric_expression": "5\u221a3 = 8.660+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.66, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@23", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5\u221a3 = 8.660+", "metric_symbol": "s", "metric_value": 8.66, "reference_text": "s = 5\u221a3 = 8.660+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "23.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/23.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 5\u221a3 = 8.660+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "31cc17034bd25d7b", "improvement": -0.0003983679346664104, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.345963802137002e-06, "max_pair_overlap_depth": -2.1349502021816846e-07, "metric_expression": "8.66040", "metric_symbol": "s", "metric_value": 8.660398367934667, "n": 23, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.66, "setup": "hexinsqu", "side": 8.660398367934667, "solution_path": "data/solutions/generated/hexinsqu_023_31cc17034bd25d7b.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/31cc17034bd25d7b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@24", "density": 0.8058676683577897, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/24.png", "friedman_metric_expression": "8.795+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.795, "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@24", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "8.795+", "metric_symbol": "s", "metric_value": 8.795, "reference_text": "s = 8.795+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "24.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/24.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 8.795+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "941fbce4f50492c6", "improvement": -0.0012932219182459903, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0969884292392119e-07, "max_pair_overlap_depth": -1.611027152126354e-05, "metric_expression": "8.79629", "metric_symbol": "s", "metric_value": 8.796293221918246, "n": 24, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.795, "setup": "hexinsqu", "side": 8.796293221918246, "solution_path": "data/solutions/generated/hexinsqu_024_941fbce4f50492c6.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/941fbce4f50492c6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexinsqu@25", "density": 0.7898968080720588, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/25.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "30(4\u221a3\u20133)/13 = 9.065+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.065, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@25", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "30(4\u221a3\u20133)/13 = 9.065+", "metric_symbol": "s", "metric_value": 9.065, "reference_text": "s = 30(4\u221a3\u20133)/13 = 9.065+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "25.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/25.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 30(4\u221a3\u20133)/13 = 9.065+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "25.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "a62e2508884336f7", "improvement": -0.00298447907218069, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.02442885507961e-06, "max_pair_overlap_depth": -5.091125714784539e-06, "metric_expression": "9.06798", "metric_symbol": "s", "metric_value": 9.06798447907218, "n": 25, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.065, "setup": "hexinsqu", "side": 9.06798447907218, "solution_path": "data/solutions/generated/hexinsqu_025_a62e2508884336f7.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/a62e2508884336f7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@1", "density": 0.6666490309389511, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/1.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "s = 3 | Trivial.", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/1.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 3 | Trivial.", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "c2fff75544b88239", "improvement": -3.9681174644368156e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.67464904574664e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "3.00004", "metric_symbol": "s", "metric_value": 3.0000396811746444, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.0, "setup": "hexintri", "side": 3.0000396811746444, "solution_path": "data/solutions/generated/hexintri_001_c2fff75544b88239.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/c2fff75544b88239.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@2", "density": 0.4799802064426444, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "b77426ecb97f3ce6", "improvement": -0.00010309463302426991, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3591084715906373e-06, "max_pair_overlap_depth": -4.2178351187804886e-05, "metric_expression": "5.00010", "metric_symbol": "s", "metric_value": 5.000103094633024, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.0, "setup": "hexintri", "side": 5.000103094633024, "solution_path": "data/solutions/generated/hexintri_002_b77426ecb97f3ce6.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/b77426ecb97f3ce6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@3", "density": 0.7199659208954582, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "748bfe1ef47ea18c", "improvement": -0.00011833442488207169, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3474135610435156e-06, "max_pair_overlap_depth": -4.4955482604913666e-05, "metric_expression": "5.00012", "metric_symbol": "s", "metric_value": 5.000118334424882, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.0, "setup": "hexintri", "side": 5.000118334424882, "solution_path": "data/solutions/generated/hexintri_003_748bfe1ef47ea18c.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/748bfe1ef47ea18c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@4", "density": 0.6666571046827545, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/4.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@4", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/4.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 6 | Trivial.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "4bf531bb9fa044b6", "improvement": -4.302939048272947e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.615149234551692e-07, "max_pair_overlap_depth": -1.1132001730862484e-05, "metric_expression": "6.00004", "metric_symbol": "s", "metric_value": 6.000043029390483, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.0, "setup": "hexintri", "side": 6.000043029390483, "solution_path": "data/solutions/generated/hexintri_004_4bf531bb9fa044b6.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4bf531bb9fa044b6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@5", "density": 0.6430466587435534, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/5.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "5(1+\u221a3)/2 = 6.8301+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.8301, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@5", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "5(1+\u221a3)/2 = 6.8301+", "metric_symbol": "s", "metric_value": 6.8301, "reference_text": "s = 5(1+\u221a3)/2 = 6.8301+ | Found by Maurizio Morandi | in April 2015.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/5.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 5(1+\u221a3)/2 = 6.8301+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "92331a16a75cf6c4", "improvement": -0.00019379102171246387, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4626103815685519e-06, "max_pair_overlap_depth": -3.302865088408366e-05, "metric_expression": "6.83029", "metric_symbol": "s", "metric_value": 6.830293791021712, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.8301, "setup": "hexintri", "side": 6.830293791021712, "solution_path": "data/solutions/generated/hexintri_005_92331a16a75cf6c4.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/92331a16a75cf6c4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@6", "density": 0.7560505607557761, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/6.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "2(1+\u221a6) = 6.89897+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.89897, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@6", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2(1+\u221a6) = 6.89897+", "metric_symbol": "s", "metric_value": 6.89897, "reference_text": "s = 2(1+\u221a6) = 6.89897+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/6.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 2(1+\u221a6) = 6.89897+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "f3621ba5529eef9a", "improvement": -0.0014548494669490708, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.849296155859392e-06, "max_pair_overlap_depth": -8.276209533908396e-05, "metric_expression": "6.90042", "metric_symbol": "s", "metric_value": 6.900424849466949, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.89897, "setup": "hexintri", "side": 6.900424849466949, "solution_path": "data/solutions/generated/hexintri_006_f3621ba5529eef9a.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/f3621ba5529eef9a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@7", "density": 0.6562369627570366, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/7.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "8", "friedman_metric_symbol": "s", "friedman_metric_value": 8.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@7", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "8", "metric_symbol": "s", "metric_value": 8.0, "reference_text": "s = 8 | Trivial. |", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/7.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 8 | Trivial. |", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "635b0cc9d15ec460", "improvement": -7.946628399579936e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.24931067292516e-06, "max_pair_overlap_depth": -1.4685785256318695e-05, "metric_expression": "8.00008", "metric_symbol": "s", "metric_value": 8.000079466283996, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.0, "setup": "hexintri", "side": 8.000079466283996, "solution_path": "data/solutions/generated/hexintri_007_635b0cc9d15ec460.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/635b0cc9d15ec460.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@8", "density": 0.6907428320047944, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/8.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "25/3 = 8.3333+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.3333, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@8", "credit": "Erich Friedman", "date": "April 2015", "family_updated": "", "metric_expression": "25/3 = 8.3333+", "metric_symbol": "s", "metric_value": 8.3333, "reference_text": "s = 25/3 = 8.3333+ | Found by Erich Friedman | in April 2015.", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/8.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 25/3 = 8.3333+ | Found by Erich Friedman | in April 2015.", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "adf439e6f7b2afb5", "improvement": -0.002790584626882975, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.227185763431761e-07, "max_pair_overlap_depth": -7.882545446008526e-05, "metric_expression": "8.33609", "metric_symbol": "s", "metric_value": 8.336090584626882, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.3333, "setup": "hexintri", "side": 8.336090584626882, "solution_path": "data/solutions/generated/hexintri_008_adf439e6f7b2afb5.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/adf439e6f7b2afb5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@9", "density": 0.7214446032247255, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/10.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "5\u221a3 = 8.6602+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.6602, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@9", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5\u221a3 = 8.6602+", "metric_symbol": "s", "metric_value": 8.6602, "reference_text": "s = 5\u221a3 = 8.6602+ | Trivial. |", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/10.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 5\u221a3 = 8.6602+ | Trivial. |", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "936a184a58977242", "improvement": 0.008620848542102877, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0939511862432736e-06, "max_pair_overlap_depth": -5.506633970053798e-05, "metric_expression": "8.65158", "metric_symbol": "s", "metric_value": 8.651579151457897, "n": 9, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 8.6602, "setup": "hexintri", "side": 8.651579151457897, "solution_path": "data/solutions/generated/hexintri_009_936a184a58977242.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/936a184a58977242.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@10", "density": 0.7999538247696885, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/10.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "5\u221a3 = 8.6602+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.6602, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@10", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5\u221a3 = 8.6602+", "metric_symbol": "s", "metric_value": 8.6602, "reference_text": "s = 5\u221a3 = 8.6602+ | Trivial. |", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/10.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 5\u221a3 = 8.6602+ | Trivial. |", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "5df6cec7a90f52fe", "improvement": -0.00030397942970239455, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2645686941820143e-06, "max_pair_overlap_depth": -4.384611814706174e-05, "metric_expression": "8.66050", "metric_symbol": "s", "metric_value": 8.660503979429702, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.6602, "setup": "hexintri", "side": 8.660503979429702, "solution_path": "data/solutions/generated/hexintri_010_5df6cec7a90f52fe.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/5df6cec7a90f52fe.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@11", "density": 0.7237571814877352, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/11.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "9.54823+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.54823, "friedman_reference": {"analytical_or_proved": false, "case": "hexintri@11", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "9.54823+", "metric_symbol": "s", "metric_value": 9.54823, "reference_text": "s = 9.54823+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/11.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 9.54823+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "d582cb032b9c575f", "improvement": -0.0011576763865779327, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.6199514834868076e-06, "max_pair_overlap_depth": -2.6419225191420814e-05, "metric_expression": "9.54939", "metric_symbol": "s", "metric_value": 9.549387676386578, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.54823, "setup": "hexintri", "side": 9.549387676386578, "solution_path": "data/solutions/generated/hexintri_011_d582cb032b9c575f.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/d582cb032b9c575f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@12", "density": 0.7199169251480841, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/12.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "10", "friedman_metric_symbol": "s", "friedman_metric_value": 10.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@12", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "10", "metric_symbol": "s", "metric_value": 10.0, "reference_text": "s = 10 | Trivial. |", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/12.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 10 | Trivial. |", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "b6e20361c3af5615", "improvement": -0.0005769586222079681, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.006918638920166e-07, "max_pair_overlap_depth": -2.082412255655086e-05, "metric_expression": "10.00058", "metric_symbol": "s", "metric_value": 10.000576958622208, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 10.0, "setup": "hexintri", "side": 10.000576958622208, "solution_path": "data/solutions/generated/hexintri_012_b6e20361c3af5615.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/b6e20361c3af5615.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@13", "density": 0.7221828032992709, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "6\u221a3 = 10.3923+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.3923, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@13", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6\u221a3 = 10.3923+", "metric_symbol": "s", "metric_value": 10.3923, "reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "da55bd8ffef5f50e", "improvement": -0.00028846326752507423, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7733151165742505e-06, "max_pair_overlap_depth": -4.4289278687159594e-05, "metric_expression": "10.39259", "metric_symbol": "s", "metric_value": 10.392588463267526, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 10.3923, "setup": "hexintri", "side": 10.392588463267526, "solution_path": "data/solutions/generated/hexintri_013_da55bd8ffef5f50e.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/da55bd8ffef5f50e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@14", "density": 0.7777237680646841, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "6\u221a3 = 10.3923+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.3923, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@14", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6\u221a3 = 10.3923+", "metric_symbol": "s", "metric_value": 10.3923, "reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "272118e9284c579f", "improvement": -0.0003656905370288399, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.442529134834328e-06, "max_pair_overlap_depth": -4.275788154761706e-05, "metric_expression": "10.39267", "metric_symbol": "s", "metric_value": 10.39266569053703, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 10.3923, "setup": "hexintri", "side": 10.39266569053703, "solution_path": "data/solutions/generated/hexintri_014_272118e9284c579f.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/272118e9284c579f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@15", "density": 0.833304219754554, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "6\u221a3 = 10.3923+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.3923, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@15", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6\u221a3 = 10.3923+", "metric_symbol": "s", "metric_value": 10.3923, "reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "83460d360e93ff66", "improvement": -0.00018638448149665976, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.672744116747984e-07, "max_pair_overlap_depth": -2.8784199847526563e-05, "metric_expression": "10.39249", "metric_symbol": "s", "metric_value": 10.392486384481497, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 10.3923, "setup": "hexintri", "side": 10.392486384481497, "solution_path": "data/solutions/generated/hexintri_015_83460d360e93ff66.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/83460d360e93ff66.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@16", "density": 0.7429369875675369, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/16.gif", "friedman_metric_expression": "11.36599+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.36599, "friedman_reference": {"analytical_or_proved": false, "case": "hexintri@16", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "11.36599+", "metric_symbol": "s", "metric_value": 11.36599, "reference_text": "s = 11.36599+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/16.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 11.36599+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "89d5bef670451c83", "improvement": -0.0013703170956897992, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.657075146936789e-07, "max_pair_overlap_depth": -2.5616124350591463e-06, "metric_expression": "11.36736", "metric_symbol": "s", "metric_value": 11.36736031709569, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 11.36599, "setup": "hexintri", "side": 11.36736031709569, "solution_path": "data/solutions/generated/hexintri_16_89d5bef670451c83.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T07:13:53+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/89d5bef670451c83.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@17", "density": 0.7525303158572544, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/17.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "11.63457+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.63457, "friedman_reference": {"analytical_or_proved": false, "case": "hexintri@17", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "11.63457+", "metric_symbol": "s", "metric_value": 11.63457, "reference_text": "s = 11.63457+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/17.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 11.63457+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "8137d039fd339f48", "improvement": -0.007711226979866481, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.447216764354318e-05, "max_pair_overlap_depth": -1.3408176938511929e-05, "metric_expression": "11.64228", "metric_symbol": "s", "metric_value": 11.642281226979867, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 11.63457, "setup": "hexintri", "side": 11.642281226979867, "solution_path": "data/solutions/generated/hexintri_017_8137d039fd339f48.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T03:07:58+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/8137d039fd339f48.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@18", "density": 0.7507767554452202, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "12", "friedman_metric_symbol": "s", "friedman_metric_value": 12.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@18", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "12", "metric_symbol": "s", "metric_value": 12.0, "reference_text": "s = 12 | Trivial. |", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 12 | Trivial. |", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "8f10cd5e01be9029", "improvement": 0.0062092209316340075, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.734105056962567e-06, "max_pair_overlap_depth": -5.8920104462956147e-05, "metric_expression": "11.99379", "metric_symbol": "s", "metric_value": 11.993790779068366, "n": 18, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 12.0, "setup": "hexintri", "side": 11.993790779068366, "solution_path": "data/solutions/generated/hexintri_018_8f10cd5e01be9029.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/8f10cd5e01be9029.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@19", "density": 0.7866173060867477, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "12", "friedman_metric_symbol": "s", "friedman_metric_value": 12.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@19", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "12", "metric_symbol": "s", "metric_value": 12.0, "reference_text": "s = 12 | Trivial. |", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 12 | Trivial. |", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "18178ad9efaf7172", "improvement": -0.0384528795380632, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.242681221171444e-06, "max_pair_overlap_depth": -3.13088544121598e-05, "metric_expression": "12.03845", "metric_symbol": "s", "metric_value": 12.038452879538063, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 12.0, "setup": "hexintri", "side": 12.038452879538063, "solution_path": "data/solutions/generated/hexintri_019_18178ad9efaf7172.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T03:07:58+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/18178ad9efaf7172.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@20", "density": 0.8162942117377381, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "7\u221a3 = 12.1243+", "friedman_metric_symbol": "s", "friedman_metric_value": 12.1243, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@20", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "7\u221a3 = 12.1243+", "metric_symbol": "s", "metric_value": 12.1243, "reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "f59179c5b6665dc4", "improvement": -0.00029566549525483765, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.116403950810266e-06, "max_pair_overlap_depth": -3.364591626842106e-05, "metric_expression": "12.12460", "metric_symbol": "s", "metric_value": 12.124595665495255, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 12.1243, "setup": "hexintri", "side": 12.124595665495255, "solution_path": "data/solutions/generated/hexintri_020_f59179c5b6665dc4.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/f59179c5b6665dc4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "hexintri@21", "density": 0.8571035425372456, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "friedman_metric_expression": "7\u221a3 = 12.1243+", "friedman_metric_symbol": "s", "friedman_metric_value": 12.1243, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@21", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "7\u221a3 = 12.1243+", "metric_symbol": "s", "metric_value": 12.1243, "reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "6cf726ac83ba7d7f", "improvement": -0.00033371669977810825, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7607980864287318e-06, "max_pair_overlap_depth": -2.977721456209892e-05, "metric_expression": "12.12463", "metric_symbol": "s", "metric_value": 12.124633716699778, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 12.1243, "setup": "hexintri", "side": 12.124633716699778, "solution_path": "data/solutions/generated/hexintri_021_6cf726ac83ba7d7f.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/6cf726ac83ba7d7f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@1", "density": 0.9999940796878448, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/1.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/1.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 1 | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "13c63959e19cfeb5", "improvement": -2.96016922152198e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.1903479056983753e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00000", "metric_symbol": "s", "metric_value": 1.0000029601692215, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.0, "setup": "octinoct", "side": 1.0000029601692215, "solution_path": "data/solutions/generated/octinoct_001_13c63959e19cfeb5.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/13c63959e19cfeb5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@2", "density": 0.4999889107582135, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/2.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/2.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 2 | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "937fb450c622d9b9", "improvement": -2.2178852493670576e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.909847599495863e-06, "max_pair_overlap_depth": -3.0343321494846753e-05, "metric_expression": "2.00002", "metric_symbol": "s", "metric_value": 2.0000221788524937, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "octinoct", "side": 2.0000221788524937, "solution_path": "data/solutions/generated/octinoct_002_937fb450c622d9b9.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/937fb450c622d9b9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@3", "density": 0.6361550822369931, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/3.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "5\u20132\u221a2 = 2.17157+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.17157, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@3", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5\u20132\u221a2 = 2.17157+", "metric_symbol": "s", "metric_value": 2.17157, "reference_text": "s = 5\u20132\u221a2 = 2.17157+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/3.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5\u20132\u221a2 = 2.17157+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "4cb37df94277ed6e", "improvement": -2.6468916854760494e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.359798521217012e-07, "max_pair_overlap_depth": -2.9093807346031175e-05, "metric_expression": "2.17160", "metric_symbol": "s", "metric_value": 2.1715964689168548, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.17157, "setup": "octinoct", "side": 2.1715964689168548, "solution_path": "data/solutions/generated/octinoct_003_4cb37df94277ed6e.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/4cb37df94277ed6e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@4", "density": 0.7008534259385343, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/4.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "\u221a(5+1/\u221a2) = 2.38895+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.38895, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@4", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "\u221a(5+1/\u221a2) = 2.38895+", "metric_symbol": "s", "metric_value": 2.38895, "reference_text": "s = \u221a(5+1/\u221a2) = 2.38895+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/4.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = \u221a(5+1/\u221a2) = 2.38895+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "8759832408431e84", "improvement": -5.1351046062464434e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.873179406841027e-06, "max_pair_overlap_depth": -4.8382172928693526e-05, "metric_expression": "2.38900", "metric_symbol": "s", "metric_value": 2.3890013510460624, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.38895, "setup": "octinoct", "side": 2.3890013510460624, "solution_path": "data/solutions/generated/octinoct_004_8759832408431e84.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/8759832408431e84.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@5", "density": 0.6822471038460284, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/5.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "2+1/\u221a2 = 2.70710+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.7071, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@5", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2+1/\u221a2 = 2.70710+", "metric_symbol": "s", "metric_value": 2.7071, "reference_text": "s = 2+1/\u221a2 = 2.70710+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/5.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 2+1/\u221a2 = 2.70710+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "d3468761b0fe9922", "improvement": -6.14172351678377e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3153662665326975e-06, "max_pair_overlap_depth": -4.586217379215496e-05, "metric_expression": "2.70716", "metric_symbol": "s", "metric_value": 2.707161417235168, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.7071, "setup": "octinoct", "side": 2.707161417235168, "solution_path": "data/solutions/generated/octinoct_005_d3468761b0fe9922.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/d3468761b0fe9922.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@6", "density": 0.6715848857993428, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/6.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "2.98915+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.98915, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@6", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.98915+", "metric_symbol": "s", "metric_value": 2.98915, "reference_text": "s = 2.98915+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/6.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 2.98915+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "3c4b2267adcca69f", "improvement": 0.0001551389501637246, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.973975728535522e-06, "max_pair_overlap_depth": -2.153911208435666e-05, "metric_expression": "2.98899", "metric_symbol": "s", "metric_value": 2.9889948610498362, "n": 6, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 2.98915, "setup": "octinoct", "side": 2.9889948610498362, "solution_path": "data/solutions/generated/octinoct_006_3c4b2267adcca69f.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/3c4b2267adcca69f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@7", "density": 0.7777522978920184, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/7.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@7", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "s = 3 | Trivial. |", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/7.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 3 | Trivial. |", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "a0053fa5c22778e9", "improvement": -4.914098707065051e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2079023857814054e-06, "max_pair_overlap_depth": -2.6395744560092638e-05, "metric_expression": "3.00005", "metric_symbol": "s", "metric_value": 3.0000491409870707, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.0, "setup": "octinoct", "side": 3.0000491409870707, "solution_path": "data/solutions/generated/octinoct_007_a0053fa5c22778e9.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/a0053fa5c22778e9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@8", "density": 0.7457363085593237, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/8.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "3.27526+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.27526, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@8", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3.27526+", "metric_symbol": "s", "metric_value": 3.27526, "reference_text": "s = 3.27526+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/8.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 3.27526+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "697fa4dfd3dbc6eb", "improvement": -4.953250458550329e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.188513199476399e-06, "max_pair_overlap_depth": -7.758148462100323e-06, "metric_expression": "3.27531", "metric_symbol": "s", "metric_value": 3.2753095325045853, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.27526, "setup": "octinoct", "side": 3.2753095325045853, "solution_path": "data/solutions/generated/octinoct_008_697fa4dfd3dbc6eb.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/697fa4dfd3dbc6eb.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@9", "density": 0.7720692797565871, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/9.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "2+\u221a2 = 3.41421+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.41421, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@9", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2+\u221a2 = 3.41421+", "metric_symbol": "s", "metric_value": 3.41421, "reference_text": "s = 2+\u221a2 = 3.41421+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/9.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 2+\u221a2 = 3.41421+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "7face58a13302eec", "improvement": -2.270780627799951e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3803938489295472e-05, "max_pair_overlap_depth": -2.6349120965107886e-06, "metric_expression": "3.41423", "metric_symbol": "s", "metric_value": 3.414232707806278, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.41421, "setup": "octinoct", "side": 3.414232707806278, "solution_path": "data/solutions/generated/octinoct_009_7face58a13302eec.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/7face58a13302eec.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@10", "density": 0.7276473732898788, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/10.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "3+1/\u221a2 = 3.70710+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.7071, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@10", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3+1/\u221a2 = 3.70710+", "metric_symbol": "s", "metric_value": 3.7071, "reference_text": "s = 3+1/\u221a2 = 3.70710+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/10.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 3+1/\u221a2 = 3.70710+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "bcfc9e294bb15f21", "improvement": -4.452047150094174e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.744023326611903e-06, "max_pair_overlap_depth": -8.094414775450254e-06, "metric_expression": "3.70714", "metric_symbol": "s", "metric_value": 3.707144520471501, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.7071, "setup": "octinoct", "side": 3.707144520471501, "solution_path": "data/solutions/generated/octinoct_010_bcfc9e294bb15f21.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/bcfc9e294bb15f21.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@11", "density": 0.7111917967389362, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/11.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "3.93270+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.9327, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@11", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3.93270+", "metric_symbol": "s", "metric_value": 3.9327, "reference_text": "s = 3.93270+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/11.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 3.93270+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "5cff1aa2d330c49e", "improvement": -0.00011007046297972778, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.479089320941585e-06, "max_pair_overlap_depth": -8.811356971838435e-06, "metric_expression": "3.93281", "metric_symbol": "s", "metric_value": 3.93281007046298, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.9327, "setup": "octinoct", "side": 3.93281007046298, "solution_path": "data/solutions/generated/octinoct_011_5cff1aa2d330c49e.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/5cff1aa2d330c49e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@12", "density": 0.7499773041118397, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/12.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@12", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "s = 4 | Trivial. |", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/12.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4 | Trivial. |", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "7bdd4832407bd3be", "improvement": -6.052374207055067e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.082066348113342e-06, "max_pair_overlap_depth": -1.2861422511445397e-05, "metric_expression": "4.00006", "metric_symbol": "s", "metric_value": 4.0000605237420706, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.0, "setup": "octinoct", "side": 4.0000605237420706, "solution_path": "data/solutions/generated/octinoct_012_7bdd4832407bd3be.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/7bdd4832407bd3be.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@13", "density": 0.7469920374756177, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/13.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "7\u20132\u221a2 = 4.17157+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.17157, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@13", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "7\u20132\u221a2 = 4.17157+", "metric_symbol": "s", "metric_value": 4.17157, "reference_text": "s = 7\u20132\u221a2 = 4.17157+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/13.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 7\u20132\u221a2 = 4.17157+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "867ad172957f0ddb", "improvement": -0.00013596034935225987, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.683174531654637e-06, "max_pair_overlap_depth": -2.596769201668181e-06, "metric_expression": "4.17171", "metric_symbol": "s", "metric_value": 4.171705960349352, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.17157, "setup": "octinoct", "side": 4.171705960349352, "solution_path": "data/solutions/generated/octinoct_013_867ad172957f0ddb.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/867ad172957f0ddb.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@14", "density": 0.7637114154056861, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/14.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4.28155+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.28155, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@14", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "4.28155+", "metric_symbol": "s", "metric_value": 4.28155, "reference_text": "s = 4.28155+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "14.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/14.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4.28155+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "190d6c8f3f4e37d6", "improvement": 1.6200963535162316e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9636658184049817e-06, "max_pair_overlap_depth": -1.2788583332312697e-05, "metric_expression": "4.28153", "metric_symbol": "s", "metric_value": 4.281533799036465, "n": 14, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 4.28155, "setup": "octinoct", "side": 4.281533799036465, "solution_path": "data/solutions/generated/octinoct_014_190d6c8f3f4e37d6.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/190d6c8f3f4e37d6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@15", "density": 0.7554665958519668, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/15.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4.45594+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.45594, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@15", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "4.45594+", "metric_symbol": "s", "metric_value": 4.45594, "reference_text": "s = 4.45594+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/15.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4.45594+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "60843ec4ea56ad88", "improvement": 1.3726756218801484e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.050759161282626e-06, "max_pair_overlap_depth": -3.648956153723404e-05, "metric_expression": "4.45593", "metric_symbol": "s", "metric_value": 4.455926273243781, "n": 15, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 4.45594, "setup": "octinoct", "side": 4.455926273243781, "solution_path": "data/solutions/generated/octinoct_015_60843ec4ea56ad88.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/60843ec4ea56ad88.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@16", "density": 0.7566625545620705, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/16.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4.59824+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.59824, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@16", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "4.59824+", "metric_symbol": "s", "metric_value": 4.59824, "reference_text": "s = 4.59824+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/16.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4.59824+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "1178c6831eb46264", "improvement": -0.00018248651533525617, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.297640975948298e-06, "max_pair_overlap_depth": -9.126693151007004e-06, "metric_expression": "4.59842", "metric_symbol": "s", "metric_value": 4.598422486515335, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.59824, "setup": "octinoct", "side": 4.598422486515335, "solution_path": "data/solutions/generated/octinoct_016_1178c6831eb46264.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/1178c6831eb46264.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@17", "density": 0.7511087688524583, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/17.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4.75741+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.75741, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@17", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "4.75741+", "metric_symbol": "s", "metric_value": 4.75741, "reference_text": "s = 4.75741+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/17.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4.75741+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "ebcfc45448cb8c5f", "improvement": -2.6985802159096295e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.580862819791944e-06, "max_pair_overlap_depth": -2.6446396224955038e-05, "metric_expression": "4.75744", "metric_symbol": "s", "metric_value": 4.757436985802159, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.75741, "setup": "octinoct", "side": 4.757436985802159, "solution_path": "data/solutions/generated/octinoct_017_ebcfc45448cb8c5f.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/ebcfc45448cb8c5f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@18", "density": 0.7629999765077309, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/18.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4.85717+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.85717, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@18", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "4.85717+", "metric_symbol": "s", "metric_value": 4.85717, "reference_text": "s = 4.85717+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/18.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4.85717+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "46f5ac176d150ffa", "improvement": 0.00010416375427002578, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.225773906749903e-06, "max_pair_overlap_depth": -2.521618462036912e-05, "metric_expression": "4.85707", "metric_symbol": "s", "metric_value": 4.85706583624573, "n": 18, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 4.85717, "setup": "octinoct", "side": 4.85706583624573, "solution_path": "data/solutions/generated/octinoct_018_46f5ac176d150ffa.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/46f5ac176d150ffa.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@19", "density": 0.7795195170060211, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/19.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4.93586+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.93586, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "4.93586+", "metric_symbol": "s", "metric_value": 4.93586, "reference_text": "s = 4.93586+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/19.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4.93586+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "4a7169be4bda1825", "improvement": -0.0011420082689239663, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1928573301213418e-05, "max_pair_overlap_depth": -1.491417372267989e-06, "metric_expression": "4.93700", "metric_symbol": "s", "metric_value": 4.937002008268924, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.93586, "setup": "octinoct", "side": 4.937002008268924, "solution_path": "data/solutions/generated/octinoct_019_4a7169be4bda1825.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/4a7169be4bda1825.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@20", "density": 0.778654925537014, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/20.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "5.06781+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.06781, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@20", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5.06781+", "metric_symbol": "s", "metric_value": 5.06781, "reference_text": "s = 5.06781+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/20.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.06781+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "ef9ffbe57f51321a", "improvement": -0.0002585475900360734, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.202696065204785e-06, "max_pair_overlap_depth": -3.692189855719619e-05, "metric_expression": "5.06807", "metric_symbol": "s", "metric_value": 5.068068547590036, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.06781, "setup": "octinoct", "side": 5.068068547590036, "solution_path": "data/solutions/generated/octinoct_020_ef9ffbe57f51321a.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/ef9ffbe57f51321a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@21", "density": 0.7774838310416734, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/21.gif", "friedman_metric_expression": "5.19715+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.19715, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@21", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5.19715+", "metric_symbol": "s", "metric_value": 5.19715, "reference_text": "s = 5.19715+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/21.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.19715+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "92c4bcf9428983c2", "improvement": 1.540400287325383e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.1696825424876755e-06, "max_pair_overlap_depth": -2.317393259165801e-05, "metric_expression": "5.19713", "metric_symbol": "s", "metric_value": 5.1971345959971265, "n": 21, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 5.19715, "setup": "octinoct", "side": 5.1971345959971265, "solution_path": "data/solutions/generated/octinoct_021_92c4bcf9428983c2.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/92c4bcf9428983c2.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@22", "density": 0.7663269933124698, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/22.gif", "friedman_metric_expression": "5.35750+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.3575, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@22", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5.35750+", "metric_symbol": "s", "metric_value": 5.3575, "reference_text": "s = 5.35750+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/22.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.35750+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "b8f2befaa2d4a75e", "improvement": -0.0005193617687213603, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.99203724676962e-06, "max_pair_overlap_depth": -1.57400449714018e-05, "metric_expression": "5.35802", "metric_symbol": "s", "metric_value": 5.358019361768721, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.3575, "setup": "octinoct", "side": 5.358019361768721, "solution_path": "data/solutions/generated/octinoct_022_b8f2befaa2d4a75e.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/b8f2befaa2d4a75e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@23", "density": 0.7845835529808874, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/23.gif", "friedman_metric_expression": "5.41440+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.4144, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@23", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5.41440+", "metric_symbol": "s", "metric_value": 5.4144, "reference_text": "s = 5.41440+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/23.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.41440+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "d6528e8801e36ce0", "improvement": 7.503853147827755e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3646686331794102e-06, "max_pair_overlap_depth": -4.536567227386712e-05, "metric_expression": "5.41432", "metric_symbol": "s", "metric_value": 5.414324961468521, "n": 23, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 5.4144, "setup": "octinoct", "side": 5.414324961468521, "solution_path": "data/solutions/generated/octinoct_023_d6528e8801e36ce0.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/d6528e8801e36ce0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@24", "density": 0.777859618157, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/24.gif", "friedman_metric_expression": "5.55464+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.55464, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@24", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5.55464+", "metric_symbol": "s", "metric_value": 5.55464, "reference_text": "s = 5.55464+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/24.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.55464+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "a34ac6a3c52f70df", "improvement": 1.1631965286973411e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.721783559078116e-06, "max_pair_overlap_depth": -2.4974900467711336e-05, "metric_expression": "5.55463", "metric_symbol": "s", "metric_value": 5.554628368034713, "n": 24, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 5.55464, "setup": "octinoct", "side": 5.554628368034713, "solution_path": "data/solutions/generated/octinoct_024_a34ac6a3c52f70df.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/a34ac6a3c52f70df.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@25", "density": 0.7805673327264805, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/25.gif", "friedman_metric_expression": "5.65593+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.65593, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@25", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5.65593+", "metric_symbol": "s", "metric_value": 5.65593, "reference_text": "s = 5.65593+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/25.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.65593+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "113492960b7e7dce", "improvement": -0.003397389940226425, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.281212189125961e-06, "max_pair_overlap_depth": -2.6024797291412938e-05, "metric_expression": "5.65933", "metric_symbol": "s", "metric_value": 5.659327389940226, "n": 25, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.65593, "setup": "octinoct", "side": 5.659327389940226, "solution_path": "data/solutions/generated/octinoct_025_113492960b7e7dce.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/113492960b7e7dce.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@26", "density": 0.7881657239941322, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/26.gif", "friedman_metric_expression": "5.73940+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.7394, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@26", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5.73940+", "metric_symbol": "s", "metric_value": 5.7394, "reference_text": "s = 5.73940+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/26.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.73940+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "581188c4895e4037", "improvement": -0.004116881359766289, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.43705423351296e-06, "max_pair_overlap_depth": -2.686615288460814e-05, "metric_expression": "5.74352", "metric_symbol": "s", "metric_value": 5.743516881359766, "n": 26, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.7394, "setup": "octinoct", "side": 5.743516881359766, "solution_path": "data/solutions/generated/octinoct_026_581188c4895e4037.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/581188c4895e4037.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@27", "density": 0.7989711846148311, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/27.gif", "friedman_metric_expression": "5.81238+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.81238, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@27", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5.81238+", "metric_symbol": "s", "metric_value": 5.81238, "reference_text": "s = 5.81238+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/27.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.81238+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "25c7f85bc0b15209", "improvement": -0.0008341744667159645, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.851030556516347e-06, "max_pair_overlap_depth": -2.4661009629944886e-05, "metric_expression": "5.81321", "metric_symbol": "s", "metric_value": 5.813214174466716, "n": 27, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.81238, "setup": "octinoct", "side": 5.813214174466716, "solution_path": "data/solutions/generated/octinoct_027_25c7f85bc0b15209.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/25c7f85bc0b15209.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@28", "density": 0.8242204012359605, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/28.gif", "friedman_metric_expression": "3+2\u221a2 = 5.82842+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.82842, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@28", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3+2\u221a2 = 5.82842+", "metric_symbol": "s", "metric_value": 5.82842, "reference_text": "s = 3+2\u221a2 = 5.82842+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/28.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 3+2\u221a2 = 5.82842+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "f8d9c8a9f9a38d45", "improvement": -8.71778893589692e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.739062384519148e-06, "max_pair_overlap_depth": -9.673739088000843e-06, "metric_expression": "5.82851", "metric_symbol": "s", "metric_value": 5.828507177889359, "n": 28, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.82842, "setup": "octinoct", "side": 5.828507177889359, "solution_path": "data/solutions/generated/octinoct_028_f8d9c8a9f9a38d45.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/f8d9c8a9f9a38d45.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@29", "density": 0.7902111886471865, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/29.gif", "friedman_metric_expression": "6.05746+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.05746, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@29", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "6.05746+", "metric_symbol": "s", "metric_value": 6.05746, "reference_text": "s = 6.05746+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/29.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 6.05746+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "30789c6bb8fd99b7", "improvement": -0.0005140918720876186, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.805265150873157e-06, "max_pair_overlap_depth": -5.6301265520808386e-05, "metric_expression": "6.05797", "metric_symbol": "s", "metric_value": 6.0579740918720875, "n": 29, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.05746, "setup": "octinoct", "side": 6.0579740918720875, "solution_path": "data/solutions/generated/octinoct_029_30789c6bb8fd99b7.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/30789c6bb8fd99b7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "octinoct@30", "density": 0.7919434557655346, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/30.gif", "friedman_metric_expression": "6.15432+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.15432, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@30", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "6.15432+", "metric_symbol": "s", "metric_value": 6.15432, "reference_text": "s = 6.15432+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/30.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 6.15432+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "1a16dc8a4d741008", "improvement": -0.00047426130353134255, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1243912272535679e-05, "max_pair_overlap_depth": -2.8046648627544357e-05, "metric_expression": "6.15479", "metric_symbol": "s", "metric_value": 6.154794261303532, "n": 30, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.15432, "setup": "octinoct", "side": 6.154794261303532, "solution_path": "data/solutions/generated/octinoct_030_1a16dc8a4d741008.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/1a16dc8a4d741008.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@1", "density": 0.7568185573097284, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/1.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a((5+\u221a5)/10) = .86065+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.86065, "friedman_reference": {"analytical_or_proved": true, "case": "penincir@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a((5+\u221a5)/10) = .86065+", "metric_symbol": "r", "metric_value": 0.86065, "reference_text": "r = \u221a((5+\u221a5)/10) = .86065+ | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/1.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = \u221a((5+\u221a5)/10) = .86065+ | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": false, "id": "ca75a5cd7cad481c", "improvement": 0.009994599443903796, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.0926430426282394e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.85066", "metric_symbol": "r", "metric_value": 0.8506554005560962, "n": 1, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.", "record_type": "verified", "reference_side": 0.86065, "setup": "penincir", "side": 1.7013108011121925, "solution_path": "data/solutions/generated/penincir_001_ca75a5cd7cad481c.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/ca75a5cd7cad481c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@2", "density": 0.462509898701161, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/2.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a(5+2\u221a5)/2 = 1.53884+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.53884, "friedman_reference": {"analytical_or_proved": true, "case": "penincir@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a(5+2\u221a5)/2 = 1.53884+", "metric_symbol": "r", "metric_value": 1.53884, "reference_text": "r = \u221a(5+2\u221a5)/2 = 1.53884+ | Trivial.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/2.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = \u221a(5+2\u221a5)/2 = 1.53884+ | Trivial.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "44da10d1d5897aae", "improvement": -3.743542237466535e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.684702690331392e-08, "max_pair_overlap_depth": -5.994543612077171e-05, "metric_expression": "1.53888", "metric_symbol": "r", "metric_value": 1.5388774354223747, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.53884, "setup": "penincir", "side": 3.0777548708447493, "solution_path": "data/solutions/generated/penincir_002_44da10d1d5897aae.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/44da10d1d5897aae.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@3", "density": 0.6275054691586099, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/3.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "(1+\u221a5)/2 = 1.61803+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.61803, "friedman_reference": {"analytical_or_proved": true, "case": "penincir@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "(1+\u221a5)/2 = 1.61803+", "metric_symbol": "r", "metric_value": 1.61803, "reference_text": "r = (1+\u221a5)/2 = 1.61803+ | Trivial.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/3.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = (1+\u221a5)/2 = 1.61803+ | Trivial.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "350d35e2110a508b", "improvement": -5.532631868709892e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.919906156253262e-06, "max_pair_overlap_depth": -5.073652219536114e-05, "metric_expression": "1.61809", "metric_symbol": "r", "metric_value": 1.6180853263186872, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.61803, "setup": "penincir", "side": 3.2361706526373744, "solution_path": "data/solutions/generated/penincir_003_350d35e2110a508b.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/350d35e2110a508b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@4", "density": 0.6542873961171766, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/4.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "1.82971+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.82971, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@4", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.82971+", "metric_symbol": "r", "metric_value": 1.82971, "reference_text": "r = 1.82971+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/4.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 1.82971+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "d03dba2c6efc98dd", "improvement": -5.479863407176211e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.02075710251404e-06, "max_pair_overlap_depth": -3.1570603938990693e-05, "metric_expression": "1.82976", "metric_symbol": "r", "metric_value": 1.8297647986340717, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.82971, "setup": "penincir", "side": 3.6595295972681434, "solution_path": "data/solutions/generated/penincir_004_d03dba2c6efc98dd.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/d03dba2c6efc98dd.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@5", "density": 0.6626607161574516, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/5.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.03271+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.03271, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@5", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.03271+", "metric_symbol": "r", "metric_value": 2.03271, "reference_text": "r = 2.03271+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "5.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/5.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 2.03271+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "97027d267cb23b7f", "improvement": -6.326016348978669e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.209947377376011e-06, "max_pair_overlap_depth": -3.7991648266566536e-05, "metric_expression": "2.03277", "metric_symbol": "r", "metric_value": 2.0327732601634896, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.03271, "setup": "penincir", "side": 4.065546520326979, "solution_path": "data/solutions/generated/penincir_005_97027d267cb23b7f.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/97027d267cb23b7f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@6", "density": 0.6624931586206462, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/6.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a((25+11\u221a5)/10) = 2.22703+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.22703, "friedman_reference": {"analytical_or_proved": true, "case": "penincir@6", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "\u221a((25+11\u221a5)/10) = 2.22703+", "metric_symbol": "r", "metric_value": 2.22703, "reference_text": "r = \u221a((25+11\u221a5)/10) = 2.22703+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/6.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = \u221a((25+11\u221a5)/10) = 2.22703+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "4b5f96ff666b1595", "improvement": -4.3119632947785647e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3229349565289112e-06, "max_pair_overlap_depth": -2.759876285962637e-05, "metric_expression": "2.22707", "metric_symbol": "r", "metric_value": 2.227073119632948, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.22703, "setup": "penincir", "side": 4.454146239265896, "solution_path": "data/solutions/generated/penincir_006_4b5f96ff666b1595.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/4b5f96ff666b1595.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@7", "density": 0.7279626259462092, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/7.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.29474+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.29474, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@7", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.29474+", "metric_symbol": "r", "metric_value": 2.29474, "reference_text": "r = 2.29474+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/7.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 2.29474+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "ef28e611d9e22eb0", "improvement": -5.570482584049685e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.717800656082403e-06, "max_pair_overlap_depth": -4.1591260455220436e-05, "metric_expression": "2.29480", "metric_symbol": "r", "metric_value": 2.2947957048258405, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.29474, "setup": "penincir", "side": 4.589591409651681, "solution_path": "data/solutions/generated/penincir_007_ef28e611d9e22eb0.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/ef28e611d9e22eb0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@8", "density": 0.7115852708183573, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/8.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.48128+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.48128, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@8", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.48128+", "metric_symbol": "r", "metric_value": 2.48128, "reference_text": "r = 2.48128+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/8.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 2.48128+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "1a134d3903b2814e", "improvement": -3.0242757913079288e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.375187333127144e-07, "max_pair_overlap_depth": -8.34480700673268e-06, "metric_expression": "2.48131", "metric_symbol": "r", "metric_value": 2.481310242757913, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.48128, "setup": "penincir", "side": 4.962620485515826, "solution_path": "data/solutions/generated/penincir_008_1a134d3903b2814e.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/1a134d3903b2814e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@9", "density": 0.674675474238072, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/9.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.70171+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.70171, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@9", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.70171+", "metric_symbol": "r", "metric_value": 2.70171, "reference_text": "r = 2.70171+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/9.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 2.70171+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "1ca74640a9bafbff", "improvement": -0.0011487048015377255, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.541032137428402e-06, "max_pair_overlap_depth": -3.412963059545859e-05, "metric_expression": "2.70286", "metric_symbol": "r", "metric_value": 2.7028587048015376, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.70171, "setup": "penincir", "side": 5.405717409603075, "solution_path": "data/solutions/generated/penincir_009_1ca74640a9bafbff.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/1ca74640a9bafbff.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@10", "density": 0.6983515169709827, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/10.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.79768+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.79768, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@10", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.79768+", "metric_symbol": "r", "metric_value": 2.79768, "reference_text": "r = 2.79768+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/10.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 2.79768+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "b50c304b68607cc4", "improvement": -0.002671254854186955, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.377527520027513e-06, "max_pair_overlap_depth": -1.3481998292097508e-05, "metric_expression": "2.80035", "metric_symbol": "r", "metric_value": 2.800351254854187, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.79768, "setup": "penincir", "side": 5.600702509708374, "solution_path": "data/solutions/generated/penincir_010_b50c304b68607cc4.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/b50c304b68607cc4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@11", "density": 0.7152777059461288, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/11.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.90180+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.9018, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@11", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.90180+", "metric_symbol": "r", "metric_value": 2.9018, "reference_text": "r = 2.90180+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "11.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/11.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 2.90180+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "11.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "37f9123e1b2153ff", "improvement": -0.0002744381126040807, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.569993058365583e-07, "max_pair_overlap_depth": -3.207817623795961e-05, "metric_expression": "2.90207", "metric_symbol": "r", "metric_value": 2.9020744381126042, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.9018, "setup": "penincir", "side": 5.8041488762252085, "solution_path": "data/solutions/generated/penincir_011_37f9123e1b2153ff.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/37f9123e1b2153ff.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@12", "density": 0.7213016172544706, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/12.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.01826+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.01826, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@12", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.01826+", "metric_symbol": "r", "metric_value": 3.01826, "reference_text": "r = 3.01826+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/12.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.01826+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "a564353850abf267", "improvement": -0.00017424806894128508, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.481723353017998e-06, "max_pair_overlap_depth": -2.751801632361328e-05, "metric_expression": "3.01843", "metric_symbol": "r", "metric_value": 3.0184342480689415, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.01826, "setup": "penincir", "side": 6.036868496137883, "solution_path": "data/solutions/generated/penincir_012_a564353850abf267.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/a564353850abf267.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@13", "density": 0.7515432650569983, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/13.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a(5+2\u221a5)/2 =3.07769+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.07769, "friedman_reference": {"analytical_or_proved": true, "case": "penincir@13", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "\u221a(5+2\u221a5)/2 =3.07769+", "metric_symbol": "r", "metric_value": 3.07769, "reference_text": "r = \u221a(5+2\u221a5)/2 =3.07769+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/13.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = \u221a(5+2\u221a5)/2 =3.07769+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "c39e9475d5bde4a6", "improvement": -0.0001371927275344298, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.94574749318366e-06, "max_pair_overlap_depth": -1.7086792766463077e-05, "metric_expression": "3.07783", "metric_symbol": "r", "metric_value": 3.0778271927275345, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.07769, "setup": "penincir", "side": 6.155654385455069, "solution_path": "data/solutions/generated/penincir_013_c39e9475d5bde4a6.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/c39e9475d5bde4a6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@14", "density": 0.7320837719347534, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/14.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.23385+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.23385, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@14", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.23385+", "metric_symbol": "r", "metric_value": 3.23385, "reference_text": "r = 3.23385+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/14.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.23385+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "4798ec354812edfb", "improvement": -0.0023337860780814346, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.2470094596680497e-07, "max_pair_overlap_depth": -1.086583313658629e-05, "metric_expression": "3.23618", "metric_symbol": "r", "metric_value": 3.2361837860780813, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.23385, "setup": "penincir", "side": 6.472367572156163, "solution_path": "data/solutions/generated/penincir_014_4798ec354812edfb.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/4798ec354812edfb.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@15", "density": 0.7364932523686155, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/15.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.33911+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.33911, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@15", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.33911+", "metric_symbol": "r", "metric_value": 3.33911, "reference_text": "r = 3.33911+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/15.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.33911+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "5fb8f24380ed14ba", "improvement": -0.0006156585665682002, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.531307800791922e-07, "max_pair_overlap_depth": -1.652091133119704e-05, "metric_expression": "3.33973", "metric_symbol": "r", "metric_value": 3.339725658566568, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.33911, "setup": "penincir", "side": 6.679451317133136, "solution_path": "data/solutions/generated/penincir_015_5fb8f24380ed14ba.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/5fb8f24380ed14ba.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@16", "density": 0.7415495303728211, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/16.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.43657+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.43657, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@16", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.43657+", "metric_symbol": "r", "metric_value": 3.43657, "reference_text": "r = 3.43657+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "16.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/16.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.43657+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "eb41133064f5f2da", "improvement": -0.0009042932667306935, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3274146969676224e-06, "max_pair_overlap_depth": -1.0162839398697443e-05, "metric_expression": "3.43747", "metric_symbol": "r", "metric_value": 3.437474293266731, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.43657, "setup": "penincir", "side": 6.874948586533462, "solution_path": "data/solutions/generated/penincir_016_eb41133064f5f2da.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/eb41133064f5f2da.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@17", "density": 0.7557819084683968, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/17.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.50958+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.50958, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@17", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.50958+", "metric_symbol": "r", "metric_value": 3.50958, "reference_text": "r = 3.50958+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/17.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.50958+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "9469ef74fc89a75b", "improvement": -0.00016662106909848262, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3042585254605683e-06, "max_pair_overlap_depth": -2.7118152433835974e-05, "metric_expression": "3.50975", "metric_symbol": "r", "metric_value": 3.5097466210690986, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.50958, "setup": "penincir", "side": 7.019493242138197, "solution_path": "data/solutions/generated/penincir_017_9469ef74fc89a75b.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/9469ef74fc89a75b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@18", "density": 0.7533573813986445, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/18.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.62080+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.6208, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.62080+", "metric_symbol": "r", "metric_value": 3.6208, "reference_text": "r = 3.62080+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/18.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.62080+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "767a627015948f32", "improvement": 0.00349375267338381, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7774333678797234e-06, "max_pair_overlap_depth": -3.109065453799076e-05, "metric_expression": "3.61731", "metric_symbol": "r", "metric_value": 3.617306247326616, "n": 18, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.6208, "setup": "penincir", "side": 7.234612494653232, "solution_path": "data/solutions/generated/penincir_018_767a627015948f32.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/767a627015948f32.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@19", "density": 0.771366675320165, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/19.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.67287+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.67287, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.67287+", "metric_symbol": "r", "metric_value": 3.67287, "reference_text": "r = 3.67287+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/19.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.67287+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "9d482c8012998879", "improvement": 8.154982387598153e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.817340790579493e-06, "max_pair_overlap_depth": -1.6517110137281854e-05, "metric_expression": "3.67279", "metric_symbol": "r", "metric_value": 3.672788450176124, "n": 19, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.67287, "setup": "penincir", "side": 7.345576900352248, "solution_path": "data/solutions/generated/penincir_019_9d482c8012998879.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/9d482c8012998879.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@20", "density": 0.7575056542556782, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/20.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.80415+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.80415, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.80415+", "metric_symbol": "r", "metric_value": 3.80415, "reference_text": "r = 3.80415+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/20.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.80415+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "5271226652403829", "improvement": 0.0016291138375779113, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.231424091092009e-06, "max_pair_overlap_depth": -3.071782635011289e-05, "metric_expression": "3.80252", "metric_symbol": "r", "metric_value": 3.802520886162422, "n": 20, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.80415, "setup": "penincir", "side": 7.605041772324844, "solution_path": "data/solutions/generated/penincir_020_5271226652403829.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/5271226652403829.svg", "tolerance": 1e-08, "verified": true}
-{"case": "penincir@21", "density": 0.7521173669587212, "friedman_analytical_or_proved": false, "friedman_credit": "Cyril Summerfield", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/21.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.90735+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.90735, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@21", "credit": "Cyril Summerfield", "date": "April 2026", "family_updated": "", "metric_expression": "3.90735+", "metric_symbol": "r", "metric_value": 3.90735, "reference_text": "r = 3.90735+ | Found by Cyril Summerfield | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/21.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.90735+ | Found by Cyril Summerfield | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "4625f732ad11a859", "improvement": -0.0030068209876064067, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9813425364011437e-06, "max_pair_overlap_depth": -1.4218243721247914e-05, "metric_expression": "3.91036", "metric_symbol": "r", "metric_value": 3.9103568209876065, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.90735, "setup": "penincir", "side": 7.820713641975213, "solution_path": "data/solutions/generated/penincir_021_4625f732ad11a859.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Cyril Summerfield", "svg_path": "data/svg/4625f732ad11a859.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@1", "density": 0.9999780359352667, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/1.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/1.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 1 | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "b3173648630fcdeb", "improvement": -1.0982213277443975e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.256503348572871e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_symbol": "s", "metric_value": 1.0000109822132774, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.0, "setup": "peninpen", "side": 1.0000109822132774, "solution_path": "data/solutions/generated/peninpen_001_b3173648630fcdeb.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/b3173648630fcdeb.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@2", "density": 0.4999891232484648, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/2.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/2.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "edac094186a54129", "improvement": -2.175385798786067e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0537211348702708e-06, "max_pair_overlap_depth": -1.9731507571563167e-05, "metric_expression": "2.00002", "metric_symbol": "s", "metric_value": 2.000021753857988, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "peninpen", "side": 2.000021753857988, "solution_path": "data/solutions/generated/peninpen_002_edac094186a54129.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/edac094186a54129.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@3", "density": 0.599978840427638, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/3.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a5 = 2.23606+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.23606, "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@3", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "\u221a5 = 2.23606+", "metric_symbol": "s", "metric_value": 2.23606, "reference_text": "s = \u221a5 = 2.23606+ | Found by Jonathan Viquerat in April 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/3.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = \u221a5 = 2.23606+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "bf261a4dce178a90", "improvement": -4.7407077830463606e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.7662857614262655e-06, "max_pair_overlap_depth": -2.7755970794667603e-05, "metric_expression": "2.23611", "metric_symbol": "s", "metric_value": 2.2361074070778306, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.23606, "setup": "peninpen", "side": 2.2361074070778306, "solution_path": "data/solutions/generated/peninpen_003_bf261a4dce178a90.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/bf261a4dce178a90.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@4", "density": 0.6678717661629443, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/4.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.44719+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.44719, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@4", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.44719+", "metric_symbol": "s", "metric_value": 2.44719, "reference_text": "s = 2.44719+ | Found by Jonathan Viquerat in April 2026.", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/4.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 2.44719+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "85435733af14070a", "improvement": -8.88306059834143e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0634336001709255e-06, "max_pair_overlap_depth": -3.575601486860425e-05, "metric_expression": "2.44728", "metric_symbol": "s", "metric_value": 2.4472788306059834, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.44719, "setup": "peninpen", "side": 2.4472788306059834, "solution_path": "data/solutions/generated/peninpen_004_85435733af14070a.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/85435733af14070a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@5", "density": 0.7294617516267693, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/6.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(3+\u221a5)/2 = 2.61803+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.61803, "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "(3+\u221a5)/2 = 2.61803+", "metric_symbol": "s", "metric_value": 2.61803, "reference_text": "s = (3+\u221a5)/2 = 2.61803+ | Trivial.", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/6.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = (3+\u221a5)/2 = 2.61803+ | Trivial.", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "28fa9f787595145b", "improvement": -5.4982701188421856e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.513169742800457e-06, "max_pair_overlap_depth": -2.4501936757292953e-06, "metric_expression": "2.61808", "metric_symbol": "s", "metric_value": 2.6180849827011885, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.61803, "setup": "peninpen", "side": 2.6180849827011885, "solution_path": "data/solutions/generated/peninpen_005_28fa9f787595145b.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/28fa9f787595145b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@6", "density": 0.8753627744848066, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/6.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(3+\u221a5)/2 = 2.61803+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.61803, "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@6", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "(3+\u221a5)/2 = 2.61803+", "metric_symbol": "s", "metric_value": 2.61803, "reference_text": "s = (3+\u221a5)/2 = 2.61803+ | Trivial.", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/6.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = (3+\u221a5)/2 = 2.61803+ | Trivial.", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "198bd12691483df1", "improvement": -4.201351602306502e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4414928963119693e-06, "max_pair_overlap_depth": -1.898562579671914e-05, "metric_expression": "2.61807", "metric_symbol": "s", "metric_value": 2.618072013516023, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.61803, "setup": "peninpen", "side": 2.618072013516023, "solution_path": "data/solutions/generated/peninpen_006_198bd12691483df1.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/198bd12691483df1.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@7", "density": 0.7384663216832239, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/7.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.07866+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.07866, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@7", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.07866+", "metric_symbol": "s", "metric_value": 3.07866, "reference_text": "s = 3.07866+ | Found by Jonathan Viquerat in April 2026.", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/7.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 3.07866+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "5b6283ab3dc4c3b5", "improvement": -0.00015556249375014986, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.964189962454e-06, "max_pair_overlap_depth": -1.5079265303863387e-05, "metric_expression": "3.07882", "metric_symbol": "s", "metric_value": 3.0788155624937503, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.07866, "setup": "peninpen", "side": 3.0788155624937503, "solution_path": "data/solutions/generated/peninpen_007_5b6283ab3dc4c3b5.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/5b6283ab3dc4c3b5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@8", "density": 0.7191427449408644, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/8.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.33514+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.33514, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@8", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.33514+", "metric_symbol": "s", "metric_value": 3.33514, "reference_text": "s = 3.33514+ | Found by Jonathan Viquerat in April 2026.", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/8.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 3.33514+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "de5f4ff90a59b8bf", "improvement": -0.00017949381007964504, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.630985964589326e-06, "max_pair_overlap_depth": -3.1607294870367175e-05, "metric_expression": "3.33532", "metric_symbol": "s", "metric_value": 3.3353194938100796, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.33514, "setup": "peninpen", "side": 3.3353194938100796, "solution_path": "data/solutions/generated/peninpen_008_de5f4ff90a59b8bf.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/de5f4ff90a59b8bf.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@9", "density": 0.756208451025979, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/9.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.44956+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.44956, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@9", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.44956+", "metric_symbol": "s", "metric_value": 3.44956, "reference_text": "s = 3.44956+ | Found by Jonathan Viquerat in April 2026.", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/9.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 3.44956+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "291eb24a57cfcd61", "improvement": -0.00029221756483766015, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.66255661877786e-06, "max_pair_overlap_depth": -4.9483298464991776e-05, "metric_expression": "3.44985", "metric_symbol": "s", "metric_value": 3.4498522175648376, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.44956, "setup": "peninpen", "side": 3.4498522175648376, "solution_path": "data/solutions/generated/peninpen_009_291eb24a57cfcd61.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/291eb24a57cfcd61.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@10", "density": 0.7370589618267208, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/10.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.68324+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.68324, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@10", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.68324+", "metric_symbol": "s", "metric_value": 3.68324, "reference_text": "s = 3.68324+ | Found by Jonathan Viquerat in April 2026.", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/10.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 3.68324+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "90badee8fc213075", "improvement": -0.0001600058005193361, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0386948383243063e-06, "max_pair_overlap_depth": -3.744974033881299e-05, "metric_expression": "3.68340", "metric_symbol": "s", "metric_value": 3.6834000058005194, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.68324, "setup": "peninpen", "side": 3.6834000058005194, "solution_path": "data/solutions/generated/peninpen_010_90badee8fc213075.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/90badee8fc213075.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@11", "density": 0.7628515256681525, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/11.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.79704+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.79704, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@11", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.79704+", "metric_symbol": "s", "metric_value": 3.79704, "reference_text": "s = 3.79704+ | Found by Jonathan Viquerat in April 2026.", "source_image": "11.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/11.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 3.79704+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "11.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "e62e9f2d5556f0f5", "improvement": -0.0002724485549276956, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.930866570871943e-06, "max_pair_overlap_depth": -3.185052846443881e-05, "metric_expression": "3.79731", "metric_symbol": "s", "metric_value": 3.7973124485549277, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.79704, "setup": "peninpen", "side": 3.7973124485549277, "solution_path": "data/solutions/generated/peninpen_011_e62e9f2d5556f0f5.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/e62e9f2d5556f0f5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@12", "density": 0.7615744792401016, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/12.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.96926+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.96926, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@12", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.96926+", "metric_symbol": "s", "metric_value": 3.96926, "reference_text": "s = 3.96926+ | Found by Jonathan Viquerat in April 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/12.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 3.96926+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "6f961579a76d6be8", "improvement": -0.00022743831780980273, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.8385847579674985e-06, "max_pair_overlap_depth": -3.1875868486519465e-05, "metric_expression": "3.96949", "metric_symbol": "s", "metric_value": 3.9694874383178096, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.96926, "setup": "peninpen", "side": 3.9694874383178096, "solution_path": "data/solutions/generated/peninpen_012_6f961579a76d6be8.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/6f961579a76d6be8.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@13", "density": 0.7865963698125578, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/13.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.06523+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.06523, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@13", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.06523+", "metric_symbol": "s", "metric_value": 4.06523, "reference_text": "s = 4.06523+ | Found by Jonathan Viquerat in April 2026.", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/13.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 4.06523+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "ce66c878ffee73fc", "improvement": -9.908623501608815e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.805365438846161e-06, "max_pair_overlap_depth": -6.344819103887289e-06, "metric_expression": "4.06533", "metric_symbol": "s", "metric_value": 4.065329086235016, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.06523, "setup": "peninpen", "side": 4.065329086235016, "solution_path": "data/solutions/generated/peninpen_013_ce66c878ffee73fc.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/ce66c878ffee73fc.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@14", "density": 0.7892057892472966, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/14.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.21120+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.2112, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@14", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.21120+", "metric_symbol": "s", "metric_value": 4.2112, "reference_text": "s = 4.21120+ | Found by Jonathan Viquerat in April 2026.", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/14.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 4.21120+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "367de42acefe1aa2", "improvement": -0.0006111178171677167, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.1042346422399235e-06, "max_pair_overlap_depth": -2.557915411749434e-05, "metric_expression": "4.21181", "metric_symbol": "s", "metric_value": 4.2118111178171675, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.2112, "setup": "peninpen", "side": 4.2118111178171675, "solution_path": "data/solutions/generated/peninpen_014_367de42acefe1aa2.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/367de42acefe1aa2.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@15", "density": 0.8358892308226911, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/15.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2+\u221a5 = 4.23606+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.23606, "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@15", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2+\u221a5 = 4.23606+", "metric_symbol": "s", "metric_value": 4.23606, "reference_text": "s = 2+\u221a5 = 4.23606+ | Trivial.", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/15.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 2+\u221a5 = 4.23606+ | Trivial.", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "251c50a18682e896", "improvement": -8.936254454106063e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.6294493786472997e-06, "max_pair_overlap_depth": -5.5218241392651635e-06, "metric_expression": "4.23615", "metric_symbol": "s", "metric_value": 4.236149362544541, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.23606, "setup": "peninpen", "side": 4.236149362544541, "solution_path": "data/solutions/generated/peninpen_015_251c50a18682e896.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/251c50a18682e896.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@16", "density": 0.8202808577467057, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/16.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.41636+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.41636, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@16", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.41636+", "metric_symbol": "s", "metric_value": 4.41636, "reference_text": "s = 4.41636+ | Found by Jonathan Viquerat in April 2026.", "source_image": "16.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/16.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 4.41636+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "e2bb776d24739328", "improvement": -0.00014476044476463557, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.7250867795500517e-06, "max_pair_overlap_depth": -1.097689597839846e-05, "metric_expression": "4.41650", "metric_symbol": "s", "metric_value": 4.416504760444765, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.41636, "setup": "peninpen", "side": 4.416504760444765, "solution_path": "data/solutions/generated/peninpen_016_e2bb776d24739328.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/e2bb776d24739328.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@17", "density": 0.7834157819221014, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/17.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.65561+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.65561, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@17", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.65561+", "metric_symbol": "s", "metric_value": 4.65561, "reference_text": "s = 4.65561+ | Found by Jonathan Viquerat in April 2026.", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/17.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 4.65561+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "54856cb865a77d57", "improvement": -0.0026991003814726966, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9034050721792276e-06, "max_pair_overlap_depth": -2.8148707974851028e-05, "metric_expression": "4.65831", "metric_symbol": "s", "metric_value": 4.658309100381473, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.65561, "setup": "peninpen", "side": 4.658309100381473, "solution_path": "data/solutions/generated/peninpen_017_54856cb865a77d57.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/54856cb865a77d57.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@18", "density": 0.7892194761771266, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/18.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.77541+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.77541, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.77541+", "metric_symbol": "s", "metric_value": 4.77541, "reference_text": "s = 4.77541+ | Found by Jonathan Viquerat in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/18.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 4.77541+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "9c442356ca78c3de", "improvement": -0.0002934971525236918, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.1318004154280254e-06, "max_pair_overlap_depth": -1.258487199295999e-05, "metric_expression": "4.77570", "metric_symbol": "s", "metric_value": 4.775703497152524, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.77541, "setup": "peninpen", "side": 4.775703497152524, "solution_path": "data/solutions/generated/peninpen_018_9c442356ca78c3de.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/9c442356ca78c3de.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@19", "density": 0.7735353200149236, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/19.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.95269+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.95269, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@19", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "4.95269+", "metric_symbol": "s", "metric_value": 4.95269, "reference_text": "s = 4.95269+ | Found by Ian Watson in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/19.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 4.95269+ | Found by Ian Watson in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "b5440311f7b9b10b", "improvement": -0.0033719480383975764, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.8067945532274755e-06, "max_pair_overlap_depth": -5.844604614307913e-06, "metric_expression": "4.95606", "metric_symbol": "s", "metric_value": 4.956061948038397, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.95269, "setup": "peninpen", "side": 4.956061948038397, "solution_path": "data/solutions/generated/peninpen_019_b5440311f7b9b10b.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/b5440311f7b9b10b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@20", "density": 0.7890584950748962, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/20.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "5.04154+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.04154, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.04154+", "metric_symbol": "s", "metric_value": 5.04154, "reference_text": "s = 5.04154+ | Found by Jonathan Viquerat in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/20.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.04154+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "74f61b73dca76fef", "improvement": 0.0069930192193110585, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.063547145356236e-06, "max_pair_overlap_depth": -1.8870971417950244e-05, "metric_expression": "5.03455", "metric_symbol": "s", "metric_value": 5.034546980780689, "n": 20, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 5.04154, "setup": "peninpen", "side": 5.034546980780689, "solution_path": "data/solutions/generated/peninpen_020_74f61b73dca76fef.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/74f61b73dca76fef.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@21", "density": 0.7887631772097712, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/21.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "5.15948+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.15948, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@21", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "5.15948+", "metric_symbol": "s", "metric_value": 5.15948, "reference_text": "s = 5.15948+ | Found by Ignacio Vallejo in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/21.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.15948+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "b731ea055eb53ce1", "improvement": -0.00036117133928748046, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.7271978645132776e-06, "max_pair_overlap_depth": -5.857494896677196e-06, "metric_expression": "5.15984", "metric_symbol": "s", "metric_value": 5.159841171339288, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.15948, "setup": "peninpen", "side": 5.159841171339288, "solution_path": "data/solutions/generated/peninpen_021_b731ea055eb53ce1.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/b731ea055eb53ce1.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@22", "density": 0.7927891464448104, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/22.png", "friedman_metric_expression": "5.26740+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.2674, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@22", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "5.26740+", "metric_symbol": "s", "metric_value": 5.2674, "reference_text": "s = 5.26740+ | Found by Ignacio Vallejo in April 2026.", "source_image": "22.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/22.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.26740+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "07e217f200bb677e", "improvement": -0.0004389908125848052, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.647717325013132e-07, "max_pair_overlap_depth": -3.201222129578518e-05, "metric_expression": "5.26784", "metric_symbol": "s", "metric_value": 5.267838990812585, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.2674, "setup": "peninpen", "side": 5.267838990812585, "solution_path": "data/solutions/generated/peninpen_022_07e217f200bb677e.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/07e217f200bb677e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@23", "density": 0.8042579677659262, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/23.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "5.34794+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.34794, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@23", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "5.34794+", "metric_symbol": "s", "metric_value": 5.34794, "reference_text": "s = 5.34794+ | Found by Ignacio Vallejo in April 2026.", "source_image": "23.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/23.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.34794+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "4286cb7dfd8b00d7", "improvement": 0.00024989883471082663, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.435117490986131e-07, "max_pair_overlap_depth": -1.717758867814112e-05, "metric_expression": "5.34769", "metric_symbol": "s", "metric_value": 5.3476901011652895, "n": 23, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 5.34794, "setup": "peninpen", "side": 5.3476901011652895, "solution_path": "data/solutions/generated/peninpen_023_4286cb7dfd8b00d7.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/4286cb7dfd8b00d7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@24", "density": 0.7956104957168404, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/24.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "5.49241+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.49241, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@24", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "5.49241+", "metric_symbol": "s", "metric_value": 5.49241, "reference_text": "s = 5.49241+ | Found by Ignacio Vallejo in April 2026.", "source_image": "24.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/24.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.49241+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "8859e051020078b2", "improvement": 9.586393159466411e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.446346359580623e-06, "max_pair_overlap_depth": -9.458275242596459e-07, "metric_expression": "5.49231", "metric_symbol": "s", "metric_value": 5.492314136068405, "n": 24, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 5.49241, "setup": "peninpen", "side": 5.492314136068405, "solution_path": "data/solutions/generated/peninpen_024_8859e051020078b2.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/8859e051020078b2.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninpen@25", "density": 0.8019460079699491, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/25.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "5.58370+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.5837, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@25", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "5.58370+", "metric_symbol": "s", "metric_value": 5.5837, "reference_text": "s = 5.58370+ | Found by Ignacio Vallejo in April 2026.", "source_image": "25.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/25.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.58370+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "25.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "0f0645180a7be991", "improvement": 0.00031674927347591364, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.618192580437412e-06, "max_pair_overlap_depth": -2.8739793660470525e-06, "metric_expression": "5.58338", "metric_symbol": "s", "metric_value": 5.583383250726524, "n": 25, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 5.5837, "setup": "peninpen", "side": 5.583383250726524, "solution_path": "data/solutions/generated/peninpen_025_0f0645180a7be991.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/0f0645180a7be991.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@1", "density": 0.6736263863631768, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/1.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.59811, "friedman_reference": {"analytical_or_proved": true, "case": "peninsqu@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "(3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+", "metric_symbol": "s", "metric_value": 1.59811, "reference_text": "s = (3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+ | Trivial. |", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/1.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = (3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+ | Trivial. |", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "ec216f3e37e16785", "improvement": -3.043902908794749e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.733207856432108e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.59814", "metric_symbol": "s", "metric_value": 1.5981404390290879, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.59811, "setup": "peninsqu", "side": 1.5981404390290879, "solution_path": "data/solutions/generated/peninsqu_001_ec216f3e37e16785.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/ec216f3e37e16785.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@2", "density": 0.5669967061443146, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/2.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2.46345+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.46345, "friedman_reference": {"analytical_or_proved": true, "case": "peninsqu@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2.46345+", "metric_symbol": "s", "metric_value": 2.46345, "reference_text": "s = 2.46345+ | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/2.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 2.46345+ | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "bb5e10eb4917963f", "improvement": -3.0994037563569776e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.416866607183818e-07, "max_pair_overlap_depth": -1.473425980974552e-05, "metric_expression": "2.46348", "metric_symbol": "s", "metric_value": 2.4634809940375635, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.46345, "setup": "peninsqu", "side": 2.4634809940375635, "solution_path": "data/solutions/generated/peninsqu_002_bb5e10eb4917963f.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/bb5e10eb4917963f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@3", "density": 0.6102674136126431, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/3.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2.90812+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.90812, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@3", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.90812+", "metric_symbol": "s", "metric_value": 2.90812, "reference_text": "s = 2.90812+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/3.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 2.90812+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "52b96ec8c7f6b741", "improvement": -8.50430757179943e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.362613813108376e-06, "max_pair_overlap_depth": -5.5799797820554886e-05, "metric_expression": "2.90821", "metric_symbol": "s", "metric_value": 2.908205043075718, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.90812, "setup": "peninsqu", "side": 2.908205043075718, "solution_path": "data/solutions/generated/peninsqu_003_52b96ec8c7f6b741.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/52b96ec8c7f6b741.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@4", "density": 0.7148924907955395, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/4.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3.10252+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.10252, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@4", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.10252+", "metric_symbol": "s", "metric_value": 3.10252, "reference_text": "s = 3.10252+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/4.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 3.10252+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "a2fcd0b0beef7a6f", "improvement": -0.00013948165686938907, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2690386136380924e-06, "max_pair_overlap_depth": -3.0975557991252956e-05, "metric_expression": "3.10266", "metric_symbol": "s", "metric_value": 3.1026594816568696, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.10252, "setup": "peninsqu", "side": 3.1026594816568696, "solution_path": "data/solutions/generated/peninsqu_004_a2fcd0b0beef7a6f.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/a2fcd0b0beef7a6f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@5", "density": 0.6829538263136812, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/5.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3.54903+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.54903, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@5", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.54903+", "metric_symbol": "s", "metric_value": 3.54903, "reference_text": "s = 3.54903+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "5.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/5.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 3.54903+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "bda3fbac20c8a756", "improvement": -3.388580996466217e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.104606408908601e-07, "max_pair_overlap_depth": -5.251218256785428e-06, "metric_expression": "3.54906", "metric_symbol": "s", "metric_value": 3.549063885809965, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.54903, "setup": "peninsqu", "side": 3.549063885809965, "solution_path": "data/solutions/generated/peninsqu_005_bda3fbac20c8a756.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/bda3fbac20c8a756.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@6", "density": 0.6845927654826146, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/6.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3.88300+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.883, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@6", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.88300+", "metric_symbol": "s", "metric_value": 3.883, "reference_text": "s = 3.88300+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/6.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 3.88300+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "a267ec5809e79964", "improvement": -0.00014813728762552714, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0190677678703185e-06, "max_pair_overlap_depth": -5.678337215275775e-05, "metric_expression": "3.88315", "metric_symbol": "s", "metric_value": 3.8831481372876255, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.883, "setup": "peninsqu", "side": 3.8831481372876255, "solution_path": "data/solutions/generated/peninsqu_006_a267ec5809e79964.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/a267ec5809e79964.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@7", "density": 0.6891282499986281, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/7.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.18038+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.18038, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@7", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.18038+", "metric_symbol": "s", "metric_value": 4.18038, "reference_text": "s = 4.18038+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/7.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 4.18038+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "b5565b951637dc85", "improvement": -7.429190517971307e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4725627916323898e-06, "max_pair_overlap_depth": -1.919059115845778e-05, "metric_expression": "4.18045", "metric_symbol": "s", "metric_value": 4.18045429190518, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.18038, "setup": "peninsqu", "side": 4.18045429190518, "solution_path": "data/solutions/generated/peninsqu_007_b5565b951637dc85.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/b5565b951637dc85.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@8", "density": 0.7167004559270932, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/8.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.38191+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.38191, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@8", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.38191+", "metric_symbol": "s", "metric_value": 4.38191, "reference_text": "s = 4.38191+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/8.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 4.38191+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "eac74e93d82a54dd", "improvement": -0.00037521167052823046, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2846178652549832e-06, "max_pair_overlap_depth": -2.0945039418324152e-05, "metric_expression": "4.38229", "metric_symbol": "s", "metric_value": 4.382285211670529, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.38191, "setup": "peninsqu", "side": 4.382285211670529, "solution_path": "data/solutions/generated/peninsqu_008_eac74e93d82a54dd.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/eac74e93d82a54dd.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@9", "density": 0.7314097601583741, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/9.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.60033+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.60033, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@9", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.60033+", "metric_symbol": "s", "metric_value": 4.60033, "reference_text": "s = 4.60033+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/9.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 4.60033+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "0270d827693b6f8d", "improvement": -0.0008091240419938472, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.8644555136003204e-06, "max_pair_overlap_depth": -1.0559011279553943e-05, "metric_expression": "4.60114", "metric_symbol": "s", "metric_value": 4.601139124041993, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.60033, "setup": "peninsqu", "side": 4.601139124041993, "solution_path": "data/solutions/generated/peninsqu_009_0270d827693b6f8d.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/0270d827693b6f8d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@10", "density": 0.7142869465585481, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/10.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.90584+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.90584, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@10", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.90584+", "metric_symbol": "s", "metric_value": 4.90584, "reference_text": "s = 4.90584+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/10.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 4.90584+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "fba502b92276222e", "improvement": -0.0019743867107484547, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.710048632437797e-06, "max_pair_overlap_depth": -3.5387419318078095e-05, "metric_expression": "4.90781", "metric_symbol": "s", "metric_value": 4.907814386710749, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.90584, "setup": "peninsqu", "side": 4.907814386710749, "solution_path": "data/solutions/generated/peninsqu_010_fba502b92276222e.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/fba502b92276222e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@11", "density": 0.7230188560400136, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/11.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5.11557+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.11557, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@11", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.11557+", "metric_symbol": "s", "metric_value": 5.11557, "reference_text": "s = 5.11557+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "11.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/11.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 5.11557+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "11.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "3596998e61e47a27", "improvement": -0.0006123708648555493, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.520631561500943e-07, "max_pair_overlap_depth": -2.3531878005744744e-05, "metric_expression": "5.11618", "metric_symbol": "s", "metric_value": 5.1161823708648555, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.11557, "setup": "peninsqu", "side": 5.1161823708648555, "solution_path": "data/solutions/generated/peninsqu_011_3596998e61e47a27.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/3596998e61e47a27.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@12", "density": 0.7539256100231233, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/12.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5.23250+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.2325, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@12", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.23250+", "metric_symbol": "s", "metric_value": 5.2325, "reference_text": "s = 5.23250+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/12.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 5.23250+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "72fe010d0104fc76", "improvement": -0.0005015230417875216, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6940168948787563e-07, "max_pair_overlap_depth": -3.660774509528508e-05, "metric_expression": "5.23300", "metric_symbol": "s", "metric_value": 5.2330015230417875, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.2325, "setup": "peninsqu", "side": 5.2330015230417875, "solution_path": "data/solutions/generated/peninsqu_012_72fe010d0104fc76.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/72fe010d0104fc76.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@13", "density": 0.7325239130137876, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/13.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5.52183+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.52183, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@13", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.52183+", "metric_symbol": "s", "metric_value": 5.52183, "reference_text": "s = 5.52183+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/13.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 5.52183+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "b54e12045e01b08b", "improvement": -0.0038439980668076856, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7653030405329436e-07, "max_pair_overlap_depth": -2.666929117722816e-05, "metric_expression": "5.52567", "metric_symbol": "s", "metric_value": 5.525673998066807, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.52183, "setup": "peninsqu", "side": 5.525673998066807, "solution_path": "data/solutions/generated/peninsqu_013_b54e12045e01b08b.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/b54e12045e01b08b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@14", "density": 0.7420924387932526, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/14.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5.69775+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.69775, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@14", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.69775+", "metric_symbol": "s", "metric_value": 5.69775, "reference_text": "s = 5.69775+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/14.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 5.69775+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "70191e649c0c34a4", "improvement": 0.0005757762276479284, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.376635005869759e-06, "max_pair_overlap_depth": -1.761308907194392e-05, "metric_expression": "5.69717", "metric_symbol": "s", "metric_value": 5.697174223772352, "n": 14, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 5.69775, "setup": "peninsqu", "side": 5.697174223772352, "solution_path": "data/solutions/generated/peninsqu_014_70191e649c0c34a4.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/70191e649c0c34a4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@15", "density": 0.737588729235034, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/15.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5.91106+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.91106, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@15", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.91106+", "metric_symbol": "s", "metric_value": 5.91106, "reference_text": "s = 5.91106+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/15.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 5.91106+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "f5d70026e15060e9", "improvement": -0.004052102776268995, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.031797802365455e-06, "max_pair_overlap_depth": -3.458627910934986e-05, "metric_expression": "5.91511", "metric_symbol": "s", "metric_value": 5.915112102776269, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.91106, "setup": "peninsqu", "side": 5.915112102776269, "solution_path": "data/solutions/generated/peninsqu_015_f5d70026e15060e9.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/f5d70026e15060e9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@16", "density": 0.7479800847585042, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/16.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.11021+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.11021, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@16", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6.11021+", "metric_symbol": "s", "metric_value": 6.11021, "reference_text": "s = 6.11021+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "16.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/16.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 6.11021+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": false, "id": "4644b3e97f0bdea2", "improvement": 0.04369242522759276, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5325677563252472e-06, "max_pair_overlap_depth": -5.091262792966678e-06, "metric_expression": "6.06652", "metric_symbol": "s", "metric_value": 6.066517574772408, "n": 16, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.", "record_type": "verified", "reference_side": 6.11021, "setup": "peninsqu", "side": 6.066517574772408, "solution_path": "data/solutions/generated/peninsqu_016_4644b3e97f0bdea2.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/4644b3e97f0bdea2.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@17", "density": 0.7514950307673967, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/17.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.26466+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.26466, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@17", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6.26466+", "metric_symbol": "s", "metric_value": 6.26466, "reference_text": "s = 6.26466+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/17.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 6.26466+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": false, "id": "a6cd0104bc26d2a0", "improvement": 0.026077965234885703, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.35268853525978e-06, "max_pair_overlap_depth": -1.565351530530279e-05, "metric_expression": "6.23858", "metric_symbol": "s", "metric_value": 6.238582034765114, "n": 17, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.", "record_type": "verified", "reference_side": 6.26466, "setup": "peninsqu", "side": 6.238582034765114, "solution_path": "data/solutions/generated/peninsqu_017_a6cd0104bc26d2a0.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/a6cd0104bc26d2a0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@18", "density": 0.7710926756280118, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/18.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.33632+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.33632, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6.33632+", "metric_symbol": "s", "metric_value": 6.33632, "reference_text": "s = 6.33632+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/18.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 6.33632+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "9705d17615c32308", "improvement": -0.0010264494540361824, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.1888526227077803e-06, "max_pair_overlap_depth": -2.3019703547788595e-06, "metric_expression": "6.33735", "metric_symbol": "s", "metric_value": 6.337346449454036, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.33632, "setup": "peninsqu", "side": 6.337346449454036, "solution_path": "data/solutions/generated/peninsqu_018_9705d17615c32308.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/9705d17615c32308.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@19", "density": 0.759469213458349, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/19.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.55939+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.55939, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6.55939+", "metric_symbol": "s", "metric_value": 6.55939, "reference_text": "s = 6.55939+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/19.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 6.55939+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "3b1113745987c1d6", "improvement": -0.0012498840705594816, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9916513391919655e-06, "max_pair_overlap_depth": -2.545361094719034e-05, "metric_expression": "6.56064", "metric_symbol": "s", "metric_value": 6.560639884070559, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.55939, "setup": "peninsqu", "side": 6.560639884070559, "solution_path": "data/solutions/generated/peninsqu_019_3b1113745987c1d6.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/3b1113745987c1d6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@20", "density": 0.7723902783602073, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/20.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.69588+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.69588, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6.69588+", "metric_symbol": "s", "metric_value": 6.69588, "reference_text": "s = 6.69588+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/20.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 6.69588+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": false, "id": "eafd28d28fb8e254", "improvement": 0.021343927884186265, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.197045603091071e-06, "max_pair_overlap_depth": -2.9426570577584243e-05, "metric_expression": "6.67454", "metric_symbol": "s", "metric_value": 6.674536072115814, "n": 20, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.", "record_type": "verified", "reference_side": 6.69588, "setup": "peninsqu", "side": 6.674536072115814, "solution_path": "data/solutions/generated/peninsqu_020_eafd28d28fb8e254.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/eafd28d28fb8e254.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@21", "density": 0.7688621226676746, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/21.png", "friedman_metric_expression": "6.85540+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.8554, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@21", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "6.85540+", "metric_symbol": "s", "metric_value": 6.8554, "reference_text": "s = 6.85540+ | Found by Emerson Connelly | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/21.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 6.85540+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "9d320f91f05e2f0e", "improvement": 0.0003614666962281632, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5104768148309566e-06, "max_pair_overlap_depth": -4.3073173047414315e-05, "metric_expression": "6.85504", "metric_symbol": "s", "metric_value": 6.855038533303772, "n": 21, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 6.8554, "setup": "peninsqu", "side": 6.855038533303772, "solution_path": "data/solutions/generated/peninsqu_21_9d320f91f05e2f0e.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T13:47:12+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/9d320f91f05e2f0e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@22", "density": 0.7625061251104759, "friedman_analytical_or_proved": false, "friedman_credit": "Teodors Smith", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/22.png", "friedman_metric_expression": "7.04532+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.04532, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@22", "credit": "Teodors Smith", "date": "April 2026", "family_updated": "", "metric_expression": "7.04532+", "metric_symbol": "s", "metric_value": 7.04532, "reference_text": "s = 7.04532+ | Found by Teodors Smith | in April 2026.", "source_image": "22.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/22.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 7.04532+ | Found by Teodors Smith | in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "70964f50e662283c", "improvement": -0.0002179452221122702, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.550099486392989e-07, "max_pair_overlap_depth": -3.276547527986118e-05, "metric_expression": "7.04554", "metric_symbol": "s", "metric_value": 7.0455379452221125, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.04532, "setup": "peninsqu", "side": 7.0455379452221125, "solution_path": "data/solutions/generated/peninsqu_22_70964f50e662283c.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T13:47:12+00:00", "submitted_by": "Teodors Smith", "svg_path": "data/svg/70964f50e662283c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@23", "density": 0.7617923823536098, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/23.png", "friedman_metric_expression": "7.20731+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.20731, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@23", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "7.20731+", "metric_symbol": "s", "metric_value": 7.20731, "reference_text": "s = 7.20731+ | Found by Emerson Connelly | in April 2026.", "source_image": "23.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/23.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 7.20731+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "5b526f4bb0fda83c", "improvement": 5.162671385594564e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.635959726042516e-06, "max_pair_overlap_depth": -3.224520897293637e-05, "metric_expression": "7.20726", "metric_symbol": "s", "metric_value": 7.207258373286144, "n": 23, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 7.20731, "setup": "peninsqu", "side": 7.207258373286144, "solution_path": "data/solutions/generated/peninsqu_23_5b526f4bb0fda83c.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T13:47:12+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/5b526f4bb0fda83c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "peninsqu@24", "density": 0.766901141845129, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/24.png", "friedman_metric_expression": "7.33823+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.33823, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@24", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "7.33823+", "metric_symbol": "s", "metric_value": 7.33823, "reference_text": "s = 7.33823+ | Found by Emerson Connelly | in April 2026.", "source_image": "24.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/24.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 7.33823+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "3e42e9e085ed4c16", "improvement": 0.0005221765418985669, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.294217705264547e-06, "max_pair_overlap_depth": -1.6096651148655994e-05, "metric_expression": "7.33771", "metric_symbol": "s", "metric_value": 7.337707823458102, "n": 24, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 7.33823, "setup": "peninsqu", "side": 7.337707823458102, "solution_path": "data/solutions/generated/peninsqu_24_3e42e9e085ed4c16.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T13:47:12+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/3e42e9e085ed4c16.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@1", "density": 0.6366152339868586, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/1.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a2 / 2 = .707+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.707, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a2 / 2 = .707+", "metric_symbol": "r", "metric_value": 0.707, "reference_text": "r = \u221a2 / 2 = .707+ | Trivial.", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/1.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a2 / 2 = .707+ | Trivial.", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "e1e16b7d18b1243e", "improvement": -0.00010930163680866745, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.331866965270656e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.70711", "metric_symbol": "r", "metric_value": 0.7071093016368086, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.707, "setup": "squincir", "side": 1.4142186032736173, "solution_path": "data/solutions/generated/squincir_001_e1e16b7d18b1243e.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/e1e16b7d18b1243e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@2", "density": 0.5092878238610891, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/2.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a5 / 2 = 1.118+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.118, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a5 / 2 = 1.118+", "metric_symbol": "r", "metric_value": 1.118, "reference_text": "r = \u221a5 / 2 = 1.118+ | Trivial.", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/2.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a5 / 2 = 1.118+ | Trivial.", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "e0e32383f27cd27d", "improvement": -4.2763322036343254e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.769902571588602e-06, "max_pair_overlap_depth": -3.18210820038356e-06, "metric_expression": "1.11804", "metric_symbol": "r", "metric_value": 1.1180427633220364, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.118, "setup": "squincir", "side": 2.236085526644073, "solution_path": "data/solutions/generated/squincir_002_e0e32383f27cd27d.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/e0e32383f27cd27d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@3", "density": 0.5751857401746373, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/3.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "5 \u221a17 / 16 = 1.288+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.288, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@3", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "5 \u221a17 / 16 = 1.288+", "metric_symbol": "r", "metric_value": 1.288, "reference_text": "r = 5 \u221a17 / 16 = 1.288+ | Found by Erich Friedman | in 1997.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/3.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 5 \u221a17 / 16 = 1.288+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "226172dcb69c3daf", "improvement": -0.0004917307904808155, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4552703365164916e-07, "max_pair_overlap_depth": -2.6483206490832134e-05, "metric_expression": "1.28849", "metric_symbol": "r", "metric_value": 1.2884917307904808, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.288, "setup": "squincir", "side": 2.5769834615809617, "solution_path": "data/solutions/generated/squincir_003_226172dcb69c3daf.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/226172dcb69c3daf.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@4", "density": 0.6365934661039774, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/4.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a2 = 1.414+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.414, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@4", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a2 = 1.414+", "metric_symbol": "r", "metric_value": 1.414, "reference_text": "r = \u221a2 = 1.414+ | Found by Erich Friedman | in 1997.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/4.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a2 = 1.414+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "59645297dac888b6", "improvement": -0.0002427821910928607, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.7659081458272254e-06, "max_pair_overlap_depth": -2.7879728913877792e-05, "metric_expression": "1.41424", "metric_symbol": "r", "metric_value": 1.4142427821910928, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.414, "setup": "squincir", "side": 2.8284855643821856, "solution_path": "data/solutions/generated/squincir_004_59645297dac888b6.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/59645297dac888b6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@5", "density": 0.6366006254695611, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/5.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a10 / 2 = 1.581+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.581, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@5", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a10 / 2 = 1.581+", "metric_symbol": "r", "metric_value": 1.581, "reference_text": "r = \u221a10 / 2 = 1.581+ | Found by Erich Friedman | in 1997.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/5.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a10 / 2 = 1.581+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "ee29f4bb5ac19bc4", "improvement": -0.00016260768909037715, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.383463508896625e-07, "max_pair_overlap_depth": -1.4376414261496606e-05, "metric_expression": "1.58116", "metric_symbol": "r", "metric_value": 1.5811626076890903, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.581, "setup": "squincir", "side": 3.1623252153781807, "solution_path": "data/solutions/generated/squincir_005_ee29f4bb5ac19bc4.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/ee29f4bb5ac19bc4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@6", "density": 0.6697921489003816, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/6.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "1.688+ *", "friedman_metric_symbol": "r", "friedman_metric_value": 1.688, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@6", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "1.688+ *", "metric_symbol": "r", "metric_value": 1.688, "reference_text": "r = 1.688+ * | Found by Erich Friedman | in 1997.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/6.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 1.688+ * | Found by Erich Friedman | in 1997.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "00816b044d90c514", "improvement": -0.0006150768345383195, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.526575301033731e-06, "max_pair_overlap_depth": -2.575413327610132e-05, "metric_expression": "1.68862", "metric_symbol": "r", "metric_value": 1.6886150768345383, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.688, "setup": "squincir", "side": 3.3772301536690765, "solution_path": "data/solutions/generated/squincir_006_00816b044d90c514.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/00816b044d90c514.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@7", "density": 0.685554128713642, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/7.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a13 / 2 = 1.802+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.802, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@7", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a13 / 2 = 1.802+", "metric_symbol": "r", "metric_value": 1.802, "reference_text": "r = \u221a13 / 2 = 1.802+ | Found by Erich Friedman | in 1997.", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/7.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a13 / 2 = 1.802+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "f533c6ece1865b92", "improvement": -0.0008234908634709992, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3338190876808227e-06, "max_pair_overlap_depth": -2.5625121306882548e-05, "metric_expression": "1.80282", "metric_symbol": "r", "metric_value": 1.802823490863471, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.802, "setup": "squincir", "side": 3.605646981726942, "solution_path": "data/solutions/generated/squincir_007_f533c6ece1865b92.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/f533c6ece1865b92.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@8", "density": 0.6501060351379704, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "March 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/8.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "1.978+ *", "friedman_metric_symbol": "r", "friedman_metric_value": 1.978, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@8", "credit": "David W. Cantrell", "date": "March 2002", "family_updated": "", "metric_expression": "1.978+ *", "metric_symbol": "r", "metric_value": 1.978, "reference_text": "r = 1.978+ * | Found by David W. Cantrell | in March 2002.", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/8.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 1.978+ * | Found by David W. Cantrell | in March 2002.", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "056dfca89502965a", "improvement": -0.0011465711618996455, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7255803199667241e-06, "max_pair_overlap_depth": -1.3772848531545812e-05, "metric_expression": "1.97915", "metric_symbol": "r", "metric_value": 1.9791465711618996, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.978, "setup": "squincir", "side": 3.9582931423237993, "solution_path": "data/solutions/generated/squincir_008_056dfca89502965a.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/056dfca89502965a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@9", "density": 0.6635107369929176, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/9.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a1105 / 16 = 2.077+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.077, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@9", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a1105 / 16 = 2.077+", "metric_symbol": "r", "metric_value": 2.077, "reference_text": "r = \u221a1105 / 16 = 2.077+ | Found by Erich Friedman | in 1997.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/9.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a1105 / 16 = 2.077+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "a0eb38ed275fd3c7", "improvement": -0.0008889848991340266, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.939578609861826e-06, "max_pair_overlap_depth": -1.5145046883935365e-05, "metric_expression": "2.07789", "metric_symbol": "r", "metric_value": 2.077888984899134, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.077, "setup": "squincir", "side": 4.155777969798268, "solution_path": "data/solutions/generated/squincir_009_a0eb38ed275fd3c7.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/a0eb38ed275fd3c7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@10", "density": 0.7072738827790132, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/10.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3 \u221a2 / 2 = 2.121+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.121, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@10", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 \u221a2 / 2 = 2.121+", "metric_symbol": "r", "metric_value": 2.121, "reference_text": "r = 3 \u221a2 / 2 = 2.121+ | Found by Erich Friedman | in 1997.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/10.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3 \u221a2 / 2 = 2.121+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "eacd7cf43d9f9c99", "improvement": -0.00044244096873002903, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.093937328557672e-07, "max_pair_overlap_depth": -1.6684797704336063e-05, "metric_expression": "2.12144", "metric_symbol": "r", "metric_value": 2.12144244096873, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.121, "setup": "squincir", "side": 4.24288488193746, "solution_path": "data/solutions/generated/squincir_010_eacd7cf43d9f9c99.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/eacd7cf43d9f9c99.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@11", "density": 0.7141684249475255, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "March 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/11.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.214+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.214, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@11", "credit": "David W. Cantrell", "date": "March 2002", "family_updated": "", "metric_expression": "2.214+", "metric_symbol": "r", "metric_value": 2.214, "reference_text": "r = 2.214+ | Found by David W. Cantrell | in March 2002.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/11.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.214+ | Found by David W. Cantrell | in March 2002.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "ed2b520c292f3457", "improvement": -0.00022160321374320446, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.710372663145449e-07, "max_pair_overlap_depth": -1.7996528127950384e-05, "metric_expression": "2.21422", "metric_symbol": "r", "metric_value": 2.214221603213743, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.214, "setup": "squincir", "side": 4.428443206427486, "solution_path": "data/solutions/generated/squincir_011_ed2b520c292f3457.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/ed2b520c292f3457.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@12", "density": 0.7638630053365897, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/12.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a5 = 2.236+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.236, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@12", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a5 = 2.236+", "metric_symbol": "r", "metric_value": 2.236, "reference_text": "r = \u221a5 = 2.236+ | Found by Erich Friedman | in 1997.", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/12.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a5 = 2.236+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "064666a02cb4bcc6", "improvement": -0.00018612303226639426, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.505810228203842e-06, "max_pair_overlap_depth": -1.897198109612752e-05, "metric_expression": "2.23619", "metric_symbol": "r", "metric_value": 2.2361861230322666, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.236, "setup": "squincir", "side": 4.472372246064533, "solution_path": "data/solutions/generated/squincir_012_064666a02cb4bcc6.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/064666a02cb4bcc6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@13", "density": 0.7419440056386433, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "November 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/13.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.3607+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.3607, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@13", "credit": "David W. Cantrell", "date": "November 2010", "family_updated": "", "metric_expression": "2.3607+", "metric_symbol": "r", "metric_value": 2.3607, "reference_text": "r = 2.3607+ | Found by David W. Cantrell | in November 2010.", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/13.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.3607+ | Found by David W. Cantrell | in November 2010.", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "1ff894504e55415a", "improvement": -0.0009262889169745492, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0049576295578788e-06, "max_pair_overlap_depth": -2.3549111853871096e-05, "metric_expression": "2.36163", "metric_symbol": "r", "metric_value": 2.3616262889169746, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.3607, "setup": "squincir", "side": 4.723252577833949, "solution_path": "data/solutions/generated/squincir_013_1ff894504e55415a.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/1ff894504e55415a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@14", "density": 0.7129258170438343, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/14.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.5", "friedman_metric_symbol": "r", "friedman_metric_value": 2.5, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@14", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "2.5", "metric_symbol": "r", "metric_value": 2.5, "reference_text": "r = 2.5 | Found by Erich Friedman | in 1997.", "source_image": "14.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/14.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.5 | Found by Erich Friedman | in 1997.", "friedman_source_image": "14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "16de07d86777c846", "improvement": -0.0001548640652071498, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.318191377805647e-07, "max_pair_overlap_depth": -1.9980447390599565e-05, "metric_expression": "2.50015", "metric_symbol": "r", "metric_value": 2.500154864065207, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.5, "setup": "squincir", "side": 5.000309728130414, "solution_path": "data/solutions/generated/squincir_014_16de07d86777c846.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/16de07d86777c846.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@15", "density": 0.7434807535174716, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "June 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/15.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.533+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.533, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@15", "credit": "David W. Cantrell", "date": "June 2002", "family_updated": "", "metric_expression": "2.533+", "metric_symbol": "r", "metric_value": 2.533, "reference_text": "r = 2.533+ | Found by by David W. Cantrell | in June 2002.", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/15.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.533+ | Found by by David W. Cantrell | in June 2002.", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "4a2ad28ea2097ba3", "improvement": -0.001170482100864234, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.5068887214985125e-06, "max_pair_overlap_depth": -8.103900655004326e-06, "metric_expression": "2.53417", "metric_symbol": "r", "metric_value": 2.534170482100864, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.533, "setup": "squincir", "side": 5.068340964201728, "solution_path": "data/solutions/generated/squincir_015_4a2ad28ea2097ba3.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/4a2ad28ea2097ba3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@16", "density": 0.7401412241351131, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/16.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a11009 / 40 = 2.623+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.623, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@16", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a11009 / 40 = 2.623+", "metric_symbol": "r", "metric_value": 2.623, "reference_text": "r = \u221a11009 / 40 = 2.623+ | Found by Erich Friedman | in 1997.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/16.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a11009 / 40 = 2.623+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "94d0a09f4c75dcc4", "improvement": -0.00017797945661435222, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.109474628753105e-06, "max_pair_overlap_depth": -5.84557896199378e-06, "metric_expression": "2.62318", "metric_symbol": "r", "metric_value": 2.6231779794566146, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.623, "setup": "squincir", "side": 5.246355958913229, "solution_path": "data/solutions/generated/squincir_016_94d0a09f4c75dcc4.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/94d0a09f4c75dcc4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@17", "density": 0.7544956917261334, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/17.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.677+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.677, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@17", "credit": "Maurizio Morandi", "date": "December 2010", "family_updated": "", "metric_expression": "2.677+", "metric_symbol": "r", "metric_value": 2.677, "reference_text": "r = 2.677+ | Found by Maurizio Morandi | in December 2010.", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/17.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.677+ | Found by Maurizio Morandi | in December 2010.", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "036910f6c0550e2f", "improvement": -0.0010651760341882088, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2297138575488873e-06, "max_pair_overlap_depth": -2.14353819976143e-05, "metric_expression": "2.67807", "metric_symbol": "r", "metric_value": 2.6780651760341883, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.677, "setup": "squincir", "side": 5.3561303520683765, "solution_path": "data/solutions/generated/squincir_017_036910f6c0550e2f.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/036910f6c0550e2f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@18", "density": 0.7617085472368383, "friedman_analytical_or_proved": true, "friedman_credit": "David W. Cantrell", "friedman_date": "March 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/18.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a481 / 8 = 2.741+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.741, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@18", "credit": "David W. Cantrell", "date": "March 2002", "family_updated": "", "metric_expression": "\u221a481 / 8 = 2.741+", "metric_symbol": "r", "metric_value": 2.741, "reference_text": "r = \u221a481 / 8 = 2.741+ | Found by David W. Cantrell | in March 2002.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/18.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a481 / 8 = 2.741+ | Found by David W. Cantrell | in March 2002.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "d726e310dc0e9eaa", "improvement": -0.001627976420446764, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.727763966399067e-06, "max_pair_overlap_depth": -2.573974201414142e-05, "metric_expression": "2.74263", "metric_symbol": "r", "metric_value": 2.742627976420447, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.741, "setup": "squincir", "side": 5.485255952840894, "solution_path": "data/solutions/generated/squincir_018_d726e310dc0e9eaa.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d726e310dc0e9eaa.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@19", "density": 0.76918194004105, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/19.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.802+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.802, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.802+", "metric_symbol": "r", "metric_value": 2.802, "reference_text": "r = 2.802+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/19.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.802+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "1966e8e14b94f055", "improvement": -0.002060145605657926, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.987997947874078e-06, "max_pair_overlap_depth": -1.7618196217927817e-05, "metric_expression": "2.80406", "metric_symbol": "r", "metric_value": 2.804060145605658, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.802, "setup": "squincir", "side": 5.608120291211316, "solution_path": "data/solutions/generated/squincir_019_1966e8e14b94f055.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:51:36+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/1966e8e14b94f055.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@20", "density": 0.7600583693203081, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "June 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/20.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.893+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.893, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@20", "credit": "David W. Cantrell", "date": "June 2002", "family_updated": "", "metric_expression": "2.893+", "metric_symbol": "r", "metric_value": 2.893, "reference_text": "r = 2.893+ | Found by David W. Cantrell | in June 2002.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/20.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.893+ | Found by David W. Cantrell | in June 2002.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "d2a3e673398d1cd8", "improvement": -0.001120361357695998, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.0691232615918125e-06, "max_pair_overlap_depth": -2.4937171242911393e-05, "metric_expression": "2.89412", "metric_symbol": "r", "metric_value": 2.894120361357696, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.893, "setup": "squincir", "side": 5.788240722715392, "solution_path": "data/solutions/generated/squincir_020_d2a3e673398d1cd8.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d2a3e673398d1cd8.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@21", "density": 0.7859297816487661, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/21.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a34 / 2 = 2.915+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.915, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@21", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a34 / 2 = 2.915+", "metric_symbol": "r", "metric_value": 2.915, "reference_text": "r = \u221a34 / 2 = 2.915+ | Found by Erich Friedman | in 1997.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/21.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a34 / 2 = 2.915+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "af376e36d9f212b7", "improvement": -0.0013714498117400886, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.2933372016152873e-06, "max_pair_overlap_depth": -5.039957310160048e-06, "metric_expression": "2.91637", "metric_symbol": "r", "metric_value": 2.91637144981174, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.915, "setup": "squincir", "side": 5.83274289962348, "solution_path": "data/solutions/generated/squincir_021_af376e36d9f212b7.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/af376e36d9f212b7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@22", "density": 0.7599553171633651, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/22.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.033+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.033, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@22", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.033+", "metric_symbol": "r", "metric_value": 3.033, "reference_text": "r = 3.033+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/22.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.033+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "d08f4c9050539106", "improvement": -0.002584838809432277, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.8140931262198308e-06, "max_pair_overlap_depth": -1.4316626561150514e-05, "metric_expression": "3.03558", "metric_symbol": "r", "metric_value": 3.035584838809432, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.033, "setup": "squincir", "side": 6.071169677618864, "solution_path": "data/solutions/generated/squincir_022_d08f4c9050539106.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:51:36+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/d08f4c9050539106.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@23", "density": 0.7743799032674085, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "June 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/23.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.073+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.073, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@23", "credit": "David W. Cantrell", "date": "June 2002", "family_updated": "", "metric_expression": "3.073+", "metric_symbol": "r", "metric_value": 3.073, "reference_text": "r = 3.073+ | Found by David W. Cantrell | in June 2002.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/23.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.073+ | Found by David W. Cantrell | in June 2002.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "3cacab4fa2a4614f", "improvement": -0.0017651132247276102, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.255819924494972e-06, "max_pair_overlap_depth": -2.255301194975523e-05, "metric_expression": "3.07477", "metric_symbol": "r", "metric_value": 3.0747651132247276, "n": 23, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.073, "setup": "squincir", "side": 6.149530226449455, "solution_path": "data/solutions/generated/squincir_023_3cacab4fa2a4614f.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/3cacab4fa2a4614f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@24", "density": 0.7887737589513796, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "October 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/24.gif", "friedman_metric_expression": "3.110+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.11, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@24", "credit": "Maurizio Morandi", "date": "October 2010", "family_updated": "", "metric_expression": "3.110+", "metric_symbol": "r", "metric_value": 3.11, "reference_text": "r = 3.110+ | Found by Maurizio Morandi | in October 2010.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/24.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.110+ | Found by Maurizio Morandi | in October 2010.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "35e22c7b35c718bd", "improvement": -0.0021065491772924716, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.225275177878075e-06, "max_pair_overlap_depth": -2.5024692080766187e-05, "metric_expression": "3.11211", "metric_symbol": "r", "metric_value": 3.1121065491772923, "n": 24, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.11, "setup": "squincir", "side": 6.224213098354585, "solution_path": "data/solutions/generated/squincir_024_35e22c7b35c718bd.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/35e22c7b35c718bd.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@25", "density": 0.7888590017487276, "friedman_analytical_or_proved": true, "friedman_credit": "David W. Cantrell", "friedman_date": "April 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/25.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a5809 / 24 = 3.175+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.175, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@25", "credit": "David W. Cantrell", "date": "April 2002", "family_updated": "", "metric_expression": "\u221a5809 / 24 = 3.175+", "metric_symbol": "r", "metric_value": 3.175, "reference_text": "r = \u221a5809 / 24 = 3.175+ | Found by David W. Cantrell | in April 2002.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/25.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a5809 / 24 = 3.175+ | Found by David W. Cantrell | in April 2002.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "0cabb86031dba8fd", "improvement": -0.0011088296688002153, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4103138832897173e-06, "max_pair_overlap_depth": -3.0578471952869e-05, "metric_expression": "3.17611", "metric_symbol": "r", "metric_value": 3.1761088296688, "n": 25, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.175, "setup": "squincir", "side": 6.3522176593376, "solution_path": "data/solutions/generated/squincir_025_0cabb86031dba8fd.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/0cabb86031dba8fd.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@26", "density": 0.806871444276765, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/26.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a41 / 2 = 3.201+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.201, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@26", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a41 / 2 = 3.201+", "metric_symbol": "r", "metric_value": 3.201, "reference_text": "r = \u221a41 / 2 = 3.201+ | Found by Erich Friedman | in 1997.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/26.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a41 / 2 = 3.201+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "d3c528742ca2afa0", "improvement": -0.0016506279557328973, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.80804369340504e-06, "max_pair_overlap_depth": -4.195014817909293e-06, "metric_expression": "3.20265", "metric_symbol": "r", "metric_value": 3.202650627955733, "n": 26, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.201, "setup": "squincir", "side": 6.405301255911466, "solution_path": "data/solutions/generated/squincir_026_d3c528742ca2afa0.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/d3c528742ca2afa0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@27", "density": 0.8080261870592086, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "September 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/27.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "13\u221a145/48 = 3.261+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.261, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@27", "credit": "Maurizio Morandi", "date": "September 2010", "family_updated": "", "metric_expression": "13\u221a145/48 = 3.261+", "metric_symbol": "r", "metric_value": 3.261, "reference_text": "r = 13\u221a145/48 = 3.261+ | Found by Maurizio Morandi | in September 2010.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/27.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 13\u221a145/48 = 3.261+ | Found by Maurizio Morandi | in September 2010.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "24101c6f5ef6d134", "improvement": -0.0003261127181617418, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.239249729032224e-06, "max_pair_overlap_depth": -1.3019517370316258e-05, "metric_expression": "3.26133", "metric_symbol": "r", "metric_value": 3.261326112718162, "n": 27, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.261, "setup": "squincir", "side": 6.522652225436324, "solution_path": "data/solutions/generated/squincir_027_24101c6f5ef6d134.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/24101c6f5ef6d134.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@28", "density": 0.8008141779745183, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/28.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.333+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.333, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@28", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.333+", "metric_symbol": "r", "metric_value": 3.333, "reference_text": "r = 3.333+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/28.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.333+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "33c1007b5e868482", "improvement": -0.0030934121555343808, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.8010138785924426e-06, "max_pair_overlap_depth": -3.2305275887267726e-05, "metric_expression": "3.33609", "metric_symbol": "r", "metric_value": 3.3360934121555346, "n": 28, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.333, "setup": "squincir", "side": 6.672186824311069, "solution_path": "data/solutions/generated/squincir_028_33c1007b5e868482.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T03:19:00+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/33c1007b5e868482.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@29", "density": 0.7983676158390189, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/29.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.401+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.401, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@29", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.401+", "metric_symbol": "r", "metric_value": 3.401, "reference_text": "r = 3.401+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/29.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.401+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "ab533ab0ad8e3eeb", "improvement": 0.000657947854124874, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.686355668135576e-06, "max_pair_overlap_depth": -1.5593607360919748e-05, "metric_expression": "3.40034", "metric_symbol": "r", "metric_value": 3.400342052145875, "n": 29, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.401, "setup": "squincir", "side": 6.80068410429175, "solution_path": "data/solutions/generated/squincir_029_ab533ab0ad8e3eeb.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:51:36+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/ab533ab0ad8e3eeb.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@30", "density": 0.7941259454921153, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/30.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.472+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.472, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@30", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.472+", "metric_symbol": "r", "metric_value": 3.472, "reference_text": "r = 3.472+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/30.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.472+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "d6d4b17471528bfa", "improvement": 0.004304153213534612, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2997799895563276e-06, "max_pair_overlap_depth": -1.7959424514213396e-05, "metric_expression": "3.46770", "metric_symbol": "r", "metric_value": 3.4676958467864654, "n": 30, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.472, "setup": "squincir", "side": 6.935391693572931, "solution_path": "data/solutions/generated/squincir_030_d6d4b17471528bfa.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:51:36+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/d6d4b17471528bfa.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@31", "density": 0.7887915525098625, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/31.gif", "friedman_metric_expression": "5 \u221a2 / 2 = 3.535+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.535, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@31", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "5 \u221a2 / 2 = 3.535+", "metric_symbol": "r", "metric_value": 3.535, "reference_text": "r = 5 \u221a2 / 2 = 3.535+ | Found by Erich Friedman | in 1997.", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/31.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 5 \u221a2 / 2 = 3.535+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "fdf9170d30584f4f", "improvement": -0.0019163212872146396, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.62119976746078e-06, "max_pair_overlap_depth": -1.7231292489316985e-05, "metric_expression": "3.53692", "metric_symbol": "r", "metric_value": 3.536916321287215, "n": 31, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.535, "setup": "squincir", "side": 7.07383264257443, "solution_path": "data/solutions/generated/squincir_031_fdf9170d30584f4f.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/fdf9170d30584f4f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@32", "density": 0.7916012707303632, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/32.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.584+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.584, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@32", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.584+", "metric_symbol": "r", "metric_value": 3.584, "reference_text": "r = 3.584+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/32.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.584+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "b8bda371acb2b492", "improvement": -0.0031274839526354015, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.2509087862826505e-06, "max_pair_overlap_depth": -6.52310694349012e-09, "metric_expression": "3.58713", "metric_symbol": "r", "metric_value": 3.5871274839526355, "n": 32, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.584, "setup": "squincir", "side": 7.174254967905271, "solution_path": "data/solutions/generated/squincir_032_b8bda371acb2b492.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/b8bda371acb2b492.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@33", "density": 0.8076634866746639, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/33.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a13 = 3.605+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.605, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@33", "credit": "Maurizio Morandi", "date": "June 2010", "family_updated": "", "metric_expression": "\u221a13 = 3.605+", "metric_symbol": "r", "metric_value": 3.605, "reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in June 2010.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/33.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in June 2010.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "e5a9fc9a4b7235a0", "improvement": -0.0013411620456880158, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.493268955270025e-06, "max_pair_overlap_depth": -1.6481229587750335e-06, "metric_expression": "3.60634", "metric_symbol": "r", "metric_value": 3.606341162045688, "n": 33, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.605, "setup": "squincir", "side": 7.212682324091376, "solution_path": "data/solutions/generated/squincir_033_e5a9fc9a4b7235a0.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/e5a9fc9a4b7235a0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@34", "density": 0.819454861319337, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif", "friedman_metric_expression": "3.629+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.629, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@34", "credit": "Maurizio Morandi", "date": "December 2010", "family_updated": "", "metric_expression": "3.629+", "metric_symbol": "r", "metric_value": 3.629, "reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "9214fdf4034b8f9a", "improvement": -0.005142931467513545, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0151594769247652e-06, "max_pair_overlap_depth": -1.71712946250846e-07, "metric_expression": "3.63414", "metric_symbol": "r", "metric_value": 3.6341429314675135, "n": 34, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.629, "setup": "squincir", "side": 7.268285862935027, "solution_path": "data/solutions/generated/squincir_34_9214fdf4034b8f9a.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T14:34:18+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/9214fdf4034b8f9a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squincir@35", "density": 0.8405414638481816, "friedman_analytical_or_proved": true, "friedman_credit": "David Eppstein", "friedman_date": "March 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/35.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a53 / 2 = 3.640+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.64, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@35", "credit": "David Eppstein", "date": "March 2002", "family_updated": "", "metric_expression": "\u221a53 / 2 = 3.640+", "metric_symbol": "r", "metric_value": 3.64, "reference_text": "r = \u221a53 / 2 = 3.640+ | Found by David Eppstein | in March 2002.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/35.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a53 / 2 = 3.640+ | Found by David Eppstein | in March 2002.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "f2d91d98b4c2ee39", "improvement": -0.0006549082553228835, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.121617296348745e-07, "max_pair_overlap_depth": -2.1344301219083928e-05, "metric_expression": "3.64065", "metric_symbol": "r", "metric_value": 3.640654908255323, "n": 35, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.64, "setup": "squincir", "side": 7.281309816510646, "solution_path": "data/solutions/generated/squincir_035_f2d91d98b4c2ee39.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David Eppstein", "svg_path": "data/svg/f2d91d98b4c2ee39.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@1", "density": 0.499990679660235, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "1-2. | | s = 1 | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "1-2. | | s = 1 | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "557f8de873a17a8e", "improvement": -9.320470070184328e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7525252651882113e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_symbol": "s", "metric_value": 1.0000093204700702, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.0, "setup": "squindom", "side": 2.0000186409401404, "solution_path": "data/solutions/generated/squindom_001_557f8de873a17a8e.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/557f8de873a17a8e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@2", "density": 0.9999882998008334, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "1-2. | | s = 1 | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "1-2. | | s = 1 | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "7684110dce2e5290", "improvement": -5.850150919473052e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.463373909884382e-07, "max_pair_overlap_depth": -9.41881114351023e-06, "metric_expression": "1.00001", "metric_symbol": "s", "metric_value": 1.0000058501509195, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.0, "setup": "squindom", "side": 2.000011700301839, "solution_path": "data/solutions/generated/squindom_002_7684110dce2e5290.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/7684110dce2e5290.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@3", "density": 0.6666417193387711, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/3.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3/2 = 1.5", "friedman_metric_symbol": "s", "friedman_metric_value": 1.5, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3/2 = 1.5", "metric_symbol": "s", "metric_value": 1.5, "reference_text": "3. | | s = 3/2 = 1.5 | Trivial. |", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/3.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "3. | | s = 3/2 = 1.5 | Trivial. |", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "3047ca63de76a853", "improvement": -2.8066531593262667e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.0617527398680835e-06, "max_pair_overlap_depth": -1.9554412996725112e-05, "metric_expression": "1.50003", "metric_symbol": "s", "metric_value": 1.5000280665315933, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.5, "setup": "squindom", "side": 3.0000561330631865, "solution_path": "data/solutions/generated/squindom_003_3047ca63de76a853.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/3047ca63de76a853.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@4", "density": 0.5367260778952853, "friedman_analytical_or_proved": false, "friedman_credit": "Evert Stenlund", "friedman_date": "June 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/4.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "1.930+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.93, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@4", "credit": "Evert Stenlund", "date": "June 2010", "family_updated": "", "metric_expression": "1.930+", "metric_symbol": "s", "metric_value": 1.93, "reference_text": "4. | | s = 1.930+ | Found by Evert Stenlund | in June 2010.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/4.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "4. | | s = 1.930+ | Found by Evert Stenlund | in June 2010.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "8d067d60c7138964", "improvement": -0.00036150970269521743, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.561542731343124e-06, "max_pair_overlap_depth": -3.757775137364083e-05, "metric_expression": "1.93036", "metric_symbol": "s", "metric_value": 1.9303615097026952, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.93, "setup": "squindom", "side": 3.8607230194053903, "solution_path": "data/solutions/generated/squindom_004_8d067d60c7138964.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Evert Stenlund", "svg_path": "data/svg/8d067d60c7138964.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@5", "density": 0.6249853765160349, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "5-8. | | s = 2 | Trivial. |", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "5-8. | | s = 2 | Trivial. |", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "05f6000ecc64a077", "improvement": -2.3397984937112426e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3736510935966635e-06, "max_pair_overlap_depth": -1.2206465427119814e-05, "metric_expression": "2.00002", "metric_symbol": "s", "metric_value": 2.000023397984937, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "squindom", "side": 4.000046795969874, "solution_path": "data/solutions/generated/squindom_005_05f6000ecc64a077.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/05f6000ecc64a077.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@6", "density": 0.749983975114432, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@6", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "5-8. | | s = 2 | Trivial. |", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "5-8. | | s = 2 | Trivial. |", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "095d951ace7a918a", "improvement": -2.136685649301029e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.707507375492412e-07, "max_pair_overlap_depth": -1.170836956105551e-05, "metric_expression": "2.00002", "metric_symbol": "s", "metric_value": 2.000021366856493, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "squindom", "side": 4.000042733712986, "solution_path": "data/solutions/generated/squindom_006_095d951ace7a918a.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/095d951ace7a918a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@7", "density": 0.8749639011598754, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@7", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "5-8. | | s = 2 | Trivial. |", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "5-8. | | s = 2 | Trivial. |", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "50aa0817a0117c40", "improvement": -4.1257093861268856e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4800520663781356e-06, "max_pair_overlap_depth": -1.885899157594295e-05, "metric_expression": "2.00004", "metric_symbol": "s", "metric_value": 2.0000412570938613, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "squindom", "side": 4.0000825141877225, "solution_path": "data/solutions/generated/squindom_007_50aa0817a0117c40.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/50aa0817a0117c40.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@8", "density": 0.9999722279382355, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@8", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "5-8. | | s = 2 | Trivial. |", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "5-8. | | s = 2 | Trivial. |", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "0b83841ee591689c", "improvement": -2.7772640243561852e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.0495464614356251e-07, "max_pair_overlap_depth": -1.777420024382249e-07, "metric_expression": "2.00003", "metric_symbol": "s", "metric_value": 2.0000277726402436, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "squindom", "side": 4.000055545280487, "solution_path": "data/solutions/generated/squindom_008_0b83841ee591689c.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/0b83841ee591689c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@9", "density": 0.7367411181657051, "friedman_analytical_or_proved": true, "friedman_credit": "Evert Stenlund", "friedman_date": "June 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/9.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "2 + \u221a2/3 = 2.471+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.471, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@9", "credit": "Evert Stenlund", "date": "June 2010", "family_updated": "", "metric_expression": "2 + \u221a2/3 = 2.471+", "metric_symbol": "s", "metric_value": 2.471, "reference_text": "9. | | s = 2 + \u221a2/3 = 2.471+ | Found by Evert Stenlund | in June 2010.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/9.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "9. | | s = 2 + \u221a2/3 = 2.471+ | Found by Evert Stenlund | in June 2010.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "2963ae62200cf2c5", "improvement": -0.000432778719658522, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.8492494266174617e-06, "max_pair_overlap_depth": -7.2416104319739105e-06, "metric_expression": "2.47143", "metric_symbol": "s", "metric_value": 2.4714327787196586, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.471, "setup": "squindom", "side": 4.942865557439317, "solution_path": "data/solutions/generated/squindom_009_2963ae62200cf2c5.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Evert Stenlund", "svg_path": "data/svg/2963ae62200cf2c5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@10", "density": 0.7999865137938963, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/10.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "5/2 = 2.5", "friedman_metric_symbol": "s", "friedman_metric_value": 2.5, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@10", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5/2 = 2.5", "metric_symbol": "s", "metric_value": 2.5, "reference_text": "10. | | s = 5/2 = 2.5 | Trivial. |", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/10.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "10. | | s = 5/2 = 2.5 | Trivial. |", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "7d3cb25d7577069f", "improvement": -2.1072463463500668e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5655128748903735e-06, "max_pair_overlap_depth": -9.554543500822632e-07, "metric_expression": "2.50002", "metric_symbol": "s", "metric_value": 2.5000210724634635, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.5, "setup": "squindom", "side": 5.000042144926927, "solution_path": "data/solutions/generated/squindom_010_7d3cb25d7577069f.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/7d3cb25d7577069f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@11", "density": 0.7109112928838592, "friedman_analytical_or_proved": false, "friedman_credit": "Evert Stenlund", "friedman_date": "June 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/11.gif", "friedman_metric_expression": "2.779+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.779, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@11", "credit": "Evert Stenlund", "date": "June 2010", "family_updated": "", "metric_expression": "2.779+", "metric_symbol": "s", "metric_value": 2.779, "reference_text": "11. | | s = 2.779+ | Found by Evert Stenlund | in June 2010. |", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/11.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "11. | | s = 2.779+ | Found by Evert Stenlund | in June 2010. |", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "eadb11fb534aa6a1", "improvement": -0.0024652481713771657, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.886034921991467e-06, "max_pair_overlap_depth": -3.432035104045106e-05, "metric_expression": "2.78147", "metric_symbol": "s", "metric_value": 2.781465248171377, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.779, "setup": "squindom", "side": 5.562930496342754, "solution_path": "data/solutions/generated/squindom_11_eadb11fb534aa6a1.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T07:13:53+00:00", "submitted_by": "Evert Stenlund", "svg_path": "data/svg/eadb11fb534aa6a1.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@12", "density": 0.7147860825866693, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/12.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "6 (1 + \u221a2) / 5 = 2.897+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.897, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@12", "credit": "Maurizio Morandi", "date": "June 2010", "family_updated": "", "metric_expression": "6 (1 + \u221a2) / 5 = 2.897+", "metric_symbol": "s", "metric_value": 2.897, "reference_text": "12. | | s = 6 (1 + \u221a2) / 5 = 2.897+ | Found by Maurizio Morandi | in June 2010. |", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/12.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "12. | | s = 6 (1 + \u221a2) / 5 = 2.897+ | Found by Maurizio Morandi | in June 2010. |", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "4c82fd3f736a139f", "improvement": -0.0002607386911455123, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.382389093311346e-06, "max_pair_overlap_depth": -2.837543626332817e-05, "metric_expression": "2.89726", "metric_symbol": "s", "metric_value": 2.8972607386911453, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.897, "setup": "squindom", "side": 5.794521477382291, "solution_path": "data/solutions/generated/squindom_012_4c82fd3f736a139f.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/4c82fd3f736a139f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@13", "density": 0.7330751854461901, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/13.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "2.976+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.976, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@13", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "2.976+", "metric_symbol": "s", "metric_value": 2.976, "reference_text": "13. | | s = 2.976+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/13.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "13. | | s = 2.976+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d738dfc349a8c940", "improvement": -0.0017101333567786092, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.7694174018241284e-06, "max_pair_overlap_depth": -2.048132261660285e-05, "metric_expression": "2.97771", "metric_symbol": "s", "metric_value": 2.9777101333567786, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.976, "setup": "squindom", "side": 5.955420266713557, "solution_path": "data/solutions/generated/squindom_013_d738dfc349a8c940.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d738dfc349a8c940.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@14", "density": 0.7777474504876777, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@14", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "14-18. | | s = 3 | Trivial. |", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "14-18. | | s = 3 | Trivial. |", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "167b47d5e39e076d", "improvement": -5.849005569213972e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0369016045785884e-06, "max_pair_overlap_depth": -1.5707310774493166e-05, "metric_expression": "3.00006", "metric_symbol": "s", "metric_value": 3.000058490055692, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.0, "setup": "squindom", "side": 6.000116980111384, "solution_path": "data/solutions/generated/squindom_014_167b47d5e39e076d.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/167b47d5e39e076d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@15", "density": 0.8333077568349537, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@15", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "14-18. | | s = 3 | Trivial. |", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "14-18. | | s = 3 | Trivial. |", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "6d686963e9ef0ece", "improvement": -4.603875684550118e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0382270816400307e-06, "max_pair_overlap_depth": -3.605764309855264e-06, "metric_expression": "3.00005", "metric_symbol": "s", "metric_value": 3.0000460387568455, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.0, "setup": "squindom", "side": 6.000092077513691, "solution_path": "data/solutions/generated/squindom_015_6d686963e9ef0ece.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/6d686963e9ef0ece.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@16", "density": 0.888839182217615, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@16", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "14-18. | | s = 3 | Trivial. |", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "14-18. | | s = 3 | Trivial. |", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "0f551306e71d2ff0", "improvement": -8.388352586674586e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4593433725073055e-06, "max_pair_overlap_depth": -5.7555123290642385e-06, "metric_expression": "3.00008", "metric_symbol": "s", "metric_value": 3.0000838835258667, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.0, "setup": "squindom", "side": 6.0001677670517335, "solution_path": "data/solutions/generated/squindom_016_0f551306e71d2ff0.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/0f551306e71d2ff0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@17", "density": 0.9444002665800334, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@17", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "14-18. | | s = 3 | Trivial. |", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "14-18. | | s = 3 | Trivial. |", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "52c5d2070c49c79c", "improvement": -7.016730512532376e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.650126292496168e-06, "max_pair_overlap_depth": -3.2807804517531736e-07, "metric_expression": "3.00007", "metric_symbol": "s", "metric_value": 3.0000701673051253, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.0, "setup": "squindom", "side": 6.000140334610251, "solution_path": "data/solutions/generated/squindom_017_52c5d2070c49c79c.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/52c5d2070c49c79c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@18", "density": 0.9999599238999353, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@18", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "14-18. | | s = 3 | Trivial. |", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "14-18. | | s = 3 | Trivial. |", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "a6900e1fd3f925c6", "improvement": -6.011595701327366e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.408701424045262e-07, "max_pair_overlap_depth": -1.079909316636929e-06, "metric_expression": "3.00006", "metric_symbol": "s", "metric_value": 3.0000601159570133, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.0, "setup": "squindom", "side": 6.0001202319140265, "solution_path": "data/solutions/generated/squindom_018_a6900e1fd3f925c6.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/a6900e1fd3f925c6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@19", "density": 0.7988013748197259, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/19.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3 + 1/\u221a5 = 3.447+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.447, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@19", "credit": "Maurizio Morandi", "date": "June 2010", "family_updated": "", "metric_expression": "3 + 1/\u221a5 = 3.447+", "metric_symbol": "s", "metric_value": 3.447, "reference_text": "19. | | s = 3 + 1/\u221a5 = 3.447+ | Found by Maurizio Morandi | in June 2010.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/19.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "19. | | s = 3 + 1/\u221a5 = 3.447+ | Found by Maurizio Morandi | in June 2010.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "cddf920bff527727", "improvement": -0.0015966406761447338, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.98512899937964e-06, "max_pair_overlap_depth": -1.3782300862574814e-05, "metric_expression": "3.44860", "metric_symbol": "s", "metric_value": 3.448596640676145, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.447, "setup": "squindom", "side": 6.89719328135229, "solution_path": "data/solutions/generated/squindom_019_cddf920bff527727.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/cddf920bff527727.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@20", "density": 0.8162860196976518, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "7/2 = 3.5", "friedman_metric_symbol": "s", "friedman_metric_value": 3.5, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@20", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "7/2 = 3.5", "metric_symbol": "s", "metric_value": 3.5, "reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "4a48c58d60a1f36b", "improvement": -8.6848505622239e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.863306484192975e-06, "max_pair_overlap_depth": -2.3696014737728532e-05, "metric_expression": "3.50009", "metric_symbol": "s", "metric_value": 3.5000868485056222, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.5, "setup": "squindom", "side": 7.0001736970112445, "solution_path": "data/solutions/generated/squindom_020_4a48c58d60a1f36b.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4a48c58d60a1f36b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@21", "density": 0.8571139620178546, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "friedman_metric_expression": "7/2 = 3.5", "friedman_metric_symbol": "s", "friedman_metric_value": 3.5, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@21", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "7/2 = 3.5", "metric_symbol": "s", "metric_value": 3.5, "reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "f91a28177536f6d3", "improvement": -5.899570515355279e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8534056853702905e-06, "max_pair_overlap_depth": -1.3464050134803784e-06, "metric_expression": "3.50006", "metric_symbol": "s", "metric_value": 3.5000589957051536, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.5, "setup": "squindom", "side": 7.000117991410307, "solution_path": "data/solutions/generated/squindom_021_f91a28177536f6d3.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/f91a28177536f6d3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@22", "density": 0.783535190077589, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/22.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3.745+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.745, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@22", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "3.745+", "metric_symbol": "s", "metric_value": 3.745, "reference_text": "22. | | s = 3.745+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/22.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "22. | | s = 3.745+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d2d5380917cfe7ce", "improvement": -0.0018567500999222553, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.72695736733975e-06, "max_pair_overlap_depth": -9.08031145729904e-06, "metric_expression": "3.74686", "metric_symbol": "s", "metric_value": 3.7468567500999224, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.745, "setup": "squindom", "side": 7.493713500199845, "solution_path": "data/solutions/generated/squindom_022_d2d5380917cfe7ce.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d2d5380917cfe7ce.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@23", "density": 0.7750857674093591, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/23.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3.849+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.849, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@23", "credit": "Maurizio Morandi", "date": "June 2010", "family_updated": "", "metric_expression": "3.849+", "metric_symbol": "s", "metric_value": 3.849, "reference_text": "23. | | s = 3.849+ | Found by Maurizio Morandi | in June 2010. |", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/23.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "23. | | s = 3.849+ | Found by Maurizio Morandi | in June 2010. |", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d12d3a9a87ba3b11", "improvement": -0.002891443742406352, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.707858897694649e-06, "max_pair_overlap_depth": -2.3445235071584136e-05, "metric_expression": "3.85189", "metric_symbol": "s", "metric_value": 3.8518914437424066, "n": 23, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.849, "setup": "squindom", "side": 7.703782887484813, "solution_path": "data/solutions/generated/squindom_023_d12d3a9a87ba3b11.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/d12d3a9a87ba3b11.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@24", "density": 0.7961447064751783, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell after Maurizio Morandi", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/24.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3.882+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.882, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@24", "credit": "David W. Cantrell after Maurizio Morandi", "date": "August 2012", "family_updated": "", "metric_expression": "3.882+", "metric_symbol": "s", "metric_value": 3.882, "reference_text": "24. | | s = 3.882+ | Found by DC after MM | in August 2012. |", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/24.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "24. | | s = 3.882+ | Found by DC after MM | in August 2012. |", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "f954e5304808181f", "improvement": -0.0003493916461954072, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7445287290307476e-06, "max_pair_overlap_depth": -1.9183513864096113e-05, "metric_expression": "3.88235", "metric_symbol": "s", "metric_value": 3.8823493916461955, "n": 24, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.882, "setup": "squindom", "side": 7.764698783292391, "solution_path": "data/solutions/generated/squindom_024_f954e5304808181f.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "David W. Cantrell after Maurizio Morandi", "svg_path": "data/svg/f954e5304808181f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@25", "density": 0.8043920132931294, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell after Maurizio Morandi", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/25.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3.939+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.939, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@25", "credit": "David W. Cantrell after Maurizio Morandi", "date": "August 2012", "family_updated": "", "metric_expression": "3.939+", "metric_symbol": "s", "metric_value": 3.939, "reference_text": "25. | | s = 3.939+ | Found by DC after MM | in August 2012. |", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/25.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "25. | | s = 3.939+ | Found by DC after MM | in August 2012. |", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "26273cb13b41bf72", "improvement": -0.003040951197706754, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.269696070480222e-06, "max_pair_overlap_depth": -2.5070959039568547e-05, "metric_expression": "3.94204", "metric_symbol": "s", "metric_value": 3.942040951197707, "n": 25, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.939, "setup": "squindom", "side": 7.884081902395414, "solution_path": "data/solutions/generated/squindom_025_26273cb13b41bf72.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "David W. Cantrell after Maurizio Morandi", "svg_path": "data/svg/26273cb13b41bf72.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@26", "density": 0.8201428647660397, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/26.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3.981+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.981, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@26", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "3.981+", "metric_symbol": "s", "metric_value": 3.981, "reference_text": "26. | | s = 3.981+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in July 2012.)", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/26.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "26. | | s = 3.981+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in July 2012.)", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "a46204eea3d7f9fe", "improvement": -0.00031848875831208545, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.947984543621445e-06, "max_pair_overlap_depth": -8.516034391559124e-06, "metric_expression": "3.98132", "metric_symbol": "s", "metric_value": 3.981318488758312, "n": 26, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.981, "setup": "squindom", "side": 7.962636977516624, "solution_path": "data/solutions/generated/squindom_026_a46204eea3d7f9fe.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/a46204eea3d7f9fe.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@27", "density": 0.8436994977206457, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@27", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "c68e03cc8f5005db", "improvement": -0.00011971448073744284, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.175631390130775e-07, "max_pair_overlap_depth": -1.4466911184563003e-06, "metric_expression": "4.00012", "metric_symbol": "s", "metric_value": 4.000119714480737, "n": 27, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.000239428961475, "solution_path": "data/solutions/generated/squindom_027_c68e03cc8f5005db.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/c68e03cc8f5005db.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@28", "density": 0.8749068629130922, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@28", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "2c8c79126d60cdac", "improvement": -0.00021290176655508475, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.243746303256302e-06, "max_pair_overlap_depth": -1.6386799395987463e-05, "metric_expression": "4.00021", "metric_symbol": "s", "metric_value": 4.000212901766555, "n": 28, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.00042580353311, "solution_path": "data/solutions/generated/squindom_028_2c8c79126d60cdac.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/2c8c79126d60cdac.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@29", "density": 0.9062096331295707, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@29", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d2548471aff7d9f5", "improvement": -8.908848335043018e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.8156140130519702e-06, "max_pair_overlap_depth": -2.026030487822794e-06, "metric_expression": "4.00009", "metric_symbol": "s", "metric_value": 4.00008908848335, "n": 29, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.0001781769667, "solution_path": "data/solutions/generated/squindom_029_d2548471aff7d9f5.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d2548471aff7d9f5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@30", "density": 0.9374597146255952, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@30", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d67a491f7b4498c0", "improvement": -8.594490193214455e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.188605266186585e-06, "max_pair_overlap_depth": -1.644068809536492e-06, "metric_expression": "4.00009", "metric_symbol": "s", "metric_value": 4.000085944901932, "n": 30, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.000171889803864, "solution_path": "data/solutions/generated/squindom_030_d67a491f7b4498c0.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d67a491f7b4498c0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@31", "density": 0.9683879031627185, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@31", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "86ec622f54cecf7c", "improvement": -0.000747764390431449, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.872732694063188e-07, "max_pair_overlap_depth": -2.9208615389531944e-06, "metric_expression": "4.00075", "metric_symbol": "s", "metric_value": 4.0007477643904314, "n": 31, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.001495528780863, "solution_path": "data/solutions/generated/squindom_031_86ec622f54cecf7c.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/86ec622f54cecf7c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@32", "density": 0.9989694769831047, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@32", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "2873ac78de186b97", "improvement": -0.0020626403695489515, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0386280700511747e-06, "max_pair_overlap_depth": -2.476940408779882e-06, "metric_expression": "4.00206", "metric_symbol": "s", "metric_value": 4.002062640369549, "n": 32, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.004125280739098, "solution_path": "data/solutions/generated/squindom_032_2873ac78de186b97.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/2873ac78de186b97.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@33", "density": 0.8455857799388354, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/33.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3 + \u221a2 = 4.414+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.414, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@33", "credit": "Maurizio Morandi", "date": "July 2012", "family_updated": "", "metric_expression": "3 + \u221a2 = 4.414+", "metric_symbol": "s", "metric_value": 4.414, "reference_text": "33. | | s = 3 + \u221a2 = 4.414+ | Found by Maurizio Morandi | in July 2012.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/33.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "33. | | s = 3 + \u221a2 = 4.414+ | Found by Maurizio Morandi | in July 2012.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "167e5e2a52e9b5fe", "improvement": -0.00336348277204479, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.856211927670387e-06, "max_pair_overlap_depth": -6.591285420576298e-06, "metric_expression": "4.41736", "metric_symbol": "s", "metric_value": 4.4173634827720445, "n": 33, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.414, "setup": "squindom", "side": 8.834726965544089, "solution_path": "data/solutions/generated/squindom_033_167e5e2a52e9b5fe.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/167e5e2a52e9b5fe.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@34", "density": 0.8499062715939519, "friedman_analytical_or_proved": true, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/34.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "4 + \u221a2/3 = 4.471+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.471, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@34", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "4 + \u221a2/3 = 4.471+", "metric_symbol": "s", "metric_value": 4.471, "reference_text": "34. | | s = 4 + \u221a2/3 = 4.471+ | Found by David W. Cantrell | in July 2012.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/34.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "34. | | s = 4 + \u221a2/3 = 4.471+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "b631e5a58c1517e1", "improvement": -0.0013825437310881483, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.603876101403557e-07, "max_pair_overlap_depth": -3.616786977911346e-06, "metric_expression": "4.47238", "metric_symbol": "s", "metric_value": 4.472382543731088, "n": 34, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.471, "setup": "squindom", "side": 8.944765087462176, "solution_path": "data/solutions/generated/squindom_034_b631e5a58c1517e1.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/b631e5a58c1517e1.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@35", "density": 0.8625827503428114, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "9/2 = 4.5", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@35", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "9/2 = 4.5", "metric_symbol": "s", "metric_value": 4.5, "reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "dcd4cfae3ff101a2", "improvement": -0.004210097373901434, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9606355010637344e-06, "max_pair_overlap_depth": -1.1537592481902781e-05, "metric_expression": "4.50421", "metric_symbol": "s", "metric_value": 4.504210097373901, "n": 35, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.5, "setup": "squindom", "side": 9.008420194747803, "solution_path": "data/solutions/generated/squindom_035_dcd4cfae3ff101a2.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/dcd4cfae3ff101a2.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@36", "density": 0.8873457711540725, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "9/2 = 4.5", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@36", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "9/2 = 4.5", "metric_symbol": "s", "metric_value": 4.5, "reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "e0fc61bd01777ea3", "improvement": -0.003911109790387002, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.310647293148122e-07, "max_pair_overlap_depth": -3.943598063660403e-06, "metric_expression": "4.50391", "metric_symbol": "s", "metric_value": 4.503911109790387, "n": 36, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.5, "setup": "squindom", "side": 9.007822219580774, "solution_path": "data/solutions/generated/squindom_036_e0fc61bd01777ea3.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/e0fc61bd01777ea3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@37", "density": 0.8199742411033116, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/37.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "10 / 3 + \u221a2 = 4.747+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.747, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@37", "credit": "Maurizio Morandi", "date": "August 2012", "family_updated": "", "metric_expression": "10 / 3 + \u221a2 = 4.747+", "metric_symbol": "s", "metric_value": 4.747, "reference_text": "37. | | s = 10 / 3 + \u221a2 = 4.747+ | Found by Maurizio Morandi | in August 2012.", "source_image": "37.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/37.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "37. | | s = 10 / 3 + \u221a2 = 4.747+ | Found by Maurizio Morandi | in August 2012.", "friedman_source_image": "37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "09a846134d0a3602", "improvement": -0.0029141409565269782, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.702594714522945e-06, "max_pair_overlap_depth": -1.6080659807293785e-05, "metric_expression": "4.74991", "metric_symbol": "s", "metric_value": 4.749914140956527, "n": 37, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.747, "setup": "squindom", "side": 9.499828281913054, "solution_path": "data/solutions/generated/squindom_037_09a846134d0a3602.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/09a846134d0a3602.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@38", "density": 0.8220103806251009, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/38.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "(13 + \u221a2) / 3 = 4.804+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.804, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@38", "credit": "Maurizio Morandi", "date": "August 2012", "family_updated": "", "metric_expression": "(13 + \u221a2) / 3 = 4.804+", "metric_symbol": "s", "metric_value": 4.804, "reference_text": "38. | | s = (13 + \u221a2) / 3 = 4.804+ | Found by Maurizio Morandi | in August 2012.", "source_image": "38.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/38.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "38. | | s = (13 + \u221a2) / 3 = 4.804+ | Found by Maurizio Morandi | in August 2012.", "friedman_source_image": "38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d4d1cf6ab169d8aa", "improvement": -0.0037087406838747228, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.518216488058613e-06, "max_pair_overlap_depth": -2.290026661011524e-05, "metric_expression": "4.80771", "metric_symbol": "s", "metric_value": 4.807708740683875, "n": 38, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.804, "setup": "squindom", "side": 9.61541748136775, "solution_path": "data/solutions/generated/squindom_038_d4d1cf6ab169d8aa.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/d4d1cf6ab169d8aa.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@39", "density": 0.8326335013079162, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/39.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "4.839+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.839, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@39", "credit": "David W. Cantrell", "date": "August 2012", "family_updated": "", "metric_expression": "4.839+", "metric_symbol": "s", "metric_value": 4.839, "reference_text": "39. | | s = 4.839+ | Found by David W. Cantrell | in August 2012.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/39.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "39. | | s = 4.839+ | Found by David W. Cantrell | in August 2012.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "a606e4f52500fa01", "improvement": -0.00038713064593576263, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.790990827618913e-06, "max_pair_overlap_depth": -1.236762303413741e-05, "metric_expression": "4.83939", "metric_symbol": "s", "metric_value": 4.839387130645936, "n": 39, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.839, "setup": "squindom", "side": 9.678774261291872, "solution_path": "data/solutions/generated/squindom_039_a606e4f52500fa01.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/a606e4f52500fa01.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@40", "density": 0.8345719865483486, "friedman_analytical_or_proved": false, "friedman_credit": "Sigvart Brendberg", "friedman_date": "June 2023", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/40.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "4.895+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.895, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@40", "credit": "Sigvart Brendberg", "date": "June 2023", "family_updated": "", "metric_expression": "4.895+", "metric_symbol": "s", "metric_value": 4.895, "reference_text": "40. | | s = 4.895+ | Found by Sigvart Brendberg | in June 2023.", "source_image": "40.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/40.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "40. | | s = 4.895+ | Found by Sigvart Brendberg | in June 2023.", "friedman_source_image": "40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "bb2811be04efb5ee", "improvement": -0.0003426573425642232, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.37233266706005e-06, "max_pair_overlap_depth": -3.9677918853286975e-06, "metric_expression": "4.89534", "metric_symbol": "s", "metric_value": 4.895342657342564, "n": 40, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.895, "setup": "squindom", "side": 9.790685314685128, "solution_path": "data/solutions/generated/squindom_040_bb2811be04efb5ee.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Sigvart Brendberg", "svg_path": "data/svg/bb2811be04efb5ee.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@41", "density": 0.8199798328031639, "friedman_analytical_or_proved": false, "friedman_credit": "Sigvart Brendberg", "friedman_date": "June 2023", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif", "friedman_metric_expression": "4.927+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.927, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@41", "credit": "Sigvart Brendberg", "date": "June 2023", "family_updated": "", "metric_expression": "4.927+", "metric_symbol": "s", "metric_value": 4.927, "reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.", "source_image": "41.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.", "friedman_source_image": "41.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "cb1462995bd3b2c0", "improvement": -0.07306148649036626, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.465020711057036e-07, "max_pair_overlap_depth": -6.131910444850952e-06, "metric_expression": "5.00006", "metric_symbol": "s", "metric_value": 5.000061486490366, "n": 41, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.927, "setup": "squindom", "side": 10.000122972980732, "solution_path": "data/solutions/generated/squindom_41_cb1462995bd3b2c0.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T13:47:12+00:00", "submitted_by": "Sigvart Brendberg", "svg_path": "data/svg/cb1462995bd3b2c0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@42", "density": 0.8472590848618945, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/42.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "4.989+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.989, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@42", "credit": "David W. Cantrell", "date": "August 2012", "family_updated": "", "metric_expression": "4.989+", "metric_symbol": "s", "metric_value": 4.989, "reference_text": "42. | | s = 4.989+ | Found by David W. Cantrell | in August 2012.", "source_image": "42.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/42.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "42. | | s = 4.989+ | Found by David W. Cantrell | in August 2012.", "friedman_source_image": "42.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": false, "id": "7faea8ae450b67a1", "improvement": 0.010465394774865189, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.54667148005916e-06, "max_pair_overlap_depth": -1.5216861767419765e-05, "metric_expression": "4.97853", "metric_symbol": "s", "metric_value": 4.978534605225135, "n": 42, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.", "record_type": "verified", "reference_side": 4.989, "setup": "squindom", "side": 9.95706921045027, "solution_path": "data/solutions/generated/squindom_042_7faea8ae450b67a1.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/7faea8ae450b67a1.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@43", "density": 0.859888117316887, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@43", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "7f9527ccddc9d648", "improvement": -0.00032527209571497906, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.1461540806485566e-08, "max_pair_overlap_depth": -2.005039219099558e-06, "metric_expression": "5.00033", "metric_symbol": "s", "metric_value": 5.000325272095715, "n": 43, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.00065054419143, "solution_path": "data/solutions/generated/squindom_043_7f9527ccddc9d648.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/7f9527ccddc9d648.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@44", "density": 0.8799631966546829, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@44", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "1ffd758f1f058de5", "improvement": -0.00010455823792376862, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.245467354557775e-06, "max_pair_overlap_depth": -3.962242465904708e-06, "metric_expression": "5.00010", "metric_symbol": "s", "metric_value": 5.000104558237924, "n": 44, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000209116475848, "solution_path": "data/solutions/generated/squindom_044_1ffd758f1f058de5.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/1ffd758f1f058de5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@45", "density": 0.8999501217119913, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@45", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d085ed9682ca2968", "improvement": -0.00013855655918781906, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0485935568738114e-06, "max_pair_overlap_depth": -1.361329106774889e-06, "metric_expression": "5.00014", "metric_symbol": "s", "metric_value": 5.000138556559188, "n": 45, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000277113118376, "solution_path": "data/solutions/generated/squindom_045_d085ed9682ca2968.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d085ed9682ca2968.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@46", "density": 0.9198953665582859, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@46", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "3b408e84cd206068", "improvement": -0.00028435426002282327, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1757865436834436e-06, "max_pair_overlap_depth": -7.423155479191479e-07, "metric_expression": "5.00028", "metric_symbol": "s", "metric_value": 5.000284354260023, "n": 46, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000568708520046, "solution_path": "data/solutions/generated/squindom_046_3b408e84cd206068.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/3b408e84cd206068.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@47", "density": 0.9398436614252309, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@47", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "2525e331a392c6b9", "improvement": -0.00041584595443833194, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3105818880431173e-06, "max_pair_overlap_depth": -3.7244704524930228e-06, "metric_expression": "5.00042", "metric_symbol": "s", "metric_value": 5.000415845954438, "n": 47, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000831691908877, "solution_path": "data/solutions/generated/squindom_047_2525e331a392c6b9.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/2525e331a392c6b9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@48", "density": 0.9599518570950978, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@48", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "0433c6294c4f3fe7", "improvement": -0.00012537686383318203, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0555756748686917e-06, "max_pair_overlap_depth": -4.3576353303542703e-07, "metric_expression": "5.00013", "metric_symbol": "s", "metric_value": 5.000125376863833, "n": 48, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000250753727666, "solution_path": "data/solutions/generated/squindom_048_0433c6294c4f3fe7.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/0433c6294c4f3fe7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@49", "density": 0.9798599360041962, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@49", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "c84a987ae840ebe3", "improvement": -0.0003573444166047324, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.316744310450815e-06, "max_pair_overlap_depth": -1.1644813818767474e-06, "metric_expression": "5.00036", "metric_symbol": "s", "metric_value": 5.000357344416605, "n": 49, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.00071468883321, "solution_path": "data/solutions/generated/squindom_049_c84a987ae840ebe3.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/c84a987ae840ebe3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squindom@50", "density": 0.9999308512263965, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@50", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "df0259815cc5320a", "improvement": -0.00017288089993794387, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.912590304139712e-09, "max_pair_overlap_depth": -7.234911549747203e-06, "metric_expression": "5.00017", "metric_symbol": "s", "metric_value": 5.000172880899938, "n": 50, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000345761799876, "solution_path": "data/solutions/generated/squindom_050_df0259815cc5320a.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/df0259815cc5320a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@1", "density": 0.6187919623349352, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/1.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(3+\u221a3)/6 = 0.778+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.778, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "(3+\u221a3)/6 = 0.778+", "metric_symbol": "s", "metric_value": 0.778, "reference_text": "s = (3+\u221a3)/6 = 0.778+ | Trivial. |", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/1.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = (3+\u221a3)/6 = 0.778+ | Trivial. |", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "7a4ae27d520be7d9", "improvement": -0.01068162910289272, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.500249687614274e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.78868", "metric_symbol": "s", "metric_value": 0.7886816291028927, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.778, "setup": "squinhex", "side": 0.7886816291028927, "solution_path": "data/solutions/generated/squinhex_001_7a4ae27d520be7d9.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T03:07:58+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/7a4ae27d520be7d9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@2", "density": 0.5773349997096187, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/2.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2/\u221a3 = 1.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.154, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2/\u221a3 = 1.154+", "metric_symbol": "s", "metric_value": 1.154, "reference_text": "s = 2/\u221a3 = 1.154+ | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/2.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2/\u221a3 = 1.154+ | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "21fb35b9b51e59c5", "improvement": -0.0007158081621452261, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.964730208767781e-07, "max_pair_overlap_depth": -4.154668371614267e-06, "metric_expression": "1.15472", "metric_symbol": "s", "metric_value": 1.1547158081621451, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.154, "setup": "squinhex", "side": 1.1547158081621451, "solution_path": "data/solutions/generated/squinhex_002_21fb35b9b51e59c5.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/21fb35b9b51e59c5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@3", "density": 0.6187647598988664, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/3.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(1+\u221a3)/2 = 1.366+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.366, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@3", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "(1+\u221a3)/2 = 1.366+", "metric_symbol": "s", "metric_value": 1.366, "reference_text": "s = (1+\u221a3)/2 = 1.366+ | Found by Maurizio Morandi | in March 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/3.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = (1+\u221a3)/2 = 1.366+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "a5c3dc7083e49634", "improvement": -6.667945486871218e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5592677317674368e-06, "max_pair_overlap_depth": -3.548280330942233e-05, "metric_expression": "1.36607", "metric_symbol": "s", "metric_value": 1.3660666794548688, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.366, "setup": "squinhex", "side": 1.3660666794548688, "solution_path": "data/solutions/generated/squinhex_003_a5c3dc7083e49634.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/a5c3dc7083e49634.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@4", "density": 0.6666229789487077, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/4.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2/3 1/4 = 1.519+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.519, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@4", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "2/3 1/4 = 1.519+", "metric_symbol": "s", "metric_value": 1.519, "reference_text": "s = 2/3 1/4 = 1.519+ | Found by Maurizio Morandi | in March 2026.", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/4.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2/3 1/4 = 1.519+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "49c10fcc6144044b", "improvement": -0.0007211669812854371, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.944520361455586e-06, "max_pair_overlap_depth": -3.91225282254104e-05, "metric_expression": "1.51972", "metric_symbol": "s", "metric_value": 1.5197211669812853, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.519, "setup": "squinhex", "side": 1.5197211669812853, "solution_path": "data/solutions/generated/squinhex_004_49c10fcc6144044b.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/49c10fcc6144044b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@5", "density": 0.6414868196410884, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/5.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a3 = 1.732+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.732, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a3 = 1.732+", "metric_symbol": "s", "metric_value": 1.732, "reference_text": "s = \u221a3 = 1.732+ | Trivial. |", "source_image": "5.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/5.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = \u221a3 = 1.732+ | Trivial. |", "friedman_source_image": "5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "1d1f44767245ecd6", "improvement": -6.900512462770791e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.1790980134561805e-06, "max_pair_overlap_depth": -6.972508607594463e-06, "metric_expression": "1.73207", "metric_symbol": "s", "metric_value": 1.7320690051246277, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.732, "setup": "squinhex", "side": 1.7320690051246277, "solution_path": "data/solutions/generated/squinhex_005_1d1f44767245ecd6.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/1d1f44767245ecd6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@6", "density": 0.6953530967749227, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/6.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.821+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.821, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@6", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "1.821+", "metric_symbol": "s", "metric_value": 1.821, "reference_text": "s = 1.821+ | Found by Maurizio Morandi | in March 2026.", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/6.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 1.821+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "974baf9dad527270", "improvement": -0.001413758154348077, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6930873179275063e-06, "max_pair_overlap_depth": -8.425702388847878e-06, "metric_expression": "1.82241", "metric_symbol": "s", "metric_value": 1.822413758154348, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.821, "setup": "squinhex", "side": 1.822413758154348, "solution_path": "data/solutions/generated/squinhex_006_974baf9dad527270.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/974baf9dad527270.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@7", "density": 0.777727236784812, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/7.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(\u221a2)3 1/4 = 1.861+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.861, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@7", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "(\u221a2)3 1/4 = 1.861+", "metric_symbol": "s", "metric_value": 1.861, "reference_text": "s = (\u221a2)3 1/4 = 1.861+ | Found by Maurizio Morandi | in March 2026.", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/7.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = (\u221a2)3 1/4 = 1.861+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "3877067eb2c9921c", "improvement": -0.0002701930433344213, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.58302978193184e-06, "max_pair_overlap_depth": -6.096494394869367e-07, "metric_expression": "1.86127", "metric_symbol": "s", "metric_value": 1.8612701930433344, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.861, "setup": "squinhex", "side": 1.8612701930433344, "solution_path": "data/solutions/generated/squinhex_007_3877067eb2c9921c.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/3877067eb2c9921c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@8", "density": 0.6631734535885272, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/8.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.15378+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.15378, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@8", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.15378+", "metric_symbol": "s", "metric_value": 2.15378, "reference_text": "s = 2.15378+ | Found by Ian Watson | in April 2026.", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/8.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.15378+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "15b61ced9a55fd6e", "improvement": -0.0010126406302717328, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9874417895385996e-06, "max_pair_overlap_depth": -2.4862858205326743e-05, "metric_expression": "2.15479", "metric_symbol": "s", "metric_value": 2.1547926406302715, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.15378, "setup": "squinhex", "side": 2.1547926406302715, "solution_path": "data/solutions/generated/squinhex_008_15b61ced9a55fd6e.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/15b61ced9a55fd6e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@9", "density": 0.6952132004138262, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/9.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1/2+\u221a3 = 2.23205+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.23205, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@9", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1/2+\u221a3 = 2.23205+", "metric_symbol": "s", "metric_value": 2.23205, "reference_text": "s = 1/2+\u221a3 = 2.23205+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/9.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 1/2+\u221a3 = 2.23205+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "55005bb44a4d74d4", "improvement": -0.00016646218885707498, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6345465208580115e-06, "max_pair_overlap_depth": -3.4334606535568746e-05, "metric_expression": "2.23222", "metric_symbol": "s", "metric_value": 2.232216462188857, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.23205, "setup": "squinhex", "side": 2.232216462188857, "solution_path": "data/solutions/generated/squinhex_009_55005bb44a4d74d4.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/55005bb44a4d74d4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@10", "density": 0.721657360923786, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/10.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4/\u221a3 = 2.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.309, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@10", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4/\u221a3 = 2.309+", "metric_symbol": "s", "metric_value": 2.309, "reference_text": "s = 4/\u221a3 = 2.309+ | Trivial. |", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/10.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 4/\u221a3 = 2.309+ | Trivial. |", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "1dc9bb5dff8e4212", "improvement": -0.0004498392040641619, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.82433796662779e-07, "max_pair_overlap_depth": -1.056245311698012e-05, "metric_expression": "2.30945", "metric_symbol": "s", "metric_value": 2.3094498392040643, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.309, "setup": "squinhex", "side": 2.3094498392040643, "solution_path": "data/solutions/generated/squinhex_010_1dc9bb5dff8e4212.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/1dc9bb5dff8e4212.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@11", "density": 0.7291333157228544, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/11.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.40944+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.40944, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@11", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.40944+", "metric_symbol": "s", "metric_value": 2.40944, "reference_text": "s = 2.40944+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "11.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/11.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.40944+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "11.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "705689a83f76dc66", "improvement": -0.00028191921915876605, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.56887695052102e-06, "max_pair_overlap_depth": -2.8090377436340574e-05, "metric_expression": "2.40972", "metric_symbol": "s", "metric_value": 2.409721919219159, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.40944, "setup": "squinhex", "side": 2.409721919219159, "solution_path": "data/solutions/generated/squinhex_011_705689a83f76dc66.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/705689a83f76dc66.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@12", "density": 0.7736310958293992, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/12.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1+5\u221a3/6 = 2.443+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.443, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@12", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "1+5\u221a3/6 = 2.443+", "metric_symbol": "s", "metric_value": 2.443, "reference_text": "s = 1+5\u221a3/6 = 2.443+ | Found by Maurizio Morandi | in March 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/12.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 1+5\u221a3/6 = 2.443+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "2605d29267e364f4", "improvement": -0.00041773030028169345, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4756288282540256e-06, "max_pair_overlap_depth": -2.0709990555811686e-06, "metric_expression": "2.44342", "metric_symbol": "s", "metric_value": 2.4434177303002818, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.443, "setup": "squinhex", "side": 2.4434177303002818, "solution_path": "data/solutions/generated/squinhex_012_2605d29267e364f4.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/2605d29267e364f4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@13", "density": 0.7555572001975633, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/13.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.572+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.572, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@13", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "2.572+", "metric_symbol": "s", "metric_value": 2.572, "reference_text": "s = 2.572+ | Found by Maurizio Morandi | in April 2026.", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/13.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.572+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "051502d315bb277c", "improvement": -0.001428217365099016, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2709109889167893e-06, "max_pair_overlap_depth": -2.7796124429491087e-05, "metric_expression": "2.57343", "metric_symbol": "s", "metric_value": 2.573428217365099, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.572, "setup": "squinhex", "side": 2.573428217365099, "solution_path": "data/solutions/generated/squinhex_013_051502d315bb277c.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/051502d315bb277c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@14", "density": 0.7839123498532168, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/14.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.62126+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.62126, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@14", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.62126+", "metric_symbol": "s", "metric_value": 2.62126, "reference_text": "s = 2.62126+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/14.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.62126+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "525e7cc585bd027c", "improvement": -0.000568749699766613, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5893267782285044e-06, "max_pair_overlap_depth": -1.4910539989809735e-05, "metric_expression": "2.62183", "metric_symbol": "s", "metric_value": 2.6218287496997665, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.62126, "setup": "squinhex", "side": 2.6218287496997665, "solution_path": "data/solutions/generated/squinhex_014_525e7cc585bd027c.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/525e7cc585bd027c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@15", "density": 0.7612787773180276, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/15.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.75365+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.75365, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@15", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.75365+", "metric_symbol": "s", "metric_value": 2.75365, "reference_text": "s = 2.75365+ | Found by Ian Watson | in April 2026.", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/15.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.75365+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "b68c71af3475ffed", "improvement": -0.00024783676108830477, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.513954837939443e-06, "max_pair_overlap_depth": -3.0296502803062175e-05, "metric_expression": "2.75390", "metric_symbol": "s", "metric_value": 2.7538978367610882, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.75365, "setup": "squinhex", "side": 2.7538978367610882, "solution_path": "data/solutions/generated/squinhex_015_b68c71af3475ffed.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/b68c71af3475ffed.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@16", "density": 0.7742958402345232, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/16.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.82004+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.82004, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@16", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.82004+", "metric_symbol": "s", "metric_value": 2.82004, "reference_text": "s = 2.82004+ | Found by Ian Watson | in April 2026.", "source_image": "16.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/16.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.82004+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "89a68dd125601a79", "improvement": -0.0001643950752789891, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.5133109066385543e-06, "max_pair_overlap_depth": -7.772490123292286e-06, "metric_expression": "2.82020", "metric_symbol": "s", "metric_value": 2.820204395075279, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.82004, "setup": "squinhex", "side": 2.820204395075279, "solution_path": "data/solutions/generated/squinhex_016_89a68dd125601a79.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/89a68dd125601a79.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@17", "density": 0.7850485918652831, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/17.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "5/\u221a3 = 2.88675+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.88675, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@17", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5/\u221a3 = 2.88675+", "metric_symbol": "s", "metric_value": 2.88675, "reference_text": "s = 5/\u221a3 = 2.88675+ | Trivial. |", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/17.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 5/\u221a3 = 2.88675+ | Trivial. |", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "68ba30b81c3844a7", "improvement": -0.0002730281066796181, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9250177449939015e-07, "max_pair_overlap_depth": -5.409854801341485e-05, "metric_expression": "2.88702", "metric_symbol": "s", "metric_value": 2.8870230281066798, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.88675, "setup": "squinhex", "side": 2.8870230281066798, "solution_path": "data/solutions/generated/squinhex_017_68ba30b81c3844a7.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/68ba30b81c3844a7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@18", "density": 0.8107158050212577, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/18.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.92111+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.92111, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@18", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.92111+", "metric_symbol": "s", "metric_value": 2.92111, "reference_text": "s = 2.92111+ | Found by Ian Watson | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/18.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.92111+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "e136eeec3de765c3", "improvement": -0.0022075205933282938, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.264526989622803e-06, "max_pair_overlap_depth": -7.64695502597501e-06, "metric_expression": "2.92332", "metric_symbol": "s", "metric_value": 2.9233175205933284, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.92111, "setup": "squinhex", "side": 2.9233175205933284, "solution_path": "data/solutions/generated/squinhex_018_e136eeec3de765c3.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/e136eeec3de765c3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@19", "density": 0.8472470384096148, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/19.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.93511+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.93511, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@19", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.93511+", "metric_symbol": "s", "metric_value": 2.93511, "reference_text": "s = 2.93511+ | Found by Ian Watson | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/19.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.93511+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "ae3850bdb0ac1880", "improvement": -0.0028496545666087947, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.965076151420116e-06, "max_pair_overlap_depth": -7.201359447650546e-06, "metric_expression": "2.93796", "metric_symbol": "s", "metric_value": 2.9379596545666087, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.93511, "setup": "squinhex", "side": 2.9379596545666087, "solution_path": "data/solutions/generated/squinhex_019_ae3850bdb0ac1880.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/ae3850bdb0ac1880.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@20", "density": 0.7690325218237841, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/20.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.16123+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.16123, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@20", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.16123+", "metric_symbol": "s", "metric_value": 3.16123, "reference_text": "s = 3.16123+ | Found by Ian Watson | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/20.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.16123+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "79028917ac70723d", "improvement": -0.0026259473298471114, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.697008230249216e-06, "max_pair_overlap_depth": -2.836652900617409e-05, "metric_expression": "3.16386", "metric_symbol": "s", "metric_value": 3.1638559473298473, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.16123, "setup": "squinhex", "side": 3.1638559473298473, "solution_path": "data/solutions/generated/squinhex_020_79028917ac70723d.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/79028917ac70723d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@21", "density": 0.7707944086673769, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png", "friedman_metric_expression": "3.23496+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.23496, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@21", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.23496+", "metric_symbol": "s", "metric_value": 3.23496, "reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "1d2ec517035658cd", "improvement": -0.0033202143530659534, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4830527974218215e-06, "max_pair_overlap_depth": -2.662964935497389e-05, "metric_expression": "3.23828", "metric_symbol": "s", "metric_value": 3.238280214353066, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.23496, "setup": "squinhex", "side": 3.238280214353066, "solution_path": "data/solutions/generated/squinhex_21_1d2ec517035658cd.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T13:47:12+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/1d2ec517035658cd.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@22", "density": 0.770525380181529, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/22.png", "friedman_metric_expression": "3.31573+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.31573, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@22", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.31573+", "metric_symbol": "s", "metric_value": 3.31573, "reference_text": "s = 3.31573+ | Found by Ian Watson | in April 2026.", "source_image": "22.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/22.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.31573+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "a1e7eaf12003fa2e", "improvement": 0.0006659560348909466, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.169977234601665e-06, "max_pair_overlap_depth": -1.9814540655582746e-05, "metric_expression": "3.31506", "metric_symbol": "s", "metric_value": 3.315064043965109, "n": 22, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.31573, "setup": "squinhex", "side": 3.315064043965109, "solution_path": "data/solutions/generated/squinhex_022_a1e7eaf12003fa2e.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/a1e7eaf12003fa2e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@23", "density": 0.7808954728618008, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/23.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.36437+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.36437, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@23", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.36437+", "metric_symbol": "s", "metric_value": 3.36437, "reference_text": "s = 3.36437+ | Found by Ian Watson | in April 2026.", "source_image": "23.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/23.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.36437+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "de78b89055181fd4", "improvement": -0.00261764110148599, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.240294795076849e-06, "max_pair_overlap_depth": -2.4390771091731267e-07, "metric_expression": "3.36699", "metric_symbol": "s", "metric_value": 3.366987641101486, "n": 23, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.36437, "setup": "squinhex", "side": 3.366987641101486, "solution_path": "data/solutions/generated/squinhex_023_de78b89055181fd4.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/de78b89055181fd4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@24", "density": 0.7904120022571139, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/24.png", "friedman_metric_expression": "3.41524+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.41524, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@24", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.41524+", "metric_symbol": "s", "metric_value": 3.41524, "reference_text": "s = 3.41524+ | Found by Ian Watson | in April 2026.", "source_image": "24.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/24.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.41524+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "73f1ceeaee97d32f", "improvement": -0.0033964158861361504, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0115328209217065e-06, "max_pair_overlap_depth": -2.5222031625055097e-05, "metric_expression": "3.41864", "metric_symbol": "s", "metric_value": 3.418636415886136, "n": 24, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.41524, "setup": "squinhex", "side": 3.418636415886136, "solution_path": "data/solutions/generated/squinhex_24_73f1ceeaee97d32f.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T14:34:18+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/73f1ceeaee97d32f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@25", "density": 0.8017157641998289, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/25.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2\u221a3 = 3.46410+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.4641, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@25", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2\u221a3 = 3.46410+", "metric_symbol": "s", "metric_value": 3.4641, "reference_text": "s = 2\u221a3 = 3.46410+ | Trivial. |", "source_image": "25.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/25.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2\u221a3 = 3.46410+ | Trivial. |", "friedman_source_image": "25.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "803edc96e272ee7a", "improvement": -0.00034642351026814566, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4684956309553432e-06, "max_pair_overlap_depth": -2.379294205911986e-05, "metric_expression": "3.46445", "metric_symbol": "s", "metric_value": 3.4644464235102683, "n": 25, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.4641, "setup": "squinhex", "side": 3.4644464235102683, "solution_path": "data/solutions/generated/squinhex_025_803edc96e272ee7a.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/803edc96e272ee7a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@26", "density": 0.8183272598135501, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/26.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.4939927+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.4939927, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@26", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.4939927+", "metric_symbol": "s", "metric_value": 3.4939927, "reference_text": "s = 3.4939927+ | Found by Ian Watson | in April 2026.", "source_image": "26.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/26.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.4939927+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "26.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "5fb7804364b5caaf", "improvement": -0.003020096739570377, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.392756549893556e-06, "max_pair_overlap_depth": -2.620566831379456e-05, "metric_expression": "3.49701", "metric_symbol": "s", "metric_value": 3.4970127967395706, "n": 26, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.4939927, "setup": "squinhex", "side": 3.4970127967395706, "solution_path": "data/solutions/generated/squinhex_026_5fb7804364b5caaf.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/5fb7804364b5caaf.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@27", "density": 0.8382703933092833, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/27.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(9+7\u221a3)/6 = 3.52072+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.52072, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@27", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "", "metric_expression": "(9+7\u221a3)/6 = 3.52072+", "metric_symbol": "s", "metric_value": 3.52072, "reference_text": "s = (9+7\u221a3)/6 = 3.52072+ | Found by Erich Friedman | in April 2026.", "source_image": "27.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/27.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = (9+7\u221a3)/6 = 3.52072+ | Found by Erich Friedman | in April 2026.", "friedman_source_image": "27.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "9cebbb5918ba8e81", "improvement": -0.00026256883024800004, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.315485793993667e-06, "max_pair_overlap_depth": -2.3466684225592616e-05, "metric_expression": "3.52098", "metric_symbol": "s", "metric_value": 3.520982568830248, "n": 27, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.52072, "setup": "squinhex", "side": 3.520982568830248, "solution_path": "data/solutions/generated/squinhex_027_9cebbb5918ba8e81.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/9cebbb5918ba8e81.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@28", "density": 0.8183465665432688, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/28.png", "friedman_metric_expression": "3.62565+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.62565, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@28", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.62565+", "metric_symbol": "s", "metric_value": 3.62565, "reference_text": "s = 3.62565+ | Found by Ian Watson | in April 2026.", "source_image": "28.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/28.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.62565+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "28.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "184baa4d16ce7f9e", "improvement": -0.00332887546169669, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.700161000518847e-07, "max_pair_overlap_depth": -3.0973746406592895e-06, "metric_expression": "3.62898", "metric_symbol": "s", "metric_value": 3.6289788754616965, "n": 28, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.62565, "setup": "squinhex", "side": 3.6289788754616965, "solution_path": "data/solutions/generated/squinhex_28_184baa4d16ce7f9e.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T14:34:18+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/184baa4d16ce7f9e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@29", "density": 0.829741145219895, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/29.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.66437+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.66437, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@29", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.66437+", "metric_symbol": "s", "metric_value": 3.66437, "reference_text": "s = 3.66437+ | Found by Ian Watson | in April 2026.", "source_image": "29.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/29.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.66437+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "29.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "3b329ff6f7babb15", "improvement": -0.0033970322125265184, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.61123003800209e-07, "max_pair_overlap_depth": -5.962934573305878e-06, "metric_expression": "3.66777", "metric_symbol": "s", "metric_value": 3.6677670322125264, "n": 29, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.66437, "setup": "squinhex", "side": 3.6677670322125264, "solution_path": "data/solutions/generated/squinhex_029_3b329ff6f7babb15.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/3b329ff6f7babb15.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@30", "density": 0.8440944212011869, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/30.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.69554+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.69554, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@30", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.69554+", "metric_symbol": "s", "metric_value": 3.69554, "reference_text": "s = 3.69554+ | Found by Ian Watson | in April 2026.", "source_image": "30.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/30.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.69554+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "30.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "0b645f27b41cbed7", "improvement": -0.0030753622873653796, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7116676711139033e-06, "max_pair_overlap_depth": -4.452216716410717e-06, "metric_expression": "3.69862", "metric_symbol": "s", "metric_value": 3.698615362287365, "n": 30, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.69554, "setup": "squinhex", "side": 3.698615362287365, "solution_path": "data/solutions/generated/squinhex_030_0b645f27b41cbed7.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/0b645f27b41cbed7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@31", "density": 0.83334567619728, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/31.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.78410+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.7841, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.78410+", "metric_symbol": "s", "metric_value": 3.7841, "reference_text": "s = 3.78410+ | Found by Emerson Connelly | in April 2026.", "source_image": "31.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/31.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.78410+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "31.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "83b47696242e2320", "improvement": 0.00017682363310500548, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.0307084382837186e-06, "max_pair_overlap_depth": -2.9858800666679453e-05, "metric_expression": "3.78392", "metric_symbol": "s", "metric_value": 3.783923176366895, "n": 31, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.7841, "setup": "squinhex", "side": 3.783923176366895, "solution_path": "data/solutions/generated/squinhex_031_83b47696242e2320.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/83b47696242e2320.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@32", "density": 0.8302114212681493, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/32.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.84795+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.84795, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.84795+", "metric_symbol": "s", "metric_value": 3.84795, "reference_text": "s = 3.84795+ | Found by Emerson Connelly | in April 2026.", "source_image": "32.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/32.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.84795+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "32.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "b233eac9bd8cc0d8", "improvement": -0.003769870972095468, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1351534734416697e-07, "max_pair_overlap_depth": -1.2013295066060081e-05, "metric_expression": "3.85172", "metric_symbol": "s", "metric_value": 3.8517198709720954, "n": 32, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.84795, "setup": "squinhex", "side": 3.8517198709720954, "solution_path": "data/solutions/generated/squinhex_032_b233eac9bd8cc0d8.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/b233eac9bd8cc0d8.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@33", "density": 0.8381951703957873, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/33.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.88897+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.88897, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.88897+", "metric_symbol": "s", "metric_value": 3.88897, "reference_text": "s = 3.88897+ | Found by Emerson Connelly | in April 2026.", "source_image": "33.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/33.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.88897+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "33.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "b14228e93eb45276", "improvement": -0.003797355726243623, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.797125554432215e-06, "max_pair_overlap_depth": -8.18730119578337e-06, "metric_expression": "3.89277", "metric_symbol": "s", "metric_value": 3.8927673557262437, "n": 33, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.88897, "setup": "squinhex", "side": 3.8927673557262437, "solution_path": "data/solutions/generated/squinhex_033_b14228e93eb45276.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/b14228e93eb45276.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@34", "density": 0.8486832973249016, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/34.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.92704+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.92704, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.92704+", "metric_symbol": "s", "metric_value": 3.92704, "reference_text": "s = 3.92704+ | Found by Emerson Connelly | in April 2026.", "source_image": "34.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/34.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.92704+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "34.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "fc2f6f3b6cabd5ed", "improvement": 0.0002227711135822652, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.30656742709778e-06, "max_pair_overlap_depth": -1.5057714820798651e-05, "metric_expression": "3.92682", "metric_symbol": "s", "metric_value": 3.9268172288864176, "n": 34, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.92704, "setup": "squinhex", "side": 3.9268172288864176, "solution_path": "data/solutions/generated/squinhex_034_fc2f6f3b6cabd5ed.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/fc2f6f3b6cabd5ed.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@35", "density": 0.8429987640989463, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/35.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.99833+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.99833, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@35", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.99833+", "metric_symbol": "s", "metric_value": 3.99833, "reference_text": "s = 3.99833+ | Found by Emerson Connelly | in April 2026.", "source_image": "35.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/35.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.99833+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "1ea058e93fb408a4", "improvement": 0.0007735056288105113, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.597269939847931e-06, "max_pair_overlap_depth": -1.4652234902046146e-05, "metric_expression": "3.99756", "metric_symbol": "s", "metric_value": 3.9975564943711897, "n": 35, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.99833, "setup": "squinhex", "side": 3.9975564943711897, "solution_path": "data/solutions/generated/squinhex_035_1ea058e93fb408a4.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/1ea058e93fb408a4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@36", "density": 0.8531956067904081, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png", "friedman_metric_expression": "2+7\u221a3/6 = 4.02072+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.02072, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@36", "credit": "Maurizio Morandi", "date": "May 2026", "family_updated": "", "metric_expression": "2+7\u221a3/6 = 4.02072+", "metric_symbol": "s", "metric_value": 4.02072, "reference_text": "s = 2+7\u221a3/6 = 4.02072+ | Found by Maurizio Morandi | in May 2026.", "source_image": "36.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2+7\u221a3/6 = 4.02072+ | Found by Maurizio Morandi | in May 2026.", "friedman_source_image": "36.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "b7083884dfb200c3", "improvement": -0.009242471992498835, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.100230231840266e-07, "max_pair_overlap_depth": -2.2076071326537772e-07, "metric_expression": "4.02996", "metric_symbol": "s", "metric_value": 4.029962471992499, "n": 36, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.02072, "setup": "squinhex", "side": 4.029962471992499, "solution_path": "data/solutions/record_hunt/squinhex_36_b7083884dfb200c3.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/b7083884dfb200c3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@37", "density": 0.8718839158050435, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/37.png", "friedman_metric_expression": "7/\u221a3 = 4.04145+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.04145, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@37", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "7/\u221a3 = 4.04145+", "metric_symbol": "s", "metric_value": 4.04145, "reference_text": "s = 7/\u221a3 = 4.04145+ | Trivial. |", "source_image": "37.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/37.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 7/\u221a3 = 4.04145+ | Trivial. |", "friedman_source_image": "37.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "a455ecb05be301ad", "improvement": -7.79426845127773e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1637259667017477e-06, "max_pair_overlap_depth": -1.0162747484221413e-05, "metric_expression": "4.04153", "metric_symbol": "s", "metric_value": 4.041527942684513, "n": 37, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.04145, "setup": "squinhex", "side": 4.041527942684513, "solution_path": "data/solutions/generated/squinhex_037_a455ecb05be301ad.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/a455ecb05be301ad.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@38", "density": 0.8354467372021385, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/38.png", "friedman_metric_expression": "4.18476+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.18476, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.18476+", "metric_symbol": "s", "metric_value": 4.18476, "reference_text": "s = 4.18476+ | Found by Emerson Connelly | in April 2026.", "source_image": "38.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/38.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 4.18476+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "38.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "657f5bc54656101d", "improvement": 0.0006174563357541629, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.3358638004937594e-07, "max_pair_overlap_depth": -2.4459335521420655e-06, "metric_expression": "4.18414", "metric_symbol": "s", "metric_value": 4.184142543664246, "n": 38, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 4.18476, "setup": "squinhex", "side": 4.184142543664246, "solution_path": "data/solutions/record_hunt/squinhex_38_657f5bc54656101d.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/657f5bc54656101d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@39", "density": 0.8275155837189719, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/39.png", "friedman_metric_expression": "4.25744+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.25744, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.25744+", "metric_symbol": "s", "metric_value": 4.25744, "reference_text": "s = 4.25744+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/39.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 4.25744+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "85e7e9eb3b3b7f5f", "improvement": -0.001664243334674076, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.204496689819836e-06, "max_pair_overlap_depth": -1.602842749781619e-05, "metric_expression": "4.25910", "metric_symbol": "s", "metric_value": 4.259104243334674, "n": 39, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.25744, "setup": "squinhex", "side": 4.259104243334674, "solution_path": "data/solutions/generated/squinhex_039_85e7e9eb3b3b7f5f.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/85e7e9eb3b3b7f5f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinhex@40", "density": 0.8288203735668404, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/40.png", "friedman_metric_expression": "4.31157+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.31157, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.31157+", "metric_symbol": "s", "metric_value": 4.31157, "reference_text": "s = 4.31157+ | Found by Emerson Connelly | in April 2026.", "source_image": "40.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/40.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 4.31157+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "40.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "9859865bba74b499", "improvement": 0.001604007461533108, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.921136271031391e-07, "max_pair_overlap_depth": -1.8467799072219293e-06, "metric_expression": "4.30997", "metric_symbol": "s", "metric_value": 4.309965992538467, "n": 40, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 4.31157, "setup": "squinhex", "side": 4.309965992538467, "solution_path": "data/solutions/record_hunt/squinhex_40_9859865bba74b499.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/9859865bba74b499.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@1", "density": 0.7071036297921394, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/1.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "1/\u221a(2+\u221a2) = .54119+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.54119, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1/\u221a(2+\u221a2) = .54119+", "metric_symbol": "s", "metric_value": 0.54119, "reference_text": "s = 1/\u221a(2+\u221a2) = .54119+ | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/1.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 1/\u221a(2+\u221a2) = .54119+ | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "b63c90f60717ba08", "improvement": -7.30613665711477e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1705346114441018e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.54120", "metric_symbol": "s", "metric_value": 0.5411973061366571, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.54119, "setup": "squinoct", "side": 0.5411973061366571, "solution_path": "data/solutions/generated/squinoct_001_b63c90f60717ba08.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/b63c90f60717ba08.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@2", "density": 0.5389047922692529, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2013", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/2.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": ".87667+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.87667, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@2", "credit": "Maurizio Morandi", "date": "December 2013", "family_updated": "", "metric_expression": ".87667+", "metric_symbol": "s", "metric_value": 0.87667, "reference_text": "s = .87667+ | Found by Maurizio Morandi | in December 2013.", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/2.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = .87667+ | Found by Maurizio Morandi | in December 2013.", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "7194ac58cba12fa7", "improvement": -4.0351762315649076e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.607981571160174e-06, "max_pair_overlap_depth": -1.1896285956325414e-06, "metric_expression": "0.87671", "metric_symbol": "s", "metric_value": 0.8767103517623156, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.87667, "setup": "squinoct", "side": 0.8767103517623156, "solution_path": "data/solutions/generated/squinoct_002_7194ac58cba12fa7.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/7194ac58cba12fa7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@3", "density": 0.5862650280603752, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "December 2013", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/3.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "18 \u2013 12\u221a2 = 1.02940+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0294, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@3", "credit": "Erich Friedman", "date": "December 2013", "family_updated": "", "metric_expression": "18 \u2013 12\u221a2 = 1.02940+", "metric_symbol": "s", "metric_value": 1.0294, "reference_text": "s = 18 \u2013 12\u221a2 = 1.02940+ | Found by Erich Friedman | in December 2013.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/3.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 18 \u2013 12\u221a2 = 1.02940+ | Found by Erich Friedman | in December 2013.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "3d85991afac60053", "improvement": -6.311956912941064e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.835100684478856e-06, "max_pair_overlap_depth": -3.4409461626638826e-05, "metric_expression": "1.02946", "metric_symbol": "s", "metric_value": 1.0294631195691295, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.0294, "setup": "squinoct", "side": 1.0294631195691295, "solution_path": "data/solutions/generated/squinoct_003_3d85991afac60053.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/3d85991afac60053.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@4", "density": 0.7070860385519216, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/4.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "\u221a(4\u20132\u221a2) = 1.08239+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.08239, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@4", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a(4\u20132\u221a2) = 1.08239+", "metric_symbol": "s", "metric_value": 1.08239, "reference_text": "s = \u221a(4\u20132\u221a2) = 1.08239+ | Trivial. |", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/4.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = \u221a(4\u20132\u221a2) = 1.08239+ | Trivial. |", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "30bfa7c46cf6dd87", "improvement": -1.8076366912644914e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.1007450963540665e-06, "max_pair_overlap_depth": -1.5610612916431253e-05, "metric_expression": "1.08241", "metric_symbol": "s", "metric_value": 1.0824080763669126, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.08239, "setup": "squinoct", "side": 1.0824080763669126, "solution_path": "data/solutions/generated/squinoct_004_30bfa7c46cf6dd87.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/30bfa7c46cf6dd87.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@5", "density": 0.6705984373456575, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/5.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "3\u221a2 \u2013 3 = 1.24261+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.24261, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3\u221a2 \u2013 3 = 1.24261+", "metric_symbol": "s", "metric_value": 1.24261, "reference_text": "s = 3\u221a2 \u2013 3 = 1.24261+ | Trivial. |", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/5.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 3\u221a2 \u2013 3 = 1.24261+ | Trivial. |", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "3bf97518bf42702c", "improvement": -4.591996404545995e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2899385621933342e-06, "max_pair_overlap_depth": -9.75715015771872e-06, "metric_expression": "1.24266", "metric_symbol": "s", "metric_value": 1.2426559199640455, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.24261, "setup": "squinoct", "side": 1.2426559199640455, "solution_path": "data/solutions/generated/squinoct_005_3bf97518bf42702c.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/3bf97518bf42702c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@6", "density": 0.6887710971991018, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2013", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/6.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "7 \u2013 4\u221a2 = 1.34314+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.34314, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@6", "credit": "Maurizio Morandi", "date": "December 2013", "family_updated": "", "metric_expression": "7 \u2013 4\u221a2 = 1.34314+", "metric_symbol": "s", "metric_value": 1.34314, "reference_text": "s = 7 \u2013 4\u221a2 = 1.34314+ | Found by Maurizio Morandi | in December 2013.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/6.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 7 \u2013 4\u221a2 = 1.34314+ | Found by Maurizio Morandi | in December 2013.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "6368fdc8880da7e0", "improvement": -4.34357115446371e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.645757686457117e-06, "max_pair_overlap_depth": -2.457675057909725e-05, "metric_expression": "1.34318", "metric_symbol": "s", "metric_value": 1.3431834357115446, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.34314, "setup": "squinoct", "side": 1.3431834357115446, "solution_path": "data/solutions/generated/squinoct_006_6368fdc8880da7e0.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/6368fdc8880da7e0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@7", "density": 0.702115846733366, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2013", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/7.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "1.43691+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.43691, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@7", "credit": "Maurizio Morandi", "date": "December 2013", "family_updated": "", "metric_expression": "1.43691+", "metric_symbol": "s", "metric_value": 1.43691, "reference_text": "s = 1.43691+ | Found by Maurizio Morandi | in December 2013.", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/7.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 1.43691+ | Found by Maurizio Morandi | in December 2013.", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "35d0c06f5c122826", "improvement": -4.0447358323758564e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.691262438170272e-07, "max_pair_overlap_depth": -1.2495412028745712e-05, "metric_expression": "1.43695", "metric_symbol": "s", "metric_value": 1.4369504473583237, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.43691, "setup": "squinoct", "side": 1.4369504473583237, "solution_path": "data/solutions/generated/squinoct_007_35d0c06f5c122826.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/35d0c06f5c122826.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@8", "density": 0.6722160358662614, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/8.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "1.56967+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.56967, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@8", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.56967+", "metric_symbol": "s", "metric_value": 1.56967, "reference_text": "s = 1.56967+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/8.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 1.56967+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "ecaef16600354c9f", "improvement": -0.00028685978676801227, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.463017743294653e-07, "max_pair_overlap_depth": -1.4183990756477804e-05, "metric_expression": "1.56996", "metric_symbol": "s", "metric_value": 1.569956859786768, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.56967, "setup": "squinoct", "side": 1.569956859786768, "solution_path": "data/solutions/generated/squinoct_008_ecaef16600354c9f.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/ecaef16600354c9f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@9", "density": 0.707064805820287, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/9.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "3/\u221a(2+\u221a2) = 1.62358+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.62358, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@9", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3/\u221a(2+\u221a2) = 1.62358+", "metric_symbol": "s", "metric_value": 1.62358, "reference_text": "s = 3/\u221a(2+\u221a2) = 1.62358+ | Trivial. |", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/9.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 3/\u221a(2+\u221a2) = 1.62358+ | Trivial. |", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "703059104a2b70f8", "improvement": -5.649241589167353e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6691071523245226e-06, "max_pair_overlap_depth": -7.928509179855325e-06, "metric_expression": "1.62364", "metric_symbol": "s", "metric_value": 1.6236364924158917, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.62358, "setup": "squinoct", "side": 1.6236364924158917, "solution_path": "data/solutions/generated/squinoct_009_703059104a2b70f8.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/703059104a2b70f8.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@10", "density": 0.732083417533705, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2013", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/10.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2^(3/4) = 1.68179+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.68179, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@10", "credit": "Maurizio Morandi", "date": "December 2013", "family_updated": "", "metric_expression": "2^(3/4) = 1.68179+", "metric_symbol": "s", "metric_value": 1.68179, "reference_text": "s = 2^(3/4) = 1.68179+ | Found by Maurizio Morandi | in December 2013.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/10.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2^(3/4) = 1.68179+ | Found by Maurizio Morandi | in December 2013.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "03facc71923f1148", "improvement": -0.00017469136174708133, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.2978224497762506e-06, "max_pair_overlap_depth": -2.3560442145575955e-05, "metric_expression": "1.68196", "metric_symbol": "s", "metric_value": 1.681964691361747, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.68179, "setup": "squinoct", "side": 1.681964691361747, "solution_path": "data/solutions/generated/squinoct_010_03facc71923f1148.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/03facc71923f1148.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@11", "density": 0.7597329550134904, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/11.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "1.73180+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.7318, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@11", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.73180+", "metric_symbol": "s", "metric_value": 1.7318, "reference_text": "s = 1.73180+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/11.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 1.73180+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "78c32afdb2263b2d", "improvement": 0.00013842799014240903, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.409684401929808e-09, "max_pair_overlap_depth": -1.1021961062729346e-05, "metric_expression": "1.73166", "metric_symbol": "s", "metric_value": 1.7316615720098576, "n": 11, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 1.7318, "setup": "squinoct", "side": 1.7316615720098576, "solution_path": "data/solutions/generated/squinoct_011_78c32afdb2263b2d.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/78c32afdb2263b2d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@12", "density": 0.8083084838512736, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2013", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/12.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "1.7533+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.7533, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@12", "credit": "Maurizio Morandi", "date": "December 2013", "family_updated": "", "metric_expression": "1.7533+", "metric_symbol": "s", "metric_value": 1.7533, "reference_text": "s = 1.7533+ | Found by Maurizio Morandi | in December 2013.", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/12.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 1.7533+ | Found by Maurizio Morandi | in December 2013.", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "7a9451cae59dbb40", "improvement": -0.00017352882969978722, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.088823188597466e-06, "max_pair_overlap_depth": -2.0797652260817756e-05, "metric_expression": "1.75347", "metric_symbol": "s", "metric_value": 1.7534735288296999, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.7533, "setup": "squinoct", "side": 1.7534735288296999, "solution_path": "data/solutions/generated/squinoct_012_7a9451cae59dbb40.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/7a9451cae59dbb40.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@13", "density": 0.7475846505942733, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/13.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "1.89760+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.8976, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@13", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.89760+", "metric_symbol": "s", "metric_value": 1.8976, "reference_text": "s = 1.89760+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/13.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 1.89760+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "c5bdcacf094e428e", "improvement": -0.00014846020367564883, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.439964464558682e-06, "max_pair_overlap_depth": -2.7883136850093138e-05, "metric_expression": "1.89775", "metric_symbol": "s", "metric_value": 1.8977484602036756, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.8976, "setup": "squinoct", "side": 1.8977484602036756, "solution_path": "data/solutions/generated/squinoct_013_c5bdcacf094e428e.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/c5bdcacf094e428e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@14", "density": 0.7369251630765782, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/14.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "1.98350+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.9835, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@14", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.98350+", "metric_symbol": "s", "metric_value": 1.9835, "reference_text": "s = 1.98350+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "14.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/14.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 1.98350+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "994e0dd57a80d4a3", "improvement": -7.891975572338339e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.49261632156563e-06, "max_pair_overlap_depth": -2.894591689805992e-05, "metric_expression": "1.98358", "metric_symbol": "s", "metric_value": 1.9835789197557234, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.9835, "setup": "squinoct", "side": 1.9835789197557234, "solution_path": "data/solutions/generated/squinoct_014_994e0dd57a80d4a3.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/994e0dd57a80d4a3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@15", "density": 0.7515649396279209, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/15.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.03259+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.03259, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@15", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.03259+", "metric_symbol": "s", "metric_value": 2.03259, "reference_text": "s = 2.03259+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/15.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.03259+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "c898d8b3cd2b55db", "improvement": -0.0005137104569299389, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7983161874182644e-07, "max_pair_overlap_depth": -1.9704810269915995e-05, "metric_expression": "2.03310", "metric_symbol": "s", "metric_value": 2.03310371045693, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.03259, "setup": "squinoct", "side": 2.03310371045693, "solution_path": "data/solutions/generated/squinoct_015_c898d8b3cd2b55db.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/c898d8b3cd2b55db.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@16", "density": 0.7725175260502497, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/16.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "5\u221a2 \u2013 5 = 2.07106+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.07106, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@16", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5\u221a2 \u2013 5 = 2.07106+", "metric_symbol": "s", "metric_value": 2.07106, "reference_text": "s = 5\u221a2 \u2013 5 = 2.07106+ | Trivial. |", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/16.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 5\u221a2 \u2013 5 = 2.07106+ | Trivial. |", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "3a2e6d99239355fd", "improvement": -4.911646819039106e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5220970331887e-06, "max_pair_overlap_depth": -8.060079695892952e-07, "metric_expression": "2.07111", "metric_symbol": "s", "metric_value": 2.0711091164681905, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.07106, "setup": "squinoct", "side": 2.0711091164681905, "solution_path": "data/solutions/generated/squinoct_016_3a2e6d99239355fd.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/3a2e6d99239355fd.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@17", "density": 0.8208079603816107, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/17.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "5\u221a2 \u2013 5 = 2.07106+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.07106, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@17", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5\u221a2 \u2013 5 = 2.07106+", "metric_symbol": "s", "metric_value": 2.07106, "reference_text": "s = 5\u221a2 \u2013 5 = 2.07106+ | Trivial. |", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/17.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 5\u221a2 \u2013 5 = 2.07106+ | Trivial. |", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "ab660f0510a3dd1c", "improvement": -3.891119068244464e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 1.368661750365744e-09, "max_pair_overlap_depth": -1.0480566122961221e-05, "metric_expression": "2.07110", "metric_symbol": "s", "metric_value": 2.0710989111906826, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.07106, "setup": "squinoct", "side": 2.0710989111906826, "solution_path": "data/solutions/generated/squinoct_017_ab660f0510a3dd1c.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/ab660f0510a3dd1c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@18", "density": 0.7934296897658486, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/18.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.16778+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.16778, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@18", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.16778+", "metric_symbol": "s", "metric_value": 2.16778, "reference_text": "s = 2.16778+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/18.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.16778+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "a7275e2ab7024187", "improvement": 0.00017977070139485463, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9711774532196686e-06, "max_pair_overlap_depth": -1.4522556675777842e-05, "metric_expression": "2.16760", "metric_symbol": "s", "metric_value": 2.167600229298605, "n": 18, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 2.16778, "setup": "squinoct", "side": 2.167600229298605, "solution_path": "data/solutions/generated/squinoct_018_a7275e2ab7024187.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/a7275e2ab7024187.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@19", "density": 0.793469906795261, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/19.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.22823+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.22823, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.22823+", "metric_symbol": "s", "metric_value": 2.22823, "reference_text": "s = 2.22823+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/19.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.22823+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "330906f1db929cdb", "improvement": 0.0012889040224068893, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0543459428412958e-06, "max_pair_overlap_depth": -1.4850274468458657e-05, "metric_expression": "2.22694", "metric_symbol": "s", "metric_value": 2.226941095977593, "n": 19, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 2.22823, "setup": "squinoct", "side": 2.226941095977593, "solution_path": "data/solutions/generated/squinoct_019_330906f1db929cdb.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/330906f1db929cdb.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@20", "density": 0.7912106699597153, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/20.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.28730+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.2873, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@20", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.28730+", "metric_symbol": "s", "metric_value": 2.2873, "reference_text": "s = 2.28730+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/20.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.28730+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "d1597d2fdf3beee1", "improvement": -0.0007530500807275686, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.367182536359887e-05, "max_pair_overlap_depth": -8.661317408398261e-06, "metric_expression": "2.28805", "metric_symbol": "s", "metric_value": 2.2880530500807277, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.2873, "setup": "squinoct", "side": 2.2880530500807277, "solution_path": "data/solutions/generated/squinoct_020_d1597d2fdf3beee1.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/d1597d2fdf3beee1.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@21", "density": 0.8091484006744551, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/21.gif", "friedman_metric_expression": "2.32167+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.32167, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@21", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.32167+", "metric_symbol": "s", "metric_value": 2.32167, "reference_text": "s = 2.32167+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/21.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.32167+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "a3759fa0325bb184", "improvement": 0.0032467851108277657, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.288437924896875e-06, "max_pair_overlap_depth": -7.589979277911052e-06, "metric_expression": "2.31842", "metric_symbol": "s", "metric_value": 2.3184232148891724, "n": 21, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 2.32167, "setup": "squinoct", "side": 2.3184232148891724, "solution_path": "data/solutions/generated/squinoct_021_a3759fa0325bb184.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/a3759fa0325bb184.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@22", "density": 0.779088370401765, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/22.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.41811+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.41811, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@22", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.41811+", "metric_symbol": "s", "metric_value": 2.41811, "reference_text": "s = 2.41811+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/22.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.41811+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "c01cc63fb6a654c8", "improvement": -0.00021763715445111131, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4586625716053672e-06, "max_pair_overlap_depth": -2.804598842454098e-05, "metric_expression": "2.41833", "metric_symbol": "s", "metric_value": 2.418327637154451, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.41811, "setup": "squinoct", "side": 2.418327637154451, "solution_path": "data/solutions/generated/squinoct_022_c01cc63fb6a654c8.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/c01cc63fb6a654c8.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@23", "density": 0.7777209980912639, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/23.gif", "friedman_metric_expression": "2.47329+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.47329, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@23", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.47329+", "metric_symbol": "s", "metric_value": 2.47329, "reference_text": "s = 2.47329+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/23.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.47329+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "004d1c5d4d7bca47", "improvement": -0.0015616154620987643, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.985478608046375e-06, "max_pair_overlap_depth": -1.4996046389881279e-05, "metric_expression": "2.47485", "metric_symbol": "s", "metric_value": 2.4748516154620988, "n": 23, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.47329, "setup": "squinoct", "side": 2.4748516154620988, "solution_path": "data/solutions/generated/squinoct_023_004d1c5d4d7bca47.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/004d1c5d4d7bca47.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@24", "density": 0.804709078453695, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/24.gif", "friedman_metric_expression": "6\u221a2 \u2013 6 = 2.48528+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.48528, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@24", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6\u221a2 \u2013 6 = 2.48528+", "metric_symbol": "s", "metric_value": 2.48528, "reference_text": "s = 6\u221a2 \u2013 6 = 2.48528+ | Trivial.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/24.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 6\u221a2 \u2013 6 = 2.48528+ | Trivial.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "4f255616aca5e547", "improvement": -4.580955124477981e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.67146332394231e-06, "max_pair_overlap_depth": -9.95881463161652e-06, "metric_expression": "2.48533", "metric_symbol": "s", "metric_value": 2.4853258095512447, "n": 24, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.48528, "setup": "squinoct", "side": 2.4853258095512447, "solution_path": "data/solutions/generated/squinoct_024_4f255616aca5e547.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4f255616aca5e547.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@25", "density": 0.8352526418920933, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/25.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "11/(3+\u221a2) = 2.49195+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.49195, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@25", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "11/(3+\u221a2) = 2.49195+", "metric_symbol": "s", "metric_value": 2.49195, "reference_text": "s = 11/(3+\u221a2) = 2.49195+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/25.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 11/(3+\u221a2) = 2.49195+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "0d3ca23da8f19da7", "improvement": 0.0021857033362460143, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.3164106628379786e-06, "max_pair_overlap_depth": -1.12459370678053e-05, "metric_expression": "2.48976", "metric_symbol": "s", "metric_value": 2.489764296663754, "n": 25, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 2.49195, "setup": "squinoct", "side": 2.489764296663754, "solution_path": "data/solutions/generated/squinoct_025_0d3ca23da8f19da7.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/0d3ca23da8f19da7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@26", "density": 0.8421766228224283, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/26.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.52841+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.52841, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@26", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.52841+", "metric_symbol": "s", "metric_value": 2.52841, "reference_text": "s = 2.52841+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/26.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.52841+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "6c0cffa2ebc39455", "improvement": -0.00020227836257324938, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3125873649857306e-07, "max_pair_overlap_depth": -6.684300461579085e-06, "metric_expression": "2.52861", "metric_symbol": "s", "metric_value": 2.5286122783625733, "n": 26, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.52841, "setup": "squinoct", "side": 2.5286122783625733, "solution_path": "data/solutions/generated/squinoct_026_6c0cffa2ebc39455.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/6c0cffa2ebc39455.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@27", "density": 0.8354347334144809, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/27.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.58695+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.58695, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@27", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.58695+", "metric_symbol": "s", "metric_value": 2.58695, "reference_text": "s = 2.58695+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/27.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.58695+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "9243c0031663b10e", "improvement": -0.0002069616913620287, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1228507689492215e-06, "max_pair_overlap_depth": -1.654834709174935e-05, "metric_expression": "2.58716", "metric_symbol": "s", "metric_value": 2.587156961691362, "n": 27, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.58695, "setup": "squinoct", "side": 2.587156961691362, "solution_path": "data/solutions/generated/squinoct_027_9243c0031663b10e.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/9243c0031663b10e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@28", "density": 0.8375235613860185, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/28.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.63116+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.63116, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@28", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.63116+", "metric_symbol": "s", "metric_value": 2.63116, "reference_text": "s = 2.63116+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/28.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.63116+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "f74e0430c683aaa0", "improvement": -0.0001841851467743183, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.686366302485504e-06, "max_pair_overlap_depth": -8.053108887406957e-06, "metric_expression": "2.63134", "metric_symbol": "s", "metric_value": 2.6313441851467743, "n": 28, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.63116, "setup": "squinoct", "side": 2.6313441851467743, "solution_path": "data/solutions/generated/squinoct_028_f74e0430c683aaa0.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/f74e0430c683aaa0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@29", "density": 0.8192713469622411, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/29.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.70811+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.70811, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@29", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.70811+", "metric_symbol": "s", "metric_value": 2.70811, "reference_text": "s = 2.70811+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/29.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.70811+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "7d4fefbdad04f318", "improvement": 0.0005239033117416803, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.8746413323634285e-06, "max_pair_overlap_depth": -4.299633667326219e-06, "metric_expression": "2.70759", "metric_symbol": "s", "metric_value": 2.7075860966882583, "n": 29, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 2.70811, "setup": "squinoct", "side": 2.7075860966882583, "solution_path": "data/solutions/generated/squinoct_029_7d4fefbdad04f318.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/7d4fefbdad04f318.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinoct@30", "density": 0.8256466842229233, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/30.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.74220+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.7422, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@30", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.74220+", "metric_symbol": "s", "metric_value": 2.7422, "reference_text": "s = 2.74220+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/30.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.74220+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "e6809975fe4af696", "improvement": -0.0010201760226595802, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.275653162265926e-06, "max_pair_overlap_depth": -1.2928136431611392e-05, "metric_expression": "2.74322", "metric_symbol": "s", "metric_value": 2.7432201760226596, "n": 30, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.7422, "setup": "squinoct", "side": 2.7432201760226596, "solution_path": "data/solutions/generated/squinoct_030_e6809975fe4af696.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/e6809975fe4af696.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@1", "density": 0.6621920830904189, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/1.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": ".936+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.936, "friedman_reference": {"analytical_or_proved": true, "case": "squinpen@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": ".936+", "metric_symbol": "s", "metric_value": 0.936, "reference_text": "s = cos(27\u00b0) / cos(18\u00b0) | s = .936+ | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/1.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = cos(27\u00b0) / cos(18\u00b0) | s = .936+ | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "7c4deaf46828e45f", "improvement": -0.0008790374068264883, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1116494686738636e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.93688", "metric_symbol": "s", "metric_value": 0.9368790374068265, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.936, "setup": "squinpen", "side": 0.9368790374068265, "solution_path": "data/solutions/generated/squinpen_001_7c4deaf46828e45f.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/7c4deaf46828e45f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@2", "density": 0.49287502021209156, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "March 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/2.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "1.535+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.535, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@2", "credit": "Erich Friedman", "date": "March 2012", "family_updated": "", "metric_expression": "1.535+", "metric_symbol": "s", "metric_value": 1.535, "reference_text": "s = 4\u221a(1\u20132/\u221a5)+\u221a5\u20132 | s = 1.535+ | Found by Erich Friedman | in March 2012.", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/2.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4\u221a(1\u20132/\u221a5)+\u221a5\u20132 | s = 1.535+ | Found by Erich Friedman | in March 2012.", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "e0d70422bfa035f2", "improvement": -0.0007556004426736429, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.603512178169518e-07, "max_pair_overlap_depth": -4.1992473865937185e-06, "metric_expression": "1.53576", "metric_symbol": "s", "metric_value": 1.5357556004426736, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.535, "setup": "squinpen", "side": 1.5357556004426736, "solution_path": "data/solutions/generated/squinpen_002_e0d70422bfa035f2.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/e0d70422bfa035f2.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@3", "density": 0.6064545372240481, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/3.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "1.695+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.695, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@3", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "1.695+", "metric_symbol": "s", "metric_value": 1.695, "reference_text": "s = 1.695+ | Found by David W. Cantrell | in July 2012. |", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/3.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 1.695+ | Found by David W. Cantrell | in July 2012. |", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "20345bd1acea07ee", "improvement": -0.0006531320538840646, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.096669049020619e-07, "max_pair_overlap_depth": -2.3507012493845236e-05, "metric_expression": "1.69565", "metric_symbol": "s", "metric_value": 1.6956531320538841, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.695, "setup": "squinpen", "side": 1.6956531320538841, "solution_path": "data/solutions/generated/squinpen_003_20345bd1acea07ee.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/20345bd1acea07ee.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@4", "density": 0.6707731008924028, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/4.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "1.861+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.861, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@4", "credit": "Maurizio Morandi", "date": "July 2012", "family_updated": "", "metric_expression": "1.861+", "metric_symbol": "s", "metric_value": 1.861, "reference_text": "s = 1.861+ | Found by Maurizio Morandi | in July 2012. |", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/4.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 1.861+ | Found by Maurizio Morandi | in July 2012. |", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "3b3728a72d1e463a", "improvement": -0.0007342580262259535, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8617284829398191e-06, "max_pair_overlap_depth": -1.61527471932571e-05, "metric_expression": "1.86173", "metric_symbol": "s", "metric_value": 1.861734258026226, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.861, "setup": "squinpen", "side": 1.861734258026226, "solution_path": "data/solutions/generated/squinpen_004_3b3728a72d1e463a.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/3b3728a72d1e463a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@5", "density": 0.7633756933560932, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "March 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/5.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "1.951+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.951, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@5", "credit": "Erich Friedman", "date": "March 2012", "family_updated": "", "metric_expression": "1.951+", "metric_symbol": "s", "metric_value": 1.951, "reference_text": "s = 1 + cos(18\u00b0) | s = 1.951+ | Found by Erich Friedman | in March 2012.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/5.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 1 + cos(18\u00b0) | s = 1.951+ | Found by Erich Friedman | in March 2012.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "dfdcf10f7cfe5f16", "improvement": -0.00015311806809270578, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.72748390891526e-06, "max_pair_overlap_depth": -2.251588894827683e-05, "metric_expression": "1.95115", "metric_symbol": "s", "metric_value": 1.9511531180680928, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.951, "setup": "squinpen", "side": 1.9511531180680928, "solution_path": "data/solutions/generated/squinpen_005_dfdcf10f7cfe5f16.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/dfdcf10f7cfe5f16.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@6", "density": 0.7300382566069571, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "March 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/6.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "2.185+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.185, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@6", "credit": "Erich Friedman", "date": "March 2012", "family_updated": "", "metric_expression": "2.185+", "metric_symbol": "s", "metric_value": 2.185, "reference_text": "s = 6\u221a(1\u20132/\u221a5)+\u221a5\u20132 | s = 2.185+ | Found by Erich Friedman | in March 2012.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/6.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 6\u221a(1\u20132/\u221a5)+\u221a5\u20132 | s = 2.185+ | Found by Erich Friedman | in March 2012.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "fbc8fa063fa8154f", "improvement": -0.0006384860733987807, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.046305607470139e-06, "max_pair_overlap_depth": -1.535481943848449e-05, "metric_expression": "2.18564", "metric_symbol": "s", "metric_value": 2.185638486073399, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.185, "setup": "squinpen", "side": 2.185638486073399, "solution_path": "data/solutions/generated/squinpen_006_fbc8fa063fa8154f.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/fbc8fa063fa8154f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@7", "density": 0.6937337333431398, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/7.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "2.421+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.421, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@7", "credit": "Erich Friedman", "date": "July 2012", "family_updated": "", "metric_expression": "2.421+", "metric_symbol": "s", "metric_value": 2.421, "reference_text": "s = 6\u221a(1\u20132/\u221a5)+2\u221a5\u20134 | s = 2.421+ | Found by Erich Friedman | in July 2012.", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/7.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 6\u221a(1\u20132/\u221a5)+2\u221a5\u20134 | s = 2.421+ | Found by Erich Friedman | in July 2012.", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "a9079c85f43f1608", "improvement": -0.0007434143519042813, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.2537276094194668e-06, "max_pair_overlap_depth": -4.1098373515402464e-05, "metric_expression": "2.42174", "metric_symbol": "s", "metric_value": 2.421743414351904, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.421, "setup": "squinpen", "side": 2.421743414351904, "solution_path": "data/solutions/generated/squinpen_007_a9079c85f43f1608.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/a9079c85f43f1608.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@8", "density": 0.7064703560745587, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/8.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "2.565+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.565, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@8", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "2.565+", "metric_symbol": "s", "metric_value": 2.565, "reference_text": "s = 2.565+ | Found by David W. Cantrell | in July 2012. |", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/8.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 2.565+ | Found by David W. Cantrell | in July 2012. |", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "eedfd38786ce3d06", "improvement": -0.0005089596009386632, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2839977085297321e-06, "max_pair_overlap_depth": -2.052513031336467e-05, "metric_expression": "2.56551", "metric_symbol": "s", "metric_value": 2.5655089596009386, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.565, "setup": "squinpen", "side": 2.5655089596009386, "solution_path": "data/solutions/generated/squinpen_008_eedfd38786ce3d06.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/eedfd38786ce3d06.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@9", "density": 0.7204851744660768, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/9.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "2.693+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.693, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@9", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "2.693+", "metric_symbol": "s", "metric_value": 2.693, "reference_text": "s = 2.693+ | Found by Timo Berthold et al | in January 2026. |", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/9.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 2.693+ | Found by Timo Berthold et al | in January 2026. |", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "b050939c544c8091", "improvement": -0.0015375753912136858, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.502705162025631e-06, "max_pair_overlap_depth": -2.4857642315079254e-05, "metric_expression": "2.69454", "metric_symbol": "s", "metric_value": 2.6945375753912137, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.693, "setup": "squinpen", "side": 2.6945375753912137, "solution_path": "data/solutions/generated/squinpen_009_b050939c544c8091.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/b050939c544c8091.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@10", "density": 0.7436124164686567, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/10.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "2.793+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.793, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@10", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "2.793+", "metric_symbol": "s", "metric_value": 2.793, "reference_text": "s = 2.793+ | Found by Timo Berthold et al | in January 2026.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/10.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 2.793+ | Found by Timo Berthold et al | in January 2026.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "5e3ff0fc92953694", "improvement": -0.0027748736770187854, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.695299675143831e-07, "max_pair_overlap_depth": -2.06179882833446e-05, "metric_expression": "2.79577", "metric_symbol": "s", "metric_value": 2.795774873677019, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.793, "setup": "squinpen", "side": 2.795774873677019, "solution_path": "data/solutions/generated/squinpen_010_5e3ff0fc92953694.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/5e3ff0fc92953694.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@11", "density": 0.7644165493663143, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/11.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "2.890+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.89, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@11", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "2.890+", "metric_symbol": "s", "metric_value": 2.89, "reference_text": "s = 2.890+ | Found by Timo Berthold et al | in January 2026.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/11.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 2.890+ | Found by Timo Berthold et al | in January 2026.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "eed6c273a2c34445", "improvement": -0.002056785153238039, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.157725543754771e-07, "max_pair_overlap_depth": -2.6396452143861993e-05, "metric_expression": "2.89206", "metric_symbol": "s", "metric_value": 2.892056785153238, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.89, "setup": "squinpen", "side": 2.892056785153238, "solution_path": "data/solutions/generated/squinpen_011_eed6c273a2c34445.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/eed6c273a2c34445.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@12", "density": 0.7899142461050866, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/12.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "2.969+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.969, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@12", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "2.969+", "metric_symbol": "s", "metric_value": 2.969, "reference_text": "s = 2.969+ | Found by Timo Berthold et al | in January 2026.", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/12.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 2.969+ | Found by Timo Berthold et al | in January 2026.", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "0dc0d2750d6b1986", "improvement": -0.0025029358297610216, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.6525891073399466e-06, "max_pair_overlap_depth": -2.2708088333933674e-05, "metric_expression": "2.97150", "metric_symbol": "s", "metric_value": 2.971502935829761, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.969, "setup": "squinpen", "side": 2.971502935829761, "solution_path": "data/solutions/generated/squinpen_012_0dc0d2750d6b1986.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/0dc0d2750d6b1986.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@13", "density": 0.7748259330672266, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/13.gif", "friedman_metric_expression": "3.121+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.121, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@13", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "3.121+", "metric_symbol": "s", "metric_value": 3.121, "reference_text": "s = 2\u221a(1\u20132/\u221a5)+2\u221a5\u20132 | s = 3.121+ | Found by David W. Cantrell | in July 2012.", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/13.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 2\u221a(1\u20132/\u221a5)+2\u221a5\u20132 | s = 3.121+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "13449338c659bacc", "improvement": -0.0018067975436526496, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.882913072523962e-06, "max_pair_overlap_depth": -3.6524180263897144e-05, "metric_expression": "3.12281", "metric_symbol": "s", "metric_value": 3.1228067975436526, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.121, "setup": "squinpen", "side": 3.1228067975436526, "solution_path": "data/solutions/generated/squinpen_13_13449338c659bacc.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T07:13:53+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/13449338c659bacc.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@14", "density": 0.8005863693145643, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/14.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.187+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.187, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@14", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "3.187+", "metric_symbol": "s", "metric_value": 3.187, "reference_text": "s = 3.187+ | Found by David W. Cantrell | in July 2012. |", "source_image": "14.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/14.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.187+ | Found by David W. Cantrell | in July 2012. |", "friedman_source_image": "14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "c910e2e69c5e952c", "improvement": -0.0011256975399334124, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.345127969056754e-07, "max_pair_overlap_depth": -6.672013015962541e-06, "metric_expression": "3.18813", "metric_symbol": "s", "metric_value": 3.1881256975399332, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.187, "setup": "squinpen", "side": 3.1881256975399332, "solution_path": "data/solutions/generated/squinpen_014_c910e2e69c5e952c.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/c910e2e69c5e952c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@15", "density": 0.8079241717093747, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/15.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.284+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.284, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@15", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "3.284+", "metric_symbol": "s", "metric_value": 3.284, "reference_text": "s = (\u221a(125\u201338\u221a5)+8\u20132\u221a5)/3 | s = 3.284+ | Found by David W. Cantrell | in July 2012.", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/15.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = (\u221a(125\u201338\u221a5)+8\u20132\u221a5)/3 | s = 3.284+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "d5cf3c3cc0980b70", "improvement": -0.001003544834322856, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.349360852435288e-06, "max_pair_overlap_depth": -2.4505079251779804e-05, "metric_expression": "3.28500", "metric_symbol": "s", "metric_value": 3.2850035448343227, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.284, "setup": "squinpen", "side": 3.2850035448343227, "solution_path": "data/solutions/generated/squinpen_015_d5cf3c3cc0980b70.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d5cf3c3cc0980b70.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@16", "density": 0.7674551673762713, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/16.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.480+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.48, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@16", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3.480+", "metric_symbol": "s", "metric_value": 3.48, "reference_text": "s = 3.480+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/16.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.480+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "9ca0c9eddf5257a6", "improvement": -0.0010398730905230025, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 5.610061847707955e-09, "max_pair_overlap_depth": -2.0020049716018562e-05, "metric_expression": "3.48104", "metric_symbol": "s", "metric_value": 3.481039873090523, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.48, "setup": "squinpen", "side": 3.481039873090523, "solution_path": "data/solutions/generated/squinpen_016_9ca0c9eddf5257a6.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/9ca0c9eddf5257a6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@17", "density": 0.7871473019367167, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/17.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.541+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.541, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@17", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3.541+", "metric_symbol": "s", "metric_value": 3.541, "reference_text": "s = 3.541+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/17.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.541+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "c1324401d6fef4ff", "improvement": -0.0020066620107224153, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3581595293550302e-06, "max_pair_overlap_depth": -1.9942519651539037e-05, "metric_expression": "3.54301", "metric_symbol": "s", "metric_value": 3.5430066620107223, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.541, "setup": "squinpen", "side": 3.5430066620107223, "solution_path": "data/solutions/generated/squinpen_017_c1324401d6fef4ff.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/c1324401d6fef4ff.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@18", "density": 0.7949963635829483, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/18.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.626+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.626, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@18", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3.626+", "metric_symbol": "s", "metric_value": 3.626, "reference_text": "s = 3.626+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/18.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.626+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "521e6ed1020d53e6", "improvement": -0.001681876520355896, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.132718950610418e-06, "max_pair_overlap_depth": -5.952134619235938e-06, "metric_expression": "3.62768", "metric_symbol": "s", "metric_value": 3.627681876520356, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.626, "setup": "squinpen", "side": 3.627681876520356, "solution_path": "data/solutions/generated/squinpen_018_521e6ed1020d53e6.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/521e6ed1020d53e6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@19", "density": 0.8016091392666894, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/19.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.710+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.71, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3.710+", "metric_symbol": "s", "metric_value": 3.71, "reference_text": "s = 3.710+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/19.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.710+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "66aeca1af6b9bf65", "improvement": -0.001683910599032501, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.240508232322902e-06, "max_pair_overlap_depth": -2.033383687716217e-05, "metric_expression": "3.71168", "metric_symbol": "s", "metric_value": 3.7116839105990325, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.71, "setup": "squinpen", "side": 3.7116839105990325, "solution_path": "data/solutions/generated/squinpen_019_66aeca1af6b9bf65.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/66aeca1af6b9bf65.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@20", "density": 0.8030009751844291, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/20.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.802+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.802, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@20", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3.802+", "metric_symbol": "s", "metric_value": 3.802, "reference_text": "s = 3.802+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/20.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.802+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "8424f972564f51a8", "improvement": -0.00280562795003636, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.488842199203112e-06, "max_pair_overlap_depth": -3.2279665458823104e-05, "metric_expression": "3.80481", "metric_symbol": "s", "metric_value": 3.8048056279500364, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.802, "setup": "squinpen", "side": 3.8048056279500364, "solution_path": "data/solutions/generated/squinpen_020_8424f972564f51a8.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/8424f972564f51a8.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@21", "density": 0.8168349282229689, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/21.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.864+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.864, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@21", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "3.864+", "metric_symbol": "s", "metric_value": 3.864, "reference_text": "s = 3.864+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/21.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.864+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "7f1bf6bbe100ca6c", "improvement": -0.0016097781764203845, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0975793470973527e-06, "max_pair_overlap_depth": -2.933142426009283e-05, "metric_expression": "3.86561", "metric_symbol": "s", "metric_value": 3.8656097781764203, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.864, "setup": "squinpen", "side": 3.8656097781764203, "solution_path": "data/solutions/generated/squinpen_021_7f1bf6bbe100ca6c.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/7f1bf6bbe100ca6c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@22", "density": 0.8236901899623935, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/22.gif", "friedman_metric_expression": "3.937+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.937, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@22", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "3.937+", "metric_symbol": "s", "metric_value": 3.937, "reference_text": "s = 3.937+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/22.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.937+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "33b95c59890c6cd7", "improvement": -0.0030787983666398233, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.1912141987053604e-06, "max_pair_overlap_depth": -2.2837560550437175e-06, "metric_expression": "3.94008", "metric_symbol": "s", "metric_value": 3.9400787983666397, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.937, "setup": "squinpen", "side": 3.9400787983666397, "solution_path": "data/solutions/generated/squinpen_022_33b95c59890c6cd7.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/33b95c59890c6cd7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@23", "density": 0.8342850114016098, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/23.gif", "friedman_metric_expression": "4.002+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.002, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@23", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.002+", "metric_symbol": "s", "metric_value": 4.002, "reference_text": "s = 4.002+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/23.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.002+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "125d15e1f42d4cc7", "improvement": -0.000968856434470311, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.142206802972531e-06, "max_pair_overlap_depth": -1.3381668518996914e-05, "metric_expression": "4.00297", "metric_symbol": "s", "metric_value": 4.00296885643447, "n": 23, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.002, "setup": "squinpen", "side": 4.00296885643447, "solution_path": "data/solutions/generated/squinpen_023_125d15e1f42d4cc7.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/125d15e1f42d4cc7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@24", "density": 0.8254992867774645, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/24.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.107+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.107, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@24", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.107+", "metric_symbol": "s", "metric_value": 4.107, "reference_text": "s = 4.107+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/24.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.107+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "7b6bed1452ec8f75", "improvement": -0.003766262034448964, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.187233974203672e-07, "max_pair_overlap_depth": -1.4055675707780324e-06, "metric_expression": "4.11077", "metric_symbol": "s", "metric_value": 4.110766262034449, "n": 24, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.107, "setup": "squinpen", "side": 4.110766262034449, "solution_path": "data/solutions/generated/squinpen_024_7b6bed1452ec8f75.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/7b6bed1452ec8f75.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@25", "density": 0.8346264431391957, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/25.gif", "friedman_metric_expression": "4.169+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.169, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@25", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.169+", "metric_symbol": "s", "metric_value": 4.169, "reference_text": "s = 4.169+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/25.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.169+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "965f543dd3a1a5b2", "improvement": -0.003529809873594303, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.8760801669609005e-06, "max_pair_overlap_depth": -9.22783607931743e-06, "metric_expression": "4.17253", "metric_symbol": "s", "metric_value": 4.172529809873594, "n": 25, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.169, "setup": "squinpen", "side": 4.172529809873594, "solution_path": "data/solutions/generated/squinpen_025_965f543dd3a1a5b2.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/965f543dd3a1a5b2.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@26", "density": 0.846720772454187, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/26.gif", "friedman_metric_expression": "4.223+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.223, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@26", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.223+", "metric_symbol": "s", "metric_value": 4.223, "reference_text": "s = 4.223+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/26.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.223+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "12ea954c92ca25d9", "improvement": -0.0016630925283189768, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.329734777233707e-07, "max_pair_overlap_depth": -5.080948892621784e-06, "metric_expression": "4.22466", "metric_symbol": "s", "metric_value": 4.224663092528319, "n": 26, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.223, "setup": "squinpen", "side": 4.224663092528319, "solution_path": "data/solutions/generated/squinpen_026_12ea954c92ca25d9.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/12ea954c92ca25d9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@27", "density": 0.8275684076653715, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/27.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.350+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.35, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@27", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.350+", "metric_symbol": "s", "metric_value": 4.35, "reference_text": "s = 4.350+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/27.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.350+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "fc7fa66fe1928440", "improvement": -0.0046719542874926745, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1174449550978842e-06, "max_pair_overlap_depth": -1.176344423625686e-05, "metric_expression": "4.35467", "metric_symbol": "s", "metric_value": 4.354671954287492, "n": 27, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.35, "setup": "squinpen", "side": 4.354671954287492, "solution_path": "data/solutions/generated/squinpen_027_fc7fa66fe1928440.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/fc7fa66fe1928440.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@28", "density": 0.8327551046015365, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/28.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.421+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.421, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@28", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.421+", "metric_symbol": "s", "metric_value": 4.421, "reference_text": "s = 4.421+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/28.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.421+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "81b95a9d0915b9b0", "improvement": 0.0002507922234444848, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3068707244667255e-06, "max_pair_overlap_depth": -1.2232567722092469e-05, "metric_expression": "4.42075", "metric_symbol": "s", "metric_value": 4.420749207776556, "n": 28, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 4.421, "setup": "squinpen", "side": 4.420749207776556, "solution_path": "data/solutions/generated/squinpen_028_81b95a9d0915b9b0.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/81b95a9d0915b9b0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@29", "density": 0.8326213695314967, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/29.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.499+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.499, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@29", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.499+", "metric_symbol": "s", "metric_value": 4.499, "reference_text": "s = 4.499+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/29.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.499+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "7cc5c6e51420a8c4", "improvement": -0.0003599298979271026, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.900416840645271e-06, "max_pair_overlap_depth": -1.3857736228028994e-05, "metric_expression": "4.49936", "metric_symbol": "s", "metric_value": 4.499359929897927, "n": 29, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.499, "setup": "squinpen", "side": 4.499359929897927, "solution_path": "data/solutions/generated/squinpen_029_7cc5c6e51420a8c4.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/7cc5c6e51420a8c4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@30", "density": 0.8380230132738162, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif", "friedman_metric_expression": "4.550+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.55, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@30", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.550+", "metric_symbol": "s", "metric_value": 4.55, "reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "45dff6d0a270c6c5", "improvement": -0.011505140806147729, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.226407328203014e-06, "max_pair_overlap_depth": -5.655700288098586e-07, "metric_expression": "4.56151", "metric_symbol": "s", "metric_value": 4.5615051408061476, "n": 30, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.55, "setup": "squinpen", "side": 4.5615051408061476, "solution_path": "data/solutions/generated/squinpen_30_45dff6d0a270c6c5.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T14:34:18+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/45dff6d0a270c6c5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@31", "density": 0.8407016075258085, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/31.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.63041+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.63041, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.63041+", "metric_symbol": "s", "metric_value": 4.63041, "reference_text": "s = 4.63041+ | Found by Emerson Connelly | in April 2026.", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/31.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.63041+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "8b17df7ad9586809", "improvement": 0.0008957860403464579, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9662880539345523e-06, "max_pair_overlap_depth": -1.825266620247845e-05, "metric_expression": "4.62951", "metric_symbol": "s", "metric_value": 4.629514213959654, "n": 31, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 4.63041, "setup": "squinpen", "side": 4.629514213959654, "solution_path": "data/solutions/generated/squinpen_031_8b17df7ad9586809.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/8b17df7ad9586809.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@32", "density": 0.839043760254319, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/32.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.70774+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.70774, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.70774+", "metric_symbol": "s", "metric_value": 4.70774, "reference_text": "s = 4.70774+ | Found by Emerson Connelly | in April 2026.", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/32.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.70774+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "ded24abc59c82646", "improvement": -0.000495710626569057, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.910425347385825e-07, "max_pair_overlap_depth": -1.0586072088480947e-05, "metric_expression": "4.70824", "metric_symbol": "s", "metric_value": 4.708235710626569, "n": 32, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.70774, "setup": "squinpen", "side": 4.708235710626569, "solution_path": "data/solutions/generated/squinpen_032_ded24abc59c82646.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/ded24abc59c82646.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@33", "density": 0.8454321018371573, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/33.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.75774+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.75774, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.75774+", "metric_symbol": "s", "metric_value": 4.75774, "reference_text": "s = 4.75774+ | Found by Emerson Connelly | in April 2026.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/33.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.75774+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "a9622b0aeea26f74", "improvement": -0.00539747702354898, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.5906514265382727e-06, "max_pair_overlap_depth": -5.445984948337923e-06, "metric_expression": "4.76314", "metric_symbol": "s", "metric_value": 4.763137477023549, "n": 33, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.75774, "setup": "squinpen", "side": 4.763137477023549, "solution_path": "data/solutions/generated/squinpen_033_a9622b0aeea26f74.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T03:19:00+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/a9622b0aeea26f74.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@34", "density": 0.8467800838831615, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.81817+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.81817, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.81817+", "metric_symbol": "s", "metric_value": 4.81817, "reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "d7af1c3ed90603fd", "improvement": -0.012747878392191048, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.414710391441419e-07, "max_pair_overlap_depth": -6.11976491438071e-06, "metric_expression": "4.83092", "metric_symbol": "s", "metric_value": 4.830917878392191, "n": 34, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.81817, "setup": "squinpen", "side": 4.830917878392191, "solution_path": "data/solutions/generated/squinpen_034_d7af1c3ed90603fd.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/d7af1c3ed90603fd.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@35", "density": 0.8578692979479161, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/35.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.86994+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.86994, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@35", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.86994+", "metric_symbol": "s", "metric_value": 4.86994, "reference_text": "s = 4.86994+ | Found by Emerson Connelly | in April 2026.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/35.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.86994+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "d0212c88c498f951", "improvement": 0.0002762594618035408, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.74898699366526e-06, "max_pair_overlap_depth": -8.959642868955342e-06, "metric_expression": "4.86966", "metric_symbol": "s", "metric_value": 4.869663740538196, "n": 35, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 4.86994, "setup": "squinpen", "side": 4.869663740538196, "solution_path": "data/solutions/generated/squinpen_035_d0212c88c498f951.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/d0212c88c498f951.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@36", "density": 0.8582852742974874, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/36.gif", "friedman_metric_expression": "4.93902+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.93902, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@36", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.93902+", "metric_symbol": "s", "metric_value": 4.93902, "reference_text": "s = 4.93902+ | Found by Emerson Connelly | in April 2026.", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/36.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.93902+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "e43d96c031faf38c", "improvement": 0.0014765141690524786, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.258589189166597e-07, "max_pair_overlap_depth": -1.4614402910062552e-07, "metric_expression": "4.93754", "metric_symbol": "s", "metric_value": 4.937543485830948, "n": 36, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 4.93902, "setup": "squinpen", "side": 4.937543485830948, "solution_path": "data/solutions/record_hunt/squinpen_36_e43d96c031faf38c.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/e43d96c031faf38c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@37", "density": 0.8661967376016183, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/37.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.98234+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.98234, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@37", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.98234+", "metric_symbol": "s", "metric_value": 4.98234, "reference_text": "s = 4.98234+ | Found by Emerson Connelly | in April 2026.", "source_image": "37.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/37.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.98234+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "dba281681536eecb", "improvement": -0.00039859816128817727, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.161377353190805e-07, "max_pair_overlap_depth": -4.181534561720213e-06, "metric_expression": "4.98274", "metric_symbol": "s", "metric_value": 4.982738598161288, "n": 37, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.98234, "setup": "squinpen", "side": 4.982738598161288, "solution_path": "data/solutions/generated/squinpen_037_dba281681536eecb.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/dba281681536eecb.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@38", "density": 0.8656682257376033, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/38.gif", "friedman_metric_expression": "5.05233+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.05233, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "5.05233+", "metric_symbol": "s", "metric_value": 5.05233, "reference_text": "s = 5.05233+ | Found by Emerson Connelly | in April 2026.", "source_image": "38.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/38.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 5.05233+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "00496638a2011285", "improvement": 0.001164786809802365, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.776103493630765e-07, "max_pair_overlap_depth": -5.692587072836375e-07, "metric_expression": "5.05117", "metric_symbol": "s", "metric_value": 5.051165213190198, "n": 38, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 5.05233, "setup": "squinpen", "side": 5.051165213190198, "solution_path": "data/solutions/record_hunt/squinpen_38_00496638a2011285.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/00496638a2011285.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@39", "density": 0.8585952949364365, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/39.gif", "friedman_metric_expression": "5.13846+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.13846, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@39", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "5.13846+", "metric_symbol": "s", "metric_value": 5.13846, "reference_text": "s = 5.13846+ | Found by Nathan Roll | in April 2026.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/39.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 5.13846+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "b01313a4744f0eda", "improvement": 0.00022970687679979562, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2716746597467209e-07, "max_pair_overlap_depth": -7.26967224418118e-07, "metric_expression": "5.13823", "metric_symbol": "s", "metric_value": 5.1382302931232005, "n": 39, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 5.13846, "setup": "squinpen", "side": 5.1382302931232005, "solution_path": "data/solutions/record_hunt/squinpen_39_b01313a4744f0eda.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/b01313a4744f0eda.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squinpen@40", "density": 0.8691683896670805, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/40.gif", "friedman_metric_expression": "5.17250+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.1725, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "5.17250+", "metric_symbol": "s", "metric_value": 5.1725, "reference_text": "s = 5.17250+ | Found by Emerson Connelly | in April 2026.", "source_image": "40.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/40.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 5.17250+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "153dbd88227e7083", "improvement": 0.0005591675539955432, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.137577186347585e-07, "max_pair_overlap_depth": -4.818340240131391e-07, "metric_expression": "5.17194", "metric_symbol": "s", "metric_value": 5.171940832446005, "n": 40, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 5.1725, "setup": "squinpen", "side": 5.171940832446005, "solution_path": "data/solutions/record_hunt/squinpen_40_153dbd88227e7083.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/153dbd88227e7083.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@1", "density": 0.49741240626661626, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts1.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "1 + 2 / \u221a3 = 2.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.154, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1 + 2 / \u221a3 = 2.154+", "metric_symbol": "s", "metric_value": 2.154, "reference_text": "s = 1 + 2 / \u221a3 = 2.154+ | Trivial.", "source_image": "ts1.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts1.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 1 + 2 / \u221a3 = 2.154+ | Trivial.", "friedman_source_image": "ts1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "bc8215883b0d29fa", "improvement": -0.0007226428063047408, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.189638991319711e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "2.15472", "metric_symbol": "s", "metric_value": 2.1547226428063047, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.154, "setup": "squintri", "side": 2.1547226428063047, "solution_path": "data/solutions/generated/squintri_001_bc8215883b0d29fa.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/bc8215883b0d29fa.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@2", "density": 0.4640775964340414, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts2.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2 + 2 / \u221a3 = 3.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.154, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2 + 2 / \u221a3 = 3.154+", "metric_symbol": "s", "metric_value": 3.154, "reference_text": "s = 2 + 2 / \u221a3 = 3.154+ | Trivial.", "source_image": "ts2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts2.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 2 + 2 / \u221a3 = 3.154+ | Trivial.", "friedman_source_image": "ts2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "9fcb7fc91bdb6f8d", "improvement": -0.000782174335970165, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.2952441585539525e-06, "max_pair_overlap_depth": -3.4919698730116744e-05, "metric_expression": "3.15478", "metric_symbol": "s", "metric_value": 3.15478217433597, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.154, "setup": "squintri", "side": 3.15478217433597, "solution_path": "data/solutions/generated/squintri_002_9fcb7fc91bdb6f8d.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/9fcb7fc91bdb6f8d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@3", "density": 0.6632023535454387, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts3.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3 / 2 + \u221a3 = 3.232+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.232, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@3", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 / 2 + \u221a3 = 3.232+", "metric_symbol": "s", "metric_value": 3.232, "reference_text": "s = 3 / 2 + \u221a3 = 3.232+ | Found by Erich Friedman | in 1997.", "source_image": "ts3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts3.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 / 2 + \u221a3 = 3.232+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "6a0fd09e2fb037d5", "improvement": -0.00011853663309757678, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.0862631378148764e-06, "max_pair_overlap_depth": -4.0896047962125925e-05, "metric_expression": "3.23212", "metric_symbol": "s", "metric_value": 3.232118536633098, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.232, "setup": "squintri", "side": 3.232118536633098, "solution_path": "data/solutions/generated/squintri_003_6a0fd09e2fb037d5.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/6a0fd09e2fb037d5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@4", "density": 0.5351297741951115, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts4.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3 + 2 / \u221a3 = 4.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.154, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@4", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 + 2 / \u221a3 = 4.154+", "metric_symbol": "s", "metric_value": 4.154, "reference_text": "s = 3 + 2 / \u221a3 = 4.154+ | Found by Erich Friedman | in 1997.", "source_image": "ts4.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts4.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 2 / \u221a3 = 4.154+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "a14dd3a45e182f53", "improvement": -0.000799971071848482, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3541096500101422e-06, "max_pair_overlap_depth": -2.3979848717270436e-05, "metric_expression": "4.15480", "metric_symbol": "s", "metric_value": 4.154799971071848, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.154, "setup": "squintri", "side": 4.154799971071848, "solution_path": "data/solutions/generated/squintri_004_a14dd3a45e182f53.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/a14dd3a45e182f53.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@5", "density": 0.6217402820027407, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts6.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2 + 4 / \u221a3 = 4.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.309, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@5", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "2 + 4 / \u221a3 = 4.309+", "metric_symbol": "s", "metric_value": 4.309, "reference_text": "s = 2 + 4 / \u221a3 = 4.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts6.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts6.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 2 + 4 / \u221a3 = 4.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "b7ec125fb5317da3", "improvement": -0.0005327081561983249, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.818148398440643e-06, "max_pair_overlap_depth": -2.4242157156018074e-05, "metric_expression": "4.30953", "metric_symbol": "s", "metric_value": 4.3095327081561985, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.309, "setup": "squintri", "side": 4.3095327081561985, "solution_path": "data/solutions/generated/squintri_005_b7ec125fb5317da3.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/b7ec125fb5317da3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@6", "density": 0.7460914321932061, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts6.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2 + 4 / \u221a3 = 4.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.309, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@6", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "2 + 4 / \u221a3 = 4.309+", "metric_symbol": "s", "metric_value": 4.309, "reference_text": "s = 2 + 4 / \u221a3 = 4.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts6.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts6.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 2 + 4 / \u221a3 = 4.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "cafd65072dcc4c6f", "improvement": -0.0005237730564999765, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6885485560193324e-06, "max_pair_overlap_depth": -3.2625800104213454e-05, "metric_expression": "4.30952", "metric_symbol": "s", "metric_value": 4.3095237730565, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.309, "setup": "squintri", "side": 4.3095237730565, "solution_path": "data/solutions/generated/squintri_006_cafd65072dcc4c6f.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/cafd65072dcc4c6f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@7", "density": 0.6083690864087284, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts7.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4 + 2 / \u221a3 = 5.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.154, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@7", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "4 + 2 / \u221a3 = 5.154+", "metric_symbol": "s", "metric_value": 5.154, "reference_text": "s = 4 + 2 / \u221a3 = 5.154+ | Found by Erich Friedman | in 1997.", "source_image": "ts7.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts7.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 2 / \u221a3 = 5.154+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "b90420d34e1bd6e3", "improvement": -0.0008393265287383045, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.7967605582714725e-06, "max_pair_overlap_depth": -3.132565940933141e-05, "metric_expression": "5.15484", "metric_symbol": "s", "metric_value": 5.154839326528738, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.154, "setup": "squintri", "side": 5.154839326528738, "solution_path": "data/solutions/generated/squintri_007_b90420d34e1bd6e3.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/b90420d34e1bd6e3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@8", "density": 0.6568042680930309, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts8.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5.301+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.301, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@8", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "5.301+", "metric_symbol": "s", "metric_value": 5.301, "reference_text": "s = 5.301+ | Found by David W. Cantrell | in July 2002.", "source_image": "ts8.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts8.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5.301+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "ts8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "9523798d0eb30de3", "improvement": -0.0026724224763796656, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4466353188141736e-06, "max_pair_overlap_depth": -2.591508822799571e-05, "metric_expression": "5.30367", "metric_symbol": "s", "metric_value": 5.30367242247638, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.301, "setup": "squintri", "side": 5.30367242247638, "solution_path": "data/solutions/generated/squintri_008_9523798d0eb30de3.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/9523798d0eb30de3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@9", "density": 0.7370953908179042, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts9.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3 + 4 / \u221a3 = 5.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.309, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@9", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 + 4 / \u221a3 = 5.309+", "metric_symbol": "s", "metric_value": 5.309, "reference_text": "s = 3 + 4 / \u221a3 = 5.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts9.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts9.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 4 / \u221a3 = 5.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "221ec438e9e78bec", "improvement": -0.0011781204346883456, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.476651564783165e-07, "max_pair_overlap_depth": -2.048243915964143e-05, "metric_expression": "5.31018", "metric_symbol": "s", "metric_value": 5.3101781204346885, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.309, "setup": "squintri", "side": 5.3101781204346885, "solution_path": "data/solutions/generated/squintri_009_221ec438e9e78bec.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/221ec438e9e78bec.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@10", "density": 0.773471405329893, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts10.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2 + 2 \u221a3 = 5.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.464, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@10", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "2 + 2 \u221a3 = 5.464+", "metric_symbol": "s", "metric_value": 5.464, "reference_text": "s = 2 + 2 \u221a3 = 5.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts10.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts10.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 2 + 2 \u221a3 = 5.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "4b92d4f5e6704540", "improvement": -0.00021212423215644094, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1415169103720102e-06, "max_pair_overlap_depth": -1.0706995126841257e-05, "metric_expression": "5.46421", "metric_symbol": "s", "metric_value": 5.464212124232157, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.464, "setup": "squintri", "side": 5.464212124232157, "solution_path": "data/solutions/generated/squintri_010_4b92d4f5e6704540.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/4b92d4f5e6704540.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@11", "density": 0.6705894339586221, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts11.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5 + 2 / \u221a3 = 6.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.154, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@11", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "5 + 2 / \u221a3 = 6.154+", "metric_symbol": "s", "metric_value": 6.154, "reference_text": "s = 5 + 2 / \u221a3 = 6.154+ | Found by Erich Friedman | in 1997.", "source_image": "ts11.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts11.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 2 / \u221a3 = 6.154+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "c18f0f7b3b1e0227", "improvement": -0.0008528095099347155, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.062945956811758e-06, "max_pair_overlap_depth": -2.0039414804218225e-05, "metric_expression": "6.15485", "metric_symbol": "s", "metric_value": 6.154852809509935, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.154, "setup": "squintri", "side": 6.154852809509935, "solution_path": "data/solutions/generated/squintri_011_c18f0f7b3b1e0227.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/c18f0f7b3b1e0227.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@12", "density": 0.6970880090801083, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts12.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.301+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.301, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@12", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "6.301+", "metric_symbol": "s", "metric_value": 6.301, "reference_text": "s = 6.301+ | Found by David W. Cantrell | in July 2002.", "source_image": "ts12.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts12.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 6.301+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "ts12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "d248ead86c97d2e6", "improvement": -0.004165620418586258, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6132876791233732e-06, "max_pair_overlap_depth": -5.9825433180948906e-05, "metric_expression": "6.30517", "metric_symbol": "s", "metric_value": 6.305165620418586, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.301, "setup": "squintri", "side": 6.305165620418586, "solution_path": "data/solutions/generated/squintri_012_d248ead86c97d2e6.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d248ead86c97d2e6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@13", "density": 0.7541442288903037, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts13.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4 + 4 / \u221a3 = 6.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.309, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@13", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "4 + 4 / \u221a3 = 6.309+", "metric_symbol": "s", "metric_value": 6.309, "reference_text": "s = 4 + 4 / \u221a3 = 6.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts13.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts13.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 4 / \u221a3 = 6.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "3b7ab78f832490ed", "improvement": -0.0004884860946248182, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1403459653225352e-06, "max_pair_overlap_depth": -1.2003638542146255e-05, "metric_expression": "6.30949", "metric_symbol": "s", "metric_value": 6.309488486094625, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.309, "setup": "squintri", "side": 6.309488486094625, "solution_path": "data/solutions/generated/squintri_013_3b7ab78f832490ed.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/3b7ab78f832490ed.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@14", "density": 0.7737221641470288, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts15.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3 + 2 \u221a3 = 6.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.464, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@14", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 + 2 \u221a3 = 6.464+", "metric_symbol": "s", "metric_value": 6.464, "reference_text": "s = 3 + 2 \u221a3 = 6.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts15.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts15.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 2 \u221a3 = 6.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "ffc152ae79167d33", "improvement": -0.00029520096988377986, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.958378324017974e-07, "max_pair_overlap_depth": -1.6732970481436737e-05, "metric_expression": "6.46430", "metric_symbol": "s", "metric_value": 6.464295200969884, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.464, "setup": "squintri", "side": 6.464295200969884, "solution_path": "data/solutions/generated/squintri_014_ffc152ae79167d33.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/ffc152ae79167d33.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@15", "density": 0.8289675963035161, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts15.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3 + 2 \u221a3 = 6.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.464, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@15", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 + 2 \u221a3 = 6.464+", "metric_symbol": "s", "metric_value": 6.464, "reference_text": "s = 3 + 2 \u221a3 = 6.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts15.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts15.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 2 \u221a3 = 6.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "37ace9570dd5c15b", "improvement": -0.0003748832881260711, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.039916977622108e-06, "max_pair_overlap_depth": -1.0702944550522453e-05, "metric_expression": "6.46437", "metric_symbol": "s", "metric_value": 6.4643748832881265, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.464, "setup": "squintri", "side": 6.4643748832881265, "solution_path": "data/solutions/generated/squintri_015_37ace9570dd5c15b.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/37ace9570dd5c15b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@16", "density": 0.7217958800018128, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts16.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6 + 2 / \u221a3 = 7.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.154, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@16", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "6 + 2 / \u221a3 = 7.154+", "metric_symbol": "s", "metric_value": 7.154, "reference_text": "s = 6 + 2 / \u221a3 = 7.154+ | Found by Erich Friedman | in 1997.", "source_image": "ts16.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts16.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 6 + 2 / \u221a3 = 7.154+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "36afe756f11f62d6", "improvement": -0.0008819711932614993, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.5571215058068575e-06, "max_pair_overlap_depth": -2.4408532427300234e-05, "metric_expression": "7.15488", "metric_symbol": "s", "metric_value": 7.154881971193261, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.154, "setup": "squintri", "side": 7.154881971193261, "solution_path": "data/solutions/generated/squintri_016_36afe756f11f62d6.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/36afe756f11f62d6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@17", "density": 0.7357616143895036, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts17.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "7.301+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.301, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@17", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "7.301+", "metric_symbol": "s", "metric_value": 7.301, "reference_text": "s = 7.301+ | Found by David W. Cantrell | in July 2002.", "source_image": "ts17.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts17.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 7.301+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "ts17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "3a2c987432da5f1d", "improvement": -0.0037537403553287163, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 2.4850519352755694e-10, "max_pair_overlap_depth": -2.8059876787889237e-05, "metric_expression": "7.30475", "metric_symbol": "s", "metric_value": 7.304753740355329, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.301, "setup": "squintri", "side": 7.304753740355329, "solution_path": "data/solutions/generated/squintri_017_3a2c987432da5f1d.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/3a2c987432da5f1d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@18", "density": 0.7780278532013658, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts18.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5 + 4 / \u221a3 = 7.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.309, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@18", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "5 + 4 / \u221a3 = 7.309+", "metric_symbol": "s", "metric_value": 7.309, "reference_text": "s = 5 + 4 / \u221a3 = 7.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts18.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 4 / \u221a3 = 7.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "e729e13f2fcc5856", "improvement": -0.0005116409635963493, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1021248752761939e-06, "max_pair_overlap_depth": -8.579145527987109e-06, "metric_expression": "7.30951", "metric_symbol": "s", "metric_value": 7.3095116409635965, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.309, "setup": "squintri", "side": 7.3095116409635965, "solution_path": "data/solutions/generated/squintri_018_e729e13f2fcc5856.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/e729e13f2fcc5856.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@19", "density": 0.787537700321716, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts19.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4 + 2 \u221a3 = 7.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.464, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@19", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "4 + 2 \u221a3 = 7.464+", "metric_symbol": "s", "metric_value": 7.464, "reference_text": "s = 4 + 2 \u221a3 = 7.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts19.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 2 \u221a3 = 7.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "805d1e50c1db2842", "improvement": -0.0003295610354463463, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0609380559736765e-06, "max_pair_overlap_depth": -1.836020690809681e-05, "metric_expression": "7.46433", "metric_symbol": "s", "metric_value": 7.464329561035447, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.464, "setup": "squintri", "side": 7.464329561035447, "solution_path": "data/solutions/generated/squintri_019_805d1e50c1db2842.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/805d1e50c1db2842.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@20", "density": 0.795657127614163, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3 + 8 / \u221a3 = 7.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@20", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 + 8 / \u221a3 = 7.618+", "metric_symbol": "s", "metric_value": 7.618, "reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "f4d21a73470ce742", "improvement": -0.0010653922379448844, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.382631857088383e-07, "max_pair_overlap_depth": -1.1470843414018717e-05, "metric_expression": "7.61907", "metric_symbol": "s", "metric_value": 7.619065392237945, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.618, "setup": "squintri", "side": 7.619065392237945, "solution_path": "data/solutions/generated/squintri_020_f4d21a73470ce742.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/f4d21a73470ce742.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@21", "density": 0.8354483980307021, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "friedman_metric_expression": "3 + 8 / \u221a3 = 7.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@21", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 + 8 / \u221a3 = 7.618+", "metric_symbol": "s", "metric_value": 7.618, "reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "a2e24601c2557198", "improvement": -0.0010270252659259071, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.8035391721895233e-06, "max_pair_overlap_depth": -9.7266150509423e-06, "metric_expression": "7.61903", "metric_symbol": "s", "metric_value": 7.619027025265926, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 7.618, "setup": "squintri", "side": 7.619027025265926, "solution_path": "data/solutions/generated/squintri_021_a2e24601c2557198.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/a2e24601c2557198.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@22", "density": 0.7639711289147475, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts22.gif", "friedman_metric_expression": "7 + 2 / \u221a3 = 8.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.154, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@22", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "7 + 2 / \u221a3 = 8.154+", "metric_symbol": "s", "metric_value": 8.154, "reference_text": "s = 7 + 2 / \u221a3 = 8.154+ | Found by Erich Friedman | in 1997.", "source_image": "ts22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts22.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 7 + 2 / \u221a3 = 8.154+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "bbb028380d997350", "improvement": -0.00097340620692421, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4334644744109685e-07, "max_pair_overlap_depth": -2.16343036094635e-05, "metric_expression": "8.15497", "metric_symbol": "s", "metric_value": 8.154973406206924, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.154, "setup": "squintri", "side": 8.154973406206924, "solution_path": "data/solutions/generated/squintri_022_bbb028380d997350.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/bbb028380d997350.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@23", "density": 0.7697946105392801, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts23.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "8.301+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.301, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@23", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "8.301+", "metric_symbol": "s", "metric_value": 8.301, "reference_text": "s = 8.301+ | Found by David W. Cantrell | in July 2002.", "source_image": "ts23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts23.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 8.301+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "ts23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "b1534ea73e00f283", "improvement": -0.005654877387726742, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7355116411507935e-05, "max_pair_overlap_depth": 9.193993899536679e-09, "metric_expression": "8.30665", "metric_symbol": "s", "metric_value": 8.306654877387727, "n": 23, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.301, "setup": "squintri", "side": 8.306654877387727, "solution_path": "data/solutions/generated/squintri_023_b1534ea73e00f283.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/b1534ea73e00f283.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@24", "density": 0.8026821430235043, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts24.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6 + 4 / \u221a3 = 8.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.309, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@24", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "6 + 4 / \u221a3 = 8.309+", "metric_symbol": "s", "metric_value": 8.309, "reference_text": "s = 6 + 4 / \u221a3 = 8.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts24.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 6 + 4 / \u221a3 = 8.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "648f7ef8ee4a197f", "improvement": -0.0006647382800331059, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.518509956206752e-06, "max_pair_overlap_depth": -1.764131142900638e-05, "metric_expression": "8.30966", "metric_symbol": "s", "metric_value": 8.309664738280032, "n": 24, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.309, "setup": "squintri", "side": 8.309664738280032, "solution_path": "data/solutions/generated/squintri_024_648f7ef8ee4a197f.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/648f7ef8ee4a197f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@25", "density": 0.8057999996349686, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts25.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5 + 2 \u221a3 = 8.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.464, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@25", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "5 + 2 \u221a3 = 8.464+", "metric_symbol": "s", "metric_value": 8.464, "reference_text": "s = 5 + 2 \u221a3 = 8.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts25.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 2 \u221a3 = 8.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "a868d8af97a256ad", "improvement": -0.0005924926961089483, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7884356498379287e-06, "max_pair_overlap_depth": -2.4212693654490636e-06, "metric_expression": "8.46459", "metric_symbol": "s", "metric_value": 8.46459249269611, "n": 25, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.464, "setup": "squintri", "side": 8.46459249269611, "solution_path": "data/solutions/generated/squintri_025_a868d8af97a256ad.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/a868d8af97a256ad.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@26", "density": 0.8076243715506172, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4 + 8 / \u221a3 = 8.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@26", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "4 + 8 / \u221a3 = 8.618+", "metric_symbol": "s", "metric_value": 8.618, "reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "249af47eefa3a74b", "improvement": -0.004469124601865104, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.4769017068652995e-06, "max_pair_overlap_depth": -2.5879119370686432e-05, "metric_expression": "8.62247", "metric_symbol": "s", "metric_value": 8.622469124601865, "n": 26, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.618, "setup": "squintri", "side": 8.622469124601865, "solution_path": "data/solutions/generated/squintri_026_249af47eefa3a74b.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/249af47eefa3a74b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@27", "density": 0.8380226358442442, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4 + 8 / \u221a3 = 8.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@27", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "4 + 8 / \u221a3 = 8.618+", "metric_symbol": "s", "metric_value": 8.618, "reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "3c62cd2126467cec", "improvement": -0.007885505517393199, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.235025861662866e-06, "max_pair_overlap_depth": -2.0721793894562524e-05, "metric_expression": "8.62589", "metric_symbol": "s", "metric_value": 8.625885505517394, "n": 27, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.618, "setup": "squintri", "side": 8.625885505517394, "solution_path": "data/solutions/generated/squintri_027_3c62cd2126467cec.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/3c62cd2126467cec.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@28", "density": 0.8400113660191094, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts28.gif", "friedman_metric_expression": "3 + 10 / \u221a3 = 8.773+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.773, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@28", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 + 10 / \u221a3 = 8.773+", "metric_symbol": "s", "metric_value": 8.773, "reference_text": "s = 3 + 10 / \u221a3 = 8.773+ | Found by Erich Friedman | in 1997.", "source_image": "ts28.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts28.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 10 / \u221a3 = 8.773+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "0d20b359435ed501", "improvement": -0.0007673944032049462, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0145694937175628e-06, "max_pair_overlap_depth": -1.3941973455278145e-05, "metric_expression": "8.77377", "metric_symbol": "s", "metric_value": 8.773767394403205, "n": 28, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 8.773, "setup": "squintri", "side": 8.773767394403205, "solution_path": "data/solutions/generated/squintri_028_0d20b359435ed501.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/0d20b359435ed501.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@29", "density": 0.7990846545133872, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts29.gif", "friedman_metric_expression": "8 + 2 / \u221a3 = 9.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.154, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@29", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "8 + 2 / \u221a3 = 9.154+", "metric_symbol": "s", "metric_value": 9.154, "reference_text": "s = 8 + 2 / \u221a3 = 9.154+ | Found by Erich Friedman | in 1997.", "source_image": "ts29.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts29.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 8 + 2 / \u221a3 = 9.154+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "3947aab39c0a1a92", "improvement": -0.000872191450978832, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2628787428294703e-06, "max_pair_overlap_depth": -1.875431036468811e-05, "metric_expression": "9.15487", "metric_symbol": "s", "metric_value": 9.154872191450979, "n": 29, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.154, "setup": "squintri", "side": 9.154872191450979, "solution_path": "data/solutions/generated/squintri_029_3947aab39c0a1a92.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/3947aab39c0a1a92.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@30", "density": 0.7992784153759376, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts30.gif", "friedman_metric_expression": "9.301+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.301, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@30", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "9.301+", "metric_symbol": "s", "metric_value": 9.301, "reference_text": "s = 9.301+ | Found by David W. Cantrell | in July 2002.", "source_image": "ts30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts30.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 9.301+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "ts30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "e0b7505d8b6b1d46", "improvement": -0.009248370808917272, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.5690858985090003e-06, "max_pair_overlap_depth": -2.654303096472077e-05, "metric_expression": "9.31025", "metric_symbol": "s", "metric_value": 9.310248370808917, "n": 30, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.301, "setup": "squintri", "side": 9.310248370808917, "solution_path": "data/solutions/generated/squintri_030_e0b7505d8b6b1d46.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/e0b7505d8b6b1d46.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@31", "density": 0.825993871568094, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts31.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "7 + 4 / \u221a3 = 9.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.309, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@31", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "7 + 4 / \u221a3 = 9.309+", "metric_symbol": "s", "metric_value": 9.309, "reference_text": "s = 7 + 4 / \u221a3 = 9.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts31.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts31.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 7 + 4 / \u221a3 = 9.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "22b5f5f5707858bb", "improvement": -0.0008378379274667225, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6472234336534766e-06, "max_pair_overlap_depth": -3.090204228461957e-05, "metric_expression": "9.30984", "metric_symbol": "s", "metric_value": 9.309837837927466, "n": 31, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.309, "setup": "squintri", "side": 9.309837837927466, "solution_path": "data/solutions/generated/squintri_031_22b5f5f5707858bb.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/22b5f5f5707858bb.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@32", "density": 0.8249717531277396, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts32.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6 + 2 \u221a3 = 9.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.464, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@32", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "6 + 2 \u221a3 = 9.464+", "metric_symbol": "s", "metric_value": 9.464, "reference_text": "s = 6 + 2 \u221a3 = 9.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts32.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 6 + 2 \u221a3 = 9.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "a44fbd99145b1ab3", "improvement": -0.0006624941961259623, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.1832282131171085e-07, "max_pair_overlap_depth": -1.699280632205813e-06, "metric_expression": "9.46466", "metric_symbol": "s", "metric_value": 9.464662494196126, "n": 32, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.464, "setup": "squintri", "side": 9.464662494196126, "solution_path": "data/solutions/generated/squintri_032_a44fbd99145b1ab3.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/a44fbd99145b1ab3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@33", "density": 0.8228028312642216, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5 + 8 / \u221a3 = 9.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@33", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "5 + 8 / \u221a3 = 9.618+", "metric_symbol": "s", "metric_value": 9.618, "reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "67de1e08be2d150c", "improvement": -0.00606977957198751, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.226435414550563e-06, "max_pair_overlap_depth": -3.0944328952564604e-06, "metric_expression": "9.62407", "metric_symbol": "s", "metric_value": 9.624069779571988, "n": 33, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.618, "setup": "squintri", "side": 9.624069779571988, "solution_path": "data/solutions/generated/squintri_033_67de1e08be2d150c.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/67de1e08be2d150c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@34", "density": 0.8485900582279403, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "friedman_metric_expression": "5 + 8 / \u221a3 = 9.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@34", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "5 + 8 / \u221a3 = 9.618+", "metric_symbol": "s", "metric_value": 9.618, "reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "3661302cdd9d0eb0", "improvement": -0.0012269381751668362, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.159334309452278e-06, "max_pair_overlap_depth": -1.741303470170763e-05, "metric_expression": "9.61923", "metric_symbol": "s", "metric_value": 9.619226938175167, "n": 34, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.618, "setup": "squintri", "side": 9.619226938175167, "solution_path": "data/solutions/generated/squintri_034_3661302cdd9d0eb0.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/3661302cdd9d0eb0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@35", "density": 0.8451911560111607, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4 + 10 / \u221a3 = 9.773+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.773, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@35", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "4 + 10 / \u221a3 = 9.773+", "metric_symbol": "s", "metric_value": 9.773, "reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "source_image": "ts36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "39d52a823b632afe", "improvement": -0.006265389488104844, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.195518233524095e-06, "max_pair_overlap_depth": -2.612964804571405e-05, "metric_expression": "9.77927", "metric_symbol": "s", "metric_value": 9.779265389488105, "n": 35, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.773, "setup": "squintri", "side": 9.779265389488105, "solution_path": "data/solutions/generated/squintri_035_39d52a823b632afe.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/39d52a823b632afe.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@36", "density": 0.8698156108347095, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4 + 10 / \u221a3 = 9.773+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.773, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@36", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "4 + 10 / \u221a3 = 9.773+", "metric_symbol": "s", "metric_value": 9.773, "reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "source_image": "ts36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "f0473aaa767ebe98", "improvement": -0.0035884436987085877, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9270562690497914e-06, "max_pair_overlap_depth": -7.45737725771356e-06, "metric_expression": "9.77659", "metric_symbol": "s", "metric_value": 9.776588443698708, "n": 36, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 9.773, "setup": "squintri", "side": 9.776588443698708, "solution_path": "data/solutions/generated/squintri_036_f0473aaa767ebe98.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/f0473aaa767ebe98.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@37", "density": 0.8285699034870297, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts37.gif", "friedman_metric_expression": "10.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.154, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@37", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "10.154+", "metric_symbol": "s", "metric_value": 10.154, "reference_text": "s = 10.154+ | Found by Emerson Connelly | in April 2026.", "source_image": "ts37.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts37.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 10.154+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "ts37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "8530be000ac2e9ed", "improvement": -0.0011412138177444575, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3566887422690367e-06, "max_pair_overlap_depth": -1.2239987045248313e-05, "metric_expression": "10.15514", "metric_symbol": "s", "metric_value": 10.155141213817744, "n": 37, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 10.154, "setup": "squintri", "side": 10.155141213817744, "solution_path": "data/solutions/generated/squintri_037_8530be000ac2e9ed.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/8530be000ac2e9ed.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@38", "density": 0.8256293316995508, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts38.gif", "friedman_metric_expression": "10.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.309, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "10.309+", "metric_symbol": "s", "metric_value": 10.309, "reference_text": "s = 10.309+ | Found by Emerson Connelly | in April 2026.", "source_image": "ts38.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts38.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 10.309+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "ts38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "896b636f9d899bf5", "improvement": -0.0007687369401132571, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.231911901047403e-06, "max_pair_overlap_depth": -1.6045122417374102e-05, "metric_expression": "10.30977", "metric_symbol": "s", "metric_value": 10.309768736940113, "n": 38, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 10.309, "setup": "squintri", "side": 10.309768736940113, "solution_path": "data/solutions/generated/squintri_038_896b636f9d899bf5.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/896b636f9d899bf5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@39", "density": 0.8473534790778084, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts39.gif", "friedman_metric_expression": "10.310+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.31, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "10.310+", "metric_symbol": "s", "metric_value": 10.31, "reference_text": "s = 10.310+ | Found by Emerson Connelly | in April 2026.", "source_image": "ts39.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts39.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 10.310+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "ts39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "c0988e1f3bf189d9", "improvement": 0.00021337573935120702, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.79079015949438e-07, "max_pair_overlap_depth": -3.1188368032619707e-06, "metric_expression": "10.30979", "metric_symbol": "s", "metric_value": 10.30978662426065, "n": 39, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 10.31, "setup": "squintri", "side": 10.30978662426065, "solution_path": "data/solutions/record_hunt/squintri_39_c0988e1f3bf189d9.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/c0988e1f3bf189d9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "squintri@40", "density": 0.8436138407048179, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts40.gif", "friedman_metric_expression": "10.46426+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.46426, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@40", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "10.46426+", "metric_symbol": "s", "metric_value": 10.46426, "reference_text": "s = 10.46426+ | Found by Nathan Roll | in April 2026.", "source_image": "ts40.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts40.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 10.46426+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "ts40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "13b03f25af76ce87", "improvement": 1.6681613434599285e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.839061064144293e-07, "max_pair_overlap_depth": -1.4626365829606414e-06, "metric_expression": "10.46424", "metric_symbol": "s", "metric_value": 10.464243318386565, "n": 40, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 10.46426, "setup": "squintri", "side": 10.464243318386565, "solution_path": "data/solutions/record_hunt/squintri_40_13b03f25af76ce87.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/13b03f25af76ce87.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@1", "density": 0.41349293224745, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc1.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1/\u221a3 = .577+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.577, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1/\u221a3 = .577+", "metric_symbol": "r", "metric_value": 0.577, "reference_text": "r = 1/\u221a3 = .577+ | Trivial.", "source_image": "tc1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc1.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1/\u221a3 = .577+ | Trivial.", "friedman_source_image": "tc1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "49954bfbb560620d", "improvement": -0.00035287974439102143, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.775275519510515e-07, "max_pair_overlap_depth": 0.0, "metric_expression": "0.57735", "metric_symbol": "r", "metric_value": 0.577352879744391, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.577, "setup": "triincir", "side": 1.154705759488782, "solution_path": "data/solutions/generated/triincir_001_49954bfbb560620d.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/49954bfbb560620d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@2", "density": 0.3675414068402789, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc2.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "\u221a3/2 = .866+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.866, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a3/2 = .866+", "metric_symbol": "r", "metric_value": 0.866, "reference_text": "r = \u221a3/2 = .866+ | Trivial.", "source_image": "tc2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc2.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = \u221a3/2 = .866+ | Trivial.", "friedman_source_image": "tc2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "92f5511b689fe041", "improvement": -3.858712037896339e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.072458078845486e-06, "max_pair_overlap_depth": -1.0890566688626091e-05, "metric_expression": "0.86604", "metric_symbol": "r", "metric_value": 0.866038587120379, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.866, "setup": "triincir", "side": 1.732077174240758, "solution_path": "data/solutions/generated/triincir_002_92f5511b689fe041.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/92f5511b689fe041.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@3", "density": 0.45476420302551357, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc3.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "3\u221a3 - 3\u221a2 = .953+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.953, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@3", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3\u221a3 - 3\u221a2 = .953+", "metric_symbol": "r", "metric_value": 0.953, "reference_text": "r = 3\u221a3 - 3\u221a2 = .953+ | Found by Erich Friedman | in 1997.", "source_image": "tc3.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc3.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 3\u221a3 - 3\u221a2 = .953+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tc3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "6ede8225b5939550", "improvement": -0.0005486885675038966, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4231654198736408e-06, "max_pair_overlap_depth": -2.0408752807413166e-05, "metric_expression": "0.95355", "metric_symbol": "r", "metric_value": 0.9535486885675039, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.953, "setup": "triincir", "side": 1.9070973771350077, "solution_path": "data/solutions/generated/triincir_003_6ede8225b5939550.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/6ede8225b5939550.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@4", "density": 0.5732690550709103, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc4.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": ".980+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.98, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@4", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": ".980+", "metric_symbol": "r", "metric_value": 0.98, "reference_text": "r = .980+ | Found by Erich Friedman | in 1997.", "source_image": "tc4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc4.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = .980+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tc4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "7f9481f33de5ecda", "improvement": -0.0006773112916812485, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.642177417024662e-06, "max_pair_overlap_depth": -2.677155749965807e-05, "metric_expression": "0.98068", "metric_symbol": "r", "metric_value": 0.9806773112916812, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.98, "setup": "triincir", "side": 1.9613546225833625, "solution_path": "data/solutions/generated/triincir_004_7f9481f33de5ecda.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/7f9481f33de5ecda.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@5", "density": 0.6891272508887964, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc5.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1", "friedman_metric_symbol": "r", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "r", "metric_value": 1.0, "reference_text": "r = 1 | Trivial.", "source_image": "tc5.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc5.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1 | Trivial.", "friedman_source_image": "tc5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "cf17d061ebfe392b", "improvement": -2.4573090296353683e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.800898255106432e-06, "max_pair_overlap_depth": -9.00554050570603e-06, "metric_expression": "1.00002", "metric_symbol": "r", "metric_value": 1.0000245730902964, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.0, "setup": "triincir", "side": 2.0000491461805927, "solution_path": "data/solutions/generated/triincir_005_cf17d061ebfe392b.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/cf17d061ebfe392b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@6", "density": 0.826963635452614, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc6.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1", "friedman_metric_symbol": "r", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@6", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "r", "metric_value": 1.0, "reference_text": "r = 1 | Trivial.", "source_image": "tc6.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc6.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1 | Trivial.", "friedman_source_image": "tc6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "fe93ba87f23c6c01", "improvement": -1.7961741001881748e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.861140867618019e-08, "max_pair_overlap_depth": -9.037179045745058e-06, "metric_expression": "1.00002", "metric_symbol": "r", "metric_value": 1.0000179617410019, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.0, "setup": "triincir", "side": 2.0000359234820038, "solution_path": "data/solutions/generated/triincir_006_fe93ba87f23c6c01.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/fe93ba87f23c6c01.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@7", "density": 0.7265087780749782, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc7.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.152+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.152, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@7", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "1.152+", "metric_symbol": "r", "metric_value": 1.152, "reference_text": "r = 1.152+ | Found by Erich Friedman | in 1997.", "source_image": "tc7.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc7.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.152+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tc7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "4d32cb6092e127b9", "improvement": -0.0004019079826915739, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.469968968942808e-06, "max_pair_overlap_depth": -4.662019983989185e-06, "metric_expression": "1.15240", "metric_symbol": "r", "metric_value": 1.1524019079826915, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.152, "setup": "triincir", "side": 2.304803815965383, "solution_path": "data/solutions/generated/triincir_007_4d32cb6092e127b9.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/4d32cb6092e127b9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@8", "density": 0.6908236123299982, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc8.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.263+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.263, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@8", "credit": "Maurizio Morandi", "date": "April 2008", "family_updated": "", "metric_expression": "1.263+", "metric_symbol": "r", "metric_value": 1.263, "reference_text": "r = 1.263+ | Found by Maurizio Morandi | in April 2008.", "source_image": "tc8.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc8.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.263+ | Found by Maurizio Morandi | in April 2008.", "friedman_source_image": "tc8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "33389e3c966a2171", "improvement": -0.0003881191911174753, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.08502399998045e-06, "max_pair_overlap_depth": -2.667573266001977e-06, "metric_expression": "1.26339", "metric_symbol": "r", "metric_value": 1.2633881191911174, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.263, "setup": "triincir", "side": 2.5267762383822348, "solution_path": "data/solutions/generated/triincir_008_33389e3c966a2171.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/33389e3c966a2171.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@9", "density": 0.7175995300521633, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc9.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.314+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.314, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@9", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "1.314+", "metric_symbol": "r", "metric_value": 1.314, "reference_text": "r = 1.314+ | Found by David W. Cantrell | in July 2002.", "source_image": "tc9.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc9.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.314+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "tc9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "68692b6dc093b182", "improvement": -0.0007874911911363025, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.28479338054899e-06, "max_pair_overlap_depth": -4.021549232235966e-06, "metric_expression": "1.31479", "metric_symbol": "r", "metric_value": 1.3147874911911364, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.314, "setup": "triincir", "side": 2.6295749823822727, "solution_path": "data/solutions/generated/triincir_009_68692b6dc093b182.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/68692b6dc093b182.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@10", "density": 0.7187883776258066, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc10.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.385+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.385, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@10", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "1.385+", "metric_symbol": "r", "metric_value": 1.385, "reference_text": "r = 1.385+ | Found by David W. Cantrell | in July 2002.", "source_image": "tc10.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc10.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.385+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "tc10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "676585e5c31a1d2f", "improvement": 0.0002388888356295027, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.405400112705848e-06, "max_pair_overlap_depth": -1.0902511275390214e-05, "metric_expression": "1.38476", "metric_symbol": "r", "metric_value": 1.3847611111643705, "n": 10, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 1.385, "setup": "triincir", "side": 2.769522222328741, "solution_path": "data/solutions/generated/triincir_010_676585e5c31a1d2f.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/676585e5c31a1d2f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@11", "density": 0.7044397586610418, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell after Maurizio Morandi", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc11.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.466+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.466, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@11", "credit": "David W. Cantrell after Maurizio Morandi", "date": "August 2012", "family_updated": "", "metric_expression": "1.466+", "metric_symbol": "r", "metric_value": 1.466, "reference_text": "r = 1.466+ | Found by DC after MM | in August 2012.", "source_image": "tc11.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc11.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.466+ | Found by DC after MM | in August 2012.", "friedman_source_image": "tc11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "27341d9b331a210b", "improvement": -0.0010664804404059147, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5710045151440255e-06, "max_pair_overlap_depth": -1.3965597729533735e-05, "metric_expression": "1.46707", "metric_symbol": "r", "metric_value": 1.4670664804404059, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.466, "setup": "triincir", "side": 2.9341329608808118, "solution_path": "data/solutions/generated/triincir_011_27341d9b331a210b.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell after Maurizio Morandi", "svg_path": "data/svg/27341d9b331a210b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@12", "density": 0.7276318026083056, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "October 2005", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc12.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.507+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.507, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@12", "credit": "David W. Cantrell", "date": "October 2005", "family_updated": "", "metric_expression": "1.507+", "metric_symbol": "r", "metric_value": 1.507, "reference_text": "r = 1.507+ | Found by David W. Cantrell | in October 2005.", "source_image": "tc12.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc12.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.507+ | Found by David W. Cantrell | in October 2005.", "friedman_source_image": "tc12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "0430950ce5a6ad65", "improvement": -0.0006834530254535842, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.988712507651542e-07, "max_pair_overlap_depth": -1.4096456774082e-06, "metric_expression": "1.50768", "metric_symbol": "r", "metric_value": 1.5076834530254535, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.507, "setup": "triincir", "side": 3.015366906050907, "solution_path": "data/solutions/generated/triincir_012_0430950ce5a6ad65.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/0430950ce5a6ad65.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@13", "density": 0.7678670311765523, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc13.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "\u221a(7/3) = 1.527+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.527, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@13", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a(7/3) = 1.527+", "metric_symbol": "r", "metric_value": 1.527, "reference_text": "r = \u221a(7/3) = 1.527+ | Found by Erich Friedman | in 1997.", "source_image": "tc13.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc13.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = \u221a(7/3) = 1.527+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tc13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "2b014eeead965100", "improvement": -0.0005802936296193106, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.995535488687807e-06, "max_pair_overlap_depth": -6.278738689302621e-06, "metric_expression": "1.52758", "metric_symbol": "r", "metric_value": 1.5275802936296192, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.527, "setup": "triincir", "side": 3.0551605872592384, "solution_path": "data/solutions/generated/triincir_013_2b014eeead965100.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/2b014eeead965100.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@14", "density": 0.7492543391037492, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell after Maurizio Morandi", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc14.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.609+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.609, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@14", "credit": "David W. Cantrell after Maurizio Morandi", "date": "August 2012", "family_updated": "", "metric_expression": "1.609+", "metric_symbol": "r", "metric_value": 1.609, "reference_text": "r = 1.609+ | Found by DC after MM | in August 2012.", "source_image": "tc14.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc14.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.609+ | Found by DC after MM | in August 2012.", "friedman_source_image": "tc14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": false, "id": "da4114b8f6b7e383", "improvement": 0.0041857717254343285, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4204418656849072e-06, "max_pair_overlap_depth": -6.9567849071972e-06, "metric_expression": "1.60481", "metric_symbol": "r", "metric_value": 1.6048142282745657, "n": 14, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.", "record_type": "verified", "reference_side": 1.609, "setup": "triincir", "side": 3.2096284565491313, "solution_path": "data/solutions/generated/triincir_014_da4114b8f6b7e383.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/da4114b8f6b7e383.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@15", "density": 0.7710002838935242, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc15.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.636+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.636, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@15", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "1.636+", "metric_symbol": "r", "metric_value": 1.636, "reference_text": "r = 1.636+ | Found by David W. Cantrell | in July 2002.", "source_image": "tc15.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc15.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.636+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "tc15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "e8f573cc9f431ed8", "improvement": -0.001546881163444036, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.392157777674768e-06, "max_pair_overlap_depth": -3.2056821285264547e-06, "metric_expression": "1.63755", "metric_symbol": "r", "metric_value": 1.637546881163444, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.636, "setup": "triincir", "side": 3.275093762326888, "solution_path": "data/solutions/generated/triincir_015_e8f573cc9f431ed8.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/e8f573cc9f431ed8.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@16", "density": 0.7739404139048575, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc16.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.687+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.687, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@16", "credit": "Maurizio Morandi", "date": "April 2008", "family_updated": "", "metric_expression": "1.687+", "metric_symbol": "r", "metric_value": 1.687, "reference_text": "r = 1.687+ | Found by Maurizio Morandi | in April 2008.", "source_image": "tc16.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc16.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.687+ | Found by Maurizio Morandi | in April 2008.", "friedman_source_image": "tc16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "8bb5531a7df45934", "improvement": -0.0010356342518775818, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.068784430077415e-07, "max_pair_overlap_depth": -9.622687440202782e-07, "metric_expression": "1.68804", "metric_symbol": "r", "metric_value": 1.6880356342518776, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.687, "setup": "triincir", "side": 3.3760712685037553, "solution_path": "data/solutions/generated/triincir_16_8bb5531a7df45934.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/8bb5531a7df45934.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@17", "density": 0.7824875965148136, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2005", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc17.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.730+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.73, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@17", "credit": "David W. Cantrell", "date": "July 2005", "family_updated": "", "metric_expression": "1.730+", "metric_symbol": "r", "metric_value": 1.73, "reference_text": "r = 1.730+ | Found by David W. Cantrell | in July 2005.", "source_image": "tc17.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc17.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.730+ | Found by David W. Cantrell | in July 2005.", "friedman_source_image": "tc17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "47c836632f7377eb", "improvement": -0.00045819251380652126, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3405989713065622e-06, "max_pair_overlap_depth": -3.2207400054717894e-06, "metric_expression": "1.73046", "metric_symbol": "r", "metric_value": 1.7304581925138065, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.73, "setup": "triincir", "side": 3.460916385027613, "solution_path": "data/solutions/generated/triincir_017_47c836632f7377eb.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/47c836632f7377eb.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@18", "density": 0.763334042584198, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc18.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "\u221a13/2 = 1.802+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.802, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@18", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a13/2 = 1.802+", "metric_symbol": "r", "metric_value": 1.802, "reference_text": "r = \u221a13/2 = 1.802+ | Found by Erich Friedman | in 1997.", "source_image": "tc18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc18.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = \u221a13/2 = 1.802+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tc18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "8d495d33c78cce38", "improvement": -0.000828100052461922, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0688499290090192e-06, "max_pair_overlap_depth": -2.7547144944017887e-06, "metric_expression": "1.80283", "metric_symbol": "r", "metric_value": 1.802828100052462, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.802, "setup": "triincir", "side": 3.605656200104924, "solution_path": "data/solutions/generated/triincir_018_8d495d33c78cce38.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/8d495d33c78cce38.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@19", "density": 0.7847061820967525, "friedman_analytical_or_proved": true, "friedman_credit": "Haym Hirsh", "friedman_date": "August 2019", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc19.gif", "friedman_metric_expression": "\u221a(10/3) = 1.825+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.825, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@19", "credit": "Haym Hirsh", "date": "August 2019", "family_updated": "", "metric_expression": "\u221a(10/3) = 1.825+", "metric_symbol": "r", "metric_value": 1.825, "reference_text": "r = \u221a(10/3) = 1.825+ | Found by Haym Hirsh | in August 2019.", "source_image": "tc19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc19.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = \u221a(10/3) = 1.825+ | Found by Haym Hirsh | in August 2019.", "friedman_source_image": "tc19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "975121af758119a3", "improvement": -0.001832145989409506, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1422789436554837e-06, "max_pair_overlap_depth": -1.3515939734642934e-06, "metric_expression": "1.82683", "metric_symbol": "r", "metric_value": 1.8268321459894095, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.825, "setup": "triincir", "side": 3.653664291978819, "solution_path": "data/solutions/generated/triincir_19_975121af758119a3.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T14:34:18+00:00", "submitted_by": "Haym Hirsh", "svg_path": "data/svg/975121af758119a3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@20", "density": 0.7838286390350678, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc20.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.874+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.874, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@20", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "1.874+", "metric_symbol": "r", "metric_value": 1.874, "reference_text": "r = 1.874+ | Found by Erich Friedman | in 1997.", "source_image": "tc20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc20.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.874+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tc20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "1217493f9010e655", "improvement": -0.0013391312177313264, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.256942872007727e-07, "max_pair_overlap_depth": -1.3401476308239069e-05, "metric_expression": "1.87534", "metric_symbol": "r", "metric_value": 1.8753391312177314, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.874, "setup": "triincir", "side": 3.750678262435463, "solution_path": "data/solutions/generated/triincir_020_1217493f9010e655.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/1217493f9010e655.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@21", "density": 0.7923995336773865, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc21.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.910+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.91, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@21", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "", "metric_expression": "1.910+", "metric_symbol": "r", "metric_value": 1.91, "reference_text": "r = 1.910+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tc21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc21.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.910+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tc21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "46b1371ff82573dd", "improvement": -0.001229866251050593, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3922552147160872e-05, "max_pair_overlap_depth": -4.454706840822942e-06, "metric_expression": "1.91123", "metric_symbol": "r", "metric_value": 1.9112298662510505, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.91, "setup": "triincir", "side": 3.822459732502101, "solution_path": "data/solutions/generated/triincir_021_46b1371ff82573dd.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/46b1371ff82573dd.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@22", "density": 0.8017796736685735, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc22.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.943+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.943, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@22", "credit": "Maurizio Morandi", "date": "June 2008", "family_updated": "", "metric_expression": "1.943+", "metric_symbol": "r", "metric_value": 1.943, "reference_text": "r = 1.943+ | Found by Maurizio Morandi | in June 2008.", "source_image": "tc22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc22.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.943+ | Found by Maurizio Morandi | in June 2008.", "friedman_source_image": "tc22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "69faaab68dcae114", "improvement": -0.0017294951342150533, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.28347034731047e-06, "max_pair_overlap_depth": -4.770520652064292e-06, "metric_expression": "1.94473", "metric_symbol": "r", "metric_value": 1.9447294951342151, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.943, "setup": "triincir", "side": 3.8894589902684302, "solution_path": "data/solutions/generated/triincir_022_69faaab68dcae114.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/69faaab68dcae114.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@23", "density": 0.8020036651008373, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc23.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.988+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.988, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@23", "credit": "Maurizio Morandi", "date": "June 2008", "family_updated": "", "metric_expression": "1.988+", "metric_symbol": "r", "metric_value": 1.988, "reference_text": "r = 1.988+ | Found by Maurizio Morandi | in June 2008.", "source_image": "tc23.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc23.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.988+ | Found by Maurizio Morandi | in June 2008.", "friedman_source_image": "tc23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "bc03a535bc1be813", "improvement": -0.0001590443736558811, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0403434641002036e-06, "max_pair_overlap_depth": -2.2042403398092603e-06, "metric_expression": "1.98816", "metric_symbol": "r", "metric_value": 1.9881590443736559, "n": 23, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.988, "setup": "triincir", "side": 3.9763180887473117, "solution_path": "data/solutions/generated/triincir_023_bc03a535bc1be813.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/bc03a535bc1be813.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@24", "density": 0.82672890671807, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc24.gif", "friedman_metric_expression": "2", "friedman_metric_symbol": "r", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@24", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "r", "metric_value": 2.0, "reference_text": "r = 2 | Trivial.", "source_image": "tc24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc24.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2 | Trivial.", "friedman_source_image": "tc24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "e1de703df3a339d6", "improvement": -0.00031983310403260745, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.886123831735148e-06, "max_pair_overlap_depth": -6.330279525013083e-07, "metric_expression": "2.00032", "metric_symbol": "r", "metric_value": 2.0003198331040326, "n": 24, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "triincir", "side": 4.000639666208065, "solution_path": "data/solutions/generated/triincir_24_e1de703df3a339d6.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/e1de703df3a339d6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@25", "density": 0.814798554480224, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2005", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc25.gif", "friedman_metric_expression": "2.055+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.055, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@25", "credit": "David W. Cantrell", "date": "July 2005", "family_updated": "", "metric_expression": "2.055+", "metric_symbol": "r", "metric_value": 2.055, "reference_text": "r = 2.055+ | Found by David W. Cantrell | in July 2005.", "source_image": "tc25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc25.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.055+ | Found by David W. Cantrell | in July 2005.", "friedman_source_image": "tc25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "460bfc63493e0a99", "improvement": -0.0014599742843675045, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.499842621325968e-07, "max_pair_overlap_depth": -5.533591762807433e-06, "metric_expression": "2.05646", "metric_symbol": "r", "metric_value": 2.0564599742843677, "n": 25, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.055, "setup": "triincir", "side": 4.112919948568735, "solution_path": "data/solutions/generated/triincir_025_460bfc63493e0a99.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/460bfc63493e0a99.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@26", "density": 0.8055666262709128, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc26.gif", "friedman_metric_expression": "2.109+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.109, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@26", "credit": "Maurizio Morandi", "date": "April 2008", "family_updated": "", "metric_expression": "2.109+", "metric_symbol": "r", "metric_value": 2.109, "reference_text": "r = 2.109+ | Found by Maurizio Morandi | in April 2008.", "source_image": "tc26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc26.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.109+ | Found by Maurizio Morandi | in April 2008.", "friedman_source_image": "tc26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "8245fa6b2a472124", "improvement": -0.00016872463985961872, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.221408735321063e-06, "max_pair_overlap_depth": -3.3631357487795555e-07, "metric_expression": "2.10917", "metric_symbol": "r", "metric_value": 2.1091687246398596, "n": 26, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.109, "setup": "triincir", "side": 4.218337449279719, "solution_path": "data/solutions/generated/triincir_26_8245fa6b2a472124.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/8245fa6b2a472124.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@27", "density": 0.8132267625810148, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2005", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc27.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "2.138+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.138, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@27", "credit": "David W. Cantrell", "date": "July 2005", "family_updated": "", "metric_expression": "2.138+", "metric_symbol": "r", "metric_value": 2.138, "reference_text": "r = 2.138+ | Found by David W. Cantrell | in July 2005.", "source_image": "tc27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc27.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.138+ | Found by David W. Cantrell | in July 2005.", "friedman_source_image": "tc27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "6af16151fd4089a6", "improvement": -0.0012002098551513463, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.142316272914286e-07, "max_pair_overlap_depth": -2.7141719629586447e-06, "metric_expression": "2.13920", "metric_symbol": "r", "metric_value": 2.1392002098551512, "n": 27, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.138, "setup": "triincir", "side": 4.2784004197103025, "solution_path": "data/solutions/generated/triincir_027_6af16151fd4089a6.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/6af16151fd4089a6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@28", "density": 0.8029867070046219, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2005", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc28.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "2.191+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.191, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@28", "credit": "David W. Cantrell", "date": "July 2005", "family_updated": "", "metric_expression": "2.191+", "metric_symbol": "r", "metric_value": 2.191, "reference_text": "r = 2.191+ | Found by David W. Cantrell | in July 2005.", "source_image": "tc28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc28.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.191+ | Found by David W. Cantrell | in July 2005.", "friedman_source_image": "tc28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "b8a030f48c690095", "improvement": -0.0013011891131600173, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3556564240069235e-06, "max_pair_overlap_depth": -5.7499508869796045e-06, "metric_expression": "2.19230", "metric_symbol": "r", "metric_value": 2.19230118911316, "n": 28, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.191, "setup": "triincir", "side": 4.38460237822632, "solution_path": "data/solutions/generated/triincir_028_b8a030f48c690095.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/b8a030f48c690095.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@29", "density": 0.8182348688742829, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc29.gif", "friedman_metric_expression": "2.215+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.215, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@29", "credit": "Maurizio Morandi", "date": "June 2008", "family_updated": "", "metric_expression": "2.215+", "metric_symbol": "r", "metric_value": 2.215, "reference_text": "r = 2.215+ | Found by Maurizio Morandi | in June 2008.", "source_image": "tc29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc29.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.215+ | Found by Maurizio Morandi | in June 2008.", "friedman_source_image": "tc29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": false, "id": "73bcaf90b9fd2226", "improvement": 0.004780586805306797, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.1271053040349273e-06, "max_pair_overlap_depth": -1.2019034158372577e-05, "metric_expression": "2.21022", "metric_symbol": "r", "metric_value": 2.210219413194693, "n": 29, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.", "record_type": "verified", "reference_side": 2.215, "setup": "triincir", "side": 4.420438826389386, "solution_path": "data/solutions/generated/triincir_029_73bcaf90b9fd2226.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/73bcaf90b9fd2226.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@30", "density": 0.8110819400631206, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc30.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "2.258+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.258, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@30", "credit": "Maurizio Morandi", "date": "July 2008", "family_updated": "", "metric_expression": "2.258+", "metric_symbol": "r", "metric_value": 2.258, "reference_text": "r = 2.258+ | Found by Maurizio Morandi | in July 2008.", "source_image": "tc30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc30.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.258+ | Found by Maurizio Morandi | in July 2008.", "friedman_source_image": "tc30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "f720ec98817b9983", "improvement": 0.00010551194829711008, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9289733554094255e-06, "max_pair_overlap_depth": -4.657725350298847e-06, "metric_expression": "2.25789", "metric_symbol": "r", "metric_value": 2.257894488051703, "n": 30, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 2.258, "setup": "triincir", "side": 4.515788976103406, "solution_path": "data/solutions/generated/triincir_030_f720ec98817b9983.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/f720ec98817b9983.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triincir@31", "density": 0.8263348764897189, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc31.gif", "friedman_metric_expression": "2.272+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.272, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@31", "credit": "Maurizio Morandi", "date": "July 2008", "family_updated": "", "metric_expression": "2.272+", "metric_symbol": "r", "metric_value": 2.272, "reference_text": "r = 2.272+ | Found by Maurizio Morandi | in July 2008.", "source_image": "tc31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc31.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.272+ | Found by Maurizio Morandi | in July 2008.", "friedman_source_image": "tc31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "ed4a5072cc8d0adf", "improvement": -0.0019357369126002943, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3803713964376527e-06, "max_pair_overlap_depth": -5.497010580973738e-06, "metric_expression": "2.27394", "metric_symbol": "r", "metric_value": 2.2739357369126, "n": 31, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.272, "setup": "triincir", "side": 4.5478714738252, "solution_path": "data/solutions/generated/triincir_31_ed4a5072cc8d0adf.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T07:13:53+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/ed4a5072cc8d0adf.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@1", "density": 0.2886702903701934, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "\u221a3/2", "friedman_metric_symbol": "s", "friedman_metric_value": 0.8660254037844386, "friedman_reference": {"analytical_or_proved": true, "case": "triindom@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a3/2", "metric_symbol": "s", "metric_value": 0.8660254037844386, "reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "37b1dca676a779e3", "improvement": -7.266428382335377e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4019537994690587e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.86603", "metric_symbol": "s", "metric_value": 0.8660326702128209, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.8660254037844386, "setup": "triindom", "side": 1.7320653404256419, "solution_path": "data/solutions/generated/triindom_001_37b1dca676a779e3.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/37b1dca676a779e3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@2", "density": 0.5773351362696808, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "\u221a3/2", "friedman_metric_symbol": "s", "friedman_metric_value": 0.8660254037844386, "friedman_reference": {"analytical_or_proved": true, "case": "triindom@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a3/2", "metric_symbol": "s", "metric_value": 0.8660254037844386, "reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "31518429031d2b51", "improvement": -1.1349913078717577e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.727531273176268e-07, "max_pair_overlap_depth": -0.13184728443338464, "metric_expression": "0.86604", "metric_symbol": "s", "metric_value": 0.8660367536975173, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.8660254037844386, "setup": "triindom", "side": 1.7320735073950346, "solution_path": "data/solutions/generated/triindom_002_31518429031d2b51.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/31518429031d2b51.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@3", "density": 0.6931800833949334, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/3.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": ".96796+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.96796, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@3", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": ".96796+", "metric_symbol": "s", "metric_value": 0.96796, "reference_text": "3. | | s = .96796+ | Found by Jonathan Viquerat | in April 2026", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/3.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "3. | | s = .96796+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "b10402bd10926cd1", "improvement": -3.454421484250236e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.601436348197538e-06, "max_pair_overlap_depth": -2.0206571078401625e-05, "metric_expression": "0.96799", "metric_symbol": "s", "metric_value": 0.9679945442148425, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.96796, "setup": "triindom", "side": 1.935989088429685, "solution_path": "data/solutions/generated/triindom_003_b10402bd10926cd1.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/b10402bd10926cd1.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@4", "density": 0.6899032945238053, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/4.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.12036+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.12036, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@4", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.12036+", "metric_symbol": "s", "metric_value": 1.12036, "reference_text": "4. | | s = 1.12036+ | Found by Jonathan Viquerat | in April 2026", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/4.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "4. | | s = 1.12036+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "daed4fc0474960d9", "improvement": -3.511453092652772e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.5154853256512695e-07, "max_pair_overlap_depth": -1.4193770285886309e-05, "metric_expression": "1.12040", "metric_symbol": "s", "metric_value": 1.1203951145309266, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.12036, "setup": "triindom", "side": 2.240790229061853, "solution_path": "data/solutions/generated/triindom_004_daed4fc0474960d9.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/daed4fc0474960d9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@5", "density": 0.6784100035927487, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/5.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.26315+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.26315, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@5", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.26315+", "metric_symbol": "s", "metric_value": 1.26315, "reference_text": "5. | | s = 1.26315+ | Found by Jonathan Viquerat | in April 2026", "source_image": "5.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/5.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "5. | | s = 1.26315+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "5f00d1fbe39c88e1", "improvement": -5.606079820497101e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.863453948036664e-06, "max_pair_overlap_depth": -2.090220821476807e-05, "metric_expression": "1.26321", "metric_symbol": "s", "metric_value": 1.263206060798205, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.26315, "setup": "triindom", "side": 2.52641212159641, "solution_path": "data/solutions/generated/triindom_005_5f00d1fbe39c88e1.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/5f00d1fbe39c88e1.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@6", "density": 0.6857340379834939, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/6.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.37629+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.37629, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@6", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.37629+", "metric_symbol": "s", "metric_value": 1.37629, "reference_text": "6. | | s = 1.37629+ | Found by Jonathan Viquerat | in April 2026", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/6.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "6. | | s = 1.37629+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "cd22df1373fe40ae", "improvement": -7.332504683676966e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4791971315062398e-06, "max_pair_overlap_depth": -2.311431619983484e-05, "metric_expression": "1.37636", "metric_symbol": "s", "metric_value": 1.3763633250468368, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.37629, "setup": "triindom", "side": 2.7527266500936736, "solution_path": "data/solutions/generated/triindom_006_cd22df1373fe40ae.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/cd22df1373fe40ae.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@7", "density": 0.6816978937448389, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/7.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.49076+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.49076, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@7", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.49076+", "metric_symbol": "s", "metric_value": 1.49076, "reference_text": "7. | | s = 1.49076+ | Found by Jonathan Viquerat | in April 2026", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/7.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "7. | | s = 1.49076+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "070c4bf393378882", "improvement": -0.0002768061413715994, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.6376140599128062e-06, "max_pair_overlap_depth": -1.7596834968304498e-05, "metric_expression": "1.49104", "metric_symbol": "s", "metric_value": 1.4910368061413717, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.49076, "setup": "triindom", "side": 2.9820736122827434, "solution_path": "data/solutions/generated/triindom_007_070c4bf393378882.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/070c4bf393378882.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@8", "density": 0.7089538292098625, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/8.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.56293+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.56293, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@8", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.56293+", "metric_symbol": "s", "metric_value": 1.56293, "reference_text": "8. | | s = 1.56293+ | Found by Jonathan Viquerat | in April 2026", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/8.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "8. | | s = 1.56293+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "dc89b8abdea24aaa", "improvement": -0.00011448128988833517, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.119934312653896e-07, "max_pair_overlap_depth": -2.4977335194534267e-05, "metric_expression": "1.56304", "metric_symbol": "s", "metric_value": 1.5630444812898883, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.56293, "setup": "triindom", "side": 3.1260889625797765, "solution_path": "data/solutions/generated/triindom_008_dc89b8abdea24aaa.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/dc89b8abdea24aaa.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@9", "density": 0.7166974833845204, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/9.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.64908+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.64908, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@9", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.64908+", "metric_symbol": "s", "metric_value": 1.64908, "reference_text": "9. | | s = 1.64908+ | Found by Jonathan Viquerat | in April 2026", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/9.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "9. | | s = 1.64908+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "9817bdf32d5c0df3", "improvement": 0.00020157610904458778, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.318788145301177e-06, "max_pair_overlap_depth": -1.0913014285005018e-05, "metric_expression": "1.64888", "metric_symbol": "s", "metric_value": 1.6488784238909555, "n": 9, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 1.64908, "setup": "triindom", "side": 3.297756847781911, "solution_path": "data/solutions/generated/triindom_009_9817bdf32d5c0df3.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/9817bdf32d5c0df3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@10", "density": 0.7634583385020529, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/10.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.68303+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.68303, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@10", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.68303+", "metric_symbol": "s", "metric_value": 1.68303, "reference_text": "10. | | s = 1.68303+ | Found by Jonathan Viquerat | in April 2026", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/10.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "10. | | s = 1.68303+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "d60b37ee7b5fe8bb", "improvement": -0.0009721776557043427, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.2406370054083306e-07, "max_pair_overlap_depth": -6.360676094274709e-06, "metric_expression": "1.68400", "metric_symbol": "s", "metric_value": 1.6840021776557044, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.68303, "setup": "triindom", "side": 3.3680043553114087, "solution_path": "data/solutions/generated/triindom_010_d60b37ee7b5fe8bb.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/d60b37ee7b5fe8bb.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@11", "density": 0.7938130122561631, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/11.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.73127+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.73127, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@11", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.73127+", "metric_symbol": "s", "metric_value": 1.73127, "reference_text": "11. | | s = 1.73127+ | Found by Jonathan Viquerat | in April 2026", "source_image": "11.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/11.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "11. | | s = 1.73127+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "11.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "92f51b49b50f6469", "improvement": -0.0008283817611449695, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.752164488808219e-06, "max_pair_overlap_depth": -9.417608768792381e-06, "metric_expression": "1.73210", "metric_symbol": "s", "metric_value": 1.732098381761145, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.73127, "setup": "triindom", "side": 3.46419676352229, "solution_path": "data/solutions/generated/triindom_011_92f51b49b50f6469.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/92f51b49b50f6469.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@12", "density": 0.8578074620402373, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/12.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.74040+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.7404, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@12", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.74040+", "metric_symbol": "s", "metric_value": 1.7404, "reference_text": "12. | | s = 1.74040+ | Found by Jonathan Viquerat | in April 2026", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/12.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "12. | | s = 1.74040+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "d4d97a50d19ba7f9", "improvement": 7.229766750849187e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6179955143756928e-06, "max_pair_overlap_depth": -3.432318619178698e-05, "metric_expression": "1.74033", "metric_symbol": "s", "metric_value": 1.7403277023324915, "n": 12, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 1.7404, "setup": "triindom", "side": 3.480655404664983, "solution_path": "data/solutions/generated/triindom_012_d4d97a50d19ba7f9.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/d4d97a50d19ba7f9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@13", "density": 0.819430202315155, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/13.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.85319+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.85319, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@13", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.85319+", "metric_symbol": "s", "metric_value": 1.85319, "reference_text": "13. | | s = 1.85319+ | Found by Jonathan Viquerat | in April 2026", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/13.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "13. | | s = 1.85319+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "734b8b487f97f149", "improvement": -0.00013256217488510913, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3279304722789718e-06, "max_pair_overlap_depth": -3.056740874492897e-05, "metric_expression": "1.85332", "metric_symbol": "s", "metric_value": 1.853322562174885, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.85319, "setup": "triindom", "side": 3.70664512434977, "solution_path": "data/solutions/generated/triindom_013_734b8b487f97f149.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/734b8b487f97f149.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@14", "density": 0.837880420446461, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/14.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "3(3\u2013\u221a3)/2 = 1.90192+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.90192, "friedman_reference": {"analytical_or_proved": true, "case": "triindom@14", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3(3\u2013\u221a3)/2 = 1.90192+", "metric_symbol": "s", "metric_value": 1.90192, "reference_text": "14. | | s = 3(3\u2013\u221a3)/2 = 1.90192+ | Found by Jonathan Viquerat | in April 2026", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/14.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "14. | | s = 3(3\u2013\u221a3)/2 = 1.90192+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "050249738efebc30", "improvement": -7.038452971785958e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.8171942911825454e-06, "max_pair_overlap_depth": -1.6337035744662387e-05, "metric_expression": "1.90199", "metric_symbol": "s", "metric_value": 1.901990384529718, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.90192, "setup": "triindom", "side": 3.803980769059436, "solution_path": "data/solutions/generated/triindom_014_050249738efebc30.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/050249738efebc30.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@15", "density": 0.827720714535801, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/15.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.97950+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.9795, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@15", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.97950+", "metric_symbol": "s", "metric_value": 1.9795, "reference_text": "15. | | s = 1.97950+ | Found by Jonathan Viquerat | in April 2026", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/15.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "15. | | s = 1.97950+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "a012f18849dc81a9", "improvement": -0.001292749811030447, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.8417244084533166e-06, "max_pair_overlap_depth": -2.1063364326057155e-05, "metric_expression": "1.98079", "metric_symbol": "s", "metric_value": 1.9807927498110305, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.9795, "setup": "triindom", "side": 3.961585499622061, "solution_path": "data/solutions/generated/triindom_015_a012f18849dc81a9.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/a012f18849dc81a9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@16", "density": 0.8658669941172707, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/16.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@16", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "16. | | s = 2 | Found by Jonathan Viquerat | in April 2026", "source_image": "16.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/16.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "16. | | s = 2 | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "97ac1b8d90281e30", "improvement": -0.0001829408254119258, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4402032156322093e-07, "max_pair_overlap_depth": -8.654468217628164e-06, "metric_expression": "2.00018", "metric_symbol": "s", "metric_value": 2.000182940825412, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "triindom", "side": 4.000365881650824, "solution_path": "data/solutions/generated/triindom_016_97ac1b8d90281e30.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/97ac1b8d90281e30.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@17", "density": 0.8312856464398565, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/17.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "2.10306+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.10306, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@17", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.10306+", "metric_symbol": "s", "metric_value": 2.10306, "reference_text": "17. | | s = 2.10306+ | Found by Jonathan Viquerat | in April 2026", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/17.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "17. | | s = 2.10306+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "3b35e95b5dec0d61", "improvement": -0.001128486819858221, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9321384165115205e-07, "max_pair_overlap_depth": -4.175356206781444e-05, "metric_expression": "2.10419", "metric_symbol": "s", "metric_value": 2.1041884868198584, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.10306, "setup": "triindom", "side": 4.208376973639717, "solution_path": "data/solutions/generated/triindom_017_3b35e95b5dec0d61.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/3b35e95b5dec0d61.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@18", "density": 0.8436836711045761, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/18.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "2.14913.+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.14913, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.14913.+", "metric_symbol": "s", "metric_value": 2.14913, "reference_text": "18. | | s = 2.14913.+ | Found by Jonathan Viquerat | in April 2026", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/18.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "18. | | s = 2.14913.+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "c7d745720c03d379", "improvement": -9.434274541320065e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.205887803834571e-06, "max_pair_overlap_depth": -1.5204184911299379e-05, "metric_expression": "2.14922", "metric_symbol": "s", "metric_value": 2.149224342745413, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.14913, "setup": "triindom", "side": 4.298448685490826, "solution_path": "data/solutions/generated/triindom_018_c7d745720c03d379.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/c7d745720c03d379.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@19", "density": 0.815605476746989, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/19.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "2.24848+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.24848, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.24848+", "metric_symbol": "s", "metric_value": 2.24848, "reference_text": "19. | | s = 2.24848+ | Found by Jonathan Viquerat | in April 2026", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/19.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "19. | | s = 2.24848+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "ccdcfac9f05e2d80", "improvement": 0.002674950513982033, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.889707633764061e-07, "max_pair_overlap_depth": -1.2330676740557323e-05, "metric_expression": "2.24581", "metric_symbol": "s", "metric_value": 2.245805049486018, "n": 19, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 2.24848, "setup": "triindom", "side": 4.491610098972036, "solution_path": "data/solutions/generated/triindom_019_ccdcfac9f05e2d80.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/ccdcfac9f05e2d80.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triindom@20", "density": 0.820310655560819, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/20.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "2.29730+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.2973, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.29730+", "metric_symbol": "s", "metric_value": 2.2973, "reference_text": "20. | | s = 2.29730+ | Found by Jonathan Viquerat | in April 2026", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/20.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "20. | | s = 2.29730+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "b651b20201d5daf5", "improvement": -0.00022973895965483493, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.6504306361575516e-06, "max_pair_overlap_depth": -2.6692790362048413e-05, "metric_expression": "2.29753", "metric_symbol": "s", "metric_value": 2.2975297389596547, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.2973, "setup": "triindom", "side": 4.5950594779193095, "solution_path": "data/solutions/generated/triindom_020_b651b20201d5daf5.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/b651b20201d5daf5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@1", "density": 0.4999941032613389, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/1.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1/\u221a3 = .577+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.577, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1/\u221a3 = .577+", "metric_symbol": "s", "metric_value": 0.577, "reference_text": "s = 1/\u221a3 = .577+ | Trivial.", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/1.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1/\u221a3 = .577+ | Trivial.", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "e9bcdcd079c1c3b7", "improvement": -0.0003536737033924542, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.663290249487904e-07, "max_pair_overlap_depth": 0.0, "metric_expression": "0.57735", "metric_symbol": "s", "metric_value": 0.5773536737033924, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.577, "setup": "triinhex", "side": 0.5773536737033924, "solution_path": "data/solutions/generated/triinhex_001_e9bcdcd079c1c3b7.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/e9bcdcd079c1c3b7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@2", "density": 0.4444266358884555, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/2.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a3/2 = .866+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.866, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a3/2 = .866+", "metric_symbol": "s", "metric_value": 0.866, "reference_text": "s = \u221a3/2 = .866+ | Trivial.", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/2.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = \u221a3/2 = .866+ | Trivial.", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "132c3ed1fad59f87", "improvement": -4.275480049964475e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.75428637420658e-06, "max_pair_overlap_depth": -4.36783093215443e-06, "metric_expression": "0.86604", "metric_symbol": "s", "metric_value": 0.8660427548004996, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.866, "setup": "triinhex", "side": 0.8660427548004996, "solution_path": "data/solutions/generated/triinhex_002_132c3ed1fad59f87.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/132c3ed1fad59f87.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@3", "density": 0.5108536175549566, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2005", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/3.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a((6+\u221a33)/12) = .989+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.989, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@3", "credit": "Erich Friedman", "date": "April 2005", "family_updated": "", "metric_expression": "\u221a((6+\u221a33)/12) = .989+", "metric_symbol": "s", "metric_value": 0.989, "reference_text": "s = \u221a((6+\u221a33)/12) = .989+ | Found by Erich Friedman | in April 2005.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/3.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = \u221a((6+\u221a33)/12) = .989+ | Found by Erich Friedman | in April 2005.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "3f19c46d9d07a54d", "improvement": -0.00031994709745319927, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.001855317125196e-07, "max_pair_overlap_depth": -5.956334362088034e-06, "metric_expression": "0.98932", "metric_symbol": "s", "metric_value": 0.9893199470974532, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.989, "setup": "triinhex", "side": 0.9893199470974532, "solution_path": "data/solutions/generated/triinhex_003_3f19c46d9d07a54d.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/3f19c46d9d07a54d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@4", "density": 0.6666347131299533, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/4.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@4", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/4.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1 | Trivial.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "9a8f72cbad0da23e", "improvement": -2.396601406218224e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.5130077190296347e-08, "max_pair_overlap_depth": -1.1324383645797624e-05, "metric_expression": "1.00002", "metric_symbol": "s", "metric_value": 1.0000239660140622, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.0, "setup": "triinhex", "side": 1.0000239660140622, "solution_path": "data/solutions/generated/triinhex_004_9a8f72cbad0da23e.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/9a8f72cbad0da23e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@5", "density": 0.8333022730508762, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/5.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/5.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1 | Trivial.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "0d61e48787b7d5d1", "improvement": -1.863669045065741e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0710555572355552e-06, "max_pair_overlap_depth": -2.545819687190834e-06, "metric_expression": "1.00002", "metric_symbol": "s", "metric_value": 1.0000186366904507, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.0, "setup": "triinhex", "side": 1.0000186366904507, "solution_path": "data/solutions/generated/triinhex_005_0d61e48787b7d5d1.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/0d61e48787b7d5d1.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@6", "density": 0.9999558832137269, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/6.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@6", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/6.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1 | Trivial.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "163de15143701be8", "improvement": -2.2059123022444282e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.751347439371281e-07, "max_pair_overlap_depth": -4.053173147537176e-06, "metric_expression": "1.00002", "metric_symbol": "s", "metric_value": 1.0000220591230224, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.0, "setup": "triinhex", "side": 1.0000220591230224, "solution_path": "data/solutions/generated/triinhex_006_163de15143701be8.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/163de15143701be8.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@7", "density": 0.7149966699512036, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "May 2005", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/7.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.277+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.277, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@7", "credit": "David W. Cantrell", "date": "May 2005", "family_updated": "", "metric_expression": "1.277+", "metric_symbol": "s", "metric_value": 1.277, "reference_text": "s = 1.277+ | Found by David W. Cantrell | in May 2005.", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/7.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.277+ | Found by David W. Cantrell | in May 2005.", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "af96c8dfd69688ff", "improvement": -0.0003837447071250999, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8980834118002716e-06, "max_pair_overlap_depth": -1.0312174508100846e-05, "metric_expression": "1.27738", "metric_symbol": "s", "metric_value": 1.277383744707125, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.277, "setup": "triinhex", "side": 1.277383744707125, "solution_path": "data/solutions/generated/triinhex_007_af96c8dfd69688ff.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/af96c8dfd69688ff.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@8", "density": 0.724469693124155, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/8.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.356+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.356, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@8", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "1.356+", "metric_symbol": "s", "metric_value": 1.356, "reference_text": "s = 1.356+ | Found by David W. Cantrell | in July 2012.", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/8.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.356+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "d557994d1935d6fb", "improvement": -0.0006232543073974028, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6958384610035216e-07, "max_pair_overlap_depth": -6.193690244168937e-06, "metric_expression": "1.35662", "metric_symbol": "s", "metric_value": 1.3566232543073975, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.356, "setup": "triinhex", "side": 1.3566232543073975, "solution_path": "data/solutions/generated/triinhex_008_d557994d1935d6fb.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d557994d1935d6fb.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@9", "density": 0.7288897241647109, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "April 2005", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/9.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.434+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.434, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@9", "credit": "Erich Friedman", "date": "April 2005", "family_updated": "", "metric_expression": "1.434+", "metric_symbol": "s", "metric_value": 1.434, "reference_text": "s = 1.434+ | Found by Erich Friedman | in April 2005.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/9.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.434+ | Found by Erich Friedman | in April 2005.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "e1592cc41ab92d4d", "improvement": -0.0005467824277936018, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.288341076546003e-06, "max_pair_overlap_depth": -3.69502244107478e-06, "metric_expression": "1.43455", "metric_symbol": "s", "metric_value": 1.4345467824277935, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.434, "setup": "triinhex", "side": 1.4345467824277935, "solution_path": "data/solutions/generated/triinhex_009_e1592cc41ab92d4d.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/e1592cc41ab92d4d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@10", "density": 0.7432082873431878, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/10.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.497+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.497, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@10", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "1.497+", "metric_symbol": "s", "metric_value": 1.497, "reference_text": "s = 1.497+ | Found by Timo Berthold et al | in January 2026.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/10.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.497+ | Found by Timo Berthold et al | in January 2026.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "27f77a1826f41a7d", "improvement": -0.0005078337450310499, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4736979206377467e-06, "max_pair_overlap_depth": -5.4498855950879665e-06, "metric_expression": "1.49751", "metric_symbol": "s", "metric_value": 1.4975078337450312, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.497, "setup": "triinhex", "side": 1.4975078337450312, "solution_path": "data/solutions/generated/triinhex_010_27f77a1826f41a7d.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/27f77a1826f41a7d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@11", "density": 0.8147753094192889, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2005", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/11.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3/2 = 1.500", "friedman_metric_symbol": "s", "friedman_metric_value": 1.5, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@11", "credit": "Erich Friedman", "date": "April 2005", "family_updated": "", "metric_expression": "3/2 = 1.500", "metric_symbol": "s", "metric_value": 1.5, "reference_text": "s = 3/2 = 1.500 | Found by Erich Friedman | in April 2005.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/11.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 3/2 = 1.500 | Found by Erich Friedman | in April 2005.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "a4d7af61e2935a14", "improvement": -3.636424319730658e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0384668058064728e-06, "max_pair_overlap_depth": -9.97710385775008e-06, "metric_expression": "1.50004", "metric_symbol": "s", "metric_value": 1.5000363642431973, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.5, "setup": "triinhex", "side": 1.5000363642431973, "solution_path": "data/solutions/generated/triinhex_011_a4d7af61e2935a14.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/a4d7af61e2935a14.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@12", "density": 0.7583806241339298, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/12.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.623+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.623, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@12", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "1.623+", "metric_symbol": "s", "metric_value": 1.623, "reference_text": "s = 1.623+ | Found by Timo Berthold et al | in January 2026.", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/12.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.623+ | Found by Timo Berthold et al | in January 2026.", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "9de540041e59931a", "improvement": -0.0009452508446496921, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.928415721340796e-06, "max_pair_overlap_depth": -1.3315156502324843e-05, "metric_expression": "1.62395", "metric_symbol": "s", "metric_value": 1.6239452508446497, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.623, "setup": "triinhex", "side": 1.6239452508446497, "solution_path": "data/solutions/generated/triinhex_012_9de540041e59931a.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/9de540041e59931a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@13", "density": 0.7821155301010267, "friedman_analytical_or_proved": true, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/13.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a(587+51\u221a17)/12\u221a2 = 1.663829+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.663829, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@13", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "\u221a(587+51\u221a17)/12\u221a2 = 1.663829+", "metric_symbol": "s", "metric_value": 1.663829, "reference_text": "s = \u221a(587+51\u221a17)/12\u221a2 = 1.663829+ | Found by Ian Watson | in April 2026.", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/13.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = \u221a(587+51\u221a17)/12\u221a2 = 1.663829+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "efc43a6cbf81ae24", "improvement": -0.0005820721473515089, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.9742574580490386e-06, "max_pair_overlap_depth": -2.1993638058326326e-05, "metric_expression": "1.66441", "metric_symbol": "s", "metric_value": 1.6644110721473515, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.663829, "setup": "triinhex", "side": 1.6644110721473515, "solution_path": "data/solutions/generated/triinhex_013_efc43a6cbf81ae24.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/efc43a6cbf81ae24.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@14", "density": 0.7828804179520853, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/14.gif", "friedman_metric_expression": "1.725+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.725, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@14", "credit": "David W. Cantrell", "date": "August 2012", "family_updated": "", "metric_expression": "1.725+", "metric_symbol": "s", "metric_value": 1.725, "reference_text": "s = 1.725+ | Found by David W. Cantrell | in August 2012.", "source_image": "14.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/14.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.725+ | Found by David W. Cantrell | in August 2012.", "friedman_source_image": "14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "dbfe389f1c3777d5", "improvement": -0.0013970193042536216, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.5600740703080906e-07, "max_pair_overlap_depth": -1.248505498985253e-07, "metric_expression": "1.72640", "metric_symbol": "s", "metric_value": 1.7263970193042537, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.725, "setup": "triinhex", "side": 1.7263970193042537, "solution_path": "data/solutions/generated/triinhex_14_dbfe389f1c3777d5.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T07:13:53+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/dbfe389f1c3777d5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@15", "density": 0.8162509918871499, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2005", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/15.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "7/4 = 1.750", "friedman_metric_symbol": "s", "friedman_metric_value": 1.75, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@15", "credit": "Erich Friedman", "date": "April 2005", "family_updated": "", "metric_expression": "7/4 = 1.750", "metric_symbol": "s", "metric_value": 1.75, "reference_text": "s = 7/4 = 1.750 | Found by Erich Friedman | in April 2005.", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/15.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 7/4 = 1.750 | Found by Erich Friedman | in April 2005.", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "20b1a0e905211ce9", "improvement": -8.097369067638915e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.758472784251539e-06, "max_pair_overlap_depth": -9.75502017092067e-06, "metric_expression": "1.75008", "metric_symbol": "s", "metric_value": 1.7500809736906764, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.75, "setup": "triinhex", "side": 1.7500809736906764, "solution_path": "data/solutions/generated/triinhex_015_20b1a0e905211ce9.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/20b1a0e905211ce9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@16", "density": 0.8229668363309378, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/16.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "9/5 = 1.800", "friedman_metric_symbol": "s", "friedman_metric_value": 1.8, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@16", "credit": "Maurizio Morandi", "date": "April 2008", "family_updated": "", "metric_expression": "9/5 = 1.800", "metric_symbol": "s", "metric_value": 1.8, "reference_text": "s = 9/5 = 1.800 | Found by Maurizio Morandi | in April 2008.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/16.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 9/5 = 1.800 | Found by Maurizio Morandi | in April 2008.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "a0b20d24de5f00ac", "improvement": -8.577060222680899e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.740972449159294e-06, "max_pair_overlap_depth": -2.3139042383268915e-06, "metric_expression": "1.80009", "metric_symbol": "s", "metric_value": 1.8000857706022269, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.8, "setup": "triinhex", "side": 1.8000857706022269, "solution_path": "data/solutions/generated/triinhex_016_a0b20d24de5f00ac.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/a0b20d24de5f00ac.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@17", "density": 0.842931104392013, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/17.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "11/6 = 1.833+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.833, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@17", "credit": "Maurizio Morandi", "date": "April 2008", "family_updated": "", "metric_expression": "11/6 = 1.833+", "metric_symbol": "s", "metric_value": 1.833, "reference_text": "s = 11/6 = 1.833+ | Found by Maurizio Morandi | in April 2008.", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/17.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 11/6 = 1.833+ | Found by Maurizio Morandi | in April 2008.", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "b8b9e4b4d61ec96c", "improvement": -0.00038129277582044097, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4990722513823532e-07, "max_pair_overlap_depth": -1.1854387088505725e-05, "metric_expression": "1.83338", "metric_symbol": "s", "metric_value": 1.8333812927758204, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.833, "setup": "triinhex", "side": 1.8333812927758204, "solution_path": "data/solutions/generated/triinhex_017_b8b9e4b4d61ec96c.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/b8b9e4b4d61ec96c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@18", "density": 0.8400311467465807, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/18.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "17/9 = 1.888+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.888, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@18", "credit": "Maurizio Morandi", "date": "April 2008", "family_updated": "", "metric_expression": "17/9 = 1.888+", "metric_symbol": "s", "metric_value": 1.888, "reference_text": "s = 17/9 = 1.888+ | Found by Maurizio Morandi | in April 2008.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/18.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 17/9 = 1.888+ | Found by Maurizio Morandi | in April 2008.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "7671cfd644a7af24", "improvement": -0.001787329223866152, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.484924045151217e-06, "max_pair_overlap_depth": -8.796062168636709e-06, "metric_expression": "1.88979", "metric_symbol": "s", "metric_value": 1.889787329223866, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.888, "setup": "triinhex", "side": 1.889787329223866, "solution_path": "data/solutions/generated/triinhex_018_7671cfd644a7af24.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/7671cfd644a7af24.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@19", "density": 0.8283361930438612, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Adri\u00e1n Nieto", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/19.gif", "friedman_metric_expression": "1.953+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.953, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@19", "credit": "Alex Adri\u00e1n Nieto", "date": "April 2026", "family_updated": "", "metric_expression": "1.953+", "metric_symbol": "s", "metric_value": 1.953, "reference_text": "s = 1.953+ | Found by Alex Adri\u00e1n Nieto | in April 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/19.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.953+ | Found by Alex Adri\u00e1n Nieto | in April 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "451018f1291a5791", "improvement": -0.0022300191069650754, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7079807782201595e-06, "max_pair_overlap_depth": -1.3478523960663846e-05, "metric_expression": "1.95523", "metric_symbol": "s", "metric_value": 1.9552300191069651, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.953, "setup": "triinhex", "side": 1.9552300191069651, "solution_path": "data/solutions/generated/triinhex_19_451018f1291a5791.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T07:13:53+00:00", "submitted_by": "Alex Adri\u00e1n Nieto", "svg_path": "data/svg/451018f1291a5791.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@20", "density": 0.8524037354438128, "friedman_analytical_or_proved": false, "friedman_credit": "Aaden Abraham", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/20.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.97591+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.97591, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@20", "credit": "Aaden Abraham", "date": "April 2026", "family_updated": "", "metric_expression": "1.97591+", "metric_symbol": "s", "metric_value": 1.97591, "reference_text": "s = 1.97591+ | Found by Aaden Abraham | in April 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/20.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.97591+ | Found by Aaden Abraham | in April 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "388fc73ef451e99b", "improvement": -0.0015909487133152211, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7558573966506123e-06, "max_pair_overlap_depth": -5.2993150605473716e-06, "metric_expression": "1.97750", "metric_symbol": "s", "metric_value": 1.9775009487133153, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.97591, "setup": "triinhex", "side": 1.9775009487133153, "solution_path": "data/solutions/generated/triinhex_020_388fc73ef451e99b.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:51:36+00:00", "submitted_by": "Aaden Abraham", "svg_path": "data/svg/388fc73ef451e99b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@21", "density": 0.8749527320468723, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/21.gif", "friedman_metric_expression": "1.99878+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.99878, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@21", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "1.99878+", "metric_symbol": "s", "metric_value": 1.99878, "reference_text": "s = 1.99878+ | Found by Ian Watson | in April 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/21.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.99878+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "96f74df50573bb81", "improvement": -0.0012740227066210252, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.545179480294009e-07, "max_pair_overlap_depth": -6.765642482919887e-06, "metric_expression": "2.00005", "metric_symbol": "s", "metric_value": 2.000054022706621, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.99878, "setup": "triinhex", "side": 2.000054022706621, "solution_path": "data/solutions/generated/triinhex_021_96f74df50573bb81.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/96f74df50573bb81.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@22", "density": 0.9166150664792877, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@22", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial. |", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2 | Trivial. |", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "38182a59461da74e", "improvement": -5.629349013291929e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.91184500961419e-07, "max_pair_overlap_depth": -9.942352799940934e-07, "metric_expression": "2.00006", "metric_symbol": "s", "metric_value": 2.000056293490133, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "triinhex", "side": 2.000056293490133, "solution_path": "data/solutions/generated/triinhex_022_38182a59461da74e.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/38182a59461da74e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@23", "density": 0.958278890368788, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@23", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial. |", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2 | Trivial. |", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "dcd331994270a997", "improvement": -5.681247061106731e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0734329507489061e-06, "max_pair_overlap_depth": -9.41664729126046e-06, "metric_expression": "2.00006", "metric_symbol": "s", "metric_value": 2.000056812470611, "n": 23, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "triinhex", "side": 2.000056812470611, "solution_path": "data/solutions/generated/triinhex_023_dcd331994270a997.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/dcd331994270a997.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@24", "density": 0.9999420291406096, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@24", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial. |", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2 | Trivial. |", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "13936a08bfd4d152", "improvement": -5.7973379977482864e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3635152509087512e-06, "max_pair_overlap_depth": -3.8859579855957235e-06, "metric_expression": "2.00006", "metric_symbol": "s", "metric_value": 2.0000579733799775, "n": 24, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "triinhex", "side": 2.0000579733799775, "solution_path": "data/solutions/generated/triinhex_024_13936a08bfd4d152.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/13936a08bfd4d152.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@25", "density": 0.8871759236838516, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/25.gif", "friedman_metric_expression": "13/6 = 2.166+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.166, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@25", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "13/6 = 2.166+", "metric_symbol": "s", "metric_value": 2.166, "reference_text": "s = 13/6 = 2.166+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/25.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 13/6 = 2.166+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "71a7801cfb4a8d31", "improvement": -0.0011526610601886311, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.780494307380179e-07, "max_pair_overlap_depth": -1.3308976067882838e-06, "metric_expression": "2.16715", "metric_symbol": "s", "metric_value": 2.1671526610601886, "n": 25, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.166, "setup": "triinhex", "side": 2.1671526610601886, "solution_path": "data/solutions/generated/triinhex_025_71a7801cfb4a8d31.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/71a7801cfb4a8d31.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@26", "density": 0.878430458154361, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/26.gif", "friedman_metric_expression": "2.21991+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.21991, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@26", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.21991+", "metric_symbol": "s", "metric_value": 2.21991, "reference_text": "s = 2.21991+ | Found by Ian Watson | in April 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/26.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.21991+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "658d7f93b604b663", "improvement": -0.0011349903788469007, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.149641376243232e-07, "max_pair_overlap_depth": -5.41804289733161e-06, "metric_expression": "2.22104", "metric_symbol": "s", "metric_value": 2.221044990378847, "n": 26, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.21991, "setup": "triinhex", "side": 2.221044990378847, "solution_path": "data/solutions/generated/triinhex_026_658d7f93b604b663.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/658d7f93b604b663.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@27", "density": 0.8525233088554102, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/27.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.29541+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.29541, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@27", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.29541+", "metric_symbol": "s", "metric_value": 2.29541, "reference_text": "s = 2.29541+ | Found by Ian Watson | in April 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/27.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.29541+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "ace1d8ac458c5bc4", "improvement": -0.0020773347367342154, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.449964623966915e-06, "max_pair_overlap_depth": -5.244956223338093e-06, "metric_expression": "2.29749", "metric_symbol": "s", "metric_value": 2.297487334736734, "n": 27, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.29541, "setup": "triinhex", "side": 2.297487334736734, "solution_path": "data/solutions/generated/triinhex_027_ace1d8ac458c5bc4.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/ace1d8ac458c5bc4.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@28", "density": 0.8636324031387004, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/28.gif", "friedman_metric_expression": "2.32289+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.32289, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@28", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.32289+", "metric_symbol": "s", "metric_value": 2.32289, "reference_text": "s = 2.32289+ | Found by Ian Watson | in April 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/28.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.32289+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "3435500023858121", "improvement": -0.0016601826518787277, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.60736131059532e-06, "max_pair_overlap_depth": -1.0038160656700157e-05, "metric_expression": "2.32455", "metric_symbol": "s", "metric_value": 2.324550182651879, "n": 28, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.32289, "setup": "triinhex", "side": 2.324550182651879, "solution_path": "data/solutions/generated/triinhex_28_3435500023858121.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/3435500023858121.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@29", "density": 0.8876189549602443, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/29.gif", "friedman_metric_expression": "7/3 = 2.333+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.333, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@29", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "7/3 = 2.333+", "metric_symbol": "s", "metric_value": 2.333, "reference_text": "s = 7/3 = 2.333+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/29.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 7/3 = 2.333+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "4339d1ebd3160f94", "improvement": -0.0005122751747741461, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.371335525980428e-06, "max_pair_overlap_depth": -4.303492490143057e-07, "metric_expression": "2.33351", "metric_symbol": "s", "metric_value": 2.3335122751747743, "n": 29, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.333, "setup": "triinhex", "side": 2.3335122751747743, "solution_path": "data/solutions/generated/triinhex_29_4339d1ebd3160f94.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/4339d1ebd3160f94.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@30", "density": 0.8862493271562808, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/30.gif", "friedman_metric_expression": "19/8 = 2.375", "friedman_metric_symbol": "s", "friedman_metric_value": 2.375, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@30", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "19/8 = 2.375", "metric_symbol": "s", "metric_value": 2.375, "reference_text": "s = 19/8 = 2.375 | Found by Ignacio Vallejo | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/30.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 19/8 = 2.375 | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "7274d354e73d8050", "improvement": -0.00023750926269094919, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.946881910542413e-07, "max_pair_overlap_depth": -3.1129912760885503e-06, "metric_expression": "2.37524", "metric_symbol": "s", "metric_value": 2.375237509262691, "n": 30, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.375, "setup": "triinhex", "side": 2.375237509262691, "solution_path": "data/solutions/generated/triinhex_30_7274d354e73d8050.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/7274d354e73d8050.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@31", "density": 0.896119877899338, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/31.gif", "friedman_metric_expression": "12/5 = 2.400", "friedman_metric_symbol": "s", "friedman_metric_value": 2.4, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "12/5 = 2.400", "metric_symbol": "s", "metric_value": 2.4, "reference_text": "s = 12/5 = 2.400 | Found by Emerson Connelly | in April 2026.", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/31.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 12/5 = 2.400 | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "cae7087451040120", "improvement": -0.0011658949471424762, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9409739826535097e-07, "max_pair_overlap_depth": -2.8541100203227643e-06, "metric_expression": "2.40117", "metric_symbol": "s", "metric_value": 2.4011658949471424, "n": 31, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.4, "setup": "triinhex", "side": 2.4011658949471424, "solution_path": "data/solutions/generated/triinhex_31_cae7087451040120.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/cae7087451040120.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@32", "density": 0.8767870241121234, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/32.gif", "friedman_metric_expression": "2.465+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.465, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "2.465+", "metric_symbol": "s", "metric_value": 2.465, "reference_text": "s = 2.465+ | Found by Emerson Connelly | in April 2026.", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/32.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.465+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "8674581436e5e74d", "improvement": -0.0013363682337788063, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.925122041572899e-07, "max_pair_overlap_depth": -1.2807310418028184e-06, "metric_expression": "2.46634", "metric_symbol": "s", "metric_value": 2.4663363682337787, "n": 32, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.465, "setup": "triinhex", "side": 2.4663363682337787, "solution_path": "data/solutions/generated/triinhex_032_8674581436e5e74d.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/8674581436e5e74d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@33", "density": 0.8799443949567897, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/33.gif", "friedman_metric_expression": "2.498+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.498, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "2.498+", "metric_symbol": "s", "metric_value": 2.498, "reference_text": "s = 2.498+ | Found by Emerson Connelly | in April 2026.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/33.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.498+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "5b836a27d2bb958c", "improvement": -0.00207898817969987, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.8634496562140136e-06, "max_pair_overlap_depth": -5.829272115620565e-06, "metric_expression": "2.50008", "metric_symbol": "s", "metric_value": 2.5000789881797, "n": 33, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.498, "setup": "triinhex", "side": 2.5000789881797, "solution_path": "data/solutions/generated/triinhex_033_5b836a27d2bb958c.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/5b836a27d2bb958c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@34", "density": 0.9066102013779274, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "friedman_metric_expression": "5/2 = 2.500", "friedman_metric_symbol": "s", "friedman_metric_value": 2.5, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "5/2 = 2.500", "metric_symbol": "s", "metric_value": 2.5, "reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "a712744ff3b5bcc9", "improvement": -7.7851001305973e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2753913921730298e-06, "max_pair_overlap_depth": -7.960301433351802e-06, "metric_expression": "2.50008", "metric_symbol": "s", "metric_value": 2.500077851001306, "n": 34, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.5, "setup": "triinhex", "side": 2.500077851001306, "solution_path": "data/solutions/generated/triinhex_034_a712744ff3b5bcc9.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/a712744ff3b5bcc9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@35", "density": 0.93316535041203, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "friedman_metric_expression": "5/2 = 2.500", "friedman_metric_symbol": "s", "friedman_metric_value": 2.5, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@35", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "5/2 = 2.500", "metric_symbol": "s", "metric_value": 2.5, "reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "ec49778cf450c37b", "improvement": -0.00022500750012577342, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6207066397040256e-06, "max_pair_overlap_depth": -1.5837731757728513e-06, "metric_expression": "2.50023", "metric_symbol": "s", "metric_value": 2.5002250075001258, "n": 35, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.5, "setup": "triinhex", "side": 2.5002250075001258, "solution_path": "data/solutions/generated/triinhex_35_ec49778cf450c37b.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/ec49778cf450c37b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@36", "density": 0.8942711196026824, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/36.gif", "friedman_metric_expression": "2.59123+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.59123, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@36", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "2.59123+", "metric_symbol": "s", "metric_value": 2.59123, "reference_text": "s = 2.59123+ | Found by Nathan Roll | in April 2026.", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/36.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.59123+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "d30ec5c19b8369f3", "improvement": 0.000983935961939686, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.744185746811731e-07, "max_pair_overlap_depth": -1.519675368655271e-06, "metric_expression": "2.59025", "metric_symbol": "s", "metric_value": 2.5902460640380602, "n": 36, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 2.59123, "setup": "triinhex", "side": 2.5902460640380602, "solution_path": "data/solutions/record_hunt/triinhex_36_d30ec5c19b8369f3.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/d30ec5c19b8369f3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@37", "density": 0.899950790089805, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/37.gif", "friedman_metric_expression": "2.61943+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.61943, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@37", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "2.61943+", "metric_symbol": "s", "metric_value": 2.61943, "reference_text": "s = 2.61943+ | Found by Nathan Roll | in April 2026.", "source_image": "37.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/37.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.61943+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "c791d76ac960cbca", "improvement": 0.0017542149405089802, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.903248309191345e-07, "max_pair_overlap_depth": -8.609976616114068e-07, "metric_expression": "2.61768", "metric_symbol": "s", "metric_value": 2.617675785059491, "n": 37, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 2.61943, "setup": "triinhex", "side": 2.617675785059491, "solution_path": "data/solutions/record_hunt/triinhex_37_c791d76ac960cbca.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/c791d76ac960cbca.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@38", "density": 0.8907392561961515, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "friedman_metric_expression": "8/3 = 2.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.666, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "8/3 = 2.666+", "metric_symbol": "s", "metric_value": 2.666, "reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "76fd196e8c79a5c9", "improvement": -0.0004956329108489754, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7850003642140776e-06, "max_pair_overlap_depth": -3.863933217385096e-06, "metric_expression": "2.66650", "metric_symbol": "s", "metric_value": 2.666495632910849, "n": 38, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.666, "setup": "triinhex", "side": 2.666495632910849, "solution_path": "data/solutions/generated/triinhex_038_76fd196e8c79a5c9.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/76fd196e8c79a5c9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@39", "density": 0.9136318214810123, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "friedman_metric_expression": "8/3 = 2.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.666, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "8/3 = 2.666+", "metric_symbol": "s", "metric_value": 2.666, "reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "a314b4bb8467e5e8", "improvement": -0.0012951149704507614, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.891404577705932e-07, "max_pair_overlap_depth": -6.19203720853001e-07, "metric_expression": "2.66730", "metric_symbol": "s", "metric_value": 2.6672951149704507, "n": 39, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.666, "setup": "triinhex", "side": 2.6672951149704507, "solution_path": "data/solutions/generated/triinhex_39_a314b4bb8467e5e8.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/a314b4bb8467e5e8.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinhex@40", "density": 0.9051419512423183, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/40.gif", "friedman_metric_expression": "2.71622+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.71622, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@40", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "2.71622+", "metric_symbol": "s", "metric_value": 2.71622, "reference_text": "s = 2.71622+ | Found by Nathan Roll | in April 2026.", "source_image": "40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/40.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.71622+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "8b6d682b66356562", "improvement": 0.0023063615780789526, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2777984478773679e-07, "max_pair_overlap_depth": -4.470141119483628e-07, "metric_expression": "2.71391", "metric_symbol": "s", "metric_value": 2.713913638421921, "n": 40, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 2.71622, "setup": "triinhex", "side": 2.713913638421921, "solution_path": "data/solutions/record_hunt/triinhex_40_8b6d682b66356562.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/8b6d682b66356562.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@1", "density": 0.4152122478191623, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/1.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": ".46470+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.4647, "friedman_reference": {"analytical_or_proved": true, "case": "triinoct@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": ".46470+", "metric_symbol": "s", "metric_value": 0.4647, "reference_text": "s = .46470+ | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/1.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = .46470+ | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "92c66f395ff03ab9", "improvement": -4.251046545072912e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3282842257895898e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.46474", "metric_symbol": "s", "metric_value": 0.46474251046545073, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.4647, "setup": "triinoct", "side": 0.46474251046545073, "solution_path": "data/solutions/generated/triinoct_001_92c66f395ff03ab9.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/92c66f395ff03ab9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@2", "density": 0.40823825072318354, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/2.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "\u221a3/\u221a(4+2\u221a2) = .66282+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.66282, "friedman_reference": {"analytical_or_proved": true, "case": "triinoct@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a3/\u221a(4+2\u221a2) = .66282+", "metric_symbol": "s", "metric_value": 0.66282, "reference_text": "s = \u221a3/\u221a(4+2\u221a2) = .66282+ | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/2.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = \u221a3/\u221a(4+2\u221a2) = .66282+ | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "5706480ca6648c20", "improvement": -1.5298424264065247e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.197393779037103e-06, "max_pair_overlap_depth": -5.033792755404498e-07, "metric_expression": "0.66284", "metric_symbol": "s", "metric_value": 0.662835298424264, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.66282, "setup": "triinoct", "side": 0.662835298424264, "solution_path": "data/solutions/generated/triinoct_002_5706480ca6648c20.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/5706480ca6648c20.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@3", "density": 0.49592364137420614, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/3.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": ".73651+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.73651, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@3", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": ".73651+", "metric_symbol": "s", "metric_value": 0.73651, "reference_text": "s = .73651+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/3.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = .73651+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "f3eee07e4d3df15b", "improvement": -3.739655668555386e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.662035887956301e-06, "max_pair_overlap_depth": -2.2250265259982083e-06, "metric_expression": "0.73655", "metric_symbol": "s", "metric_value": 0.7365473965566856, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.73651, "setup": "triinoct", "side": 0.7365473965566856, "solution_path": "data/solutions/generated/triinoct_003_f3eee07e4d3df15b.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/f3eee07e4d3df15b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@4", "density": 0.593540115018531, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/4.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": ".77733+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.77733, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@4", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": ".77733+", "metric_symbol": "s", "metric_value": 0.77733, "reference_text": "s = .77733+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/4.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = .77733+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "daeed392d4fde104", "improvement": -8.413889807601382e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.025085624522854e-06, "max_pair_overlap_depth": -2.0675467336764286e-05, "metric_expression": "0.77741", "metric_symbol": "s", "metric_value": 0.777414138898076, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.77733, "setup": "triinoct", "side": 0.777414138898076, "solution_path": "data/solutions/generated/triinoct_004_daeed392d4fde104.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/daeed392d4fde104.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@5", "density": 0.6941546982548611, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/5.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": ".80367+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.80367, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@5", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": ".80367+", "metric_symbol": "s", "metric_value": 0.80367, "reference_text": "s = .80367+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/5.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = .80367+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "a0addde9772ff582", "improvement": -4.920494762683525e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.8458025218911135e-06, "max_pair_overlap_depth": -2.636296310584707e-05, "metric_expression": "0.80372", "metric_symbol": "s", "metric_value": 0.8037192049476268, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.80367, "setup": "triinoct", "side": 0.8037192049476268, "solution_path": "data/solutions/generated/triinoct_005_a0addde9772ff582.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/a0addde9772ff582.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@6", "density": 0.8085136476900721, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/6.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": ".81574+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.81574, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@6", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": ".81574+", "metric_symbol": "s", "metric_value": 0.81574, "reference_text": "s = .81574+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/6.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = .81574+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "e7ac2b490b8118b6", "improvement": -5.196804299267832e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.999019070763348e-06, "max_pair_overlap_depth": -1.523375553563397e-05, "metric_expression": "0.81579", "metric_symbol": "s", "metric_value": 0.8157919680429927, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.81574, "setup": "triinoct", "side": 0.8157919680429927, "solution_path": "data/solutions/generated/triinoct_006_e7ac2b490b8118b6.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/e7ac2b490b8118b6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@7", "density": 0.7344053269175495, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/7.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": ".92453+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.92453, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@7", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": ".92453+", "metric_symbol": "s", "metric_value": 0.92453, "reference_text": "s = .92453+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/7.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = .92453+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "f1951fc893682894", "improvement": -1.6137063615029312e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.877767128601322e-06, "max_pair_overlap_depth": -4.487804835917597e-06, "metric_expression": "0.92455", "metric_symbol": "s", "metric_value": 0.924546137063615, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.92453, "setup": "triinoct", "side": 0.924546137063615, "solution_path": "data/solutions/generated/triinoct_007_f1951fc893682894.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/f1951fc893682894.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@8", "density": 0.7351940708693757, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/8.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": ".98782+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.98782, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@8", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": ".98782+", "metric_symbol": "s", "metric_value": 0.98782, "reference_text": "s = .98782+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/8.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = .98782+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "cdfdb28bbd7c958a", "improvement": -3.106647506945226e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6027742606714177e-06, "max_pair_overlap_depth": -8.534452089259403e-06, "metric_expression": "0.98785", "metric_symbol": "s", "metric_value": 0.9878510664750695, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.98782, "setup": "triinoct", "side": 0.9878510664750695, "solution_path": "data/solutions/generated/triinoct_008_cdfdb28bbd7c958a.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/cdfdb28bbd7c958a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@9", "density": 0.7931382286148597, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/9.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.00875+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.00875, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@9", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.00875+", "metric_symbol": "s", "metric_value": 1.00875, "reference_text": "s = 1.00875+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/9.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.00875+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "0a4766beda41f84b", "improvement": -2.4953411784212065e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.992353374519455e-07, "max_pair_overlap_depth": -5.523000253249144e-06, "metric_expression": "1.00877", "metric_symbol": "s", "metric_value": 1.0087749534117842, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.00875, "setup": "triinoct", "side": 1.0087749534117842, "solution_path": "data/solutions/generated/triinoct_009_0a4766beda41f84b.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/0a4766beda41f84b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@10", "density": 0.7747683390429897, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/10.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.07565+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.07565, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@10", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.07565+", "metric_symbol": "s", "metric_value": 1.07565, "reference_text": "s = 1.07565+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/10.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.07565+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "df6976316812d041", "improvement": -0.00022432883231693346, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3385179497460716e-06, "max_pair_overlap_depth": -1.8668924055276204e-05, "metric_expression": "1.07587", "metric_symbol": "s", "metric_value": 1.075874328832317, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.07565, "setup": "triinoct", "side": 1.075874328832317, "solution_path": "data/solutions/generated/triinoct_010_df6976316812d041.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/df6976316812d041.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@11", "density": 0.7515390994133405, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/11.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.14571+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.14571, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@11", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.14571+", "metric_symbol": "s", "metric_value": 1.14571, "reference_text": "s = 1.14571+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/11.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.14571+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "11036479a300844a", "improvement": 1.760556295749005e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.2318282708152993e-06, "max_pair_overlap_depth": -7.937162014970411e-06, "metric_expression": "1.14569", "metric_symbol": "s", "metric_value": 1.1456923944370425, "n": 11, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 1.14571, "setup": "triinoct", "side": 1.1456923944370425, "solution_path": "data/solutions/generated/triinoct_011_11036479a300844a.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/11036479a300844a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@12", "density": 0.74788706506276, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/12.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.19929+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.19929, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@12", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.19929+", "metric_symbol": "s", "metric_value": 1.19929, "reference_text": "s = 1.19929+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/12.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.19929+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "1fa5264e0f579a94", "improvement": -0.0002647906752053508, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2204761718366964e-06, "max_pair_overlap_depth": -1.4073169272155184e-06, "metric_expression": "1.19955", "metric_symbol": "s", "metric_value": 1.1995547906752053, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.19929, "setup": "triinoct", "side": 1.1995547906752053, "solution_path": "data/solutions/generated/triinoct_012_1fa5264e0f579a94.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/1fa5264e0f579a94.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@13", "density": 0.7604201292225432, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/13.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.23759+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.23759, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@13", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.23759+", "metric_symbol": "s", "metric_value": 1.23759, "reference_text": "s = 1.23759+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/13.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.23759+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "ebb5825b80b24749", "improvement": -0.0006144239243295324, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.763415979262496e-06, "max_pair_overlap_depth": -3.350137919300167e-06, "metric_expression": "1.23820", "metric_symbol": "s", "metric_value": 1.2382044239243295, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.23759, "setup": "triinoct", "side": 1.2382044239243295, "solution_path": "data/solutions/generated/triinoct_013_ebb5825b80b24749.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/ebb5825b80b24749.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@14", "density": 0.7704458772851622, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/14.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.27677+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.27677, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@14", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.27677+", "metric_symbol": "s", "metric_value": 1.27677, "reference_text": "s = 1.27677+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "14.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/14.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.27677+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "e00a18106d2fcfee", "improvement": 0.00021236461691676034, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.593194459024069e-06, "max_pair_overlap_depth": -5.874056281496287e-06, "metric_expression": "1.27656", "metric_symbol": "s", "metric_value": 1.2765576353830832, "n": 14, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 1.27677, "setup": "triinoct", "side": 1.2765576353830832, "solution_path": "data/solutions/generated/triinoct_014_e00a18106d2fcfee.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/e00a18106d2fcfee.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@15", "density": 0.7924237027261557, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/15.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.30275+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.30275, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@15", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.30275+", "metric_symbol": "s", "metric_value": 1.30275, "reference_text": "s = 1.30275+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/15.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.30275+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "e14eda962017d06d", "improvement": -0.0001598827367932376, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3032093708899356e-06, "max_pair_overlap_depth": -6.895788391969582e-06, "metric_expression": "1.30291", "metric_symbol": "s", "metric_value": 1.3029098827367933, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.30275, "setup": "triinoct", "side": 1.3029098827367933, "solution_path": "data/solutions/generated/triinoct_015_e14eda962017d06d.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/e14eda962017d06d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@16", "density": 0.7920450821484247, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/16.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.34584+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.34584, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@16", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.34584+", "metric_symbol": "s", "metric_value": 1.34584, "reference_text": "s = 1.34584+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/16.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.34584+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "640352ab60961c58", "improvement": -0.00012112963758759143, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.464975954309231e-06, "max_pair_overlap_depth": -7.38266966116008e-07, "metric_expression": "1.34596", "metric_symbol": "s", "metric_value": 1.3459611296375875, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.34584, "setup": "triinoct", "side": 1.3459611296375875, "solution_path": "data/solutions/generated/triinoct_16_640352ab60961c58.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/640352ab60961c58.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@17", "density": 0.7893502976721624, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/17.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.38964+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.38964, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@17", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.38964+", "metric_symbol": "s", "metric_value": 1.38964, "reference_text": "s = 1.38964+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/17.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.38964+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "6f00b933407c7c80", "improvement": -0.0001111742572472707, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.693112749768053e-07, "max_pair_overlap_depth": -2.384134229149737e-06, "metric_expression": "1.38975", "metric_symbol": "s", "metric_value": 1.3897511742572473, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.38964, "setup": "triinoct", "side": 1.3897511742572473, "solution_path": "data/solutions/generated/triinoct_017_6f00b933407c7c80.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/6f00b933407c7c80.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@18", "density": 0.8027011318687396, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/18.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.41836+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.41836, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@18", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.41836+", "metric_symbol": "s", "metric_value": 1.41836, "reference_text": "s = 1.41836+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/18.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.41836+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "91a694d1aa76789c", "improvement": 0.0002602110634655208, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.835525154559248e-06, "max_pair_overlap_depth": -9.960192069113916e-06, "metric_expression": "1.41810", "metric_symbol": "s", "metric_value": 1.4180997889365345, "n": 18, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 1.41836, "setup": "triinoct", "side": 1.4180997889365345, "solution_path": "data/solutions/generated/triinoct_018_91a694d1aa76789c.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/91a694d1aa76789c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@19", "density": 0.7911354610751659, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/19.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.46749+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.46749, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.46749+", "metric_symbol": "s", "metric_value": 1.46749, "reference_text": "s = 1.46749+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/19.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.46749+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "f92a5a5a3b54909a", "improvement": -8.00911599283527e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.983793930902579e-06, "max_pair_overlap_depth": -8.286875174401409e-06, "metric_expression": "1.46757", "metric_symbol": "s", "metric_value": 1.4675700911599283, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.46749, "setup": "triinoct", "side": 1.4675700911599283, "solution_path": "data/solutions/generated/triinoct_019_f92a5a5a3b54909a.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/f92a5a5a3b54909a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@20", "density": 0.7990175319982477, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/20.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.49832+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.49832, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@20", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.49832+", "metric_symbol": "s", "metric_value": 1.49832, "reference_text": "s = 1.49832+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/20.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.49832+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "ead92a925f9f00a7", "improvement": 6.988050923584233e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3276003687482804e-06, "max_pair_overlap_depth": -2.2158170135400113e-06, "metric_expression": "1.49825", "metric_symbol": "s", "metric_value": 1.4982501194907643, "n": 20, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 1.49832, "setup": "triinoct", "side": 1.4982501194907643, "solution_path": "data/solutions/generated/triinoct_020_ead92a925f9f00a7.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/ead92a925f9f00a7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@21", "density": 0.8078137663314585, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/21.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.52615+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.52615, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@21", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.52615+", "metric_symbol": "s", "metric_value": 1.52615, "reference_text": "s = 1.52615+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/21.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.52615+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "e350f46688d32a68", "improvement": -0.0007180233722772211, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.407426670083604e-06, "max_pair_overlap_depth": -1.1097264517423433e-05, "metric_expression": "1.52687", "metric_symbol": "s", "metric_value": 1.5268680233722771, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.52615, "setup": "triinoct", "side": 1.5268680233722771, "solution_path": "data/solutions/generated/triinoct_021_e350f46688d32a68.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/e350f46688d32a68.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@22", "density": 0.8155579012833859, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/22.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.55545+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.55545, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@22", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.55545+", "metric_symbol": "s", "metric_value": 1.55545, "reference_text": "s = 1.55545+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/22.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.55545+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "c1314ed0099ebdb6", "improvement": 8.823677085589843e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.5323101194107617e-06, "max_pair_overlap_depth": -6.490133103720375e-06, "metric_expression": "1.55536", "metric_symbol": "s", "metric_value": 1.555361763229144, "n": 22, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 1.55545, "setup": "triinoct", "side": 1.555361763229144, "solution_path": "data/solutions/generated/triinoct_022_c1314ed0099ebdb6.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/c1314ed0099ebdb6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@23", "density": 0.8210902170609379, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/23.gif", "friedman_metric_expression": "1.58458+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.58458, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@23", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.58458+", "metric_symbol": "s", "metric_value": 1.58458, "reference_text": "s = 1.58458+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/23.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.58458+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "4ca1a825a22b1f04", "improvement": -0.0003714249913302492, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.321393677649287e-06, "max_pair_overlap_depth": -1.5960535921788477e-06, "metric_expression": "1.58495", "metric_symbol": "s", "metric_value": 1.5849514249913303, "n": 23, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.58458, "setup": "triinoct", "side": 1.5849514249913303, "solution_path": "data/solutions/generated/triinoct_023_4ca1a825a22b1f04.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/4ca1a825a22b1f04.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@24", "density": 0.8373304168984339, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/24.gif", "friedman_metric_expression": "1.60261+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.60261, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@24", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.60261+", "metric_symbol": "s", "metric_value": 1.60261, "reference_text": "s = 1.60261+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.60261+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "e197b92ecac28558", "improvement": -0.0006526103809141315, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.085338835265612e-06, "max_pair_overlap_depth": -9.98840296584369e-06, "metric_expression": "1.60326", "metric_symbol": "s", "metric_value": 1.6032626103809142, "n": 24, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.60261, "setup": "triinoct", "side": 1.6032626103809142, "solution_path": "data/solutions/generated/triinoct_024_e197b92ecac28558.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/e197b92ecac28558.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@25", "density": 0.8354970198268096, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/25.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.63797+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.63797, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@25", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.63797+", "metric_symbol": "s", "metric_value": 1.63797, "reference_text": "s = 1.63797+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/25.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.63797+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "e322401fc5bafe4d", "improvement": -0.00014742221399233202, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.350806641875647e-06, "max_pair_overlap_depth": -2.3762008580785476e-06, "metric_expression": "1.63812", "metric_symbol": "s", "metric_value": 1.6381174222139923, "n": 25, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.63797, "setup": "triinoct", "side": 1.6381174222139923, "solution_path": "data/solutions/generated/triinoct_025_e322401fc5bafe4d.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/e322401fc5bafe4d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@26", "density": 0.8292613760828756, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/26.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.67666+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.67666, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@26", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.67666+", "metric_symbol": "s", "metric_value": 1.67666, "reference_text": "s = 1.67666+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/26.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.67666+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "7cb3797cd10b21d8", "improvement": -0.0001676725391090983, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.6314473196666756e-05, "max_pair_overlap_depth": -5.591511314406716e-06, "metric_expression": "1.67683", "metric_symbol": "s", "metric_value": 1.6768276725391091, "n": 26, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.67666, "setup": "triinoct", "side": 1.6768276725391091, "solution_path": "data/solutions/generated/triinoct_026_7cb3797cd10b21d8.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/7cb3797cd10b21d8.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@27", "density": 0.8297818493323376, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/27.gif", "friedman_metric_expression": "1.70882+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.70882, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@27", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.70882+", "metric_symbol": "s", "metric_value": 1.70882, "reference_text": "s = 1.70882+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/27.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.70882+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "c7748eb19b34ff2e", "improvement": 0.0005858720037632548, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.055699391789948e-06, "max_pair_overlap_depth": -3.877030372301249e-07, "metric_expression": "1.70823", "metric_symbol": "s", "metric_value": 1.7082341279962368, "n": 27, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 1.70882, "setup": "triinoct", "side": 1.7082341279962368, "solution_path": "data/solutions/generated/triinoct_27_c7748eb19b34ff2e.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/c7748eb19b34ff2e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@28", "density": 0.8299146316504411, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/28.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.73954+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.73954, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@28", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.73954+", "metric_symbol": "s", "metric_value": 1.73954, "reference_text": "s = 1.73954+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/28.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.73954+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "26e8795d82a701d8", "improvement": 9.867973407984287e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2195571711171888e-06, "max_pair_overlap_depth": -8.650951147992636e-06, "metric_expression": "1.73944", "metric_symbol": "s", "metric_value": 1.7394413202659202, "n": 28, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 1.73954, "setup": "triinoct", "side": 1.7394413202659202, "solution_path": "data/solutions/generated/triinoct_028_26e8795d82a701d8.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/26e8795d82a701d8.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@29", "density": 0.8439313801960897, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/29.gif", "friedman_metric_expression": "1.75576+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.75576, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@29", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.75576+", "metric_symbol": "s", "metric_value": 1.75576, "reference_text": "s = 1.75576+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/29.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.75576+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "0575780ea85d68dd", "improvement": 0.00029203482208850495, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.530531415212805e-06, "max_pair_overlap_depth": -1.1528245769332202e-05, "metric_expression": "1.75547", "metric_symbol": "s", "metric_value": 1.7554679651779115, "n": 29, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 1.75576, "setup": "triinoct", "side": 1.7554679651779115, "solution_path": "data/solutions/generated/triinoct_29_0575780ea85d68dd.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/0575780ea85d68dd.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinoct@30", "density": 0.8466211131481989, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/30.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.78101+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.78101, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@30", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.78101+", "metric_symbol": "s", "metric_value": 1.78101, "reference_text": "s = 1.78101+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/30.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.78101+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "4c08385c68f67e77", "improvement": -0.0016296314900829945, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.472767326523421e-06, "max_pair_overlap_depth": -3.1822885246945987e-06, "metric_expression": "1.78264", "metric_symbol": "s", "metric_value": 1.782639631490083, "n": 30, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.78101, "setup": "triinoct", "side": 1.782639631490083, "solution_path": "data/solutions/generated/triinoct_030_4c08385c68f67e77.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/4c08385c68f67e77.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@1", "density": 0.4121951299103008, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/1.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": ".781+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.781, "friedman_reference": {"analytical_or_proved": true, "case": "triinpen@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": ".781+", "metric_symbol": "s", "metric_value": 0.781, "reference_text": "s = cos(42\u00b0) / cos(18\u00b0) | s = .781+ | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/1.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = cos(42\u00b0) / cos(18\u00b0) | s = .781+ | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "6d3af7533c544064", "improvement": -0.0004017935524769367, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.010333690326338e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.78140", "metric_symbol": "s", "metric_value": 0.781401793552477, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.781, "setup": "triinpen", "side": 0.781401793552477, "solution_path": "data/solutions/generated/triinpen_001_6d3af7533c544064.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/6d3af7533c544064.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@2", "density": 0.4392461428307515, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/2.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.070+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.07, "friedman_reference": {"analytical_or_proved": true, "case": "triinpen@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1.070+", "metric_symbol": "s", "metric_value": 1.07, "reference_text": "s = \u221a(6/(3+\u221a5)) | s = 1.070+ | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/2.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = \u221a(6/(3+\u221a5)) | s = 1.070+ | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "eebb278fed1959e5", "improvement": -0.0005004432401414238, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.540244142797655e-06, "max_pair_overlap_depth": -4.677606255020384e-06, "metric_expression": "1.07050", "metric_symbol": "s", "metric_value": 1.0705004432401415, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.07, "setup": "triinpen", "side": 1.0705004432401415, "solution_path": "data/solutions/generated/triinpen_002_eebb278fed1959e5.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/eebb278fed1959e5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@3", "density": 0.5773621092377123, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/3.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.143+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.143, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@3", "credit": "Maurizio Morandi", "date": "August 2012", "family_updated": "", "metric_expression": "1.143+", "metric_symbol": "s", "metric_value": 1.143, "reference_text": "s = 1.143+ | Found by Maurizio Morandi | in August 2012. |", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/3.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.143+ | Found by Maurizio Morandi | in August 2012. |", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "6ec3c588fb678646", "improvement": -0.0005688574140261249, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4403665141977852e-06, "max_pair_overlap_depth": -4.738354987265936e-06, "metric_expression": "1.14357", "metric_symbol": "s", "metric_value": 1.1435688574140261, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.143, "setup": "triinpen", "side": 1.1435688574140261, "solution_path": "data/solutions/generated/triinpen_003_6ec3c588fb678646.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/6ec3c588fb678646.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@4", "density": 0.6999227205319379, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/4.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.199+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.199, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@4", "credit": "Maurizio Morandi", "date": "July 2012", "family_updated": "", "metric_expression": "1.199+", "metric_symbol": "s", "metric_value": 1.199, "reference_text": "s = 1.199+ | Found by Maurizio Morandi | in July 2012. |", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/4.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.199+ | Found by Maurizio Morandi | in July 2012. |", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "c45dd63fd5a8806b", "improvement": -0.0003081410566185827, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9487802360351315e-06, "max_pair_overlap_depth": -2.0674441409240796e-05, "metric_expression": "1.19931", "metric_symbol": "s", "metric_value": 1.1993081410566186, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.199, "setup": "triinpen", "side": 1.1993081410566186, "solution_path": "data/solutions/generated/triinpen_004_c45dd63fd5a8806b.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/c45dd63fd5a8806b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@5", "density": 0.818292233169356, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "March 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/5.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.240+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.24, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@5", "credit": "Erich Friedman", "date": "March 2012", "family_updated": "", "metric_expression": "1.240+", "metric_symbol": "s", "metric_value": 1.24, "reference_text": "s = 1 + 2sin(12\u00b0)/\u221a3 | s = 1.240+ | Found by Erich Friedman | in March 2012.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/5.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1 + 2sin(12\u00b0)/\u221a3 | s = 1.240+ | Found by Erich Friedman | in March 2012.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "a99f063702c9d4e8", "improvement": -9.974870359874544e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.477405190997757e-06, "max_pair_overlap_depth": -1.386320747689962e-05, "metric_expression": "1.24010", "metric_symbol": "s", "metric_value": 1.2400997487035987, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.24, "setup": "triinpen", "side": 1.2400997487035987, "solution_path": "data/solutions/generated/triinpen_005_a99f063702c9d4e8.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/a99f063702c9d4e8.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@6", "density": 0.7771309707429922, "friedman_analytical_or_proved": false, "friedman_credit": "Dominik Kamp", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/6.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.393+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.393, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@6", "credit": "Dominik Kamp", "date": "April 2026", "family_updated": "", "metric_expression": "1.393+", "metric_symbol": "s", "metric_value": 1.393, "reference_text": "s = 1.393+ | Found by Dominik Kamp | in April 2026.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/6.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.393+ | Found by Dominik Kamp | in April 2026.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "8d12939187f41554", "improvement": -0.0009729568537997224, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4992545061493154e-06, "max_pair_overlap_depth": -6.033095825291185e-06, "metric_expression": "1.39397", "metric_symbol": "s", "metric_value": 1.3939729568537997, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.393, "setup": "triinpen", "side": 1.3939729568537997, "solution_path": "data/solutions/generated/triinpen_006_8d12939187f41554.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Dominik Kamp", "svg_path": "data/svg/8d12939187f41554.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@7", "density": 0.7037922543518549, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/7.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.581+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.581, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@7", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "1.581+", "metric_symbol": "s", "metric_value": 1.581, "reference_text": "s = 1.581+ | Found by David W. Cantrell | in July 2012.", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/7.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.581+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "d149692a95cde76c", "improvement": -0.0011680508685436575, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5825119043122948e-06, "max_pair_overlap_depth": -1.774591125650038e-05, "metric_expression": "1.58217", "metric_symbol": "s", "metric_value": 1.5821680508685436, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.581, "setup": "triinpen", "side": 1.5821680508685436, "solution_path": "data/solutions/generated/triinpen_007_d149692a95cde76c.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d149692a95cde76c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@8", "density": 0.7311911118691055, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/8.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.659+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.659, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@8", "credit": "Maurizio Morandi", "date": "July 2012", "family_updated": "", "metric_expression": "1.659+", "metric_symbol": "s", "metric_value": 1.659, "reference_text": "s = 1.659+ | Found by Maurizio Morandi | in July 2012.", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/8.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.659+ | Found by Maurizio Morandi | in July 2012.", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "2ac4629603f9ce00", "improvement": -0.0004163833859911481, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2708160845523109e-06, "max_pair_overlap_depth": -2.147963686768839e-05, "metric_expression": "1.65942", "metric_symbol": "s", "metric_value": 1.6594163833859912, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.659, "setup": "triinpen", "side": 1.6594163833859912, "solution_path": "data/solutions/generated/triinpen_008_2ac4629603f9ce00.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/2ac4629603f9ce00.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@9", "density": 0.7240666005522262, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/9.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.767+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.767, "friedman_reference": {"analytical_or_proved": true, "case": "triinpen@9", "credit": "Maurizio Morandi", "date": "July 2012", "family_updated": "", "metric_expression": "1.767+", "metric_symbol": "s", "metric_value": 1.767, "reference_text": "s = 1.767+ | Found by Maurizio Morandi in July 2012. | Improved slightly by David W. Cantrell in August 2012.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/9.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.767+ | Found by Maurizio Morandi in July 2012. | Improved slightly by David W. Cantrell in August 2012.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "72279a3b92ae69ca", "improvement": -0.0017148783247660226, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.918216101924126e-06, "max_pair_overlap_depth": -2.2857021414468548e-08, "metric_expression": "1.76871", "metric_symbol": "s", "metric_value": 1.768714878324766, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.767, "setup": "triinpen", "side": 1.768714878324766, "solution_path": "data/solutions/generated/triinpen_009_72279a3b92ae69ca.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/72279a3b92ae69ca.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@10", "density": 0.7626299188806616, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/10.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.815+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.815, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@10", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "1.815+", "metric_symbol": "s", "metric_value": 1.815, "reference_text": "s = 1.815+ | Found by Timo Berthold et al | in January 2026.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/10.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.815+ | Found by Timo Berthold et al | in January 2026.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "f05f442bda1c650b", "improvement": -0.0016401662315850274, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.176875820916777e-06, "max_pair_overlap_depth": -3.546498963225009e-06, "metric_expression": "1.81664", "metric_symbol": "s", "metric_value": 1.816640166231585, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.815, "setup": "triinpen", "side": 1.816640166231585, "solution_path": "data/solutions/generated/triinpen_010_f05f442bda1c650b.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/f05f442bda1c650b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@11", "density": 0.7898687600512876, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/11.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.871+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.871, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@11", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "1.871+", "metric_symbol": "s", "metric_value": 1.871, "reference_text": "s = 1.871+ | Found by Timo Berthold et al | in January 2026.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/11.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.871+ | Found by Timo Berthold et al | in January 2026.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "ca41afc6c9b25b21", "improvement": -0.0011675168118052692, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.191218876790302e-06, "max_pair_overlap_depth": -1.6407344776342425e-05, "metric_expression": "1.87217", "metric_symbol": "s", "metric_value": 1.8721675168118053, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.871, "setup": "triinpen", "side": 1.8721675168118053, "solution_path": "data/solutions/generated/triinpen_011_ca41afc6c9b25b21.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/ca41afc6c9b25b21.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@12", "density": 0.774567014021955, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/12.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.973+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.973, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@12", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.973+", "metric_symbol": "s", "metric_value": 1.973, "reference_text": "s = 1.973+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/12.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.973+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "bf7ddcc735398246", "improvement": -0.0016355699317964767, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.087403974087953e-06, "max_pair_overlap_depth": -1.3435552785878713e-05, "metric_expression": "1.97464", "metric_symbol": "s", "metric_value": 1.9746355699317966, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.973, "setup": "triinpen", "side": 1.9746355699317966, "solution_path": "data/solutions/generated/triinpen_012_bf7ddcc735398246.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/bf7ddcc735398246.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@13", "density": 0.8029051605923488, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/13.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.017+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.017, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@13", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "2.017+", "metric_symbol": "s", "metric_value": 2.017, "reference_text": "s = 2.017+ | Found by Timo Berthold et al | in January 2026.", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/13.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.017+ | Found by Timo Berthold et al | in January 2026.", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "ff07ea08219353cb", "improvement": -0.0016702531518792973, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.615779077054135e-07, "max_pair_overlap_depth": -4.3930654851198625e-05, "metric_expression": "2.01867", "metric_symbol": "s", "metric_value": 2.018670253151879, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.017, "setup": "triinpen", "side": 2.018670253151879, "solution_path": "data/solutions/generated/triinpen_013_ff07ea08219353cb.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/ff07ea08219353cb.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@14", "density": 0.8070990172681682, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/14.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.088+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.088, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@14", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "2.088+", "metric_symbol": "s", "metric_value": 2.088, "reference_text": "s = 2.088+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "14.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/14.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.088+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "bc900c323229ee0c", "improvement": -0.0014233339778941811, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2035527022044616e-06, "max_pair_overlap_depth": -3.9869300561434784e-05, "metric_expression": "2.08942", "metric_symbol": "s", "metric_value": 2.0894233339778943, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.088, "setup": "triinpen", "side": 2.0894233339778943, "solution_path": "data/solutions/generated/triinpen_014_bc900c323229ee0c.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/bc900c323229ee0c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@15", "density": 0.8370246386712876, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/15.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.123+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.123, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@15", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.123+", "metric_symbol": "s", "metric_value": 2.123, "reference_text": "s = 2.123+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/15.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.123+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "39b13eec51bf2ea6", "improvement": -0.000744857935933041, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.959192129393714e-06, "max_pair_overlap_depth": -3.112528873211451e-05, "metric_expression": "2.12374", "metric_symbol": "s", "metric_value": 2.1237448579359333, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.123, "setup": "triinpen", "side": 2.1237448579359333, "solution_path": "data/solutions/generated/triinpen_015_39b13eec51bf2ea6.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/39b13eec51bf2ea6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@16", "density": 0.8497807683719915, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/16.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.17598+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.17598, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@16", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.17598+", "metric_symbol": "s", "metric_value": 2.17598, "reference_text": "s = 2.17598+ | Found by Ian Watson | in April 2026.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/16.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.17598+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "852225bc33edeebe", "improvement": -0.0008893975034314217, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.337598971955443e-06, "max_pair_overlap_depth": -3.396060024770525e-05, "metric_expression": "2.17687", "metric_symbol": "s", "metric_value": 2.1768693975034314, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.17598, "setup": "triinpen", "side": 2.1768693975034314, "solution_path": "data/solutions/generated/triinpen_016_852225bc33edeebe.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/852225bc33edeebe.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@17", "density": 0.8546812093159708, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/17.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.23658+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.23658, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@17", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.23658+", "metric_symbol": "s", "metric_value": 2.23658, "reference_text": "s = 2.23658+ | Found by Ian Watson | in April 2026.", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/17.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.23658+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "a8618eee7fdaba2a", "improvement": -0.0008435999825509022, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.39992551681681e-07, "max_pair_overlap_depth": -1.7412872881594765e-05, "metric_expression": "2.23742", "metric_symbol": "s", "metric_value": 2.237423599982551, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.23658, "setup": "triinpen", "side": 2.237423599982551, "solution_path": "data/solutions/generated/triinpen_017_a8618eee7fdaba2a.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/a8618eee7fdaba2a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@18", "density": 0.8594655455888001, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/18.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.29382+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.29382, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@18", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.29382+", "metric_symbol": "s", "metric_value": 2.29382, "reference_text": "s = 2.29382+ | Found by Ian Watson | in April 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/18.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.29382+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "6bf4f9b0915d39ee", "improvement": -0.0020529370652000445, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4774387061990001e-05, "max_pair_overlap_depth": -2.9541451285197695e-08, "metric_expression": "2.29587", "metric_symbol": "s", "metric_value": 2.2958729370652002, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.29382, "setup": "triinpen", "side": 2.2958729370652002, "solution_path": "data/solutions/generated/triinpen_018_6bf4f9b0915d39ee.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/6bf4f9b0915d39ee.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@19", "density": 0.868021512388566, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.344+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.344, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.344+", "metric_symbol": "s", "metric_value": 2.344, "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "eaa1430599d74148", "improvement": -0.003131316702724707, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9139572150349214e-06, "max_pair_overlap_depth": -1.0705368373109536e-05, "metric_expression": "2.34713", "metric_symbol": "s", "metric_value": 2.3471313167027246, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.344, "setup": "triinpen", "side": 2.3471313167027246, "solution_path": "data/solutions/generated/triinpen_19_eaa1430599d74148.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/eaa1430599d74148.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@20", "density": 0.8487102106795418, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/20.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.43350+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.4335, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@20", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.43350+", "metric_symbol": "s", "metric_value": 2.4335, "reference_text": "s = 2.43350+ | Found by Ian Watson | in April 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/20.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.43350+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "760faebc4d0b131b", "improvement": -0.001848490502489586, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.176183787084704e-07, "max_pair_overlap_depth": -8.807499014995557e-06, "metric_expression": "2.43535", "metric_symbol": "s", "metric_value": 2.4353484905024896, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.4335, "setup": "triinpen", "side": 2.4353484905024896, "solution_path": "data/solutions/generated/triinpen_020_760faebc4d0b131b.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/760faebc4d0b131b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@21", "density": 0.8589998748063701, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/21.gif", "friedman_metric_expression": "2.479+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.479, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@21", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.479+", "metric_symbol": "s", "metric_value": 2.479, "reference_text": "s = 2.479+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/21.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.479+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "115c20fad199fe9d", "improvement": -0.0014982727861765355, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.811024693767028e-06, "max_pair_overlap_depth": -2.8209410938284663e-06, "metric_expression": "2.48050", "metric_symbol": "s", "metric_value": 2.4804982727861766, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.479, "setup": "triinpen", "side": 2.4804982727861766, "solution_path": "data/solutions/generated/triinpen_021_115c20fad199fe9d.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/115c20fad199fe9d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@22", "density": 0.8389716031782235, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/22.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.56740+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.5674, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@22", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.56740+", "metric_symbol": "s", "metric_value": 2.5674, "reference_text": "s = 2.56740+ | Found by Ian Watson | in April 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/22.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.56740+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "929a1aedb3cfabb6", "improvement": -0.0015966714037367602, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.137059676377362e-07, "max_pair_overlap_depth": -8.172541590134585e-06, "metric_expression": "2.56900", "metric_symbol": "s", "metric_value": 2.568996671403737, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.5674, "setup": "triinpen", "side": 2.568996671403737, "solution_path": "data/solutions/generated/triinpen_022_929a1aedb3cfabb6.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/929a1aedb3cfabb6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@23", "density": 0.8432972889244729, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/23.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.61831+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.61831, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@23", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.61831+", "metric_symbol": "s", "metric_value": 2.61831, "reference_text": "s = 2.61831+ | Found by Ian Watson | in April 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/23.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.61831+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "c0d3905a26f7ef33", "improvement": -0.001678576890473682, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.992582537021139e-06, "max_pair_overlap_depth": -4.362218652298466e-06, "metric_expression": "2.61999", "metric_symbol": "s", "metric_value": 2.619988576890474, "n": 23, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.61831, "setup": "triinpen", "side": 2.619988576890474, "solution_path": "data/solutions/generated/triinpen_023_c0d3905a26f7ef33.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/c0d3905a26f7ef33.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@24", "density": 0.8488309418600493, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/24.gif", "friedman_metric_expression": "2.66641+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.66641, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@24", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.66641+", "metric_symbol": "s", "metric_value": 2.66641, "reference_text": "s = 2.66641+ | Found by Ian Watson | in April 2026.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.66641+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "7bc3466b163ec849", "improvement": -0.0011908775198370414, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.421732660736982e-06, "max_pair_overlap_depth": -3.3708625798434255e-05, "metric_expression": "2.66760", "metric_symbol": "s", "metric_value": 2.667600877519837, "n": 24, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.66641, "setup": "triinpen", "side": 2.667600877519837, "solution_path": "data/solutions/generated/triinpen_24_7bc3466b163ec849.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/7bc3466b163ec849.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@25", "density": 0.8491607934363294, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/25.gif", "friedman_metric_expression": "2.720+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.72, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@25", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.720+", "metric_symbol": "s", "metric_value": 2.72, "reference_text": "s = 2.720+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/25.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.720+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "0f20f89eba855e21", "improvement": -0.0020799025832594076, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.997044244500036e-06, "max_pair_overlap_depth": -8.121085018242269e-06, "metric_expression": "2.72208", "metric_symbol": "s", "metric_value": 2.7220799025832596, "n": 25, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.72, "setup": "triinpen", "side": 2.7220799025832596, "solution_path": "data/solutions/generated/triinpen_25_0f20f89eba855e21.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T13:47:12+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/0f20f89eba855e21.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@26", "density": 0.8520841245254238, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/26.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.771+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.771, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@26", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.771+", "metric_symbol": "s", "metric_value": 2.771, "reference_text": "s = 2.771+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/26.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.771+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "f991467944e6e634", "improvement": -0.00022168609627781777, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2986540650513047e-06, "max_pair_overlap_depth": -8.90414151222263e-06, "metric_expression": "2.77122", "metric_symbol": "s", "metric_value": 2.7712216860962777, "n": 26, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.771, "setup": "triinpen", "side": 2.7712216860962777, "solution_path": "data/solutions/generated/triinpen_026_f991467944e6e634.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/f991467944e6e634.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@27", "density": 0.8551322064876743, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/27.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.81761+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.81761, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@27", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.81761+", "metric_symbol": "s", "metric_value": 2.81761, "reference_text": "s = 2.81761+ | Found by Ian Watson | in April 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/27.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.81761+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "d6f1d3073209f163", "improvement": -0.0013640775641627911, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.642891580892597e-06, "max_pair_overlap_depth": -2.2253597504739986e-06, "metric_expression": "2.81897", "metric_symbol": "s", "metric_value": 2.818974077564163, "n": 27, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.81761, "setup": "triinpen", "side": 2.818974077564163, "solution_path": "data/solutions/generated/triinpen_027_d6f1d3073209f163.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/d6f1d3073209f163.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@28", "density": 0.8558072548880046, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/28.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.868+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.868, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@28", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.868+", "metric_symbol": "s", "metric_value": 2.868, "reference_text": "s = 2.868+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/28.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.868+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "2caa877f5aa08139", "improvement": -0.0015702794780372287, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.305293369328324e-06, "max_pair_overlap_depth": -1.9072024115107666e-05, "metric_expression": "2.86957", "metric_symbol": "s", "metric_value": 2.869570279478037, "n": 28, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.868, "setup": "triinpen", "side": 2.869570279478037, "solution_path": "data/solutions/generated/triinpen_028_2caa877f5aa08139.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T03:19:00+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/2caa877f5aa08139.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@29", "density": 0.8642558401713053, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/29.gif", "friedman_metric_expression": "2.903+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.903, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@29", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "2.903+", "metric_symbol": "s", "metric_value": 2.903, "reference_text": "s = 2.903+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/29.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.903+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "9730db96941e5b52", "improvement": -0.003053928319848076, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.800701997238751e-06, "max_pair_overlap_depth": -5.0014115865471e-06, "metric_expression": "2.90605", "metric_symbol": "s", "metric_value": 2.906053928319848, "n": 29, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.903, "setup": "triinpen", "side": 2.906053928319848, "solution_path": "data/solutions/generated/triinpen_29_9730db96941e5b52.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T07:13:53+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/9730db96941e5b52.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@30", "density": 0.8662355090431414, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/30.gif", "friedman_metric_expression": "2.952+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.952, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@30", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "2.952+", "metric_symbol": "s", "metric_value": 2.952, "reference_text": "s = 2.952+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/30.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.952+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "29e4e0e684891d8a", "improvement": -0.00035425771249730786, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.990812967166742e-06, "max_pair_overlap_depth": -2.800943013125945e-05, "metric_expression": "2.95235", "metric_symbol": "s", "metric_value": 2.9523542577124973, "n": 30, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.952, "setup": "triinpen", "side": 2.9523542577124973, "solution_path": "data/solutions/generated/triinpen_30_29e4e0e684891d8a.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/29e4e0e684891d8a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@31", "density": 0.8713888671331285, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/31.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.992+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.992, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "2.992+", "metric_symbol": "s", "metric_value": 2.992, "reference_text": "s = 2.992+ | Found by Emerson Connelly | in April 2026.", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/31.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.992+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "44a0bb3f581e92e2", "improvement": -0.0002692889761504169, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.7795814276238894e-06, "max_pair_overlap_depth": -1.3596177029562284e-05, "metric_expression": "2.99227", "metric_symbol": "s", "metric_value": 2.9922692889761504, "n": 31, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.992, "setup": "triinpen", "side": 2.9922692889761504, "solution_path": "data/solutions/generated/triinpen_031_44a0bb3f581e92e2.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/44a0bb3f581e92e2.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@32", "density": 0.8781198099192385, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/32.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.029+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.029, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.029+", "metric_symbol": "s", "metric_value": 3.029, "reference_text": "s = 3.029+ | Found by Emerson Connelly | in April 2026.", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/32.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.029+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "310badf403ba4fce", "improvement": 0.0005254132016050406, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.877563686504985e-07, "max_pair_overlap_depth": -2.5172545809359903e-05, "metric_expression": "3.02847", "metric_symbol": "s", "metric_value": 3.028474586798395, "n": 32, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.029, "setup": "triinpen", "side": 3.028474586798395, "solution_path": "data/solutions/generated/triinpen_032_310badf403ba4fce.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/310badf403ba4fce.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@33", "density": 0.8767362450469284, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/33.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.078+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.078, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.078+", "metric_symbol": "s", "metric_value": 3.078, "reference_text": "s = 3.078+ | Found by Emerson Connelly | in April 2026.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/33.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.078+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "2cf1b1f38810795d", "improvement": 0.00014382895343612034, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9579559668821387e-06, "max_pair_overlap_depth": -6.152141676318834e-06, "metric_expression": "3.07786", "metric_symbol": "s", "metric_value": 3.0778561710465637, "n": 33, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.078, "setup": "triinpen", "side": 3.0778561710465637, "solution_path": "data/solutions/generated/triinpen_033_2cf1b1f38810795d.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/2cf1b1f38810795d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@34", "density": 0.8805067280135348, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/34.gif", "friedman_metric_expression": "3.114+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.114, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.114+", "metric_symbol": "s", "metric_value": 3.114, "reference_text": "s = 3.114+ | Found by Emerson Connelly | in April 2026.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/34.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.114+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "faff9872314d8b1a", "improvement": -0.003446083050953952, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4825467113644516e-07, "max_pair_overlap_depth": -8.773672566686486e-06, "metric_expression": "3.11745", "metric_symbol": "s", "metric_value": 3.117446083050954, "n": 34, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.114, "setup": "triinpen", "side": 3.117446083050954, "solution_path": "data/solutions/generated/triinpen_34_faff9872314d8b1a.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T14:34:18+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/faff9872314d8b1a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@35", "density": 0.8875886550862264, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/35.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.150+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.15, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@35", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.150+", "metric_symbol": "s", "metric_value": 3.15, "reference_text": "s = 3.150+ | Found by Emerson Connelly | in April 2026.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/35.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.150+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "8fe5da1df972c0b3", "improvement": -0.0003150122852528803, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4152162741179605e-06, "max_pair_overlap_depth": -9.46789992128938e-06, "metric_expression": "3.15032", "metric_symbol": "s", "metric_value": 3.150315012285253, "n": 35, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.15, "setup": "triinpen", "side": 3.150315012285253, "solution_path": "data/solutions/generated/triinpen_035_8fe5da1df972c0b3.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/8fe5da1df972c0b3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@36", "density": 0.8985572699958073, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/36.gif", "friedman_metric_expression": "3.177+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.177, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@36", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.177+", "metric_symbol": "s", "metric_value": 3.177, "reference_text": "s = 3.177+ | Found by Emerson Connelly | in April 2026.", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/36.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.177+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "5183a03ffc16bcf9", "improvement": 0.0015578799748001693, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.498547309348074e-07, "max_pair_overlap_depth": -2.3029919912209706e-06, "metric_expression": "3.17544", "metric_symbol": "s", "metric_value": 3.1754421200252, "n": 36, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.177, "setup": "triinpen", "side": 3.1754421200252, "solution_path": "data/solutions/record_hunt/triinpen_36_5183a03ffc16bcf9.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/5183a03ffc16bcf9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@37", "density": 0.9016389565813171, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/37.gif", "friedman_metric_expression": "3.21529+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.21529, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@37", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "3.21529+", "metric_symbol": "s", "metric_value": 3.21529, "reference_text": "s = 3.21529+ | Found by Nathan Roll | in April 2026.", "source_image": "37.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/37.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.21529+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "08996b45ff04652c", "improvement": 0.0015527990845791706, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.641732962649716e-07, "max_pair_overlap_depth": -1.845774424413804e-07, "metric_expression": "3.21374", "metric_symbol": "s", "metric_value": 3.213737200915421, "n": 37, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.21529, "setup": "triinpen", "side": 3.213737200915421, "solution_path": "data/solutions/record_hunt/triinpen_37_08996b45ff04652c.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/08996b45ff04652c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@38", "density": 0.9010687984988149, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/38.gif", "friedman_metric_expression": "3.25877+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.25877, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@38", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "3.25877+", "metric_symbol": "s", "metric_value": 3.25877, "reference_text": "s = 3.25877+ | Found by Nathan Roll | in April 2026.", "source_image": "38.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/38.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.25877+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "cca381f54ee9b299", "improvement": 0.0008632130758914336, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.177049878621715e-07, "max_pair_overlap_depth": -8.114145322313249e-07, "metric_expression": "3.25791", "metric_symbol": "s", "metric_value": 3.2579067869241087, "n": 38, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.25877, "setup": "triinpen", "side": 3.2579067869241087, "solution_path": "data/solutions/record_hunt/triinpen_38_cca381f54ee9b299.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/cca381f54ee9b299.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@39", "density": 0.9025101556269666, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/39.gif", "friedman_metric_expression": "3.295+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.295, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.295+", "metric_symbol": "s", "metric_value": 3.295, "reference_text": "s = 3.295+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/39.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.295+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "67a6bbf24108966a", "improvement": -0.002859023967915597, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9740347935670834e-06, "max_pair_overlap_depth": -1.0007850107629501e-05, "metric_expression": "3.29786", "metric_symbol": "s", "metric_value": 3.2978590239679155, "n": 39, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.295, "setup": "triinpen", "side": 3.2978590239679155, "solution_path": "data/solutions/generated/triinpen_039_67a6bbf24108966a.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/67a6bbf24108966a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinpen@40", "density": 0.9091859235070038, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/40.gif", "friedman_metric_expression": "3.32786+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.32786, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@40", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "3.32786+", "metric_symbol": "s", "metric_value": 3.32786, "reference_text": "s = 3.32786+ | Found by Nathan Roll | in April 2026.", "source_image": "40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/40.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.32786+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "032ceee4e789eff6", "improvement": 0.0002725631872593226, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4037127820689358e-07, "max_pair_overlap_depth": -1.074379339049969e-06, "metric_expression": "3.32759", "metric_symbol": "s", "metric_value": 3.3275874368127405, "n": 40, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.32786, "setup": "triinpen", "side": 3.3275874368127405, "solution_path": "data/solutions/record_hunt/triinpen_40_032ceee4e789eff6.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/032ceee4e789eff6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@1", "density": 0.4640965865243202, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t1.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(\u221a2+\u221a6)/4 = .965+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.965, "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "(\u221a2+\u221a6)/4 = .965+", "metric_symbol": "s", "metric_value": 0.965, "reference_text": "s = (\u221a2+\u221a6)/4 = .965+ | Trivial.", "source_image": "t1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t1.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = (\u221a2+\u221a6)/4 = .965+ | Trivial.", "friedman_source_image": "t1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "d0da9c9aae58c37e", "improvement": -0.0009310593101359288, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.031269735994051e-07, "max_pair_overlap_depth": 0.0, "metric_expression": "0.96593", "metric_symbol": "s", "metric_value": 0.9659310593101359, "n": 1, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 0.965, "setup": "triinsqu", "side": 0.9659310593101359, "solution_path": "data/solutions/generated/triinsqu_001_d0da9c9aae58c37e.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d0da9c9aae58c37e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@2", "density": 0.5773345801938596, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t2.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a6/2 = 1.224+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.224, "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a6/2 = 1.224+", "metric_symbol": "s", "metric_value": 1.224, "reference_text": "s = \u221a6/2 = 1.224+ | Trivial.", "source_image": "t2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t2.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = \u221a6/2 = 1.224+ | Trivial.", "friedman_source_image": "t2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "536a8bec14614050", "improvement": -0.0007615124236886039, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.5296142902332335e-06, "max_pair_overlap_depth": -8.602274652714007e-06, "metric_expression": "1.22476", "metric_symbol": "s", "metric_value": 1.2247615124236886, "n": 2, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.224, "setup": "triinsqu", "side": 1.2247615124236886, "solution_path": "data/solutions/generated/triinsqu_002_536a8bec14614050.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/536a8bec14614050.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@3", "density": 0.594304450868366, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1996", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t3.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a3/2+\u221a6/4 = 1.478+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.478, "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@3", "credit": "Erich Friedman", "date": "1996", "family_updated": "", "metric_expression": "\u221a3/2+\u221a6/4 = 1.478+", "metric_symbol": "s", "metric_value": 1.478, "reference_text": "s = \u221a3/2+\u221a6/4 = 1.478+ | Found by Erich Friedman | in 1996.", "source_image": "t3.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t3.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = \u221a3/2+\u221a6/4 = 1.478+ | Found by Erich Friedman | in 1996.", "friedman_source_image": "t3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "85d51e7a9d3c3790", "improvement": -0.00044936123470140643, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.5025974997417175e-07, "max_pair_overlap_depth": -2.9708917167997617e-05, "metric_expression": "1.47845", "metric_symbol": "s", "metric_value": 1.4784493612347014, "n": 3, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.478, "setup": "triinsqu", "side": 1.4784493612347014, "solution_path": "data/solutions/generated/triinsqu_003_85d51e7a9d3c3790.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/85d51e7a9d3c3790.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@4", "density": 0.6961073829345906, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1996", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t4.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1+1/\u221a3 = 1.577+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.577, "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@4", "credit": "Erich Friedman", "date": "1996", "family_updated": "", "metric_expression": "1+1/\u221a3 = 1.577+", "metric_symbol": "s", "metric_value": 1.577, "reference_text": "s = 1+1/\u221a3 = 1.577+ | Found by Erich Friedman | in 1996.", "source_image": "t4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t4.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 1+1/\u221a3 = 1.577+ | Found by Erich Friedman | in 1996.", "friedman_source_image": "t4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "10004832454b0f3c", "improvement": -0.00040129748580719493, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.301219061208287e-07, "max_pair_overlap_depth": -2.378752457826705e-05, "metric_expression": "1.57740", "metric_symbol": "s", "metric_value": 1.5774012974858072, "n": 4, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.577, "setup": "triinsqu", "side": 1.5774012974858072, "solution_path": "data/solutions/generated/triinsqu_004_10004832454b0f3c.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/10004832454b0f3c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@5", "density": 0.6658433228069607, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1996", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t5.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.803+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.803, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@5", "credit": "Erich Friedman", "date": "1996", "family_updated": "", "metric_expression": "1.803+", "metric_symbol": "s", "metric_value": 1.803, "reference_text": "s = 1.803+ | Found by Erich Friedman | in 1996.", "source_image": "t5.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t5.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 1.803+ | Found by Erich Friedman | in 1996.", "friedman_source_image": "t5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "f41eeaee150f1c15", "improvement": -0.0002224086857132157, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.6751531743821273e-06, "max_pair_overlap_depth": -2.226142234541817e-05, "metric_expression": "1.80322", "metric_symbol": "s", "metric_value": 1.8032224086857132, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.803, "setup": "triinsqu", "side": 1.8032224086857132, "solution_path": "data/solutions/generated/triinsqu_005_f41eeaee150f1c15.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/f41eeaee150f1c15.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@6", "density": 0.7181966221398873, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1996", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t6.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "9/2\u20133\u221a3/2 = 1.901+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.901, "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@6", "credit": "Erich Friedman", "date": "1996", "family_updated": "", "metric_expression": "9/2\u20133\u221a3/2 = 1.901+", "metric_symbol": "s", "metric_value": 1.901, "reference_text": "s = 9/2\u20133\u221a3/2 = 1.901+ | Found by Erich Friedman | in 1996.", "source_image": "t6.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t6.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 9/2\u20133\u221a3/2 = 1.901+ | Found by Erich Friedman | in 1996.", "friedman_source_image": "t6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "47de8ba8f0c9310c", "improvement": -0.0009726348176062327, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.131503356462894e-07, "max_pair_overlap_depth": -1.0226066655058541e-06, "metric_expression": "1.90197", "metric_symbol": "s", "metric_value": 1.9019726348176063, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 1.901, "setup": "triinsqu", "side": 1.9019726348176063, "solution_path": "data/solutions/generated/triinsqu_006_47de8ba8f0c9310c.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/47de8ba8f0c9310c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@7", "density": 0.7576992844833931, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1996", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t7.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@7", "credit": "Erich Friedman", "date": "1996", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Found by Erich Friedman | in 1996.", "source_image": "t7.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t7.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2 | Found by Erich Friedman | in 1996.", "friedman_source_image": "t7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "d4eecc11473f7bf7", "improvement": -9.626783869354227e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.867700488247924e-07, "max_pair_overlap_depth": -1.9950288099523666e-05, "metric_expression": "2.00010", "metric_symbol": "s", "metric_value": 2.0000962678386935, "n": 7, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.0, "setup": "triinsqu", "side": 2.0000962678386935, "solution_path": "data/solutions/generated/triinsqu_007_d4eecc11473f7bf7.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/d4eecc11473f7bf7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@8", "density": 0.7868902975296777, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1996", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t8.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3\u221a3/2\u20131/2 = 2.098+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.098, "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@8", "credit": "Erich Friedman", "date": "1996", "family_updated": "", "metric_expression": "3\u221a3/2\u20131/2 = 2.098+", "metric_symbol": "s", "metric_value": 2.098, "reference_text": "s = 3\u221a3/2\u20131/2 = 2.098+ | Found by Erich Friedman | in 1996.", "source_image": "t8.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t8.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3\u221a3/2\u20131/2 = 2.098+ | Found by Erich Friedman | in 1996.", "friedman_source_image": "t8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "bd28b88a6ba9b99d", "improvement": -0.00015813059780489525, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0169734543243664e-06, "max_pair_overlap_depth": -2.636538231393093e-05, "metric_expression": "2.09816", "metric_symbol": "s", "metric_value": 2.0981581305978048, "n": 8, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.098, "setup": "triinsqu", "side": 2.0981581305978048, "solution_path": "data/solutions/generated/triinsqu_008_bd28b88a6ba9b99d.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/bd28b88a6ba9b99d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@9", "density": 0.7446998211864622, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t9.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.287+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.287, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@9", "credit": "Maurizio Morandi", "date": "July 2008", "family_updated": "", "metric_expression": "2.287+", "metric_symbol": "s", "metric_value": 2.287, "reference_text": "s = 2.287+ | Found by Maurizio Morandi | in July 2008.", "source_image": "t9.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t9.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.287+ | Found by Maurizio Morandi | in July 2008.", "friedman_source_image": "t9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "458e49fec5e5573c", "improvement": -0.0006045303821253789, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.745466993473377e-07, "max_pair_overlap_depth": -5.124657140087585e-06, "metric_expression": "2.28760", "metric_symbol": "s", "metric_value": 2.2876045303821253, "n": 9, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.287, "setup": "triinsqu", "side": 2.2876045303821253, "solution_path": "data/solutions/generated/triinsqu_009_458e49fec5e5573c.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/458e49fec5e5573c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@10", "density": 0.7662234065167978, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t10.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.377+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.377, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@10", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "2.377+", "metric_symbol": "s", "metric_value": 2.377, "reference_text": "s = 2.377+ | Found by David W. Cantrell | in July 2002.", "source_image": "t10.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t10.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.377+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "t10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "5b0eaf84f54fe48c", "improvement": -0.00023770927049060475, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.324926068512563e-07, "max_pair_overlap_depth": -1.1896205976635876e-05, "metric_expression": "2.37724", "metric_symbol": "s", "metric_value": 2.3772377092704904, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.377, "setup": "triinsqu", "side": 2.3772377092704904, "solution_path": "data/solutions/generated/triinsqu_10_5b0eaf84f54fe48c.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/5b0eaf84f54fe48c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@11", "density": 0.7671858882860172, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t11.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.490+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.49, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@11", "credit": "Maurizio Morandi", "date": "June 2008", "family_updated": "", "metric_expression": "2.490+", "metric_symbol": "s", "metric_value": 2.49, "reference_text": "s = 2.490+ | Found by Maurizio Morandi | in June 2008.", "source_image": "t11.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t11.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.490+ | Found by Maurizio Morandi | in June 2008.", "friedman_source_image": "t11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "b95fbc7e7009bb63", "improvement": -0.0017034740442234408, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.171896607131735e-07, "max_pair_overlap_depth": -3.917476745979309e-05, "metric_expression": "2.49170", "metric_symbol": "s", "metric_value": 2.4917034740442237, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.49, "setup": "triinsqu", "side": 2.4917034740442237, "solution_path": "data/solutions/generated/triinsqu_011_b95fbc7e7009bb63.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/b95fbc7e7009bb63.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@12", "density": 0.792908624011719, "friedman_analytical_or_proved": false, "friedman_credit": "Dominik Kamp", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t12.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.558+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.558, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@12", "credit": "Dominik Kamp", "date": "April 2026", "family_updated": "", "metric_expression": "2.558+", "metric_symbol": "s", "metric_value": 2.558, "reference_text": "s = 2.558+ | Found by Dominik Kamp | in April 2026.", "source_image": "t12.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t12.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.558+ | Found by Dominik Kamp | in April 2026.", "friedman_source_image": "t12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "297283972e34795d", "improvement": -0.0019375473066665094, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.5442542765183254e-06, "max_pair_overlap_depth": -1.2119755173123359e-05, "metric_expression": "2.55994", "metric_symbol": "s", "metric_value": 2.5599375473066663, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.558, "setup": "triinsqu", "side": 2.5599375473066663, "solution_path": "data/solutions/generated/triinsqu_012_297283972e34795d.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Dominik Kamp", "svg_path": "data/svg/297283972e34795d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@13", "density": 0.8355745862678572, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t13.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.595+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.595, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@13", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "2.595+", "metric_symbol": "s", "metric_value": 2.595, "reference_text": "s = 2.595+ | Found by David W. Cantrell | in July 2002.", "source_image": "t13.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t13.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.595+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "t13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "7628e283de25ee68", "improvement": -0.0005499010705918295, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8264727928819919e-06, "max_pair_overlap_depth": -1.755464108432747e-05, "metric_expression": "2.59555", "metric_symbol": "s", "metric_value": 2.595549901070592, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.595, "setup": "triinsqu", "side": 2.595549901070592, "solution_path": "data/solutions/generated/triinsqu_13_7628e283de25ee68.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/7628e283de25ee68.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@14", "density": 0.8144966370845219, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t14.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.726+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.726, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@14", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "2.726+", "metric_symbol": "s", "metric_value": 2.726, "reference_text": "s = 2.726+ | Found by David W. Cantrell | in July 2002.", "source_image": "t14.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t14.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.726+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "t14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "601dc4458719752d", "improvement": -0.0021590642579867314, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4175513847981196e-06, "max_pair_overlap_depth": -2.112817484914431e-05, "metric_expression": "2.72816", "metric_symbol": "s", "metric_value": 2.7281590642579867, "n": 14, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.726, "setup": "triinsqu", "side": 2.7281590642579867, "solution_path": "data/solutions/generated/triinsqu_014_601dc4458719752d.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/601dc4458719752d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@15", "density": 0.8108430550585584, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t15.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.8299+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.8299, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@15", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.8299+", "metric_symbol": "s", "metric_value": 2.8299, "reference_text": "s = 2.8299+ | Found by Ian Watson | in April 2026.", "source_image": "t15.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t15.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.8299+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "430e70d954ae3759", "improvement": -0.0003679073759270679, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0258685225063818e-06, "max_pair_overlap_depth": -3.8614458098606974e-05, "metric_expression": "2.83027", "metric_symbol": "s", "metric_value": 2.830267907375927, "n": 15, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.8299, "setup": "triinsqu", "side": 2.830267907375927, "solution_path": "data/solutions/generated/triinsqu_015_430e70d954ae3759.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/430e70d954ae3759.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@16", "density": 0.8226134516626242, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t16.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.9000+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.9, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@16", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.9000+", "metric_symbol": "s", "metric_value": 2.9, "reference_text": "s = 2.9000+ | Found by Ian Watson | in April 2026.", "source_image": "t16.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t16.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.9000+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "2350476c07d7060c", "improvement": -0.002100218284964317, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.0129376531587966e-06, "max_pair_overlap_depth": -5.176872598853383e-06, "metric_expression": "2.90210", "metric_symbol": "s", "metric_value": 2.9021002182849642, "n": 16, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.9, "setup": "triinsqu", "side": 2.9021002182849642, "solution_path": "data/solutions/generated/triinsqu_016_2350476c07d7060c.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/2350476c07d7060c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@17", "density": 0.8272516069770434, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t17.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.982+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.982, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@17", "credit": "Maurizio Morandi", "date": "July 2008", "family_updated": "", "metric_expression": "2.982+", "metric_symbol": "s", "metric_value": 2.982, "reference_text": "s = 2.982+ | Found by Maurizio Morandi | in July 2008.", "source_image": "t17.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t17.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.982+ | Found by Maurizio Morandi | in July 2008.", "friedman_source_image": "t17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "79a5506fa7f0974c", "improvement": -0.0010186525102788835, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8787966733926961e-06, "max_pair_overlap_depth": -9.562062775358982e-06, "metric_expression": "2.98302", "metric_symbol": "s", "metric_value": 2.983018652510279, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.982, "setup": "triinsqu", "side": 2.983018652510279, "solution_path": "data/solutions/generated/triinsqu_017_79a5506fa7f0974c.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/79a5506fa7f0974c.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@18", "density": 0.8369229075763384, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t18.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.051+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.051, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@18", "credit": "Maurizio Morandi", "date": "July 2008", "family_updated": "", "metric_expression": "3.051+", "metric_symbol": "s", "metric_value": 3.051, "reference_text": "s = 3.051+ | Found by Maurizio Morandi | in July 2008.", "source_image": "t18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t18.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3.051+ | Found by Maurizio Morandi | in July 2008.", "friedman_source_image": "t18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "0d24ad1cca3bbb64", "improvement": -0.0007140908076439523, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6577344713731995e-06, "max_pair_overlap_depth": -7.637757528100586e-06, "metric_expression": "3.05171", "metric_symbol": "s", "metric_value": 3.051714090807644, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.051, "setup": "triinsqu", "side": 3.051714090807644, "solution_path": "data/solutions/generated/triinsqu_018_0d24ad1cca3bbb64.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/0d24ad1cca3bbb64.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@19", "density": 0.8400046005998116, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t19.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.12930+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.1293, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@19", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.12930+", "metric_symbol": "s", "metric_value": 3.1293, "reference_text": "s = 3.12930+ | Found by Ian Watson | in April 2026.", "source_image": "t19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t19.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3.12930+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "def5af7572515998", "improvement": -0.0002816463880579434, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.93050707669818e-06, "max_pair_overlap_depth": -4.5439275512260124e-06, "metric_expression": "3.12958", "metric_symbol": "s", "metric_value": 3.129581646388058, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.1293, "setup": "triinsqu", "side": 3.129581646388058, "solution_path": "data/solutions/generated/triinsqu_019_def5af7572515998.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/def5af7572515998.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@20", "density": 0.8288697801794981, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t20.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.2305+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.2305, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@20", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.2305+", "metric_symbol": "s", "metric_value": 3.2305, "reference_text": "s = 3.2305+ | Found by Ian Watson | in April 2026.", "source_image": "t20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t20.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3.2305+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "43e53f43942a4488", "improvement": -0.0018781535798377824, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.815940991194715e-07, "max_pair_overlap_depth": -1.1219130352735363e-05, "metric_expression": "3.23238", "metric_symbol": "s", "metric_value": 3.232378153579838, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.2305, "setup": "triinsqu", "side": 3.232378153579838, "solution_path": "data/solutions/generated/triinsqu_020_43e53f43942a4488.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/43e53f43942a4488.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@21", "density": 0.8291397947988184, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t21.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.3111+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.3111, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@21", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.3111+", "metric_symbol": "s", "metric_value": 3.3111, "reference_text": "s = 3.3111+ | Found by Ian Watson | in April 2026.", "source_image": "t21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t21.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3.3111+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "986572060ddb345a", "improvement": -0.0005626159903786565, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2145623034941338e-06, "max_pair_overlap_depth": -2.9730022631513364e-06, "metric_expression": "3.31166", "metric_symbol": "s", "metric_value": 3.311662615990379, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.3111, "setup": "triinsqu", "side": 3.311662615990379, "solution_path": "data/solutions/generated/triinsqu_021_986572060ddb345a.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/986572060ddb345a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@22", "density": 0.8356286267983878, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t22.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.3757+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.3757, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@22", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.3757+", "metric_symbol": "s", "metric_value": 3.3757, "reference_text": "22. | | s = 3.3757+ | Found by Ian Watson | in April 2026.", "source_image": "t22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t22.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "22. | | s = 3.3757+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "4d69d20a7a35e585", "improvement": -0.0007086456724314516, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2855965547198588e-06, "max_pair_overlap_depth": -1.8710922459974633e-05, "metric_expression": "3.37641", "metric_symbol": "s", "metric_value": 3.3764086456724316, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.3757, "setup": "triinsqu", "side": 3.3764086456724316, "solution_path": "data/solutions/generated/triinsqu_022_4d69d20a7a35e585.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/4d69d20a7a35e585.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@23", "density": 0.8452320475065837, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t23.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.4311+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.4311, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@23", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.4311+", "metric_symbol": "s", "metric_value": 3.4311, "reference_text": "23. | | s = 3.4311+ | Found by Ian Watson | in April 2026.", "source_image": "t23.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t23.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "23. | | s = 3.4311+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "959574dda9a01133", "improvement": -0.001524187888661821, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.8602101761622194e-08, "max_pair_overlap_depth": -2.5255431334025857e-06, "metric_expression": "3.43262", "metric_symbol": "s", "metric_value": 3.4326241878886616, "n": 23, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.4311, "setup": "triinsqu", "side": 3.4326241878886616, "solution_path": "data/solutions/generated/triinsqu_023_959574dda9a01133.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/959574dda9a01133.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@24", "density": 0.8636751606923448, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t24.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.468+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.468, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@24", "credit": "Maurizio Morandi", "date": "August 2008", "family_updated": "", "metric_expression": "3.468+", "metric_symbol": "s", "metric_value": 3.468, "reference_text": "24. | | s = 3.468+ | Found by Maurizio Morandi | in August 2008.", "source_image": "t24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t24.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "24. | | s = 3.468+ | Found by Maurizio Morandi | in August 2008.", "friedman_source_image": "t24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "d96b5ad8b1001b9a", "improvement": -0.0008116902395634007, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1658397103314651e-06, "max_pair_overlap_depth": -6.191240536246312e-06, "metric_expression": "3.46881", "metric_symbol": "s", "metric_value": 3.4688116902395634, "n": 24, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.468, "setup": "triinsqu", "side": 3.4688116902395634, "solution_path": "data/solutions/generated/triinsqu_024_d96b5ad8b1001b9a.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/d96b5ad8b1001b9a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@25", "density": 0.8645393394550887, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t25.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.537+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.537, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@25", "credit": "David W. Cantrell", "date": "August 2012", "family_updated": "", "metric_expression": "3.537+", "metric_symbol": "s", "metric_value": 3.537, "reference_text": "25. | | s = 3.537+ | Found by David W. Cantrell | in August 2012.", "source_image": "t25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t25.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "25. | | s = 3.537+ | Found by David W. Cantrell | in August 2012.", "friedman_source_image": "t25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "8da962f4a2ed3f11", "improvement": -0.0015712315473748184, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.272129416634903e-07, "max_pair_overlap_depth": -1.1961418790784606e-05, "metric_expression": "3.53857", "metric_symbol": "s", "metric_value": 3.5385712315473747, "n": 25, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.537, "setup": "triinsqu", "side": 3.5385712315473747, "solution_path": "data/solutions/generated/triinsqu_025_8da962f4a2ed3f11.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/8da962f4a2ed3f11.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@26", "density": 0.8796434821316925, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "September 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t26.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.575+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.575, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@26", "credit": "Maurizio Morandi", "date": "September 2008", "family_updated": "", "metric_expression": "3.575+", "metric_symbol": "s", "metric_value": 3.575, "reference_text": "26. | | s = 3.575+ | Found by Maurizio Morandi | in September 2008.", "source_image": "t26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t26.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "26. | | s = 3.575+ | Found by Maurizio Morandi | in September 2008.", "friedman_source_image": "t26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "c36ce120aca7c2e7", "improvement": -0.002532991640289417, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0954385221262358e-06, "max_pair_overlap_depth": -5.476191583808632e-07, "metric_expression": "3.57753", "metric_symbol": "s", "metric_value": 3.5775329916402896, "n": 26, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.575, "setup": "triinsqu", "side": 3.5775329916402896, "solution_path": "data/solutions/generated/triinsqu_026_c36ce120aca7c2e7.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/c36ce120aca7c2e7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@27", "density": 0.8658956992776567, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t27.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.6726+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.6726, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@27", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.6726+", "metric_symbol": "s", "metric_value": 3.6726, "reference_text": "27. | | s = 3.6726+ | Found by Ian Watson | in April 2026.", "source_image": "t27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t27.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "27. | | s = 3.6726+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "4c91417b38b8be95", "improvement": -0.0019097898938134072, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.750472262434879e-07, "max_pair_overlap_depth": -1.515528041828862e-05, "metric_expression": "3.67451", "metric_symbol": "s", "metric_value": 3.6745097898938135, "n": 27, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.6726, "setup": "triinsqu", "side": 3.6745097898938135, "solution_path": "data/solutions/generated/triinsqu_027_4c91417b38b8be95.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/4c91417b38b8be95.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@28", "density": 0.8583067572738268, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t28.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.7571+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.7571, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@28", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.7571+", "metric_symbol": "s", "metric_value": 3.7571, "reference_text": "28. | | s = 3.7571+ | Found by Ian Watson | in April 2026.", "source_image": "t28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t28.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "28. | | s = 3.7571+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "9b7285926a894eec", "improvement": -0.0013438626171571322, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7756377540625622e-06, "max_pair_overlap_depth": -5.481622750158621e-06, "metric_expression": "3.75844", "metric_symbol": "s", "metric_value": 3.758443862617157, "n": 28, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.7571, "setup": "triinsqu", "side": 3.758443862617157, "solution_path": "data/solutions/generated/triinsqu_028_9b7285926a894eec.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/9b7285926a894eec.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@29", "density": 0.8613056568479127, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t29.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.818+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.818, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@29", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "3.818+", "metric_symbol": "s", "metric_value": 3.818, "reference_text": "29. | | s = 3.818+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "t29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t29.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "29. | | s = 3.818+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "t29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "a02ae61c838755d7", "improvement": -0.0003054483997071422, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.731563201531232e-06, "max_pair_overlap_depth": -2.352291984759891e-06, "metric_expression": "3.81831", "metric_symbol": "s", "metric_value": 3.818305448399707, "n": 29, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.818, "setup": "triinsqu", "side": 3.818305448399707, "solution_path": "data/solutions/generated/triinsqu_029_a02ae61c838755d7.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/a02ae61c838755d7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@30", "density": 0.868927959047152, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t30.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.8662+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.8662, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@30", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.8662+", "metric_symbol": "s", "metric_value": 3.8662, "reference_text": "30. | | s = 3.8662+ | Found by Ian Watson | in April 2026.", "source_image": "t30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t30.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "30. | | s = 3.8662+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "d3cf7ea5ce255135", "improvement": -0.00030930450574828683, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.0741990212131443e-07, "max_pair_overlap_depth": -7.811820435188466e-06, "metric_expression": "3.86651", "metric_symbol": "s", "metric_value": 3.8665093045057484, "n": 30, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.8662, "setup": "triinsqu", "side": 3.8665093045057484, "solution_path": "data/solutions/generated/triinsqu_030_d3cf7ea5ce255135.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/d3cf7ea5ce255135.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@31", "density": 0.8672905272682435, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t31.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.936+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.936, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.936+", "metric_symbol": "s", "metric_value": 3.936, "reference_text": "31. | | s = 3.936+ | Found by Emerson Connelly | in April 2026.", "source_image": "t31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t31.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "31. | | s = 3.936+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "90f4b9b8010910a7", "improvement": 0.001868580153832955, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.1286553127417914e-06, "max_pair_overlap_depth": -1.3206709677193729e-05, "metric_expression": "3.93413", "metric_symbol": "s", "metric_value": 3.934131419846167, "n": 31, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.936, "setup": "triinsqu", "side": 3.934131419846167, "solution_path": "data/solutions/generated/triinsqu_031_90f4b9b8010910a7.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/90f4b9b8010910a7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@32", "density": 0.8675921732131934, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t32.gif", "friedman_metric_expression": "6\u20137\u221a3/6 = 3.979+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.979, "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@32", "credit": "Maurizio Morandi", "date": "May 2026", "family_updated": "", "metric_expression": "6\u20137\u221a3/6 = 3.979+", "metric_symbol": "s", "metric_value": 3.979, "reference_text": "32. | | s = 6\u20137\u221a3/6 = 3.979+ | Found by Maurizio Morandi | in May 2026.", "source_image": "t32.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t32.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "32. | | s = 6\u20137\u221a3/6 = 3.979+ | Found by Maurizio Morandi | in May 2026.", "friedman_source_image": "t32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "f42801b713b9238d", "improvement": -0.01738660313705287, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.208596980261035e-06, "max_pair_overlap_depth": -2.3341135757526388e-06, "metric_expression": "3.99639", "metric_symbol": "s", "metric_value": 3.996386603137053, "n": 32, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.979, "setup": "triinsqu", "side": 3.996386603137053, "solution_path": "data/solutions/generated/triinsqu_32_f42801b713b9238d.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/f42801b713b9238d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@33", "density": 0.8675949776849048, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t33.gif", "friedman_metric_expression": "4.058+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.058, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.058+", "metric_symbol": "s", "metric_value": 4.058, "reference_text": "33. | | s = 4.058+ | Found by Emerson Connelly | in April 2026.", "source_image": "t33.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t33.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "33. | | s = 4.058+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "a6f49f2f24228d1b", "improvement": -0.00034322121207797096, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0747182587902822e-06, "max_pair_overlap_depth": -2.8024820216354662e-05, "metric_expression": "4.05834", "metric_symbol": "s", "metric_value": 4.058343221212078, "n": 33, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.058, "setup": "triinsqu", "side": 4.058343221212078, "solution_path": "data/solutions/generated/triinsqu_33_a6f49f2f24228d1b.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/a6f49f2f24228d1b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@34", "density": 0.8767333914896571, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t34.gif", "friedman_metric_expression": "4.098+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.098, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.098+", "metric_symbol": "s", "metric_value": 4.098, "reference_text": "34. | | s = 4.098+ | Found by Emerson Connelly | in April 2026.", "source_image": "t34.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t34.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "34. | | s = 4.098+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "61b4d5d6bf22a206", "improvement": 0.00015051348449990343, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6262786795626285e-06, "max_pair_overlap_depth": -1.499292058504409e-05, "metric_expression": "4.09785", "metric_symbol": "s", "metric_value": 4.0978494865155, "n": 34, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 4.098, "setup": "triinsqu", "side": 4.0978494865155, "solution_path": "data/solutions/generated/triinsqu_34_61b4d5d6bf22a206.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/61b4d5d6bf22a206.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@35", "density": 0.8677502962014568, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t35.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "9(2\u221a3\u20133) = 4.176+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.176, "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@35", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "", "metric_expression": "9(2\u221a3\u20133) = 4.176+", "metric_symbol": "s", "metric_value": 4.176, "reference_text": "35. | | s = 9(2\u221a3\u20133) = 4.176+ | Found by Erich Friedman | in April 2026.", "source_image": "t35.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t35.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "35. | | s = 9(2\u221a3\u20133) = 4.176+ | Found by Erich Friedman | in April 2026.", "friedman_source_image": "t35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "ab6aa3f219e08b42", "improvement": -0.0031403345722011977, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.770482464101941e-07, "max_pair_overlap_depth": -3.3297730506198775e-06, "metric_expression": "4.17914", "metric_symbol": "s", "metric_value": 4.179140334572201, "n": 35, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.176, "setup": "triinsqu", "side": 4.179140334572201, "solution_path": "data/solutions/generated/triinsqu_035_ab6aa3f219e08b42.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/ab6aa3f219e08b42.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@36", "density": 0.8790676097280682, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t36.gif", "friedman_metric_expression": "4.214+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.214, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@36", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.214+", "metric_symbol": "s", "metric_value": 4.214, "reference_text": "36. | | s = 4.214+ | Found by Emerson Connelly | in April 2026.", "source_image": "t36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t36.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "36. | | s = 4.214+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "aae755b2130a7a83", "improvement": 0.0029496973593481357, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.160284450281608e-07, "max_pair_overlap_depth": -9.933313802612531e-07, "metric_expression": "4.21105", "metric_symbol": "s", "metric_value": 4.211050302640652, "n": 36, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 4.214, "setup": "triinsqu", "side": 4.211050302640652, "solution_path": "data/solutions/record_hunt/triinsqu_36_aae755b2130a7a83.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/aae755b2130a7a83.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@37", "density": 0.8782570037473258, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t37.gif", "friedman_metric_expression": "4.27233+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.27233, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@37", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "4.27233+", "metric_symbol": "s", "metric_value": 4.27233, "reference_text": "37. | | s = 4.27233+ | Found by Nathan Roll | in April 2026.", "source_image": "t37.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t37.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "37. | | s = 4.27233+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "t37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "46406dc33c9746a7", "improvement": 0.0012238102051549404, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.826527513923834e-07, "max_pair_overlap_depth": -6.105510335085995e-07, "metric_expression": "4.27111", "metric_symbol": "s", "metric_value": 4.271106189794845, "n": 37, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 4.27233, "setup": "triinsqu", "side": 4.271106189794845, "solution_path": "data/solutions/record_hunt/triinsqu_37_46406dc33c9746a7.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/46406dc33c9746a7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@38", "density": 0.87940001283733, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t38.gif", "friedman_metric_expression": "4.327+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.327, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.327+", "metric_symbol": "s", "metric_value": 4.327, "reference_text": "38. | | s = 4.327+ | Found by Emerson Connelly | in April 2026.", "source_image": "t38.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t38.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "38. | | s = 4.327+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "f44a4bd75616bc73", "improvement": 0.0013748413573368978, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0707071410413964e-07, "max_pair_overlap_depth": -1.0916553592199563e-06, "metric_expression": "4.32563", "metric_symbol": "s", "metric_value": 4.325625158642663, "n": 38, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 4.327, "setup": "triinsqu", "side": 4.325625158642663, "solution_path": "data/solutions/record_hunt/triinsqu_38_f44a4bd75616bc73.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/f44a4bd75616bc73.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@39", "density": 0.880118042721229, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t39.gif", "friedman_metric_expression": "4.383+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.383, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.383+", "metric_symbol": "s", "metric_value": 4.383, "reference_text": "39. | | s = 4.383+ | Found by Emerson Connelly | in April 2026.", "source_image": "t39.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t39.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "39. | | s = 4.383+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "263f7876a25d297b", "improvement": 0.002616247848735931, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.607883972834501e-07, "max_pair_overlap_depth": -1.86255866918561e-06, "metric_expression": "4.38038", "metric_symbol": "s", "metric_value": 4.380383752151264, "n": 39, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 4.383, "setup": "triinsqu", "side": 4.380383752151264, "solution_path": "data/solutions/record_hunt/triinsqu_39_263f7876a25d297b.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/263f7876a25d297b.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triinsqu@40", "density": 0.878868813713771, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t40.gif", "friedman_metric_expression": "4.437+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.437, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.437+", "metric_symbol": "s", "metric_value": 4.437, "reference_text": "40. | | s = 4.437+ | Found by Emerson Connelly | in April 2026.", "source_image": "t40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t40.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "40. | | s = 4.437+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "ccf2360cc8917adc", "improvement": -0.002338759632142029, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.520888573265893e-06, "max_pair_overlap_depth": -1.6780429565876886e-05, "metric_expression": "4.43934", "metric_symbol": "s", "metric_value": 4.439338759632142, "n": 40, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.437, "setup": "triinsqu", "side": 4.439338759632142, "solution_path": "data/solutions/generated/triinsqu_040_ccf2360cc8917adc.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/ccf2360cc8917adc.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@1", "density": 1.0, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt1.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial.", "source_image": "tt1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt1.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 1 | Trivial.", "friedman_source_image": "tt1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "b09a5ce4a2c03ad3", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 5.551115123125788e-17, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00000", "metric_symbol": "s", "metric_value": 1.0, "n": 1, "notes": "Exact triangular subdivision coordinate JSON; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 1.0, "setup": "triintri", "side": 1.0, "solution_path": "data/solutions/generated/triintri_001_b09a5ce4a2c03ad3.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T15:42:49+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/b09a5ce4a2c03ad3.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@2", "density": 0.5, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "tt4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "tt4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "2d6f654db11412d8", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 1.6653345369377346e-16, "max_pair_overlap_depth": 0.0, "metric_expression": "2.00000", "metric_symbol": "s", "metric_value": 2.0, "n": 2, "notes": "Exact triangular subdivision coordinate JSON; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 2.0, "setup": "triintri", "side": 2.0, "solution_path": "data/solutions/generated/triintri_002_2d6f654db11412d8.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T15:42:49+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/2d6f654db11412d8.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@3", "density": 0.75, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "tt4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "tt4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "76381d42f8f17f41", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 1.6653345369377346e-16, "max_pair_overlap_depth": 3.3306690738754696e-16, "metric_expression": "2.00000", "metric_symbol": "s", "metric_value": 2.0, "n": 3, "notes": "Exact triangular subdivision coordinate JSON; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 2.0, "setup": "triintri", "side": 2.0, "solution_path": "data/solutions/generated/triintri_003_76381d42f8f17f41.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T15:42:49+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/76381d42f8f17f41.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@4", "density": 1.0, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@4", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "tt4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "tt4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "be1b0b4b1802d8fa", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 1.6653345369377346e-16, "max_pair_overlap_depth": 3.3306690738754696e-16, "metric_expression": "2.00000", "metric_symbol": "s", "metric_value": 2.0, "n": 4, "notes": "Exact triangular subdivision coordinate JSON; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 2.0, "setup": "triintri", "side": 2.0, "solution_path": "data/solutions/generated/triintri_004_be1b0b4b1802d8fa.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T15:42:49+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/be1b0b4b1802d8fa.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@5", "density": 0.66984024663198, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt5.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "1 + \u221a3 = 2.732+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.732, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@5", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "1 + \u221a3 = 2.732+", "metric_symbol": "s", "metric_value": 2.732, "reference_text": "s = 1 + \u221a3 = 2.732+ | Proved by Erich Friedman | in 1997.", "source_image": "tt5.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt5.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 1 + \u221a3 = 2.732+ | Proved by Erich Friedman | in 1997.", "friedman_source_image": "tt5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "b4ac2c13e986485e", "improvement": -0.00011756309530053244, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.644640909821311e-06, "max_pair_overlap_depth": -6.265774057961264e-06, "metric_expression": "2.73212", "metric_symbol": "s", "metric_value": 2.7321175630953007, "n": 5, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.732, "setup": "triintri", "side": 2.7321175630953007, "solution_path": "data/solutions/generated/triintri_005_b4ac2c13e986485e.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/b4ac2c13e986485e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@6", "density": 0.6768918015337515, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt6.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "13/8 + 3\u221a13/8 = 2.977+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.977, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@6", "credit": "Maurizio Morandi", "date": "August 2008", "family_updated": "", "metric_expression": "13/8 + 3\u221a13/8 = 2.977+", "metric_symbol": "s", "metric_value": 2.977, "reference_text": "s = 13/8 + 3\u221a13/8 = 2.977+ | Found by Maurizio Morandi | in August 2008.", "source_image": "tt6.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt6.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 13/8 + 3\u221a13/8 = 2.977+ | Found by Maurizio Morandi | in August 2008.", "friedman_source_image": "tt6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "df20f3104adbd6a1", "improvement": -0.00025475946622810497, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3999156171376625e-07, "max_pair_overlap_depth": -1.9147124426771578e-05, "metric_expression": "2.97725", "metric_symbol": "s", "metric_value": 2.977254759466228, "n": 6, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 2.977, "setup": "triintri", "side": 2.977254759466228, "solution_path": "data/solutions/generated/triintri_006_df20f3104adbd6a1.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/df20f3104adbd6a1.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@7", "density": 0.777777777777778, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@7", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "s = 3 | Trivial.", "source_image": "tt9.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 3 | Trivial.", "friedman_source_image": "tt9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "355f218b5ea40614", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 2.9605947323337506e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "3.00000", "metric_symbol": "s", "metric_value": 3.0, "n": 7, "notes": "Exact triangular subdivision coordinate JSON; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.0, "setup": "triintri", "side": 3.0, "solution_path": "data/solutions/generated/triintri_007_355f218b5ea40614.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T15:42:49+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/355f218b5ea40614.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@8", "density": 0.8888888888888892, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@8", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "s = 3 | Trivial.", "source_image": "tt9.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 3 | Trivial.", "friedman_source_image": "tt9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "43e3200cf32d77a9", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 2.9605947323337506e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "3.00000", "metric_symbol": "s", "metric_value": 3.0, "n": 8, "notes": "Exact triangular subdivision coordinate JSON; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.0, "setup": "triintri", "side": 3.0, "solution_path": "data/solutions/generated/triintri_008_43e3200cf32d77a9.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T15:42:49+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/43e3200cf32d77a9.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@9", "density": 1.0000000000000004, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@9", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "s = 3 | Trivial.", "source_image": "tt9.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 3 | Trivial.", "friedman_source_image": "tt9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "4242c6a66848e1ea", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 2.9605947323337516e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "3.00000", "metric_symbol": "s", "metric_value": 3.0, "n": 9, "notes": "Exact triangular subdivision coordinate JSON; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 3.0, "setup": "triintri", "side": 3.0, "solution_path": "data/solutions/generated/triintri_009_4242c6a66848e1ea.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T15:42:49+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4242c6a66848e1ea.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@10", "density": 0.8162770652591925, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt10.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "7/2 = 3.500", "friedman_metric_symbol": "s", "friedman_metric_value": 3.5, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@10", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "7/2 = 3.500", "metric_symbol": "s", "metric_value": 3.5, "reference_text": "s = 7/2 = 3.500 | Found by Erich Friedman | in 1997.", "source_image": "tt10.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt10.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 7/2 = 3.500 | Found by Erich Friedman | in 1997.", "friedman_source_image": "tt10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "bcf7fa93627e2e22", "improvement": -0.00010604617003595607, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.918936789115156e-08, "max_pair_overlap_depth": -1.2701382657187565e-05, "metric_expression": "3.50011", "metric_symbol": "s", "metric_value": 3.500106046170036, "n": 10, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.5, "setup": "triintri", "side": 3.500106046170036, "solution_path": "data/solutions/generated/triintri_010_bcf7fa93627e2e22.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/bcf7fa93627e2e22.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@11", "density": 0.792568600317471, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt11.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "9/4 + 9\u221a21/28 = 3.722+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.722, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@11", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "9/4 + 9\u221a21/28 = 3.722+", "metric_symbol": "s", "metric_value": 3.722, "reference_text": "s = 9/4 + 9\u221a21/28 = 3.722+ | Found by Erich Friedman | in 1997.", "source_image": "tt11.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt11.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 9/4 + 9\u221a21/28 = 3.722+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tt11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "8c37202a929dc807", "improvement": -0.0034428993959463305, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.7247990718051686e-06, "max_pair_overlap_depth": -2.4227159337045223e-05, "metric_expression": "3.72544", "metric_symbol": "s", "metric_value": 3.7254428993959463, "n": 11, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.722, "setup": "triintri", "side": 3.7254428993959463, "solution_path": "data/solutions/generated/triintri_11_8c37202a929dc807.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/8c37202a929dc807.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@12", "density": 0.7960259433336867, "friedman_analytical_or_proved": true, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2007", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt12.gif", "friedman_metric_expression": "2 + 2cos(\u03c0/9) = 3.879+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.879, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@12", "credit": "David W. Cantrell", "date": "July 2007", "family_updated": "", "metric_expression": "2 + 2cos(\u03c0/9) = 3.879+", "metric_symbol": "s", "metric_value": 3.879, "reference_text": "s = 2 + 2cos(\u03c0/9) = 3.879+ | Found by David W. Cantrell | in July 2007.", "source_image": "tt12.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt12.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 2 + 2cos(\u03c0/9) = 3.879+ | Found by David W. Cantrell | in July 2007.", "friedman_source_image": "tt12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "7642b05605706588", "improvement": -0.0036389945275763225, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.358547413541538e-08, "max_pair_overlap_depth": -4.590975868801195e-06, "metric_expression": "3.88264", "metric_symbol": "s", "metric_value": 3.8826389945275763, "n": 12, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.879, "setup": "triintri", "side": 3.8826389945275763, "solution_path": "data/solutions/generated/triintri_12_7642b05605706588.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T07:13:53+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/7642b05605706588.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@13", "density": 0.8146483132163195, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt13.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "3.992+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.992, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@13", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "", "metric_expression": "3.992+", "metric_symbol": "s", "metric_value": 3.992, "reference_text": "s = 3.992+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt13.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt13.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 3.992+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "afe3e3dc6de1bc36", "improvement": -0.0027223080586638027, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.48838412272174e-06, "max_pair_overlap_depth": -3.9197094850562664e-05, "metric_expression": "3.99472", "metric_symbol": "s", "metric_value": 3.994722308058664, "n": 13, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 3.992, "setup": "triintri", "side": 3.994722308058664, "solution_path": "data/solutions/generated/triintri_013_afe3e3dc6de1bc36.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/afe3e3dc6de1bc36.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@14", "density": 0.875, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@14", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "s = 4 | Trivial.", "source_image": "tt16.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 4 | Trivial.", "friedman_source_image": "tt16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "8676384ad0301449", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 2.775557561562891e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "4.00000", "metric_symbol": "s", "metric_value": 4.0, "n": 14, "notes": "Exact triangular subdivision coordinate JSON; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 4.0, "setup": "triintri", "side": 4.0, "solution_path": "data/solutions/generated/triintri_014_8676384ad0301449.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T15:42:49+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/8676384ad0301449.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@15", "density": 0.9375, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@15", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "s = 4 | Trivial.", "source_image": "tt16.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 4 | Trivial.", "friedman_source_image": "tt16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "31db3ec76cc0421f", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 2.775557561562891e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "4.00000", "metric_symbol": "s", "metric_value": 4.0, "n": 15, "notes": "Exact triangular subdivision coordinate JSON; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 4.0, "setup": "triintri", "side": 4.0, "solution_path": "data/solutions/generated/triintri_015_31db3ec76cc0421f.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T15:42:49+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/31db3ec76cc0421f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@16", "density": 1.0, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@16", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "s = 4 | Trivial.", "source_image": "tt16.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 4 | Trivial.", "friedman_source_image": "tt16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "2ffa329b602032d6", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 2.775557561562891e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "4.00000", "metric_symbol": "s", "metric_value": 4.0, "n": 16, "notes": "Exact triangular subdivision coordinate JSON; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 4.0, "setup": "triintri", "side": 4.0, "solution_path": "data/solutions/generated/triintri_016_2ffa329b602032d6.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T15:42:49+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/2ffa329b602032d6.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@17", "density": 0.8524249732795084, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt17.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "4.465+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.465, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@17", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "", "metric_expression": "4.465+", "metric_symbol": "s", "metric_value": 4.465, "reference_text": "s = 4.465+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt17.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt17.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 4.465+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "ad8aac0e4c06f7d0", "improvement": -0.0007702721912288268, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8241570152012174e-06, "max_pair_overlap_depth": -7.389272764501964e-06, "metric_expression": "4.46577", "metric_symbol": "s", "metric_value": 4.465770272191229, "n": 17, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.465, "setup": "triintri", "side": 4.465770272191229, "solution_path": "data/solutions/generated/triintri_017_ad8aac0e4c06f7d0.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/ad8aac0e4c06f7d0.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@18", "density": 0.8888203671574908, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt18.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "9/2 = 4.500", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@18", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "9/2 = 4.500", "metric_symbol": "s", "metric_value": 4.5, "reference_text": "s = 9/2 = 4.500 | Found by Erich Friedman | in 1997.", "source_image": "tt18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt18.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 9/2 = 4.500 | Found by Erich Friedman | in 1997.", "friedman_source_image": "tt18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "b4cfb14015aca75a", "improvement": -0.00017345566104154386, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.575746594607548e-06, "max_pair_overlap_depth": -5.0550449839370515e-06, "metric_expression": "4.50017", "metric_symbol": "s", "metric_value": 4.5001734556610415, "n": 18, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.5, "setup": "triintri", "side": 4.5001734556610415, "solution_path": "data/solutions/generated/triintri_018_b4cfb14015aca75a.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/b4cfb14015aca75a.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@19", "density": 0.872322152073677, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt19.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "14/3 = 4.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.666, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@19", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "", "metric_expression": "14/3 = 4.666+", "metric_symbol": "s", "metric_value": 4.666, "reference_text": "s = 14/3 = 4.666+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt19.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 14/3 = 4.666+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "bf4e89c9b4dd8ae2", "improvement": -0.0010058992763006813, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.331642222161759e-07, "max_pair_overlap_depth": -9.690072424628493e-06, "metric_expression": "4.66701", "metric_symbol": "s", "metric_value": 4.667005899276301, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.666, "setup": "triintri", "side": 4.667005899276301, "solution_path": "data/solutions/generated/triintri_019_bf4e89c9b4dd8ae2.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/bf4e89c9b4dd8ae2.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@20", "density": 0.845304928058783, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt20.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "33/8 + 9\u221a21/56 = 4.861+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.861, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@20", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "", "metric_expression": "33/8 + 9\u221a21/56 = 4.861+", "metric_symbol": "s", "metric_value": 4.861, "reference_text": "s = 33/8 + 9\u221a21/56 = 4.861+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt20.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 33/8 + 9\u221a21/56 = 4.861+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "4dff2c76e1273753", "improvement": -0.00316498806837906, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.619234998604407e-06, "max_pair_overlap_depth": -7.278337082583519e-06, "metric_expression": "4.86416", "metric_symbol": "s", "metric_value": 4.864164988068379, "n": 20, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.861, "setup": "triintri", "side": 4.864164988068379, "solution_path": "data/solutions/generated/triintri_020_4dff2c76e1273753.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/4dff2c76e1273753.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@21", "density": 0.8650098201747314, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt21.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "4.923+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.923, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@21", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "", "metric_expression": "4.923+", "metric_symbol": "s", "metric_value": 4.923, "reference_text": "s = 4.923+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt21.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 4.923+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "4dc62e9e9421c0aa", "improvement": -0.004187943781052361, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4013824985741632e-06, "max_pair_overlap_depth": -4.2136074186321926e-06, "metric_expression": "4.92719", "metric_symbol": "s", "metric_value": 4.927187943781052, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.923, "setup": "triintri", "side": 4.927187943781052, "solution_path": "data/solutions/generated/triintri_021_4dc62e9e9421c0aa.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/4dc62e9e9421c0aa.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@22", "density": 0.8799245341930954, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt22.gif", "friedman_metric_expression": "4.996+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.996, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@22", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "", "metric_expression": "4.996+", "metric_symbol": "s", "metric_value": 4.996, "reference_text": "s = 4.996+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt22.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 4.996+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "2122d833c6fcab70", "improvement": -0.004214405286988132, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.380108740330726e-08, "max_pair_overlap_depth": -8.335028905959163e-07, "metric_expression": "5.00021", "metric_symbol": "s", "metric_value": 5.000214405286989, "n": 22, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 4.996, "setup": "triintri", "side": 5.000214405286989, "solution_path": "data/solutions/generated/triintri_022_2122d833c6fcab70.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/2122d833c6fcab70.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@23", "density": 0.9200000000000002, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@23", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "tt25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "tt25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "4f1bdd5d6c07f589", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 7.105427357601002e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "5.00000", "metric_symbol": "s", "metric_value": 5.0, "n": 23, "notes": "Exact triangular subdivision coordinate JSON; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 5.0, "setup": "triintri", "side": 5.0, "solution_path": "data/solutions/generated/triintri_023_4f1bdd5d6c07f589.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T15:42:49+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4f1bdd5d6c07f589.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@24", "density": 0.9600000000000002, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@24", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "tt25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "tt25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "64d77fbf13ae0be7", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 7.105427357601002e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "5.00000", "metric_symbol": "s", "metric_value": 5.0, "n": 24, "notes": "Exact triangular subdivision coordinate JSON; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 5.0, "setup": "triintri", "side": 5.0, "solution_path": "data/solutions/generated/triintri_024_64d77fbf13ae0be7.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T15:42:49+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/64d77fbf13ae0be7.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@25", "density": 1.0000000000000002, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@25", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "tt25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "tt25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "9c4806b8b37c5d37", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 7.105427357601002e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "5.00000", "metric_symbol": "s", "metric_value": 5.0, "n": 25, "notes": "Exact triangular subdivision coordinate JSON; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 5.0, "setup": "triintri", "side": 5.0, "solution_path": "data/solutions/generated/triintri_025_9c4806b8b37c5d37.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T15:42:49+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/9c4806b8b37c5d37.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@26", "density": 0.8884053356293824, "friedman_analytical_or_proved": false, "friedman_credit": "Joah Frenzley", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt26.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "5.406+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.406, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@26", "credit": "Joah Frenzley", "date": "April 2026", "family_updated": "", "metric_expression": "5.406+", "metric_symbol": "s", "metric_value": 5.406, "reference_text": "s = 5.406+ | Found by Joah Frenzley | in April 2026.", "source_image": "tt26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt26.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5.406+ | Found by Joah Frenzley | in April 2026.", "friedman_source_image": "tt26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "0af5a3765ecc4828", "improvement": -0.0037985715923722907, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.296466577480461e-06, "max_pair_overlap_depth": -2.0400569136769242e-05, "metric_expression": "5.40980", "metric_symbol": "s", "metric_value": 5.409798571592372, "n": 26, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.406, "setup": "triintri", "side": 5.409798571592372, "solution_path": "data/solutions/generated/triintri_026_0af5a3765ecc4828.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Joah Frenzley", "svg_path": "data/svg/0af5a3765ecc4828.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@27", "density": 0.8924996192164427, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "friedman_metric_expression": "11/2 = 5.500", "friedman_metric_symbol": "s", "friedman_metric_value": 5.5, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@27", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "11/2 = 5.500", "metric_symbol": "s", "metric_value": 5.5, "reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "source_image": "tt28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "friedman_source_image": "tt28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "f1c2be61e829f1e2", "improvement": -0.00019215549305418023, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8365186496628e-06, "max_pair_overlap_depth": -1.8064988390742442e-06, "metric_expression": "5.50019", "metric_symbol": "s", "metric_value": 5.500192155493054, "n": 27, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.5, "setup": "triintri", "side": 5.500192155493054, "solution_path": "data/solutions/generated/triintri_027_f1c2be61e829f1e2.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/f1c2be61e829f1e2.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@28", "density": 0.9255631973649003, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "friedman_metric_expression": "11/2 = 5.500", "friedman_metric_symbol": "s", "friedman_metric_value": 5.5, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@28", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "11/2 = 5.500", "metric_symbol": "s", "metric_value": 5.5, "reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "source_image": "tt28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "friedman_source_image": "tt28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "9562d7d6e075a347", "improvement": -0.00016827626559567932, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.296352348617567e-06, "max_pair_overlap_depth": -7.147352432124165e-08, "metric_expression": "5.50017", "metric_symbol": "s", "metric_value": 5.500168276265596, "n": 28, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.5, "setup": "triintri", "side": 5.500168276265596, "solution_path": "data/solutions/generated/triintri_028_9562d7d6e075a347.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/9562d7d6e075a347.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@29", "density": 0.9023512759650716, "friedman_analytical_or_proved": true, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2007", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt29.gif", "friedman_metric_expression": "17/3 = 5.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.666, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@29", "credit": "David W. Cantrell", "date": "July 2007", "family_updated": "", "metric_expression": "17/3 = 5.666+", "metric_symbol": "s", "metric_value": 5.666, "reference_text": "s = 17/3 = 5.666+ | Found by David W. Cantrell | in July 2007.", "source_image": "tt29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt29.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 17/3 = 5.666+ | Found by David W. Cantrell | in July 2007.", "friedman_source_image": "tt29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "38c7a009f9059275", "improvement": -0.0030616587354490576, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9275914294015247e-06, "max_pair_overlap_depth": -5.088073942505211e-06, "metric_expression": "5.66906", "metric_symbol": "s", "metric_value": 5.669061658735449, "n": 29, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.666, "setup": "triintri", "side": 5.669061658735449, "solution_path": "data/solutions/generated/triintri_29_38c7a009f9059275.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T13:47:12+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/38c7a009f9059275.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@30", "density": 0.9060985977127352, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt30.gif", "friedman_metric_expression": "23/4 = 5.75", "friedman_metric_symbol": "s", "friedman_metric_value": 5.75, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@30", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "", "metric_expression": "23/4 = 5.75", "metric_symbol": "s", "metric_value": 5.75, "reference_text": "s = 23/4 = 5.75 | Found by Maurizio Morandi | in May 2008.", "source_image": "tt30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt30.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 23/4 = 5.75 | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "149a91e0248df04e", "improvement": -0.004040286099913359, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2882428961650933e-06, "max_pair_overlap_depth": -6.414942533283785e-06, "metric_expression": "5.75404", "metric_symbol": "s", "metric_value": 5.754040286099913, "n": 30, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.75, "setup": "triintri", "side": 5.754040286099913, "solution_path": "data/solutions/generated/triintri_30_149a91e0248df04e.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/149a91e0248df04e.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@31", "density": 0.8852772627280384, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt31.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "5.912+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.912, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "5.912+", "metric_symbol": "s", "metric_value": 5.912, "reference_text": "s = 5.912+ | Found by Emerson Connelly | in April 2026.", "source_image": "tt31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt31.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5.912+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "tt31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "c729ec2b23a32942", "improvement": -0.005539858919105356, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9513696602846134e-06, "max_pair_overlap_depth": -3.7790737070775293e-06, "metric_expression": "5.91754", "metric_symbol": "s", "metric_value": 5.917539858919105, "n": 31, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.912, "setup": "triintri", "side": 5.917539858919105, "solution_path": "data/solutions/generated/triintri_031_c729ec2b23a32942.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T02:51:36+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/c729ec2b23a32942.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@32", "density": 0.9021138463561595, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt32.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "5.951+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.951, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@32", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "5.951+", "metric_symbol": "s", "metric_value": 5.951, "reference_text": "s = 5.951+ | Found by Ian Watson | in April 2026.", "source_image": "tt32.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt32.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5.951+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "tt32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "fa640909a0850f97", "improvement": -0.004857726462081935, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.7950535548187937e-06, "max_pair_overlap_depth": -4.900081183589755e-06, "metric_expression": "5.95586", "metric_symbol": "s", "metric_value": 5.955857726462082, "n": 32, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 5.951, "setup": "triintri", "side": 5.955857726462082, "solution_path": "data/solutions/generated/triintri_032_fa640909a0850f97.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/fa640909a0850f97.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@33", "density": 0.9166666666666669, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@33", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial. |", "source_image": "tt36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6 | Trivial. |", "friedman_source_image": "tt36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "34a5032aebc12aff", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 5.921189464667501e-16, "max_pair_overlap_depth": 6.661338147750939e-16, "metric_expression": "6.00000", "metric_symbol": "s", "metric_value": 6.0, "n": 33, "notes": "Exact triangular subdivision coordinate JSON; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 6.0, "setup": "triintri", "side": 6.0, "solution_path": "data/solutions/generated/triintri_033_34a5032aebc12aff.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T15:42:49+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/34a5032aebc12aff.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@34", "density": 0.9444444444444448, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@34", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial. |", "source_image": "tt36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6 | Trivial. |", "friedman_source_image": "tt36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "a2ccd0a19cfa1b75", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 5.921189464667501e-16, "max_pair_overlap_depth": 6.661338147750939e-16, "metric_expression": "6.00000", "metric_symbol": "s", "metric_value": 6.0, "n": 34, "notes": "Exact triangular subdivision coordinate JSON; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 6.0, "setup": "triintri", "side": 6.0, "solution_path": "data/solutions/generated/triintri_034_a2ccd0a19cfa1b75.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T15:42:49+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/a2ccd0a19cfa1b75.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@35", "density": 0.9722222222222225, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@35", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial. |", "source_image": "tt36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6 | Trivial. |", "friedman_source_image": "tt36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "6325f936448cdf94", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 5.921189464667503e-16, "max_pair_overlap_depth": 6.661338147750939e-16, "metric_expression": "6.00000", "metric_symbol": "s", "metric_value": 6.0, "n": 35, "notes": "Exact triangular subdivision coordinate JSON; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 6.0, "setup": "triintri", "side": 6.0, "solution_path": "data/solutions/generated/triintri_035_6325f936448cdf94.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T15:42:49+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/6325f936448cdf94.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@36", "density": 1.0000000000000004, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@36", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial. |", "source_image": "tt36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6 | Trivial. |", "friedman_source_image": "tt36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "4b90836bf07f8a65", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 6.661338147750939e-16, "max_pair_overlap_depth": 6.661338147750939e-16, "metric_expression": "6.00000", "metric_symbol": "s", "metric_value": 6.0, "n": 36, "notes": "Exact triangular subdivision coordinate JSON; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 6.0, "setup": "triintri", "side": 6.0, "solution_path": "data/solutions/generated/triintri_036_4b90836bf07f8a65.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T15:42:49+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4b90836bf07f8a65.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@37", "density": 0.9223731676430976, "friedman_analytical_or_proved": true, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt37.gif", "friedman_metric_expression": "19/3 = 6.333+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.333, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@37", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "19/3 = 6.333+", "metric_symbol": "s", "metric_value": 6.333, "reference_text": "s = 19/3 = 6.333+ | Found by Ian Watson | in April 2026.", "source_image": "tt37.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt37.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 19/3 = 6.333+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "tt37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "a824891b660555f5", "improvement": -0.0005547879590457327, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.1058084789851627e-06, "max_pair_overlap_depth": -1.0503324543442716e-06, "metric_expression": "6.33355", "metric_symbol": "s", "metric_value": 6.333554787959046, "n": 37, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.333, "setup": "triintri", "side": 6.333554787959046, "solution_path": "data/solutions/generated/triintri_037_a824891b660555f5.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/a824891b660555f5.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@38", "density": 0.9184187453437659, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt38.gif", "friedman_metric_expression": "6.43454+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.43454, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@38", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "6.43454+", "metric_symbol": "s", "metric_value": 6.43454, "reference_text": "s = 6.43454+ | Found by Nathan Roll | in April 2026.", "source_image": "tt38.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt38.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6.43454+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "tt38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "b1563d97c893e28d", "improvement": 0.002163914058151306, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.8714774987883973e-07, "max_pair_overlap_depth": -1.6883301962034025e-06, "metric_expression": "6.43238", "metric_symbol": "s", "metric_value": 6.432376085941849, "n": 38, "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.", "record_type": "verified", "reference_side": 6.43454, "setup": "triintri", "side": 6.432376085941849, "solution_path": "data/solutions/record_hunt/triintri_38_b1563d97c893e28d.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/b1563d97c893e28d.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@39", "density": 0.922995893638428, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "friedman_metric_expression": "13/2 = 6.500", "friedman_metric_symbol": "s", "friedman_metric_value": 6.5, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@39", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "", "metric_expression": "13/2 = 6.500", "metric_symbol": "s", "metric_value": 6.5, "reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "source_image": "tt40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "friedman_source_image": "tt40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "5ff069bd30790b7f", "improvement": -0.0002853099319573005, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.7141701112233934e-06, "max_pair_overlap_depth": -2.524988351737534e-07, "metric_expression": "6.50029", "metric_symbol": "s", "metric_value": 6.500285309931957, "n": 39, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.5, "setup": "triintri", "side": 6.500285309931957, "solution_path": "data/solutions/generated/triintri_039_5ff069bd30790b7f.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/5ff069bd30790b7f.svg", "tolerance": 1e-08, "verified": true}
-{"case": "triintri@40", "density": 0.9466291268019702, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "friedman_metric_expression": "13/2 = 6.500", "friedman_metric_symbol": "s", "friedman_metric_value": 6.5, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@40", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "", "metric_expression": "13/2 = 6.500", "metric_symbol": "s", "metric_value": 6.5, "reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "source_image": "tt40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "friedman_source_image": "tt40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "7890a1da940c9143", "improvement": -0.00039973752172350885, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4343626129297504e-07, "max_pair_overlap_depth": -3.1212060811469655e-06, "metric_expression": "6.50040", "metric_symbol": "s", "metric_value": 6.5003997375217235, "n": 40, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.", "record_type": "verified", "reference_side": 6.5, "setup": "triintri", "side": 6.5003997375217235, "solution_path": "data/solutions/generated/triintri_040_7890a1da940c9143.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/7890a1da940c9143.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@1", "density": 0.9999989965161072, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc1.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "1", "friedman_metric_symbol": "r", "friedman_metric_value": 1.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "r", "metric_value": 1.0, "reference_text": "r = 1 | Trivial.", "source_image": "ccc1.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc1.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 1 | Trivial.", "friedman_source_image": "ccc1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "d8dddd0385fd067c", "improvement": -5.017423239106478e-07, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1979053238242443e-07, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.000000501742324, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.0, "setup": "cirincir", "side": 2.000001003484648, "solution_path": "data/solutions/generated/cirincir_001_d8dddd0385fd067c.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d8dddd0385fd067c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@2", "density": 0.4999800974887553, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc2.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "2", "friedman_metric_symbol": "r", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "r", "metric_value": 2.0, "reference_text": "r = 2 | Trivial.", "source_image": "ccc2.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc2.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 2 | Trivial.", "friedman_source_image": "ccc2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "ab9a33067266df01", "improvement": -3.9806210858639446e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.204627911923552e-06, "max_pair_overlap_depth": -5.010172176866945e-05, "metric_expression": "2.00004", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.0000398062108586, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "cirincir", "side": 4.000079612421717, "solution_path": "data/solutions/generated/cirincir_002_ab9a33067266df01.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/ab9a33067266df01.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@3", "density": 0.646133359064875, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc3.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "1 + 2 / \u221a3 = 2.154+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.1547005383792515, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1 + 2 / \u221a3 = 2.154+", "metric_symbol": "r", "metric_value": 2.154, "reference_text": "r = 1 + 2 / \u221a3 = 2.154+ | Trivial.", "source_image": "ccc3.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc3.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 1 + 2 / \u221a3 = 2.154+ | Trivial.", "friedman_source_image": "ccc3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "fe973ff9a23dc34c", "improvement": -6.264000582900664e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.918381111833185e-06, "max_pair_overlap_depth": -9.100356622360195e-05, "metric_expression": "2.15476", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.1547631783850805, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.1547005383792515, "setup": "cirincir", "side": 4.309526356770161, "solution_path": "data/solutions/generated/cirincir_003_fe973ff9a23dc34c.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/fe973ff9a23dc34c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@4", "density": 0.6862704996379871, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.414, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc4.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "1 + \u221a2 = 2.414+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.414213562373095, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@4", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1 + \u221a2 = 2.414+", "metric_symbol": "r", "metric_value": 2.414, "reference_text": "r = 1 + \u221a2 = 2.414+ | Trivial.", "source_image": "ccc4.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc4.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 1 + \u221a2 = 2.414+ | Trivial.", "friedman_source_image": "ccc4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "9d3e9e7ea6ba298b", "improvement": -3.693982323849099e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.985176337373275e-06, "max_pair_overlap_depth": -4.660490859054178e-05, "metric_expression": "2.41425", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.4142505021963334, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.414213562373095, "setup": "cirincir", "side": 4.828501004392667, "solution_path": "data/solutions/generated/cirincir_004_9d3e9e7ea6ba298b.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/9d3e9e7ea6ba298b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@5", "density": 0.6851849889863537, "friedman_analytical_or_proved": true, "friedman_credit": "Graham", "friedman_date": "1968", "friedman_display_metric_value": 2.701, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc5.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "2.701+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.701, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@5", "credit": "Graham", "date": "1968", "family_updated": "", "metric_expression": "2.701+", "metric_symbol": "r", "metric_value": 2.701, "reference_text": "r = 2.701+ | Proved by Graham in 1968.", "source_image": "ccc5.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc5.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 2.701+ | Proved by Graham in 1968.", "friedman_source_image": "ccc5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "9c2ab1f687c06eec", "improvement": -0.0003514001027240532, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.911145805306603e-06, "max_pair_overlap_depth": -4.497481208476373e-05, "metric_expression": "2.70135", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.701351400102724, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.701, "setup": "cirincir", "side": 5.402702800205448, "solution_path": "data/solutions/generated/cirincir_005_9c2ab1f687c06eec.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Graham", "svg_path": "data/svg/9c2ab1f687c06eec.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@6", "density": 0.6666416612940322, "friedman_analytical_or_proved": true, "friedman_credit": "Graham", "friedman_date": "1968", "friedman_display_metric_value": 3.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc6.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "3", "friedman_metric_symbol": "r", "friedman_metric_value": 3.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@6", "credit": "Graham", "date": "1968", "family_updated": "", "metric_expression": "3", "metric_symbol": "r", "metric_value": 3.0, "reference_text": "r = 3 | Proved by Graham in 1968.", "source_image": "ccc6.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc6.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 3 | Proved by Graham in 1968.", "friedman_source_image": "ccc6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "5d3d5beee3c5f33c", "improvement": -5.626367118827247e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.011848064282674e-06, "max_pair_overlap_depth": -4.5345095143201064e-05, "metric_expression": "3.00006", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.0000562636711883, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.0, "setup": "cirincir", "side": 6.0001125273423765, "solution_path": "data/solutions/generated/cirincir_006_5d3d5beee3c5f33c.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Graham", "svg_path": "data/svg/5d3d5beee3c5f33c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@7", "density": 0.77774147574625, "friedman_analytical_or_proved": true, "friedman_credit": "Graham", "friedman_date": "1968", "friedman_display_metric_value": 3.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc7.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "3", "friedman_metric_symbol": "r", "friedman_metric_value": 3.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@7", "credit": "Graham", "date": "1968", "family_updated": "", "metric_expression": "3", "metric_symbol": "r", "metric_value": 3.0, "reference_text": "r = 3 | Proved by Graham in 1968.", "source_image": "ccc7.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc7.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 3 | Proved by Graham in 1968.", "friedman_source_image": "ccc7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "2b1985e4094e6893", "improvement": -7.001351167312819e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.2947164267690425e-06, "max_pair_overlap_depth": -6.231680049051391e-05, "metric_expression": "3.00007", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.000070013511673, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.0, "setup": "cirincir", "side": 6.000140027023346, "solution_path": "data/solutions/generated/cirincir_007_2b1985e4094e6893.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Graham", "svg_path": "data/svg/2b1985e4094e6893.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@8", "density": 0.7324681263291527, "friedman_analytical_or_proved": true, "friedman_credit": "Braaksma", "friedman_date": "1963", "friedman_display_metric_value": 3.304, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc8.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "3.304+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.304, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@8", "credit": "Braaksma", "date": "1963", "family_updated": "", "metric_expression": "3.304+", "metric_symbol": "r", "metric_value": 3.304, "reference_text": "r = 3.304+ | Proved by Braaksma in 1963.", "source_image": "ccc8.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc8.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 3.304+ | Proved by Braaksma in 1963.", "friedman_source_image": "ccc8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "0193661647fd3854", "improvement": -0.0008414425517750956, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.96872891495326e-06, "max_pair_overlap_depth": -4.3191348294779885e-05, "metric_expression": "3.30484", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.304841442551775, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.304, "setup": "cirincir", "side": 6.60968288510355, "solution_path": "data/solutions/generated/cirincir_008_0193661647fd3854.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Braaksma", "svg_path": "data/svg/0193661647fd3854.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@9", "density": 0.6893878045655164, "friedman_analytical_or_proved": true, "friedman_credit": "Pirl", "friedman_date": "1969", "friedman_display_metric_value": 3.613, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc9.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "3.613+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.613, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@9", "credit": "Pirl", "date": "1969", "family_updated": "", "metric_expression": "3.613+", "metric_symbol": "r", "metric_value": 3.613, "reference_text": "r = 3.613+ | Proved by Pirl in 1969.", "source_image": "ccc9.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc9.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 3.613+ | Proved by Pirl in 1969.", "friedman_source_image": "ccc9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "b51df67181f6833b", "improvement": -0.00017882622267562098, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.656082665643879e-06, "max_pair_overlap_depth": -2.396342999144707e-05, "metric_expression": "3.61318", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.6131788262226756, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.613, "setup": "cirincir", "side": 7.226357652445351, "solution_path": "data/solutions/generated/cirincir_009_b51df67181f6833b.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Pirl", "svg_path": "data/svg/b51df67181f6833b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@10", "density": 0.6877649990272218, "friedman_analytical_or_proved": true, "friedman_credit": "Pirl", "friedman_date": "1969", "friedman_display_metric_value": 3.813, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc10.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "3.813+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.813, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@10", "credit": "Pirl", "date": "1969", "family_updated": "", "metric_expression": "3.813+", "metric_symbol": "r", "metric_value": 3.813, "reference_text": "r = 3.813+ | Proved by Pirl in 1969.", "source_image": "ccc10.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc10.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 3.813+ | Proved by Pirl in 1969.", "friedman_source_image": "ccc10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "be14c55679a54b28", "improvement": -0.00011553912424266954, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.081326946625552e-06, "max_pair_overlap_depth": -3.967607896537828e-05, "metric_expression": "3.81312", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.813115539124243, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.813, "setup": "cirincir", "side": 7.626231078248486, "solution_path": "data/solutions/generated/cirincir_10_be14c55679a54b28.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Pirl", "svg_path": "data/svg/be14c55679a54b28.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@11", "density": 0.714418364520267, "friedman_analytical_or_proved": true, "friedman_credit": "Melissen", "friedman_date": "1994", "friedman_display_metric_value": 3.923, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc11.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "3.923+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.923, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@11", "credit": "Melissen", "date": "1994", "family_updated": "", "metric_expression": "3.923+", "metric_symbol": "r", "metric_value": 3.923, "reference_text": "r = 3.923+ | Proved by Melissen in 1994.", "source_image": "ccc11.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc11.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 3.923+ | Proved by Melissen in 1994.", "friedman_source_image": "ccc11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "e624f391927921fb", "improvement": -0.0009190348380849755, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.92009600810772e-06, "max_pair_overlap_depth": -4.346382940223492e-05, "metric_expression": "3.92392", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.923919034838085, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.923, "setup": "cirincir", "side": 7.84783806967617, "solution_path": "data/solutions/generated/cirincir_011_e624f391927921fb.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Melissen", "svg_path": "data/svg/e624f391927921fb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@12", "density": 0.7389828254275508, "friedman_analytical_or_proved": false, "friedman_credit": "Kravitz", "friedman_date": "1967", "friedman_display_metric_value": 4.029, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc12.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "4.029+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.029, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirincir@12", "credit": "Kravitz", "date": "1967", "family_updated": "", "metric_expression": "4.029+", "metric_symbol": "r", "metric_value": 4.029, "reference_text": "r = 4.029+ | Found by Kravitz in 1967.", "source_image": "ccc12.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc12.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 4.029+ | Found by Kravitz in 1967.", "friedman_source_image": "ccc12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "0d7fc8a14b1c4e0e", "improvement": -0.0007068210362959348, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.338373973515445e-06, "max_pair_overlap_depth": -5.019209633871924e-05, "metric_expression": "4.02971", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.029706821036296, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.029, "setup": "cirincir", "side": 8.059413642072592, "solution_path": "data/solutions/generated/cirincir_012_0d7fc8a14b1c4e0e.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Kravitz", "svg_path": "data/svg/0d7fc8a14b1c4e0e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@13", "density": 0.7244255598642273, "friedman_analytical_or_proved": true, "friedman_credit": "F. Fodor", "friedman_date": "2003", "friedman_display_metric_value": 4.236, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc13.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "2 + \u221a5 = 4.236+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.23606797749979, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@13", "credit": "F. Fodor", "date": "2003", "family_updated": "", "metric_expression": "2 + \u221a5 = 4.236+", "metric_symbol": "r", "metric_value": 4.236, "reference_text": "r = 2 + \u221a5 = 4.236+ | Proved by F. Fodor in 2003.", "source_image": "ccc13.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc13.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 2 + \u221a5 = 4.236+ | Proved by F. Fodor in 2003.", "friedman_source_image": "ccc13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "a118f33872e0cb30", "improvement": -0.00011580829680202243, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.324667153277062e-06, "max_pair_overlap_depth": -4.7467215169572086e-05, "metric_expression": "4.23618", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.236183785796592, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.23606797749979, "setup": "cirincir", "side": 8.472367571593184, "solution_path": "data/solutions/generated/cirincir_013_a118f33872e0cb30.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "F. Fodor", "svg_path": "data/svg/a118f33872e0cb30.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@14", "density": 0.7472109217319929, "friedman_analytical_or_proved": false, "friedman_credit": "Goldberg", "friedman_date": "1971", "friedman_display_metric_value": 4.328, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc14.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "4.328+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.328, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirincir@14", "credit": "Goldberg", "date": "1971", "family_updated": "", "metric_expression": "4.328+", "metric_symbol": "r", "metric_value": 4.328, "reference_text": "r = 4.328+ | Found by Goldberg in 1971.", "source_image": "ccc14.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc14.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 4.328+ | Found by Goldberg in 1971.", "friedman_source_image": "ccc14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "b2ec44e582e5ab93", "improvement": -0.000549738133919675, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.732062089120916e-06, "max_pair_overlap_depth": -4.9839299053555663e-05, "metric_expression": "4.32855", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.32854973813392, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.328, "setup": "cirincir", "side": 8.65709947626784, "solution_path": "data/solutions/generated/cirincir_014_b2ec44e582e5ab93.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Goldberg", "svg_path": "data/svg/b2ec44e582e5ab93.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@15", "density": 0.7334069336541974, "friedman_analytical_or_proved": false, "friedman_credit": "Kravitz", "friedman_date": "1967", "friedman_display_metric_value": 4.521, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc15.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "4.521+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.521, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirincir@15", "credit": "Kravitz", "date": "1967", "family_updated": "", "metric_expression": "4.521+", "metric_symbol": "r", "metric_value": 4.521, "reference_text": "r = 4.521+ | Found by Kravitz in 1967.", "source_image": "ccc15.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc15.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 4.521+ | Found by Kravitz in 1967.", "friedman_source_image": "ccc15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "eeff7b918e6d6618", "improvement": -0.00144322894722837, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.2291583220711573e-06, "max_pair_overlap_depth": -2.9276985216153406e-05, "metric_expression": "4.52244", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.522443228947228, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.521, "setup": "cirincir", "side": 9.044886457894457, "solution_path": "data/solutions/generated/cirincir_015_eeff7b918e6d6618.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Kravitz", "svg_path": "data/svg/eeff7b918e6d6618.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@16", "density": 0.7510554296860762, "friedman_analytical_or_proved": false, "friedman_credit": "Goldberg", "friedman_date": "1971", "friedman_display_metric_value": 4.615, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc16.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "4.615+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.615, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirincir@16", "credit": "Goldberg", "date": "1971", "family_updated": "", "metric_expression": "4.615+", "metric_symbol": "r", "metric_value": 4.615, "reference_text": "r = 4.615+ | Found by Goldberg in 1971.", "source_image": "ccc16.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc16.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 4.615+ | Found by Goldberg in 1971.", "friedman_source_image": "ccc16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "7824261a02b5ed90", "improvement": -0.0005556989154120728, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.219226596077988e-06, "max_pair_overlap_depth": -4.8324434488655754e-05, "metric_expression": "4.61556", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.615555698915412, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.615, "setup": "cirincir", "side": 9.231111397830825, "solution_path": "data/solutions/generated/cirincir_016_7824261a02b5ed90.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Goldberg", "svg_path": "data/svg/7824261a02b5ed90.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@17", "density": 0.7402604737017356, "friedman_analytical_or_proved": false, "friedman_credit": "Reis", "friedman_date": "1975", "friedman_display_metric_value": 4.792, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc17.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "4.792+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.792, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirincir@17", "credit": "Reis", "date": "1975", "family_updated": "", "metric_expression": "4.792+", "metric_symbol": "r", "metric_value": 4.792, "reference_text": "r = 4.792+ | Found by Reis in 1975.", "source_image": "ccc17.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc17.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 4.792+ | Found by Reis in 1975.", "friedman_source_image": "ccc17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "68c41c427924b99a", "improvement": -0.00016960544150546042, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.357123401303568e-06, "max_pair_overlap_depth": -5.05938755308577e-05, "metric_expression": "4.79217", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.792169605441505, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.792, "setup": "cirincir", "side": 9.58433921088301, "solution_path": "data/solutions/generated/cirincir_017_68c41c427924b99a.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Reis", "svg_path": "data/svg/68c41c427924b99a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@18", "density": 0.7608872603215449, "friedman_analytical_or_proved": true, "friedman_credit": "Kravitz", "friedman_date": "1967", "friedman_display_metric_value": 4.863, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc18.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "1 + \u221a2 + \u221a6 = 4.863+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.863703305156273, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@18", "credit": "Kravitz", "date": "1967", "family_updated": "", "metric_expression": "1 + \u221a2 + \u221a6 = 4.863+", "metric_symbol": "r", "metric_value": 4.863, "reference_text": "r = 1 + \u221a2 + \u221a6 = 4.863+ | Found by Kravitz in 1967.", "source_image": "ccc18.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc18.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 1 + \u221a2 + \u221a6 = 4.863+ | Found by Kravitz in 1967.", "friedman_source_image": "ccc18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "6acc78721c0b4ca1", "improvement": -0.00010103809458961166, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.509170524220508e-07, "max_pair_overlap_depth": -3.6364882113559815e-05, "metric_expression": "4.86380", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.863804343250862, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.863703305156273, "setup": "cirincir", "side": 9.727608686501725, "solution_path": "data/solutions/generated/cirincir_018_6acc78721c0b4ca1.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Kravitz", "svg_path": "data/svg/6acc78721c0b4ca1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@19", "density": 0.8031578398507155, "friedman_analytical_or_proved": true, "friedman_credit": "F. Fodor", "friedman_date": "1999", "friedman_display_metric_value": 4.863, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc19.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "1 + \u221a2 + \u221a6 = 4.863+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.863703305156273, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirincir@19", "credit": "F. Fodor", "date": "1999", "family_updated": "", "metric_expression": "1 + \u221a2 + \u221a6 = 4.863+", "metric_symbol": "r", "metric_value": 4.863, "reference_text": "r = 1 + \u221a2 + \u221a6 = 4.863+ | Proved by F. Fodor in 1999.", "source_image": "ccc19.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc19.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 1 + \u221a2 + \u221a6 = 4.863+ | Proved by F. Fodor in 1999.", "friedman_source_image": "ccc19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "8325b5bff319f74f", "improvement": -0.00010386900173209312, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.170379222960378e-06, "max_pair_overlap_depth": -3.89864445309307e-05, "metric_expression": "4.86381", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.863807174158005, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.863703305156273, "setup": "cirincir", "side": 9.72761434831601, "solution_path": "data/solutions/generated/cirincir_019_8325b5bff319f74f.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "F. Fodor", "svg_path": "data/svg/8325b5bff319f74f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirincir@20", "density": 0.7622179661920169, "friedman_analytical_or_proved": false, "friedman_credit": "Goldberg", "friedman_date": "1971", "friedman_display_metric_value": 5.122, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc20.gif", "friedman_family_updated": "6/27/05", "friedman_metric_expression": "5.122+", "friedman_metric_symbol": "r", "friedman_metric_value": 5.122, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirincir@20", "credit": "Goldberg", "date": "1971", "family_updated": "", "metric_expression": "5.122+", "metric_symbol": "r", "metric_value": 5.122, "reference_text": "r = 5.122+ | Found by Goldberg in 1971.", "source_image": "ccc20.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc20.gif", "source_page": "https://erich-friedman.github.io/packing/cirincir/", "title": "Circles in Circles"}, "friedman_reference_text": "r = 5.122+ | Found by Goldberg in 1971.", "friedman_source_image": "ccc20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirincir/", "friedman_title": "Circles in Circles", "frontend_seed": true, "id": "f0718319f5a05220", "improvement": -0.0004226268079490225, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.474954062416714e-06, "max_pair_overlap_depth": -3.4642111702343215e-05, "metric_expression": "5.12242", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 5.122422626807949, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.122, "setup": "cirincir", "side": 10.244845253615898, "solution_path": "data/solutions/generated/cirincir_020_f0718319f5a05220.json", "source_url": "https://erich-friedman.github.io/packing/cirincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Goldberg", "svg_path": "data/svg/f0718319f5a05220.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@1", "density": 0.9068802327278791, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc1.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "2/\u221a3 = 1.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.1547005383792515, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2/\u221a3 = 1.154+", "metric_symbol": "s", "metric_value": 1.154, "reference_text": "s = 2/\u221a3 = 1.154+ | Trivial.", "source_image": "hc1.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc1.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 2/\u221a3 = 1.154+ | Trivial.", "friedman_source_image": "hc1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "37d86bed2252b572", "improvement": -1.238206490383753e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.894559686663413e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.15471", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.1547129204441553, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.1547005383792515, "setup": "cirinhex", "side": 1.1547129204441553, "solution_path": "data/solutions/generated/cirinhex_001_37d86bed2252b572.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/37d86bed2252b572.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@2", "density": 0.5208916187605724, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc2.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "1 + 2/\u221a3 = 2.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.1547005383792515, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1 + 2/\u221a3 = 2.154+", "metric_symbol": "s", "metric_value": 2.154, "reference_text": "s = 1 + 2/\u221a3 = 2.154+ | Trivial.", "source_image": "hc2.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc2.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 1 + 2/\u221a3 = 2.154+ | Trivial.", "friedman_source_image": "hc2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "4ba45a45587fd527", "improvement": -1.6799259586974813e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.535667492477913e-06, "max_pair_overlap_depth": -1.2900139699567603e-05, "metric_expression": "2.15472", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.1547173376388384, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.1547005383792515, "setup": "cirinhex", "side": 2.1547173376388384, "solution_path": "data/solutions/generated/cirinhex_002_4ba45a45587fd527.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4ba45a45587fd527.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@3", "density": 0.6801656739683151, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.309, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc3.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "4/\u221a3 = 2.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4/\u221a3 = 2.309+", "metric_symbol": "s", "metric_value": 2.309, "reference_text": "s = 4/\u221a3 = 2.309+ | Trivial.", "source_image": "hc3.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc3.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 4/\u221a3 = 2.309+ | Trivial.", "friedman_source_image": "hc3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "fa4a26f729d80904", "improvement": -1.5427776642873425e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3364075199806535e-06, "max_pair_overlap_depth": -1.818559246702378e-05, "metric_expression": "2.30942", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.309416504535146, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.309401076758503, "setup": "cirinhex", "side": 2.309416504535146, "solution_path": "data/solutions/generated/cirinhex_003_fa4a26f729d80904.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/fa4a26f729d80904.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@4", "density": 0.6802066538449848, "friedman_analytical_or_proved": true, "friedman_credit": "Shahriar Manzoor", "friedman_date": "April 2002", "friedman_display_metric_value": 2.666, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc4.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "2/\u221a3 + 4/\u221a7 = 2.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.6665584304161603, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@4", "credit": "Shahriar Manzoor", "date": "April 2002", "family_updated": "", "metric_expression": "2/\u221a3 + 4/\u221a7 = 2.666+", "metric_symbol": "s", "metric_value": 2.666, "reference_text": "s = 2/\u221a3 + 4/\u221a7 = 2.666+ | Found by Shahriar Manzoor | in April 2002.", "source_image": "hc4.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc4.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 2/\u221a3 + 4/\u221a7 = 2.666+ | Found by Shahriar Manzoor | in April 2002.", "friedman_source_image": "hc4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "4ea68db180a8d4c4", "improvement": -4.572067859331952e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3940250920849735e-07, "max_pair_overlap_depth": -4.6158989302380604e-05, "metric_expression": "2.66660", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.6666041510947536, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.6665584304161603, "setup": "cirinhex", "side": 2.6666041510947536, "solution_path": "data/solutions/generated/cirinhex_004_4ea68db180a8d4c4.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Shahriar Manzoor", "svg_path": "data/svg/4ea68db180a8d4c4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@5", "density": 0.672041103262025, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1999", "friedman_display_metric_value": 2.999, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc5.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "2.999+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.999, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@5", "credit": "Erich Friedman", "date": "1999", "family_updated": "", "metric_expression": "2.999+", "metric_symbol": "s", "metric_value": 2.999, "reference_text": "s = 2.999+ | Found by Erich Friedman | in 1999.", "source_image": "hc5.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc5.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 2.999+ | Found by Erich Friedman | in 1999.", "friedman_source_image": "hc5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "eb88c54ef20a6355", "improvement": -0.00041167259487728813, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6369105032841844e-07, "max_pair_overlap_depth": -3.862655436481788e-05, "metric_expression": "2.99941", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.9994116725948774, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.999, "setup": "cirinhex", "side": 2.9994116725948774, "solution_path": "data/solutions/generated/cirinhex_005_eb88c54ef20a6355.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/eb88c54ef20a6355.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@6", "density": 0.7289750468062609, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc6.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "2 + 2/\u221a3 = 3.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.1547005383792515, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@6", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2 + 2/\u221a3 = 3.154+", "metric_symbol": "s", "metric_value": 3.154, "reference_text": "s = 2 + 2/\u221a3 = 3.154+ | Trivial. |", "source_image": "hc6.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc6.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 2 + 2/\u221a3 = 3.154+ | Trivial. |", "friedman_source_image": "hc6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "9b7724fab73c49c1", "improvement": -7.370981566001689e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.7088474341983044e-06, "max_pair_overlap_depth": -4.5158069021944414e-05, "metric_expression": "3.15477", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.1547742481949115, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.1547005383792515, "setup": "cirinhex", "side": 3.1547742481949115, "solution_path": "data/solutions/generated/cirinhex_006_9b7724fab73c49c1.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/9b7724fab73c49c1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@7", "density": 0.8504825176668179, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc7.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "2 + 2/\u221a3 = 3.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.1547005383792515, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@7", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2 + 2/\u221a3 = 3.154+", "metric_symbol": "s", "metric_value": 3.154, "reference_text": "s = 2 + 2/\u221a3 = 3.154+ | Trivial. |", "source_image": "hc7.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc7.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 2 + 2/\u221a3 = 3.154+ | Trivial. |", "friedman_source_image": "hc7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "7368090471750227", "improvement": -5.2140127083433185e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.857578518338343e-06, "max_pair_overlap_depth": -3.893260533160969e-05, "metric_expression": "3.15475", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.154752678506335, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.1547005383792515, "setup": "cirinhex", "side": 3.154752678506335, "solution_path": "data/solutions/generated/cirinhex_007_7368090471750227.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/7368090471750227.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@8", "density": 0.7030218969047355, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_display_metric_value": 3.709, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc8.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "3.709+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.709, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@8", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "3.709+", "metric_symbol": "s", "metric_value": 3.709, "reference_text": "s = 3.709+ | Found by David W. Cantrell | in July 2002.", "source_image": "hc8.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc8.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 3.709+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "hc8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "afebd04e4720460b", "improvement": -0.0004503331818734857, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.1028444985304873e-08, "max_pair_overlap_depth": -2.2199913737530608e-05, "metric_expression": "3.70945", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.7094503331818736, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.709, "setup": "cirinhex", "side": 3.7094503331818736, "solution_path": "data/solutions/generated/cirinhex_008_afebd04e4720460b.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/afebd04e4720460b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@9", "density": 0.6761453195206264, "friedman_analytical_or_proved": true, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_display_metric_value": 4.011, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc9.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "20/7 + 2/\u221a3 = 4.011+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.011843395522108, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@9", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "20/7 + 2/\u221a3 = 4.011+", "metric_symbol": "s", "metric_value": 4.011, "reference_text": "s = 20/7 + 2/\u221a3 = 4.011+ | Found by David W. Cantrell | in July 2002.", "source_image": "hc9.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc9.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 20/7 + 2/\u221a3 = 4.011+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "hc9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "64b59a5605599f8e", "improvement": -5.776381833300093e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.491846259144452e-06, "max_pair_overlap_depth": -2.6999063512000987e-05, "metric_expression": "4.01190", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.011901159340441, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.011843395522108, "setup": "cirinhex", "side": 4.011901159340441, "solution_path": "data/solutions/generated/cirinhex_009_64b59a5605599f8e.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/64b59a5605599f8e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@10", "density": 0.7125686135385136, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_display_metric_value": 4.119, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc10.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "4.119+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.119, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@10", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "4.119+", "metric_symbol": "s", "metric_value": 4.119, "reference_text": "s = 4.119+ | Found by David W. Cantrell | in July 2002.", "source_image": "hc10.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc10.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 4.119+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "hc10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "cd79fdfeb9e3f24b", "improvement": -0.00041597258721015606, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.240617525155585e-06, "max_pair_overlap_depth": -1.610926851469685e-05, "metric_expression": "4.11942", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.11941597258721, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.119, "setup": "cirinhex", "side": 4.11941597258721, "solution_path": "data/solutions/generated/cirinhex_010_cd79fdfeb9e3f24b.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/cd79fdfeb9e3f24b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@11", "density": 0.7162109607848701, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1999", "friedman_display_metric_value": 4.309, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc11.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "2 + 4/\u221a3 = 4.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@11", "credit": "Erich Friedman", "date": "1999", "family_updated": "", "metric_expression": "2 + 4/\u221a3 = 4.309+", "metric_symbol": "s", "metric_value": 4.309, "reference_text": "s = 2 + 4/\u221a3 = 4.309+ | Found by Erich Friedman | in 1999.", "source_image": "hc11.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc11.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 2 + 4/\u221a3 = 4.309+ | Found by Erich Friedman | in 1999.", "friedman_source_image": "hc11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "cda2ccbbf4de67aa", "improvement": -7.877087278718164e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.3670191174924895e-06, "max_pair_overlap_depth": -2.2677850788799248e-05, "metric_expression": "4.30948", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.30947984763129, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.309401076758503, "setup": "cirinhex", "side": 4.30947984763129, "solution_path": "data/solutions/generated/cirinhex_011_cda2ccbbf4de67aa.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/cda2ccbbf4de67aa.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@12", "density": 0.7813203208949625, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1999", "friedman_display_metric_value": 4.309, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc12.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "2 + 4/\u221a3 = 4.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@12", "credit": "Erich Friedman", "date": "1999", "family_updated": "", "metric_expression": "2 + 4/\u221a3 = 4.309+", "metric_symbol": "s", "metric_value": 4.309, "reference_text": "s = 2 + 4/\u221a3 = 4.309+ | Found by Erich Friedman | in 1999.", "source_image": "hc12.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc12.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 2 + 4/\u221a3 = 4.309+ | Found by Erich Friedman | in 1999.", "friedman_source_image": "hc12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "c3d795864cfeb74c", "improvement": -8.07764519317189e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.009897945360223e-06, "max_pair_overlap_depth": -3.7913329796079864e-05, "metric_expression": "4.30948", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.309481853210435, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.309401076758503, "setup": "cirinhex", "side": 4.309481853210435, "solution_path": "data/solutions/generated/cirinhex_012_c3d795864cfeb74c.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/c3d795864cfeb74c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@13", "density": 0.7368031353920613, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1999", "friedman_display_metric_value": 4.618, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc13.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "8/\u221a3 = 4.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.618802153517006, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@13", "credit": "Erich Friedman", "date": "1999", "family_updated": "", "metric_expression": "8/\u221a3 = 4.618+", "metric_symbol": "s", "metric_value": 4.618, "reference_text": "s = 8/\u221a3 = 4.618+ | Found by Erich Friedman | in 1999.", "source_image": "hc13.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc13.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 8/\u221a3 = 4.618+ | Found by Erich Friedman | in 1999.", "friedman_source_image": "hc13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "62c003d981fbe524", "improvement": -0.0001656674164873806, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.589858579651107e-06, "max_pair_overlap_depth": -5.483667702588235e-05, "metric_expression": "4.61897", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.618967820933493, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.618802153517006, "setup": "cirinhex", "side": 4.618967820933493, "solution_path": "data/solutions/generated/cirinhex_013_62c003d981fbe524.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/62c003d981fbe524.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@14", "density": 0.7773468150841377, "friedman_analytical_or_proved": true, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_display_metric_value": 4.666, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc14.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "2 + 2/\u221a3 + 4/\u221a7 = 4.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.666558430416161, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@14", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "2 + 2/\u221a3 + 4/\u221a7 = 4.666+", "metric_symbol": "s", "metric_value": 4.666, "reference_text": "s = 2 + 2/\u221a3 + 4/\u221a7 = 4.666+ | Found by David W. Cantrell | in July 2002.", "source_image": "hc14.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc14.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 2 + 2/\u221a3 + 4/\u221a7 = 4.666+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "hc14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "d3d8d6f246feeaad", "improvement": -9.55379601901285e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4490171600378687e-06, "max_pair_overlap_depth": -3.940553381864831e-05, "metric_expression": "4.66665", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.666653968376351, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.666558430416161, "setup": "cirinhex", "side": 4.666653968376351, "solution_path": "data/solutions/generated/cirinhex_014_d3d8d6f246feeaad.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d3d8d6f246feeaad.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@15", "density": 0.7368006709671345, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "January 2006", "friedman_display_metric_value": 4.961, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc15.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "4.961+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.961, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@15", "credit": "David W. Cantrell", "date": "January 2006", "family_updated": "", "metric_expression": "4.961+", "metric_symbol": "s", "metric_value": 4.961, "reference_text": "s = 4.961+ | Found by David W. Cantrell | in January 2006.", "source_image": "hc15.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc15.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 4.961+ | Found by David W. Cantrell | in January 2006.", "friedman_source_image": "hc15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "d923ba7fbcb56e93", "improvement": -0.0005756365508533534, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.177000685334775e-07, "max_pair_overlap_depth": -3.4253106946380285e-05, "metric_expression": "4.96158", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.961575636550854, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.961, "setup": "cirinhex", "side": 4.961575636550854, "solution_path": "data/solutions/generated/cirinhex_015_d923ba7fbcb56e93.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d923ba7fbcb56e93.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@16", "density": 0.774039756730763, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_display_metric_value": 4.999, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc16.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "4.999+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.999, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@16", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "4.999+", "metric_symbol": "s", "metric_value": 4.999, "reference_text": "s = 4.999+ | Found by David W. Cantrell | in July 2002.", "source_image": "hc16.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc16.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 4.999+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "hc16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "b6a042d1d6eee5a4", "improvement": -0.0005089546268814971, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.665337648678829e-06, "max_pair_overlap_depth": -4.998313684900779e-05, "metric_expression": "4.99951", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.999508954626881, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.999, "setup": "cirinhex", "side": 4.999508954626881, "solution_path": "data/solutions/generated/cirinhex_016_b6a042d1d6eee5a4.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/b6a042d1d6eee5a4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@17", "density": 0.7801137203230791, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "January 2006", "friedman_display_metric_value": 5.133, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc17.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "5.133+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.133, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@17", "credit": "David W. Cantrell", "date": "January 2006", "family_updated": "", "metric_expression": "5.133+", "metric_symbol": "s", "metric_value": 5.133, "reference_text": "s = 5.133+ | Found by David W. Cantrell | in January 2006.", "source_image": "hc17.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc17.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 5.133+ | Found by David W. Cantrell | in January 2006.", "friedman_source_image": "hc17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "4927714d5d50ab2b", "improvement": -0.00027458420964432406, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.495950815863736e-06, "max_pair_overlap_depth": -5.684433644859155e-05, "metric_expression": "5.13327", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.133274584209644, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.133, "setup": "cirinhex", "side": 5.133274584209644, "solution_path": "data/solutions/generated/cirinhex_017_4927714d5d50ab2b.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/4927714d5d50ab2b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@18", "density": 0.81913146509039, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc18.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "4 + 2/\u221a3 = 5.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.1547005383792515, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@18", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4 + 2/\u221a3 = 5.154+", "metric_symbol": "s", "metric_value": 5.154, "reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "source_image": "hc18.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc18.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "friedman_source_image": "hc18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "223b1a3f7b7d0e67", "improvement": -5.9361077508590654e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.33856736717064e-06, "max_pair_overlap_depth": -1.657857602177515e-05, "metric_expression": "5.15476", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.15475989945676, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.1547005383792515, "setup": "cirinhex", "side": 5.15475989945676, "solution_path": "data/solutions/generated/cirinhex_018_223b1a3f7b7d0e67.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/223b1a3f7b7d0e67.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@19", "density": 0.8646358262071194, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc19.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "4 + 2/\u221a3 = 5.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.1547005383792515, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@19", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4 + 2/\u221a3 = 5.154+", "metric_symbol": "s", "metric_value": 5.154, "reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "source_image": "hc19.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc19.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "friedman_source_image": "hc19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "78f9327e80d8ab20", "improvement": -6.813232232882882e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.035946609195264e-07, "max_pair_overlap_depth": -1.6136694912294303e-05, "metric_expression": "5.15477", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.15476867070158, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.1547005383792515, "setup": "cirinhex", "side": 5.15476867070158, "solution_path": "data/solutions/generated/cirinhex_019_78f9327e80d8ab20.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/78f9327e80d8ab20.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@20", "density": 0.7503080962551325, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 5.676, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc20.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "5.676+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.676, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@20", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "5.676+", "metric_symbol": "s", "metric_value": 5.676, "reference_text": "s = 5.676+ | Found by David W. Cantrell | in July 2012.", "source_image": "hc20.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc20.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 5.676+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "hc20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "247c6c06779a7d8b", "improvement": -0.0013304688728235092, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.66649728101143e-06, "max_pair_overlap_depth": -2.983410910761819e-05, "metric_expression": "5.67733", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.677330468872824, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.676, "setup": "cirinhex", "side": 5.677330468872824, "solution_path": "data/solutions/generated/cirinhex_020_247c6c06779a7d8b.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/247c6c06779a7d8b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@21", "density": 0.7789652581067265, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 5.709, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc21.gif", "friedman_metric_expression": "5.709+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.709, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@21", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "5.709+", "metric_symbol": "s", "metric_value": 5.709, "reference_text": "s = 5.709+ | Found by David W. Cantrell | in July 2012.", "source_image": "hc21.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc21.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 5.709+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "hc21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "38040eceeb63c1e3", "improvement": -0.0005199689632231497, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.315374129847953e-06, "max_pair_overlap_depth": -3.751451804223649e-05, "metric_expression": "5.70952", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.709519968963223, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.709, "setup": "cirinhex", "side": 5.709519968963223, "solution_path": "data/solutions/generated/cirinhex_021_38040eceeb63c1e3.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/38040eceeb63c1e3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@22", "density": 0.7509530082141859, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 5.952, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc22.gif", "friedman_metric_expression": "5.952+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.952, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@22", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "5.952+", "metric_symbol": "s", "metric_value": 5.952, "reference_text": "s = 5.952+ | Found by David W. Cantrell | in July 2012.", "source_image": "hc22.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc22.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 5.952+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "hc22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "cd7262f9f7d0d279", "improvement": 0.0001229278734493633, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.663138574891647e-06, "max_pair_overlap_depth": -3.268885699680979e-05, "metric_expression": "5.95188", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.951877072126551, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.952, "setup": "cirinhex", "side": 5.951877072126551, "solution_path": "data/solutions/generated/cirinhex_022_cd7262f9f7d0d279.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/cd7262f9f7d0d279.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@23", "density": 0.7694641578789073, "friedman_analytical_or_proved": true, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 6.011, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc23.gif", "friedman_metric_expression": "34/7 + 2/\u221a3 = 6.011+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.011843395522108, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@23", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "34/7 + 2/\u221a3 = 6.011+", "metric_symbol": "s", "metric_value": 6.011, "reference_text": "s = 34/7 + 2/\u221a3 = 6.011+ | Found by David W. Cantrell | in July 2012.", "source_image": "hc23.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc23.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 34/7 + 2/\u221a3 = 6.011+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "hc23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "de2d2aabdc650ad2", "improvement": -0.00015302973728736902, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.1931154748950945e-06, "max_pair_overlap_depth": -3.920500316656472e-05, "metric_expression": "6.01200", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.011996425259396, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.011843395522108, "setup": "cirinhex", "side": 6.011996425259396, "solution_path": "data/solutions/generated/cirinhex_023_de2d2aabdc650ad2.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/de2d2aabdc650ad2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@24", "density": 0.7747882438352293, "friedman_analytical_or_proved": false, "friedman_credit": "Rob Pratt", "friedman_date": "March 2020", "friedman_display_metric_value": 6.117, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc24.gif", "friedman_metric_expression": "6.117+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.117, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@24", "credit": "Rob Pratt", "date": "March 2020", "family_updated": "", "metric_expression": "6.117+", "metric_symbol": "s", "metric_value": 6.117, "reference_text": "s = 6.117+ | Found by Rob Pratt | in March 2020.", "source_image": "hc24.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc24.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 6.117+ | Found by Rob Pratt | in March 2020.", "friedman_source_image": "hc24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "61a86ae12328c1ca", "improvement": -0.003164603994216364, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4542492504119338e-06, "max_pair_overlap_depth": -2.04098607499148e-05, "metric_expression": "6.12016", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.120164603994216, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.117, "setup": "cirinhex", "side": 6.120164603994216, "solution_path": "data/solutions/generated/cirinhex_024_61a86ae12328c1ca.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Rob Pratt", "svg_path": "data/svg/61a86ae12328c1ca.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@1", "density": 0.8647965566225578, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.453, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.1.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "1.453+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.453, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirinpen@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1.453+", "metric_symbol": "s", "metric_value": 1.453, "reference_text": "s = 2tan(36\u00b0) | s = 1.453+ | Trivial.", "source_image": "pent.1.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.1.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 2tan(36\u00b0) | s = 1.453+ | Trivial.", "friedman_source_image": "pent.1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "2249439da521383e", "improvement": -9.321311914245456e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.798939718275719e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.45309", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.4530932131191425, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.453, "setup": "cirinpen", "side": 1.4530932131191425, "solution_path": "data/solutions/generated/cirinpen_001_2249439da521383e.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/2249439da521383e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@2", "density": 0.5049856179230741, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.689, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.2.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "2.689+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.689, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirinpen@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2.689+", "metric_symbol": "s", "metric_value": 2.689, "reference_text": "s = 2tan(36\u00b0) + \u221a5 - 1 | s = 2.689+ | Trivial.", "source_image": "pent.2.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.2.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 2tan(36\u00b0) + \u221a5 - 1 | s = 2.689+ | Trivial.", "friedman_source_image": "pent.2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "042df6c460b769f5", "improvement": -0.00021758992828191381, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.904067621218203e-06, "max_pair_overlap_depth": -5.9422400474407056e-05, "metric_expression": "2.68922", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.689217589928282, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.689, "setup": "cirinpen", "side": 2.689217589928282, "solution_path": "data/solutions/generated/cirinpen_002_042df6c460b769f5.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/042df6c460b769f5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@3", "density": 0.6022625992350803, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_display_metric_value": 3.015, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.3.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "3.015+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.015, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@3", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "3.015+", "metric_symbol": "s", "metric_value": 3.015, "reference_text": "s = 3.015+ | Found by George Sicherman | in July 2012.", "source_image": "pent.3.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.3.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 3.015+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "7afe63c4f78d1c3c", "improvement": -0.0009082861357154748, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.348511423333477e-06, "max_pair_overlap_depth": -3.760319804513301e-05, "metric_expression": "3.01591", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0159082861357156, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.015, "setup": "cirinpen", "side": 3.0159082861357156, "solution_path": "data/solutions/generated/cirinpen_003_7afe63c4f78d1c3c.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/7afe63c4f78d1c3c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@4", "density": 0.6648380416307991, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_display_metric_value": 3.314, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.4.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "3.314+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.314, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@4", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "3.314+", "metric_symbol": "s", "metric_value": 3.314, "reference_text": "s = 3.314+ | Found by George Sicherman | in July 2012.", "source_image": "pent.4.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.4.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 3.314+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "3b6f81450d56967c", "improvement": -0.0005342806983965609, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4291241632899983e-06, "max_pair_overlap_depth": -5.729132607923404e-05, "metric_expression": "3.31453", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.3145342806983966, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.314, "setup": "cirinpen", "side": 3.3145342806983966, "solution_path": "data/solutions/generated/cirinpen_004_3b6f81450d56967c.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/3b6f81450d56967c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@5", "density": 0.7656755676390014, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.453, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.5.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "3.453+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.453, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirinpen@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3.453+", "metric_symbol": "s", "metric_value": 3.453, "reference_text": "s = 2tan(36\u00b0) + 2 | s = 3.453+ | Trivial.", "source_image": "pent.5.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.5.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 2tan(36\u00b0) + 2 | s = 3.453+ | Trivial.", "friedman_source_image": "pent.5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "6a788c9a1ab05f1f", "improvement": -0.00013102756244531832, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4842628671150067e-07, "max_pair_overlap_depth": -2.3617760550376232e-05, "metric_expression": "3.45313", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.453131027562445, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.453, "setup": "cirinpen", "side": 3.453131027562445, "solution_path": "data/solutions/generated/cirinpen_005_6a788c9a1ab05f1f.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/6a788c9a1ab05f1f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@6", "density": 0.7570230558933833, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.804, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.6.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "3.804+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.804, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirinpen@6", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3.804+", "metric_symbol": "s", "metric_value": 3.804, "reference_text": "s = 2tan(36\u00b0) + 4sin(36\u00b0) | s = 3.804+ | Trivial.", "source_image": "pent.6.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.6.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 2tan(36\u00b0) + 4sin(36\u00b0) | s = 3.804+ | Trivial.", "friedman_source_image": "pent.6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "a73fe466a153c6dc", "improvement": -0.0002716609440795992, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.235659036235575e-06, "max_pair_overlap_depth": -1.860019961119619e-05, "metric_expression": "3.80427", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.8042716609440794, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.804, "setup": "cirinpen", "side": 3.8042716609440794, "solution_path": "data/solutions/generated/cirinpen_006_a73fe466a153c6dc.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/a73fe466a153c6dc.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@7", "density": 0.7122554139396908, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_display_metric_value": 4.236, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.7.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "4.236+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.236, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@7", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "4.236+", "metric_symbol": "s", "metric_value": 4.236, "reference_text": "s = 4.236+ | Found by George Sicherman | in July 2012.", "source_image": "pent.7.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.7.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 4.236+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "f2fb4964063d721f", "improvement": -0.0002500861768837126, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.256168874145928e-06, "max_pair_overlap_depth": -7.389596920859276e-05, "metric_expression": "4.23625", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.2362500861768835, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.236, "setup": "cirinpen", "side": 4.2362500861768835, "solution_path": "data/solutions/generated/cirinpen_007_f2fb4964063d721f.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/f2fb4964063d721f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@8", "density": 0.7010960627351681, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_display_metric_value": 4.564, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.8.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "4.564+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.564, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@8", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "4.564+", "metric_symbol": "s", "metric_value": 4.564, "reference_text": "s = 4.564+ | Found by George Sicherman | in July 2012.", "source_image": "pent.8.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.8.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 4.564+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "7550c7a4a15ba971", "improvement": -0.0006415548993858877, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.759741664666194e-07, "max_pair_overlap_depth": -2.5138721591932978e-05, "metric_expression": "4.56464", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.564641554899386, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.564, "setup": "cirinpen", "side": 4.564641554899386, "solution_path": "data/solutions/generated/cirinpen_008_7550c7a4a15ba971.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/7550c7a4a15ba971.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@9", "density": 0.7058543729480167, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_display_metric_value": 4.825, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.9.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "4.825+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.825, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@9", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "4.825+", "metric_symbol": "s", "metric_value": 4.825, "reference_text": "s = 4.825+ | Found by George Sicherman | in July 2012.", "source_image": "pent.9.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.9.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 4.825+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "44a9c06211e4a669", "improvement": -0.0001870114230673181, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.33965970525874e-06, "max_pair_overlap_depth": -6.87249875483964e-05, "metric_expression": "4.82519", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.8251870114230675, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.825, "setup": "cirinpen", "side": 4.8251870114230675, "solution_path": "data/solutions/generated/cirinpen_009_44a9c06211e4a669.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/44a9c06211e4a669.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@10", "density": 0.7033183837462447, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_display_metric_value": 5.095, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.10.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "5.095+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.095, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@10", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "5.095+", "metric_symbol": "s", "metric_value": 5.095, "reference_text": "s = 5.095+ | Found by George Sicherman | in July 2012.", "source_image": "pent.10.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.10.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 5.095+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "38c046e395ee0204", "improvement": -0.0003552139806179966, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.918153382491795e-06, "max_pair_overlap_depth": -5.2545257565039805e-05, "metric_expression": "5.09536", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.095355213980618, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.095, "setup": "cirinpen", "side": 5.095355213980618, "solution_path": "data/solutions/generated/cirinpen_010_38c046e395ee0204.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/38c046e395ee0204.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@11", "density": 0.7314145264425335, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 5.24, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.11.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "5.240+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.24, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@11", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "5.240+", "metric_symbol": "s", "metric_value": 5.24, "reference_text": "s = 5.240+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.11.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.11.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 5.240+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "3c4a20ceb03b166b", "improvement": -0.0004068061718305316, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.25538255039082e-06, "max_pair_overlap_depth": -4.98370515433777e-05, "metric_expression": "5.24041", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.240406806171831, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.24, "setup": "cirinpen", "side": 5.240406806171831, "solution_path": "data/solutions/generated/cirinpen_011_3c4a20ceb03b166b.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/3c4a20ceb03b166b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@12", "density": 0.7492511392398852, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_display_metric_value": 5.407, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.12.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "5.407+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.407, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@12", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "5.407+", "metric_symbol": "s", "metric_value": 5.407, "reference_text": "s = 5.407+ | Found by George Sicherman | in July 2012.", "source_image": "pent.12.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.12.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 5.407+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "1156bc3b50d815fe", "improvement": -0.0008839986719992865, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7054584944851143e-06, "max_pair_overlap_depth": -3.0020938044383882e-05, "metric_expression": "5.40788", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.407883998671999, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.407, "setup": "cirinpen", "side": 5.407883998671999, "solution_path": "data/solutions/generated/cirinpen_012_1156bc3b50d815fe.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/1156bc3b50d815fe.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@13", "density": 0.7430341365754948, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_display_metric_value": 5.651, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.13.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "5.651+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.651, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@13", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "5.651+", "metric_symbol": "s", "metric_value": 5.651, "reference_text": "s = 5.651+ | Found by George Sicherman | in July 2012.", "source_image": "pent.13.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.13.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 5.651+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "213cdbfbbdb494b1", "improvement": -0.0012028933276413412, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.063538795673338e-06, "max_pair_overlap_depth": -3.936589445130423e-05, "metric_expression": "5.65220", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.652202893327641, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.651, "setup": "cirinpen", "side": 5.652202893327641, "solution_path": "data/solutions/generated/cirinpen_013_213cdbfbbdb494b1.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/213cdbfbbdb494b1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@14", "density": 0.7576628256268029, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_display_metric_value": 5.808, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.14.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "5.808+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.808, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@14", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "5.808+", "metric_symbol": "s", "metric_value": 5.808, "reference_text": "s = 5.808+ | Found by George Sicherman | in July 2012.", "source_image": "pent.14.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.14.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 5.808+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "44805be876ac7787", "improvement": -0.0006669796446772125, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.282572655998294e-06, "max_pair_overlap_depth": -2.37953924338008e-05, "metric_expression": "5.80867", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.808666979644677, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.808, "setup": "cirinpen", "side": 5.808666979644677, "solution_path": "data/solutions/generated/cirinpen_014_44805be876ac7787.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/44805be876ac7787.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@15", "density": 0.7748926471130506, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_display_metric_value": 5.945, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.15.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "5.945+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.945, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@15", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "5.945+", "metric_symbol": "s", "metric_value": 5.945, "reference_text": "s = 5.945+ | Found by George Sicherman | in July 2012.", "source_image": "pent.15.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.15.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 5.945+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "36fcf02cb6fd9f92", "improvement": -0.0003210236521935528, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.123112133491702e-06, "max_pair_overlap_depth": -5.711461050461608e-05, "metric_expression": "5.94532", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.945321023652194, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.945, "setup": "cirinpen", "side": 5.945321023652194, "solution_path": "data/solutions/generated/cirinpen_015_36fcf02cb6fd9f92.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/36fcf02cb6fd9f92.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@16", "density": 0.7775664873268765, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_display_metric_value": 6.129, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.16.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "6.129+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.129, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@16", "credit": "George Sicherman", "date": "July 2012", "family_updated": "", "metric_expression": "6.129+", "metric_symbol": "s", "metric_value": 6.129, "reference_text": "s = 6.129+ | Found by George Sicherman | in July 2012.", "source_image": "pent.16.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.16.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 6.129+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "39b6519b6fb7eef4", "improvement": -0.0007346433642512196, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.515317749508867e-06, "max_pair_overlap_depth": -2.965957000666819e-05, "metric_expression": "6.12973", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.129734643364251, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.129, "setup": "cirinpen", "side": 6.129734643364251, "solution_path": "data/solutions/generated/cirinpen_016_39b6519b6fb7eef4.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "George Sicherman", "svg_path": "data/svg/39b6519b6fb7eef4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@17", "density": 0.7527556084558986, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 6.419, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.17.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "6.419+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.419, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@17", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "6.419+", "metric_symbol": "s", "metric_value": 6.419, "reference_text": "s = 6.419+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.17.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.17.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 6.419+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "5e677c639e143e85", "improvement": -0.0026689184768269314, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.2234530213948176e-06, "max_pair_overlap_depth": -4.317787105012627e-05, "metric_expression": "6.42167", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.4216689184768265, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.419, "setup": "cirinpen", "side": 6.4216689184768265, "solution_path": "data/solutions/generated/cirinpen_017_5e677c639e143e85.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/5e677c639e143e85.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@18", "density": 0.7574722105185439, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 6.586, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.18.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "6.586+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.586, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@18", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "6.586+", "metric_symbol": "s", "metric_value": 6.586, "reference_text": "s = 6.586+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.18.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.18.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 6.586+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "34fda06736bbaaf7", "improvement": -0.0012379322999080955, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.803338162222119e-06, "max_pair_overlap_depth": -4.5158559001112764e-05, "metric_expression": "6.58724", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.587237932299908, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.586, "setup": "cirinpen", "side": 6.587237932299908, "solution_path": "data/solutions/generated/cirinpen_018_34fda06736bbaaf7.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/34fda06736bbaaf7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@19", "density": 0.7551620068495595, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 6.777, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.19.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "6.777+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.777, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@19", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "6.777+", "metric_symbol": "s", "metric_value": 6.777, "reference_text": "s = 6.777+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.19.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.19.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 6.777+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "dfaba7cef14e53f5", "improvement": -0.0010877146457399789, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.911905938958071e-06, "max_pair_overlap_depth": -5.528697090007029e-05, "metric_expression": "6.77809", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.77808771464574, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.777, "setup": "cirinpen", "side": 6.77808771464574, "solution_path": "data/solutions/generated/cirinpen_019_dfaba7cef14e53f5.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/dfaba7cef14e53f5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@20", "density": 0.7572204985441312, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 6.944, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.20.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "6.944+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.944, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@20", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "6.944+", "metric_symbol": "s", "metric_value": 6.944, "reference_text": "s = 6.944+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.20.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.20.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 6.944+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "d513055d785b23f7", "improvement": -0.0007124298362715109, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4085836122521584e-06, "max_pair_overlap_depth": -2.3984136221066876e-05, "metric_expression": "6.94471", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.9447124298362715, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.944, "setup": "cirinpen", "side": 6.9447124298362715, "solution_path": "data/solutions/generated/cirinpen_020_d513055d785b23f7.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d513055d785b23f7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@21", "density": 0.7590915818467144, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 7.107, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.21.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "7.107+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.107, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@21", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "7.107+", "metric_symbol": "s", "metric_value": 7.107, "reference_text": "s = 7.107+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.21.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.21.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 7.107+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "71add6eacc6c4fb9", "improvement": -0.0004368549852129533, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.952484924405695e-06, "max_pair_overlap_depth": -3.840822292655588e-05, "metric_expression": "7.10744", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.107436854985213, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.107, "setup": "cirinpen", "side": 7.107436854985213, "solution_path": "data/solutions/generated/cirinpen_021_71add6eacc6c4fb9.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/71add6eacc6c4fb9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@22", "density": 0.7595290345154431, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 7.271, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.22.gif", "friedman_metric_expression": "7.271+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.271, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@22", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "7.271+", "metric_symbol": "s", "metric_value": 7.271, "reference_text": "s = 7.271+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.22.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.22.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 7.271+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "ebdb05232e56526e", "improvement": -0.0015983061562394596, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.413438632810411e-06, "max_pair_overlap_depth": -6.856237147889743e-05, "metric_expression": "7.27260", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.272598306156239, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.271, "setup": "cirinpen", "side": 7.272598306156239, "solution_path": "data/solutions/generated/cirinpen_022_ebdb05232e56526e.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/ebdb05232e56526e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@23", "density": 0.7675010590620791, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 7.397, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.23.gif", "friedman_metric_expression": "7.397+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.397, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@23", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "7.397+", "metric_symbol": "s", "metric_value": 7.397, "reference_text": "s = 7.397+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.23.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.23.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 7.397+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "0115bd21477c01e6", "improvement": -0.0003280102549396702, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.583943801847681e-07, "max_pair_overlap_depth": -3.4243400256706025e-05, "metric_expression": "7.39733", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.39732801025494, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.397, "setup": "cirinpen", "side": 7.39732801025494, "solution_path": "data/solutions/generated/cirinpen_023_0115bd21477c01e6.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/0115bd21477c01e6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@24", "density": 0.7719374015643087, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 7.534, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.24.gif", "friedman_metric_expression": "7.534+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.534, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@24", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "7.534+", "metric_symbol": "s", "metric_value": 7.534, "reference_text": "s = 7.534+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.24.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.24.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 7.534+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "9eb26a95274f1d1d", "improvement": -0.0006837609794780874, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.468927518428643e-06, "max_pair_overlap_depth": -2.3713548386705696e-05, "metric_expression": "7.53468", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.534683760979478, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.534, "setup": "cirinpen", "side": 7.534683760979478, "solution_path": "data/solutions/generated/cirinpen_024_9eb26a95274f1d1d.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/9eb26a95274f1d1d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@1", "density": 0.7853971453379307, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs1.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "cs1.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs1.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "cs1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "329c377d412c468f", "improvement": -1.2962348967526793e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0795596527835016e-07, "max_pair_overlap_depth": 0.0, "metric_expression": "2.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0000012962348968, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "cirinsqu", "side": 2.0000012962348968, "solution_path": "data/solutions/generated/cirinsqu_001_329c377d412c468f.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/329c377d412c468f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@2", "density": 0.5390070210000131, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.414, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs2.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + \u221a2 = 3.414+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.414213562373095, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2 + \u221a2 = 3.414+", "metric_symbol": "s", "metric_value": 3.414, "reference_text": "s = 2 + \u221a2 = 3.414+ | Trivial.", "source_image": "cs2.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs2.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + \u221a2 = 3.414+ | Trivial.", "friedman_source_image": "cs2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "e3bab8445b304ebe", "improvement": -1.6036588933232565e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.1788679802625666e-06, "max_pair_overlap_depth": -1.6252235923275293e-05, "metric_expression": "3.41423", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.414229598962028, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.414213562373095, "setup": "cirinsqu", "side": 3.414229598962028, "solution_path": "data/solutions/generated/cirinsqu_002_e3bab8445b304ebe.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/e3bab8445b304ebe.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@3", "density": 0.6096071430698954, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.931, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs3.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + 1/\u221a2 + \u221a6/2 = 3.931+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.9318516525781364, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2 + 1/\u221a2 + \u221a6/2 = 3.931+", "metric_symbol": "s", "metric_value": 3.931, "reference_text": "s = 2 + 1/\u221a2 + \u221a6/2 = 3.931+ | Trivial.", "source_image": "cs3.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs3.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + 1/\u221a2 + \u221a6/2 = 3.931+ | Trivial.", "friedman_source_image": "cs3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "63c314af1da3741c", "improvement": -0.00012146637938892368, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.540614135605807e-06, "max_pair_overlap_depth": -7.777950709542125e-05, "metric_expression": "3.93197", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.9319731189575253, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.9318516525781364, "setup": "cirinsqu", "side": 3.9319731189575253, "solution_path": "data/solutions/generated/cirinsqu_003_63c314af1da3741c.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/63c314af1da3741c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@4", "density": 0.7853846601471004, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs4.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@4", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "s = 4 | Trivial.", "source_image": "cs4.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs4.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 4 | Trivial.", "friedman_source_image": "cs4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "9917d423eeeb95cb", "improvement": -3.438618804896265e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3561316251363706e-06, "max_pair_overlap_depth": -2.9461600919766795e-05, "metric_expression": "4.00003", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.000034386188049, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.0, "setup": "cirinsqu", "side": 4.000034386188049, "solution_path": "data/solutions/generated/cirinsqu_004_9917d423eeeb95cb.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/9917d423eeeb95cb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@5", "density": 0.6737513675455145, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.828, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs5.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + 2\u221a2 = 4.828+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.82842712474619, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2 + 2\u221a2 = 4.828+", "metric_symbol": "s", "metric_value": 4.828, "reference_text": "s = 2 + 2\u221a2 = 4.828+ | Trivial.", "source_image": "cs5.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs5.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + 2\u221a2 = 4.828+ | Trivial.", "friedman_source_image": "cs5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "f91bd37c36f9320b", "improvement": -4.922638742588248e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.7157366511154635e-07, "max_pair_overlap_depth": -2.294469225416762e-05, "metric_expression": "4.82848", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.828476351133616, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.82842712474619, "setup": "cirinsqu", "side": 4.828476351133616, "solution_path": "data/solutions/generated/cirinsqu_005_f91bd37c36f9320b.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/f91bd37c36f9320b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@6", "density": 0.6639170340529372, "friedman_analytical_or_proved": true, "friedman_credit": "Graham", "friedman_date": "1963", "friedman_display_metric_value": 5.328, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs6.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + 12/\u221a13 = 5.328+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.328201177351374, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@6", "credit": "Graham", "date": "1963", "family_updated": "", "metric_expression": "2 + 12/\u221a13 = 5.328+", "metric_symbol": "s", "metric_value": 5.328, "reference_text": "s = 2 + 12/\u221a13 = 5.328+ | Proved by Graham in 1963.", "source_image": "cs6.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs6.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + 12/\u221a13 = 5.328+ | Proved by Graham in 1963.", "friedman_source_image": "cs6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "96dda57e28868925", "improvement": -0.00016000570243512868, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.928735258591388e-06, "max_pair_overlap_depth": -7.200734794432506e-05, "metric_expression": "5.32836", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.32836118305381, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.328201177351374, "setup": "cirinsqu", "side": 5.32836118305381, "solution_path": "data/solutions/generated/cirinsqu_006_96dda57e28868925.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Graham", "svg_path": "data/svg/96dda57e28868925.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@7", "density": 0.669268877528072, "friedman_analytical_or_proved": true, "friedman_credit": "Schaer", "friedman_date": "1964", "friedman_display_metric_value": 5.732, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs7.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "4 + \u221a3 = 5.732+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.732050807568878, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@7", "credit": "Schaer", "date": "1964", "family_updated": "", "metric_expression": "4 + \u221a3 = 5.732+", "metric_symbol": "s", "metric_value": 5.732, "reference_text": "s = 4 + \u221a3 = 5.732+ | Proved by Schaer in 1964.", "source_image": "cs7.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs7.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 4 + \u221a3 = 5.732+ | Proved by Schaer in 1964.", "friedman_source_image": "cs7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "7e4d3361af467e5d", "improvement": -0.0001796376853517856, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.33238067148811e-06, "max_pair_overlap_depth": -6.633595249638802e-05, "metric_expression": "5.73223", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.732230445254229, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.732050807568878, "setup": "cirinsqu", "side": 5.732230445254229, "solution_path": "data/solutions/generated/cirinsqu_007_7e4d3361af467e5d.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Schaer", "svg_path": "data/svg/7e4d3361af467e5d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@8", "density": 0.7309263604724501, "friedman_analytical_or_proved": true, "friedman_credit": "Schaer/Meir", "friedman_date": "1964", "friedman_display_metric_value": 5.863, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs8.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + \u221a2 + \u221a6 = 5.863+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.863703305156273, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@8", "credit": "Schaer/Meir", "date": "1964", "family_updated": "", "metric_expression": "2 + \u221a2 + \u221a6 = 5.863+", "metric_symbol": "s", "metric_value": 5.863, "reference_text": "s = 2 + \u221a2 + \u221a6 = 5.863+ | Proved by Schaer/Meir in 1964.", "source_image": "cs8.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs8.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + \u221a2 + \u221a6 = 5.863+ | Proved by Schaer/Meir in 1964.", "friedman_source_image": "cs8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "67f6750a9af94d2c", "improvement": -0.0001502747470683019, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.247320970871769e-06, "max_pair_overlap_depth": -5.202375940349668e-05, "metric_expression": "5.86385", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.863853579903341, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.863703305156273, "setup": "cirinsqu", "side": 5.863853579903341, "solution_path": "data/solutions/generated/cirinsqu_008_67f6750a9af94d2c.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Schaer/Meir", "svg_path": "data/svg/67f6750a9af94d2c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@9", "density": 0.7853720614609764, "friedman_analytical_or_proved": true, "friedman_credit": "Schaer", "friedman_date": "1964", "friedman_display_metric_value": 6.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs9.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@9", "credit": "Schaer", "date": "1964", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Proved by Schaer in 1964.", "source_image": "cs9.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs9.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 6 | Proved by Schaer in 1964.", "friedman_source_image": "cs9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "a35561fa5a518c8b", "improvement": -9.970453832330861e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.26657331825875e-06, "max_pair_overlap_depth": -3.06706256441025e-05, "metric_expression": "6.00010", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.000099704538323, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.0, "setup": "cirinsqu", "side": 6.000099704538323, "solution_path": "data/solutions/generated/cirinsqu_009_a35561fa5a518c8b.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Schaer", "svg_path": "data/svg/a35561fa5a518c8b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@10", "density": 0.6900075339157021, "friedman_analytical_or_proved": true, "friedman_credit": "De Groot", "friedman_date": "1990", "friedman_display_metric_value": 6.747, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs10.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "6.747+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.747, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@10", "credit": "De Groot", "date": "1990", "family_updated": "", "metric_expression": "6.747+", "metric_symbol": "s", "metric_value": 6.747, "reference_text": "s = 6.747+ | Proved by De Groot in 1990.", "source_image": "cs10.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs10.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 6.747+ | Proved by De Groot in 1990.", "friedman_source_image": "cs10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "522948d614943781", "improvement": -0.0005796538825402209, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.6772848518975536e-06, "max_pair_overlap_depth": -4.0928067794876455e-05, "metric_expression": "6.74758", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.74757965388254, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.747, "setup": "cirinsqu", "side": 6.74757965388254, "solution_path": "data/solutions/generated/cirinsqu_10_522948d614943781.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "De Groot", "svg_path": "data/svg/522948d614943781.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@11", "density": 0.7006956988559802, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_display_metric_value": 7.022, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs11.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "7.022+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.022, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@11", "credit": "Peikert", "date": "1991", "family_updated": "", "metric_expression": "7.022+", "metric_symbol": "s", "metric_value": 7.022, "reference_text": "s = 7.022+ | Proved by Peikert in 1991.", "source_image": "cs11.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs11.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 7.022+ | Proved by Peikert in 1991.", "friedman_source_image": "cs11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "b0ae38086de8cdf9", "improvement": -0.0007394033277021705, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.667419736983149e-06, "max_pair_overlap_depth": -2.585792898823769e-05, "metric_expression": "7.02274", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.022739403327702, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.022, "setup": "cirinsqu", "side": 7.022739403327702, "solution_path": "data/solutions/generated/cirinsqu_011_b0ae38086de8cdf9.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Peikert", "svg_path": "data/svg/b0ae38086de8cdf9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@12", "density": 0.7384288108172983, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_display_metric_value": 7.144, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs12.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + 15\u221a(2/17) = 7.144+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.1449575542752655, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@12", "credit": "Peikert", "date": "1991", "family_updated": "", "metric_expression": "2 + 15\u221a(2/17) = 7.144+", "metric_symbol": "s", "metric_value": 7.144, "reference_text": "s = 2 + 15\u221a(2/17) = 7.144+ | Proved by Peikert in 1991.", "source_image": "cs12.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs12.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + 15\u221a(2/17) = 7.144+ | Proved by Peikert in 1991.", "friedman_source_image": "cs12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "e58733a8646795ab", "improvement": -0.0001906757478522536, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.939770909988098e-06, "max_pair_overlap_depth": -5.93949466169974e-05, "metric_expression": "7.14515", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.145148230023118, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.1449575542752655, "setup": "cirinsqu", "side": 7.145148230023118, "solution_path": "data/solutions/generated/cirinsqu_012_e58733a8646795ab.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Peikert", "svg_path": "data/svg/e58733a8646795ab.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@13", "density": 0.7332320892098975, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_display_metric_value": 7.463, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs13.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "7.463+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.463, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@13", "credit": "Peikert", "date": "1991", "family_updated": "", "metric_expression": "7.463+", "metric_symbol": "s", "metric_value": 7.463, "reference_text": "s = 7.463+ | Proved by Peikert in 1991.", "source_image": "cs13.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs13.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 7.463+ | Proved by Peikert in 1991.", "friedman_source_image": "cs13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "60997371c312edb4", "improvement": -0.0002137620977080701, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.323292483705444e-06, "max_pair_overlap_depth": -3.8715255959331785e-05, "metric_expression": "7.46321", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.463213762097708, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.463, "setup": "cirinsqu", "side": 7.463213762097708, "solution_path": "data/solutions/generated/cirinsqu_013_60997371c312edb4.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Peikert", "svg_path": "data/svg/60997371c312edb4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@14", "density": 0.7356508336971848, "friedman_analytical_or_proved": true, "friedman_credit": "Wengerodt", "friedman_date": "1987", "friedman_display_metric_value": 7.732, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs14.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "6 + \u221a3 = 7.732+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.732050807568878, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@14", "credit": "Wengerodt", "date": "1987", "family_updated": "", "metric_expression": "6 + \u221a3 = 7.732+", "metric_symbol": "s", "metric_value": 7.732, "reference_text": "s = 6 + \u221a3 = 7.732+ | Proved by Wengerodt in 1987.", "source_image": "cs14.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs14.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 6 + \u221a3 = 7.732+ | Proved by Wengerodt in 1987.", "friedman_source_image": "cs14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "2ccdf5f3d4bee77b", "improvement": -0.0001493623202817318, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.480532338595026e-07, "max_pair_overlap_depth": -3.0206326999682176e-05, "metric_expression": "7.73220", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.732200169889159, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.732050807568878, "setup": "cirinsqu", "side": 7.732200169889159, "solution_path": "data/solutions/generated/cirinsqu_014_2ccdf5f3d4bee77b.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Wengerodt", "svg_path": "data/svg/2ccdf5f3d4bee77b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@15", "density": 0.7620259985870776, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_display_metric_value": 7.863, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs15.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "4 + \u221a2 + \u221a6 = 7.863+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.863703305156273, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@15", "credit": "Peikert", "date": "1991", "family_updated": "", "metric_expression": "4 + \u221a2 + \u221a6 = 7.863+", "metric_symbol": "s", "metric_value": 7.863, "reference_text": "s = 4 + \u221a2 + \u221a6 = 7.863+ | Proved by Peikert in 1991.", "source_image": "cs15.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs15.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 4 + \u221a2 + \u221a6 = 7.863+ | Proved by Peikert in 1991.", "friedman_source_image": "cs15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "edc16b42d64e4d82", "improvement": -0.00015485417222382836, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.610873706565542e-06, "max_pair_overlap_depth": -3.564256081922679e-05, "metric_expression": "7.86386", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.863858159328497, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.863703305156273, "setup": "cirinsqu", "side": 7.863858159328497, "solution_path": "data/solutions/generated/cirinsqu_015_edc16b42d64e4d82.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Peikert", "svg_path": "data/svg/edc16b42d64e4d82.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@16", "density": 0.7853654831135446, "friedman_analytical_or_proved": true, "friedman_credit": "Wengerodt", "friedman_date": "1983", "friedman_display_metric_value": 8.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs16.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "8", "friedman_metric_symbol": "s", "friedman_metric_value": 8.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@16", "credit": "Wengerodt", "date": "1983", "family_updated": "", "metric_expression": "8", "metric_symbol": "s", "metric_value": 8.0, "reference_text": "s = 8 | Proved by Wengerodt in 1983.", "source_image": "cs16.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs16.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 8 | Proved by Wengerodt in 1983.", "friedman_source_image": "cs16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "6ef91613d0db44e8", "improvement": -0.00016644451351055523, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.383802090528576e-06, "max_pair_overlap_depth": -3.451016213729119e-05, "metric_expression": "8.00017", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.00016644451351, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.0, "setup": "cirinsqu", "side": 8.00016644451351, "solution_path": "data/solutions/generated/cirinsqu_016_6ef91613d0db44e8.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Wengerodt", "svg_path": "data/svg/6ef91613d0db44e8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@17", "density": 0.7333955245290497, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_display_metric_value": 8.532, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs17.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "8.532+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.532, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@17", "credit": "Peikert", "date": "1991", "family_updated": "", "metric_expression": "8.532+", "metric_symbol": "s", "metric_value": 8.532, "reference_text": "s = 8.532+ | Proved by Peikert in 1991.", "source_image": "cs17.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs17.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 8.532+ | Proved by Peikert in 1991.", "friedman_source_image": "cs17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "9211255584acb7a4", "improvement": -0.001560450998908891, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6768059695481128e-06, "max_pair_overlap_depth": -3.5588125128604986e-05, "metric_expression": "8.53356", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.533560450998909, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.532, "setup": "cirinsqu", "side": 8.533560450998909, "solution_path": "data/solutions/generated/cirinsqu_017_9211255584acb7a4.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Peikert", "svg_path": "data/svg/9211255584acb7a4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@18", "density": 0.7546080214690231, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_display_metric_value": 8.656, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs18.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + 24/\u221a13 = 8.656+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.656402354702749, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@18", "credit": "Peikert", "date": "1991", "family_updated": "", "metric_expression": "2 + 24/\u221a13 = 8.656+", "metric_symbol": "s", "metric_value": 8.656, "reference_text": "s = 2 + 24/\u221a13 = 8.656+ | Proved by Peikert in 1991.", "source_image": "cs18.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs18.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + 24/\u221a13 = 8.656+ | Proved by Peikert in 1991.", "friedman_source_image": "cs18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "4872462eca76de82", "improvement": -0.0002600318786036837, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.585640835636951e-06, "max_pair_overlap_depth": -5.7251545610981225e-05, "metric_expression": "8.65666", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.656662386581353, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.656402354702749, "setup": "cirinsqu", "side": 8.656662386581353, "solution_path": "data/solutions/generated/cirinsqu_018_4872462eca76de82.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Peikert", "svg_path": "data/svg/4872462eca76de82.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@19", "density": 0.752224113091453, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_display_metric_value": 8.907, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs19.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "8.907+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.907, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@19", "credit": "Peikert", "date": "1991", "family_updated": "", "metric_expression": "8.907+", "metric_symbol": "s", "metric_value": 8.907, "reference_text": "s = 8.907+ | Proved by Peikert in 1991.", "source_image": "cs19.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs19.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 8.907+ | Proved by Peikert in 1991.", "friedman_source_image": "cs19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "72fa8cf8e074fd32", "improvement": -0.0009569875134012307, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.019564082723974e-06, "max_pair_overlap_depth": -6.564483433546542e-05, "metric_expression": "8.90796", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.907956987513401, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.907, "setup": "cirinsqu", "side": 8.907956987513401, "solution_path": "data/solutions/generated/cirinsqu_019_72fa8cf8e074fd32.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Peikert", "svg_path": "data/svg/72fa8cf8e074fd32.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@20", "density": 0.7794478091956536, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_display_metric_value": 8.978, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs20.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "130/17 + 16/17\u221a2 = 8.978+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.978083352821736, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@20", "credit": "Peikert", "date": "1991", "family_updated": "", "metric_expression": "130/17 + 16/17\u221a2 = 8.978+", "metric_symbol": "s", "metric_value": 8.978, "reference_text": "s = 130/17 + 16/17\u221a2 = 8.978+ | Proved by Peikert in 1991.", "source_image": "cs20.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs20.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 130/17 + 16/17\u221a2 = 8.978+ | Proved by Peikert in 1991.", "friedman_source_image": "cs20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "ed16784370181dab", "improvement": -0.00026421749945981787, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3975782322539487e-06, "max_pair_overlap_depth": -5.140241392753708e-05, "metric_expression": "8.97835", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.978347570321196, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.978083352821736, "setup": "cirinsqu", "side": 8.978347570321196, "solution_path": "data/solutions/generated/cirinsqu_020_ed16784370181dab.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Peikert", "svg_path": "data/svg/ed16784370181dab.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@21", "density": 0.7531827030031223, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman Packing Center", "friedman_date": "", "friedman_display_metric_value": 9.358, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs21.gif", "friedman_metric_expression": "9.358+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.358, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinsqu@21", "credit": "Erich Friedman Packing Center", "date": "", "family_updated": "", "metric_expression": "9.358+", "metric_symbol": "s", "metric_value": 9.358, "reference_text": "s = 9.358+", "source_image": "cs21.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs21.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 9.358+", "friedman_source_image": "cs21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "65afc927a4d3cb10", "improvement": -0.0011070505635846217, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.857662265602471e-06, "max_pair_overlap_depth": -3.291297220409106e-05, "metric_expression": "9.35911", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.359107050563585, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.358, "setup": "cirinsqu", "side": 9.359107050563585, "solution_path": "data/solutions/generated/cirinsqu_021_65afc927a4d3cb10.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman Packing Center", "svg_path": "data/svg/65afc927a4d3cb10.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@22", "density": 0.7716499915329439, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman Packing Center", "friedman_date": "", "friedman_display_metric_value": 9.463, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs22.gif", "friedman_metric_expression": "9.463+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.463, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "cirinsqu@22", "credit": "Erich Friedman Packing Center", "date": "", "family_updated": "", "metric_expression": "9.463+", "metric_symbol": "s", "metric_value": 9.463, "reference_text": "s = 9.463+", "source_image": "cs22.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs22.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 9.463+", "friedman_source_image": "cs22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "27d48d864449f174", "improvement": -0.0010297949122062278, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1647620365984324e-06, "max_pair_overlap_depth": -2.796224374757017e-05, "metric_expression": "9.46403", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.464029794912205, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.463, "setup": "cirinsqu", "side": 9.464029794912205, "solution_path": "data/solutions/generated/cirinsqu_022_27d48d864449f174.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman Packing Center", "svg_path": "data/svg/27d48d864449f174.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@23", "density": 0.7628623175184639, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman Packing Center", "friedman_date": "", "friedman_display_metric_value": 9.727, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs23.gif", "friedman_metric_expression": "2 + 2\u221a2 + 2\u221a6 = 9.727+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.727406610312546, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@23", "credit": "Erich Friedman Packing Center", "date": "", "family_updated": "", "metric_expression": "2 + 2\u221a2 + 2\u221a6 = 9.727+", "metric_symbol": "s", "metric_value": 9.727, "reference_text": "s = 2 + 2\u221a2 + 2\u221a6 = 9.727+", "source_image": "cs23.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs23.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + 2\u221a2 + 2\u221a6 = 9.727+", "friedman_source_image": "cs23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "cfa99060ee2203a1", "improvement": -0.004899781121649127, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8298221013957061e-06, "max_pair_overlap_depth": -2.6081243190478887e-05, "metric_expression": "9.73231", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.732306391434195, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.727406610312546, "setup": "cirinsqu", "side": 9.732306391434195, "solution_path": "data/solutions/generated/cirinsqu_023_cfa99060ee2203a1.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman Packing Center", "svg_path": "data/svg/cfa99060ee2203a1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@24", "density": 0.7749295071503051, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman Packing Center", "friedman_date": "", "friedman_display_metric_value": 9.863, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs24.gif", "friedman_metric_expression": "6 + \u221a2 + \u221a6 = 9.863+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.863703305156273, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@24", "credit": "Erich Friedman Packing Center", "date": "", "family_updated": "", "metric_expression": "6 + \u221a2 + \u221a6 = 9.863+", "metric_symbol": "s", "metric_value": 9.863, "reference_text": "s = 6 + \u221a2 + \u221a6 = 9.863+", "source_image": "cs24.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs24.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 6 + \u221a2 + \u221a6 = 9.863+", "friedman_source_image": "cs24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "e2eca298edbdb88c", "improvement": -0.0002148079781072454, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.506144878683841e-06, "max_pair_overlap_depth": -4.0021533562306644e-05, "metric_expression": "9.86392", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.86391811313438, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.863703305156273, "setup": "cirinsqu", "side": 9.86391811313438, "solution_path": "data/solutions/generated/cirinsqu_024_e2eca298edbdb88c.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman Packing Center", "svg_path": "data/svg/e2eca298edbdb88c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirintri@1", "density": 0.6045962978262086, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.464, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct1.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "2\u221a3 = 3.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.4641016151377544, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2\u221a3 = 3.464+", "metric_symbol": "s", "metric_value": 3.464, "reference_text": "s = 2\u221a3 = 3.464+ | Trivial.", "source_image": "ct1.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct1.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 2\u221a3 = 3.464+ | Trivial.", "friedman_source_image": "ct1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "10a7a380c7f5376a", "improvement": -9.998878353734142e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7091087705090047e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "3.46411", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.464111614016108, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.4641016151377544, "setup": "cirintri", "side": 3.464111614016108, "solution_path": "data/solutions/generated/cirintri_001_10a7a380c7f5376a.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/10a7a380c7f5376a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirintri@2", "density": 0.48598475821399, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.464, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct2.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "2 + 2\u221a3 = 5.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.464101615137754, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2 + 2\u221a3 = 5.464+", "metric_symbol": "s", "metric_value": 5.464, "reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "source_image": "ct2.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct2.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "friedman_source_image": "ct2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "f5cde1b8295da3ad", "improvement": -0.00011983415381777718, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7587277048611867e-06, "max_pair_overlap_depth": -7.068795172848752e-05, "metric_expression": "5.46422", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.464221449291572, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.464101615137754, "setup": "cirintri", "side": 5.464221449291572, "solution_path": "data/solutions/generated/cirintri_002_f5cde1b8295da3ad.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/f5cde1b8295da3ad.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirintri@3", "density": 0.7289907317557431, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.464, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct3.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "2 + 2\u221a3 = 5.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.464101615137754, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2 + 2\u221a3 = 5.464+", "metric_symbol": "s", "metric_value": 5.464, "reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "source_image": "ct3.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct3.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "friedman_source_image": "ct3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "fcee9d6e8b7c5ce0", "improvement": -6.888470749721876e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0755666179917966e-07, "max_pair_overlap_depth": -5.0474041760395494e-05, "metric_expression": "5.46417", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.464170499845252, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.464101615137754, "setup": "cirintri", "side": 5.464170499845252, "solution_path": "data/solutions/generated/cirintri_003_fcee9d6e8b7c5ce0.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/fcee9d6e8b7c5ce0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirintri@4", "density": 0.6045810458812538, "friedman_analytical_or_proved": true, "friedman_credit": "Milano", "friedman_date": "1987", "friedman_display_metric_value": 6.928, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct4.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "4\u221a3 = 6.928+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.928203230275509, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@4", "credit": "Milano", "date": "1987", "family_updated": "", "metric_expression": "4\u221a3 = 6.928+", "metric_symbol": "s", "metric_value": 6.928, "reference_text": "s = 4\u221a3 = 6.928+ | Proved by Milano in 1987.", "source_image": "ct4.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct4.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 4\u221a3 = 6.928+ | Proved by Milano in 1987.", "friedman_source_image": "ct4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "9e0c39beb3cc8aa7", "improvement": -0.00010738737436177814, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7330840119143005e-06, "max_pair_overlap_depth": -4.49553106092182e-05, "metric_expression": "6.92831", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.9283106176498706, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.928203230275509, "setup": "cirintri", "side": 6.9283106176498706, "solution_path": "data/solutions/generated/cirintri_004_9e0c39beb3cc8aa7.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Milano", "svg_path": "data/svg/9e0c39beb3cc8aa7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirintri@5", "density": 0.6510985676665063, "friedman_analytical_or_proved": true, "friedman_credit": "Milano", "friedman_date": "1987", "friedman_display_metric_value": 7.464, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct5.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "4 + 2\u221a3 = 7.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.464101615137754, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@5", "credit": "Milano", "date": "1987", "family_updated": "", "metric_expression": "4 + 2\u221a3 = 7.464+", "metric_symbol": "s", "metric_value": 7.464, "reference_text": "s = 4 + 2\u221a3 = 7.464+ | Proved by Milano in 1987.", "source_image": "ct5.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct5.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 4 + 2\u221a3 = 7.464+ | Proved by Milano in 1987.", "friedman_source_image": "ct5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "ad32c3b8e4c714b5", "improvement": -0.0001496519183588063, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.12146637612598e-06, "max_pair_overlap_depth": -3.650753517803196e-05, "metric_expression": "7.46425", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.464251267056113, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.464101615137754, "setup": "cirintri", "side": 7.464251267056113, "solution_path": "data/solutions/generated/cirintri_005_ad32c3b8e4c714b5.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Milano", "svg_path": "data/svg/ad32c3b8e4c714b5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirintri@6", "density": 0.7813295579764934, "friedman_analytical_or_proved": true, "friedman_credit": "Oler/Groemer", "friedman_date": "1961", "friedman_display_metric_value": 7.464, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct6.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "4 + 2\u221a3 = 7.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.464101615137754, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@6", "credit": "Oler/Groemer", "date": "1961", "family_updated": "", "metric_expression": "4 + 2\u221a3 = 7.464+", "metric_symbol": "s", "metric_value": 7.464, "reference_text": "s = 4 + 2\u221a3 = 7.464+ | Proved by Oler/Groemer in 1961.", "source_image": "ct6.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct6.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 4 + 2\u221a3 = 7.464+ | Proved by Oler/Groemer in 1961.", "friedman_source_image": "ct6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "09bddcb97a85d368", "improvement": -9.578668471910134e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.6105130511423482e-06, "max_pair_overlap_depth": -3.3410124574029254e-05, "metric_expression": "7.46420", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.4641974018224735, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.464101615137754, "setup": "cirintri", "side": 7.4641974018224735, "solution_path": "data/solutions/generated/cirintri_006_09bddcb97a85d368.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Oler/Groemer", "svg_path": "data/svg/09bddcb97a85d368.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirintri@7", "density": 0.6370913423934993, "friedman_analytical_or_proved": true, "friedman_credit": "Melissen", "friedman_date": "1993", "friedman_display_metric_value": 8.928, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct7.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "2 + 4\u221a3 = 8.928+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.928203230275509, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@7", "credit": "Melissen", "date": "1993", "family_updated": "", "metric_expression": "2 + 4\u221a3 = 8.928+", "metric_symbol": "s", "metric_value": 8.928, "reference_text": "s = 2 + 4\u221a3 = 8.928+ | Proved by Melissen in 1993.", "source_image": "ct7.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct7.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 2 + 4\u221a3 = 8.928+ | Proved by Melissen in 1993.", "friedman_source_image": "ct7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "1d479488f6f25560", "improvement": -0.00017925098356919023, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.6242968528307244e-06, "max_pair_overlap_depth": -4.768068922000879e-05, "metric_expression": "8.92838", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.928382481259078, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.928203230275509, "setup": "cirintri", "side": 8.928382481259078, "solution_path": "data/solutions/generated/cirintri_007_1d479488f6f25560.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Melissen", "svg_path": "data/svg/1d479488f6f25560.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirintri@8", "density": 0.6718185539703104, "friedman_analytical_or_proved": true, "friedman_credit": "Melissen", "friedman_date": "1993", "friedman_display_metric_value": 9.293, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct8.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "2 + 2\u221a3 + 2\u221a33/3 = 9.293+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.293810046163108, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@8", "credit": "Melissen", "date": "1993", "family_updated": "", "metric_expression": "2 + 2\u221a3 + 2\u221a33/3 = 9.293+", "metric_symbol": "s", "metric_value": 9.293, "reference_text": "s = 2 + 2\u221a3 + 2\u221a33/3 = 9.293+ | Proved by Melissen in 1993.", "source_image": "ct8.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct8.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 2 + 2\u221a3 + 2\u221a33/3 = 9.293+ | Proved by Melissen in 1993.", "friedman_source_image": "ct8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "ad6e4ca149e6364f", "improvement": -0.0010662654394817395, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.090428418316975e-06, "max_pair_overlap_depth": -4.461887232398709e-05, "metric_expression": "9.29488", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.29487631160259, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.293810046163108, "setup": "cirintri", "side": 9.29487631160259, "solution_path": "data/solutions/generated/cirintri_008_ad6e4ca149e6364f.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Melissen", "svg_path": "data/svg/ad6e4ca149e6364f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirintri@9", "density": 0.728985395977573, "friedman_analytical_or_proved": true, "friedman_credit": "Melissen", "friedman_date": "1993", "friedman_display_metric_value": 9.464, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct9.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "6 + 2\u221a3 = 9.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.464101615137755, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@9", "credit": "Melissen", "date": "1993", "family_updated": "", "metric_expression": "6 + 2\u221a3 = 9.464+", "metric_symbol": "s", "metric_value": 9.464, "reference_text": "s = 6 + 2\u221a3 = 9.464+ | Proved by Melissen in 1993.", "source_image": "ct9.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct9.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 6 + 2\u221a3 = 9.464+ | Proved by Melissen in 1993.", "friedman_source_image": "ct9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "108d2156f1819ef5", "improvement": -0.00015394823483561026, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.43897889048894e-06, "max_pair_overlap_depth": -2.63301951002326e-05, "metric_expression": "9.46426", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.46425556337259, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.464101615137755, "setup": "cirintri", "side": 9.46425556337259, "solution_path": "data/solutions/generated/cirintri_009_108d2156f1819ef5.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Melissen", "svg_path": "data/svg/108d2156f1819ef5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirintri@10", "density": 0.8099824382101458, "friedman_analytical_or_proved": true, "friedman_credit": "Oler/Groemer", "friedman_date": "1961", "friedman_display_metric_value": 9.464, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct10.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "6 + 2\u221a3 = 9.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.464101615137755, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@10", "credit": "Oler/Groemer", "date": "1961", "family_updated": "", "metric_expression": "6 + 2\u221a3 = 9.464+", "metric_symbol": "s", "metric_value": 9.464, "reference_text": "s = 6 + 2\u221a3 = 9.464+ | Proved by Oler/Groemer in 1961.", "source_image": "ct10.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct10.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 6 + 2\u221a3 = 9.464+ | Proved by Oler/Groemer in 1961.", "friedman_source_image": "ct10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "abf88e494059d012", "improvement": -0.00016174822247450038, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.885918628489861e-06, "max_pair_overlap_depth": -4.501428401626484e-05, "metric_expression": "9.46426", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.46426336336023, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.464101615137755, "setup": "cirintri", "side": 9.46426336336023, "solution_path": "data/solutions/generated/cirintri_010_abf88e494059d012.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Oler/Groemer", "svg_path": "data/svg/abf88e494059d012.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirintri@11", "density": 0.693141460882906, "friedman_analytical_or_proved": true, "friedman_credit": "Melissen", "friedman_date": "1993", "friedman_display_metric_value": 10.73, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct11.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "4 + 2\u221a3 + 4\u221a6/3 = 10.730+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.730087938848659, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@11", "credit": "Melissen", "date": "1993", "family_updated": "", "metric_expression": "4 + 2\u221a3 + 4\u221a6/3 = 10.730+", "metric_symbol": "s", "metric_value": 10.73, "reference_text": "s = 4 + 2\u221a3 + 4\u221a6/3 = 10.730+ | Proved by Melissen in 1993.", "source_image": "ct11.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct11.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 4 + 2\u221a3 + 4\u221a6/3 = 10.730+ | Proved by Melissen in 1993.", "friedman_source_image": "ct11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "64f835afcfaa2245", "improvement": -0.00016655033577173128, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7228747402064926e-06, "max_pair_overlap_depth": -3.113241300978231e-05, "metric_expression": "10.73025", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.73025448918443, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 10.730087938848659, "setup": "cirintri", "side": 10.73025448918443, "solution_path": "data/solutions/generated/cirintri_011_64f835afcfaa2245.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Melissen", "svg_path": "data/svg/64f835afcfaa2245.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirintri@12", "density": 0.7289832647467578, "friedman_analytical_or_proved": true, "friedman_credit": "Melissen", "friedman_date": "1994", "friedman_display_metric_value": 10.928, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct12.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "4 + 4\u221a3 = 10.928+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.928203230275509, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@12", "credit": "Melissen", "date": "1994", "family_updated": "", "metric_expression": "4 + 4\u221a3 = 10.928+", "metric_symbol": "s", "metric_value": 10.928, "reference_text": "s = 4 + 4\u221a3 = 10.928+ | Proved by Melissen in 1994.", "source_image": "ct12.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct12.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 4 + 4\u221a3 = 10.928+ | Proved by Melissen in 1994.", "friedman_source_image": "ct12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "c94cd40d17cad41e", "improvement": -0.0001937390204851397, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.790000236816084e-06, "max_pair_overlap_depth": -3.824380327710486e-05, "metric_expression": "10.92840", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.928396969295994, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 10.928203230275509, "setup": "cirintri", "side": 10.928396969295994, "solution_path": "data/solutions/generated/cirintri_012_c94cd40d17cad41e.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Melissen", "svg_path": "data/svg/c94cd40d17cad41e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirintri@13", "density": 0.7248761583522253, "friedman_analytical_or_proved": true, "friedman_credit": "Melissen", "friedman_date": "1993", "friedman_display_metric_value": 11.406, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct13.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "4 + 2\u221a6/3 + 10\u221a3/3 = 11.406+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.406495853751709, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@13", "credit": "Melissen", "date": "1993", "family_updated": "", "metric_expression": "4 + 2\u221a6/3 + 10\u221a3/3 = 11.406+", "metric_symbol": "s", "metric_value": 11.406, "reference_text": "s = 4 + 2\u221a6/3 + 10\u221a3/3 = 11.406+ | Found by Melissen in 1993.", "source_image": "ct13.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct13.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 4 + 2\u221a6/3 + 10\u221a3/3 = 11.406+ | Found by Melissen in 1993.", "friedman_source_image": "ct13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "4ca74ad9707b79ad", "improvement": -0.0003188455403364543, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.27136224545599e-06, "max_pair_overlap_depth": -4.371332125208127e-05, "metric_expression": "11.40681", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 11.406814699292045, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 11.406495853751709, "setup": "cirintri", "side": 11.406814699292045, "solution_path": "data/solutions/generated/cirintri_013_4ca74ad9707b79ad.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Melissen", "svg_path": "data/svg/4ca74ad9707b79ad.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirintri@14", "density": 0.7728234005113342, "friedman_analytical_or_proved": true, "friedman_credit": "Erd\u0151s/Oler", "friedman_date": "1961", "friedman_display_metric_value": 11.464, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct14.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "8 + 2\u221a3 = 11.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.464101615137755, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@14", "credit": "Erd\u0151s/Oler", "date": "1961", "family_updated": "", "metric_expression": "8 + 2\u221a3 = 11.464+", "metric_symbol": "s", "metric_value": 11.464, "reference_text": "s = 8 + 2\u221a3 = 11.464+ | Found by Erd\u0151s/Oler in 1961.", "source_image": "ct14.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct14.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 8 + 2\u221a3 = 11.464+ | Found by Erd\u0151s/Oler in 1961.", "friedman_source_image": "ct14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "67743153538612b8", "improvement": -0.00022378122726074423, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.0042126467086945e-06, "max_pair_overlap_depth": -3.7763457817252544e-05, "metric_expression": "11.46433", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 11.464325396365016, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 11.464101615137755, "setup": "cirintri", "side": 11.464325396365016, "solution_path": "data/solutions/generated/cirintri_014_67743153538612b8.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erd\u0151s/Oler", "svg_path": "data/svg/67743153538612b8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirintri@15", "density": 0.82802371463932, "friedman_analytical_or_proved": true, "friedman_credit": "Erd\u0151s/Groemer", "friedman_date": "1961", "friedman_display_metric_value": 11.464, "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct15.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "8 + 2\u221a3 = 11.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.464101615137755, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@15", "credit": "Erd\u0151s/Groemer", "date": "1961", "family_updated": "", "metric_expression": "8 + 2\u221a3 = 11.464+", "metric_symbol": "s", "metric_value": 11.464, "reference_text": "s = 8 + 2\u221a3 = 11.464+ | Proved by Erd\u0151s/Groemer in 1961.", "source_image": "ct15.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct15.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 8 + 2\u221a3 = 11.464+ | Proved by Erd\u0151s/Groemer in 1961.", "friedman_source_image": "ct15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "2a26f9d337f635e0", "improvement": -0.0002331776658177631, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.377565219179871e-06, "max_pair_overlap_depth": -4.0761680023315705e-05, "metric_expression": "11.46433", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 11.464334792803573, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 11.464101615137755, "setup": "cirintri", "side": 11.464334792803573, "solution_path": "data/solutions/generated/cirintri_015_2a26f9d337f635e0.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erd\u0151s/Groemer", "svg_path": "data/svg/2a26f9d337f635e0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domindom@1", "density": 0.9999892980292665, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/1.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "domindom@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "1. | | s = 1 | Trivial.", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/1.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "1. | | s = 1 | Trivial.", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "6b50d5741feee5dc", "improvement": -5.351028316669115e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6755141583345576e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0000053510283167, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.0, "setup": "domindom", "side": 2.0000107020566333, "solution_path": "data/solutions/generated/domindom_001_6b50d5741feee5dc.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/6b50d5741feee5dc.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domindom@2", "density": 0.5146978614404703, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_display_metric_value": 1.971, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/2.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "(2+\u221a2)/\u221a3 = 1.971+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.9711971193069775, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domindom@2", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "", "metric_expression": "(2+\u221a2)/\u221a3 = 1.971+", "metric_symbol": "s", "metric_value": 1.971, "reference_text": "2. | | s = (2+\u221a2)/\u221a3 = 1.971+ | Found by Erich Friedman in April 2026.", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/2.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "2. | | s = (2+\u221a2)/\u221a3 = 1.971+ | Found by Erich Friedman in April 2026.", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "e1760976ec64bd64", "improvement": -3.97613434226507e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9155926735958673e-06, "max_pair_overlap_depth": -6.0125633082330765e-06, "metric_expression": "1.97124", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.9712368806504001, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.9711971193069775, "setup": "domindom", "side": 3.9424737613008003, "solution_path": "data/solutions/generated/domindom_002_e1760976ec64bd64.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/e1760976ec64bd64.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domindom@3", "density": 0.7499858951262421, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/4.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "domindom@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "3.-4. | | s = 2 | Trivial.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/4.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "3.-4. | | s = 2 | Trivial.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "5194ab3dddc343bb", "improvement": -1.8806763611323163e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3349574317089719e-06, "max_pair_overlap_depth": -6.50598393479697e-06, "metric_expression": "2.00002", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0000188067636113, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "domindom", "side": 4.000037613527223, "solution_path": "data/solutions/generated/domindom_003_5194ab3dddc343bb.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/5194ab3dddc343bb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domindom@4", "density": 0.9999632147512098, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/4.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "domindom@4", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "3.-4. | | s = 2 | Trivial.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/4.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "3.-4. | | s = 2 | Trivial.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "14a703d2c83d5b43", "improvement": -3.6786263687194065e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.672168442576563e-06, "max_pair_overlap_depth": -2.5740489017265176e-05, "metric_expression": "2.00004", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.000036786263687, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "domindom", "side": 4.000073572527374, "solution_path": "data/solutions/generated/domindom_004_14a703d2c83d5b43.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/14a703d2c83d5b43.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domindom@5", "density": 0.7999239260919105, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/5.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "5/2 = 2.5", "friedman_metric_symbol": "s", "friedman_metric_value": 2.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domindom@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5/2 = 2.5", "metric_symbol": "s", "metric_value": 2.5, "reference_text": "5. | | s = 5/2 = 2.5 | Trivial.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/5.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "5. | | s = 5/2 = 2.5 | Trivial.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "af0995e19f0dc8ce", "improvement": -0.00011887395946308388, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.6075584103633105e-07, "max_pair_overlap_depth": -2.297221660940707e-05, "metric_expression": "2.50012", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.500118873959463, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.5, "setup": "domindom", "side": 5.000237747918926, "solution_path": "data/solutions/generated/domindom_005_af0995e19f0dc8ce.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/af0995e19f0dc8ce.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domindom@6", "density": 0.7051360525077088, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_display_metric_value": 2.916, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/6.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "2.916+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.916, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "domindom@6", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "", "metric_expression": "2.916+", "metric_symbol": "s", "metric_value": 2.916, "reference_text": "6. | | s = 2.916+ | Found by Erich Friedman in April 2026.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/6.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "6. | | s = 2.916+ | Found by Erich Friedman in April 2026.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "0f3d5defa1e042a8", "improvement": -0.001018377106842383, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.01302900812739e-06, "max_pair_overlap_depth": -7.57681649177222e-06, "metric_expression": "2.91702", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.9170183771068423, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.916, "setup": "domindom", "side": 5.834036754213685, "solution_path": "data/solutions/generated/domindom_006_0f3d5defa1e042a8.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/0f3d5defa1e042a8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domindom@7", "density": 0.777726224180711, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "domindom@7", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "7.-9. | | s = 3 | Trivial.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "7.-9. | | s = 3 | Trivial.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "7b5335d8b8c4a5db", "improvement": -9.942973726095872e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3331344280185253e-06, "max_pair_overlap_depth": -2.1961883454491016e-05, "metric_expression": "3.00010", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.000099429737261, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.0, "setup": "domindom", "side": 6.000198859474522, "solution_path": "data/solutions/generated/domindom_007_7b5335d8b8c4a5db.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/7b5335d8b8c4a5db.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domindom@8", "density": 0.8888442639489805, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "domindom@8", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "7.-9. | | s = 3 | Trivial.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "7.-9. | | s = 3 | Trivial.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "953d10b3e926402a", "improvement": -7.530742160444248e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.80012014980602e-06, "max_pair_overlap_depth": -1.8965164302886528e-05, "metric_expression": "3.00008", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0000753074216044, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.0, "setup": "domindom", "side": 6.000150614843209, "solution_path": "data/solutions/generated/domindom_008_953d10b3e926402a.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/953d10b3e926402a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domindom@9", "density": 0.9999668695349745, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "domindom@9", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "7.-9. | | s = 3 | Trivial.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/9.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "7.-9. | | s = 3 | Trivial.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "43b9630822b40990", "improvement": -4.9696932403531235e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7542337882889854e-07, "max_pair_overlap_depth": -3.0527855267026283e-06, "metric_expression": "3.00005", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0000496969324035, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.0, "setup": "domindom", "side": 6.000099393864807, "solution_path": "data/solutions/generated/domindom_009_43b9630822b40990.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/43b9630822b40990.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domindom@10", "density": 0.8162099861183555, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/10.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "7/2 = 3.5", "friedman_metric_symbol": "s", "friedman_metric_value": 3.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domindom@10", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "7/2 = 3.5", "metric_symbol": "s", "metric_value": 3.5, "reference_text": "10. | | s = 7/2 = 3.5 | Trivial.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/10.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "10. | | s = 7/2 = 3.5 | Trivial.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "d7508c45c3f18a7c", "improvement": -0.0002498690138819093, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5739397918324016e-07, "max_pair_overlap_depth": -9.291197802940854e-05, "metric_expression": "3.50025", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.500249869013882, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.5, "setup": "domindom", "side": 7.000499738027764, "solution_path": "data/solutions/generated/domindom_010_d7508c45c3f18a7c.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d7508c45c3f18a7c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domindom@11", "density": 0.7611589259525644, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_display_metric_value": 3.801, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/11.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "(5+\u221a41)/3 = 3.801+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.801041412477616, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domindom@11", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "(5+\u221a41)/3 = 3.801+", "metric_symbol": "s", "metric_value": 3.801, "reference_text": "11. | | s = (5+\u221a41)/3 = 3.801+ | Found by Maurizio Morandi in April 2026.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/11.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "11. | | s = (5+\u221a41)/3 = 3.801+ | Found by Maurizio Morandi in April 2026.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "0fa9d3de612fbf03", "improvement": -0.0004907598320262885, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0757791549262947e-06, "max_pair_overlap_depth": -0.0001019023981195799, "metric_expression": "3.80153", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.8015321723096425, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.801041412477616, "setup": "domindom", "side": 7.603064344619285, "solution_path": "data/solutions/generated/domindom_011_0fa9d3de612fbf03.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/0fa9d3de612fbf03.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domindom@12", "density": 0.7822558234911755, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_display_metric_value": 3.914, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/12.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "5/2+\u221a2 = 3.914+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.914213562373095, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domindom@12", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "5/2+\u221a2 = 3.914+", "metric_symbol": "s", "metric_value": 3.914, "reference_text": "12. | | s = 5/2+\u221a2 = 3.914+ | Found by Maurizio Morandi in April 2026.", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/12.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "12. | | s = 5/2+\u221a2 = 3.914+ | Found by Maurizio Morandi in April 2026.", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "3a75d33bd56228b0", "improvement": -0.0024495751142099564, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.0673284962267076e-07, "max_pair_overlap_depth": -1.4217486933421064e-05, "metric_expression": "3.91666", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.916663137487305, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.914213562373095, "setup": "domindom", "side": 7.83332627497461, "solution_path": "data/solutions/generated/domindom_012_3a75d33bd56228b0.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T03:07:58+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/3a75d33bd56228b0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domindom@14", "density": 0.8749484114386541, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "domindom@14", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "14.-16 | | s = 4 | Trivial.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "14.-16 | | s = 4 | Trivial.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "8be6cbfdbea40909", "improvement": -0.00011792192603543583, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.966859551203129e-06, "max_pair_overlap_depth": -1.688780940467538e-05, "metric_expression": "4.00012", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.000117921926035, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.0, "setup": "domindom", "side": 8.00023584385207, "solution_path": "data/solutions/generated/domindom_014_8be6cbfdbea40909.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/8be6cbfdbea40909.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domindom@15", "density": 0.9374471956142247, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "domindom@15", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "14.-16 | | s = 4 | Trivial.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "14.-16 | | s = 4 | Trivial.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "d2b8e4757dde349c", "improvement": -0.00011265411524785662, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.415030228686277e-06, "max_pair_overlap_depth": -1.0456826571081379e-05, "metric_expression": "4.00011", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.000112654115248, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.0, "setup": "domindom", "side": 8.000225308230496, "solution_path": "data/solutions/generated/domindom_015_d2b8e4757dde349c.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d2b8e4757dde349c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domindom@16", "density": 0.9999595560012681, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "domindom@16", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "14.-16 | | s = 4 | Trivial.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/16.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "14.-16 | | s = 4 | Trivial.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "5102d8436800a7ff", "improvement": -8.08904511222508e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.23688533190969e-06, "max_pair_overlap_depth": -4.621969549978289e-06, "metric_expression": "4.00008", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.000080890451122, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.0, "setup": "domindom", "side": 8.000161780902245, "solution_path": "data/solutions/generated/domindom_016_5102d8436800a7ff.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/5102d8436800a7ff.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domindom@17", "density": 0.8394293686085971, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/18.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "9/2 = 4.5", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domindom@17", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "9/2 = 4.5", "metric_symbol": "s", "metric_value": 4.5, "reference_text": "17.-18 | | s = 9/2 = 4.5 | Trivial.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/18.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "17.-18 | | s = 9/2 = 4.5 | Trivial.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "3b388ddd068a843f", "improvement": -0.00020586075893191946, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.953267209728551e-07, "max_pair_overlap_depth": -5.000451830872166e-05, "metric_expression": "4.50021", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.500205860758932, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.5, "setup": "domindom", "side": 9.000411721517864, "solution_path": "data/solutions/generated/domindom_017_3b388ddd068a843f.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/3b388ddd068a843f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domindom@18", "density": 0.887184224626392, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domindom/18.gif", "friedman_family_updated": "4/3/26", "friedman_metric_expression": "9/2 = 4.5", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domindom@18", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "9/2 = 4.5", "metric_symbol": "s", "metric_value": 4.5, "reference_text": "17.-18 | | s = 9/2 = 4.5 | Trivial.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/domindom/18.gif", "source_page": "https://erich-friedman.github.io/packing/domindom/", "title": "Dominoes in Dominoes"}, "friedman_reference_text": "17.-18 | | s = 9/2 = 4.5 | Trivial.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/domindom/", "friedman_title": "Dominoes in Dominoes", "frontend_seed": true, "id": "6a5fcb6ec4e55187", "improvement": -0.004321147560441219, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4781434060372476e-06, "max_pair_overlap_depth": -4.894490537976637e-05, "metric_expression": "4.50432", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.504321147560441, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.5, "setup": "domindom", "side": 9.008642295120882, "solution_path": "data/solutions/generated/domindom_018_6a5fcb6ec4e55187.json", "source_url": "https://erich-friedman.github.io/packing/domindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/6a5fcb6ec4e55187.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@1", "density": 0.46408935997723705, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.1547, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/1.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "2+2/\u221a3 = 3.15470+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.1547005383792515, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2+2/\u221a3 = 3.15470+", "metric_symbol": "s", "metric_value": 3.1547, "reference_text": "s = 2+2/\u221a3 = 3.15470+ | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/1.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 2+2/\u221a3 = 3.15470+ | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "6121ec989c6c813b", "improvement": -4.165265311817379e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.613940413552034e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "3.15474", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.1547421910323696, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.1547005383792515, "setup": "domintri", "side": 3.1547421910323696, "solution_path": "data/solutions/generated/domintri_001_6121ec989c6c813b.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/6121ec989c6c813b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@2", "density": 0.4973974214603669, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.3094, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/2.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "2+4/\u221a3 = 4.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2+4/\u221a3 = 4.30940+", "metric_symbol": "s", "metric_value": 4.3094, "reference_text": "s = 2+4/\u221a3 = 4.30940+ | Trivial.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/2.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 2+4/\u221a3 = 4.30940+ | Trivial.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "75b0ecc0320e01de", "improvement": -0.00010912245589178582, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.546312299587745e-06, "max_pair_overlap_depth": -2.318487220109855e-05, "metric_expression": "4.30951", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.309510199214395, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.309401076758503, "setup": "domintri", "side": 4.309510199214395, "solution_path": "data/solutions/generated/domintri_002_75b0ecc0320e01de.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/75b0ecc0320e01de.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@3", "density": 0.746073641317824, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.30934, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/3.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "2+4/\u221a3 = 4.30934+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2+4/\u221a3 = 4.30934+", "metric_symbol": "s", "metric_value": 4.30934, "reference_text": "s = 2+4/\u221a3 = 4.30934+ | Trivial.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/3.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 2+4/\u221a3 = 4.30934+ | Trivial.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "ecf54a038a2d7184", "improvement": -0.00017407845325045912, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2511235262659097e-06, "max_pair_overlap_depth": -8.934604283755698e-05, "metric_expression": "4.30958", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.309575155211753, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.309401076758503, "setup": "domintri", "side": 4.309575155211753, "solution_path": "data/solutions/generated/domintri_003_ecf54a038a2d7184.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/ecf54a038a2d7184.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@4", "density": 0.6377999539199563, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 5.38188, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/4.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "5.38188+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.38188, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "domintri@4", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.38188+", "metric_symbol": "s", "metric_value": 5.38188, "reference_text": "s = 5.38188+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/4.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 5.38188+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "6f3730492b03ce4f", "improvement": -0.0002283152146249634, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.401205447247945e-07, "max_pair_overlap_depth": -4.238554796887062e-05, "metric_expression": "5.38211", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.382108315214625, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.38188, "setup": "domintri", "side": 5.382108315214625, "solution_path": "data/solutions/generated/domintri_004_6f3730492b03ce4f.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/6f3730492b03ce4f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@5", "density": 0.7734497127773695, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 5.4641, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/5.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "2+2\u221a3 = 5.46410+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.464101615137754, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@5", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2+2\u221a3 = 5.46410+", "metric_symbol": "s", "metric_value": 5.4641, "reference_text": "s = 2+2\u221a3 = 5.46410+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "5.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/5.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 2+2\u221a3 = 5.46410+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "272a5ede0aa9a415", "improvement": -0.00018713455268937196, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.315600305266359e-07, "max_pair_overlap_depth": -2.2346020378205544e-05, "metric_expression": "5.46429", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.464288749690444, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.464101615137754, "setup": "domintri", "side": 5.464288749690444, "solution_path": "data/solutions/generated/domintri_005_272a5ede0aa9a415.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/272a5ede0aa9a415.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@6", "density": 0.6961017329945272, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 6.3094, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/6.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "4+4/\u221a3 = 6.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@6", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4+4/\u221a3 = 6.30940+", "metric_symbol": "s", "metric_value": 6.3094, "reference_text": "s = 4+4/\u221a3 = 6.30940+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/6.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 4+4/\u221a3 = 6.30940+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "5709487003259292", "improvement": -0.00022971922556713764, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1058985619703807e-06, "max_pair_overlap_depth": -5.695799924376743e-05, "metric_expression": "6.30963", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.30963079598407, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.309401076758503, "setup": "domintri", "side": 6.30963079598407, "solution_path": "data/solutions/generated/domintri_006_5709487003259292.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/5709487003259292.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@7", "density": 0.7379982685276676, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 6.61409, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/7.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "6.61409+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.61409, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "domintri@7", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6.61409+", "metric_symbol": "s", "metric_value": 6.61409, "reference_text": "s = 6.61409+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/7.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 6.61409+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "4f3a41ae14776742", "improvement": -0.004813180227946745, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.155481361422797e-07, "max_pair_overlap_depth": -2.185552101252597e-05, "metric_expression": "6.61890", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.618903180227947, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.61409, "setup": "domintri", "side": 6.618903180227947, "solution_path": "data/solutions/generated/domintri_007_4f3a41ae14776742.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/4f3a41ae14776742.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@8", "density": 0.7218039663224785, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 7.1547, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/8.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "6+2/\u221a3 = 7.15470+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.1547005383792515, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@8", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6+2/\u221a3 = 7.15470+", "metric_symbol": "s", "metric_value": 7.1547, "reference_text": "s = 6+2/\u221a3 = 7.15470+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/8.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 6+2/\u221a3 = 7.15470+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "6c005b2a9a930ec2", "improvement": -0.0001413548740938353, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4194624753243232e-06, "max_pair_overlap_depth": -3.0722639065561275e-05, "metric_expression": "7.15484", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.154841893253345, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.1547005383792515, "setup": "domintri", "side": 7.154841893253345, "solution_path": "data/solutions/generated/domintri_008_6c005b2a9a930ec2.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/6c005b2a9a930ec2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@9", "density": 0.7778159590517906, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 7.3094, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/9.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "5+4/\u221a3 = 7.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@9", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5+4/\u221a3 = 7.30940+", "metric_symbol": "s", "metric_value": 7.3094, "reference_text": "s = 5+4/\u221a3 = 7.30940+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/9.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 5+4/\u221a3 = 7.30940+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "efd3c01a911fbe39", "improvement": -0.0011061321570089433, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4249809133477843e-06, "max_pair_overlap_depth": -9.12510211048545e-05, "metric_expression": "7.31051", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.310507208915512, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.309401076758503, "setup": "domintri", "side": 7.310507208915512, "solution_path": "data/solutions/generated/domintri_009_efd3c01a911fbe39.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/efd3c01a911fbe39.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@10", "density": 0.7955429934788115, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 7.61885, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/10.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "3+8/\u221a3 = 7.61885+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.618802153517006, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@10", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3+8/\u221a3 = 7.61885+", "metric_symbol": "s", "metric_value": 7.61885, "reference_text": "s = 3+8/\u221a3 = 7.61885+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/10.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 3+8/\u221a3 = 7.61885+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "0ce8e56f538c019b", "improvement": -0.0008097611971216168, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.832683484389887e-07, "max_pair_overlap_depth": -3.7959726496283874e-06, "metric_expression": "7.61961", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.6196119147141275, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.618802153517006, "setup": "domintri", "side": 7.6196119147141275, "solution_path": "data/solutions/generated/domintri_010_0ce8e56f538c019b.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/0ce8e56f538c019b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@11", "density": 0.7639001254938724, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 8.1547, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/11.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "7+2/\u221a3 = 8.15470+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.154700538379252, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@11", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "7+2/\u221a3 = 8.15470+", "metric_symbol": "s", "metric_value": 8.1547, "reference_text": "s = 7+2/\u221a3 = 8.15470+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "11.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/11.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 7+2/\u221a3 = 8.15470+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "11.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "9dea260c7a23e4ab", "improvement": -0.0006518555613173049, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.1114403341932665e-06, "max_pair_overlap_depth": -5.305705658820159e-06, "metric_expression": "8.15535", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.15535239394057, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.154700538379252, "setup": "domintri", "side": 8.15535239394057, "solution_path": "data/solutions/generated/domintri_011_9dea260c7a23e4ab.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/9dea260c7a23e4ab.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@12", "density": 0.8025727620592626, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 8.3094, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/12.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "6+4/\u221a3 = 8.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@12", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6+4/\u221a3 = 8.30940+", "metric_symbol": "s", "metric_value": 8.3094, "reference_text": "s = 6+4/\u221a3 = 8.30940+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/12.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 6+4/\u221a3 = 8.30940+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "c7b6e34fcb0ca6b3", "improvement": -0.0008298956488257403, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.6999836404354686e-06, "max_pair_overlap_depth": -5.386448125865861e-06, "metric_expression": "8.31023", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.310230972407329, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.309401076758503, "setup": "domintri", "side": 8.310230972407329, "solution_path": "data/solutions/generated/domintri_012_c7b6e34fcb0ca6b3.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/c7b6e34fcb0ca6b3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@13", "density": 0.8080926405411509, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 8.61885, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/13.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "4+8/\u221a3 = 8.61885+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.618802153517006, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@13", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4+8/\u221a3 = 8.61885+", "metric_symbol": "s", "metric_value": 8.61885, "reference_text": "s = 4+8/\u221a3 = 8.61885+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/13.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 4+8/\u221a3 = 8.61885+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "9f9d19c6f117401b", "improvement": -0.0011683590406832423, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.5415762652602807e-06, "max_pair_overlap_depth": -3.765847597092531e-05, "metric_expression": "8.61997", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.619970512557689, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.618802153517006, "setup": "domintri", "side": 8.619970512557689, "solution_path": "data/solutions/generated/domintri_013_9f9d19c6f117401b.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/9f9d19c6f117401b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@14", "density": 0.8398945758370188, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_display_metric_value": 8.7735, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/14.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "3+10/\u221a3 = 8.77350+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.773502691896258, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@14", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "3+10/\u221a3 = 8.77350+", "metric_symbol": "s", "metric_value": 8.7735, "reference_text": "s = 3+10/\u221a3 = 8.77350+ | Found by Maurizio Morandi | in April 2026.", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/14.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 3+10/\u221a3 = 8.77350+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "333566d5c4b3657c", "improvement": -0.0008746923210960489, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 2.796172321890858e-09, "max_pair_overlap_depth": -3.2457310312317134e-05, "metric_expression": "8.77438", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.774377384217354, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.773502691896258, "setup": "domintri", "side": 8.774377384217354, "solution_path": "data/solutions/generated/domintri_014_333566d5c4b3657c.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/333566d5c4b3657c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@15", "density": 0.7991843102868493, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 9.3094, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/15.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "7+4/\u221a3 = 9.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@15", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "7+4/\u221a3 = 9.30940+", "metric_symbol": "s", "metric_value": 9.3094, "reference_text": "s = 7+4/\u221a3 = 9.30940+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/15.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 7+4/\u221a3 = 9.30940+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "2da1308626a02461", "improvement": -0.001395425408144746, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.5011317742776256e-06, "max_pair_overlap_depth": -8.262234862044249e-05, "metric_expression": "9.31080", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.310796502166648, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.309401076758503, "setup": "domintri", "side": 9.310796502166648, "solution_path": "data/solutions/generated/domintri_015_2da1308626a02461.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/2da1308626a02461.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@16", "density": 0.8249213221645568, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_display_metric_value": 9.4641, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/16.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "6+2\u221a3 = 9.46410+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.464101615137755, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@16", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "6+2\u221a3 = 9.46410+", "metric_symbol": "s", "metric_value": 9.4641, "reference_text": "s = 6+2\u221a3 = 9.46410+ | Found by Maurizio Morandi | in April 2026.", "source_image": "16.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/16.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 6+2\u221a3 = 9.46410+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "cc2a76b6a75c7120", "improvement": -0.0008501822550215365, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.428695004104409e-06, "max_pair_overlap_depth": -2.0153462060745753e-05, "metric_expression": "9.46495", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.464951797392777, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.464101615137755, "setup": "domintri", "side": 9.464951797392777, "solution_path": "data/solutions/generated/domintri_016_cc2a76b6a75c7120.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/cc2a76b6a75c7120.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@17", "density": 0.8218638425440753, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 9.7735, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/17.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "4+10/\u221a3 = 9.77350+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.773502691896258, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@17", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4+10/\u221a3 = 9.77350+", "metric_symbol": "s", "metric_value": 9.7735, "reference_text": "s = 4+10/\u221a3 = 9.77350+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/17.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 4+10/\u221a3 = 9.77350+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "842ace76b15a5c6d", "improvement": -0.0008769524247327354, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.8870325675374086e-06, "max_pair_overlap_depth": -2.297706007370337e-05, "metric_expression": "9.77438", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.774379644320991, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.773502691896258, "setup": "domintri", "side": 9.774379644320991, "solution_path": "data/solutions/generated/domintri_017_842ace76b15a5c6d.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/842ace76b15a5c6d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@18", "density": 0.8433917909368376, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 9.9282, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/18.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "3+4\u221a3 = 9.92820+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.928203230275509, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3+4\u221a3 = 9.92820+", "metric_symbol": "s", "metric_value": 9.9282, "reference_text": "s = 3+4\u221a3 = 9.92820+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/18.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 3+4\u221a3 = 9.92820+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "286272298adf99a4", "improvement": -0.00035637945903843615, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.814371048432239e-06, "max_pair_overlap_depth": -1.8972863250255045e-05, "metric_expression": "9.92856", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.928559609734547, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.928203230275509, "setup": "domintri", "side": 9.928559609734547, "solution_path": "data/solutions/generated/domintri_018_286272298adf99a4.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/286272298adf99a4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@19", "density": 0.8255562955017095, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 10.3094, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/19.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "8+4/\u221a3 = 10.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "8+4/\u221a3 = 10.30940+", "metric_symbol": "s", "metric_value": 10.3094, "reference_text": "s = 8+4/\u221a3 = 10.30940+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/19.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 8+4/\u221a3 = 10.30940+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "77c1eb98f0e7fed4", "improvement": -0.0008236979224669483, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.73171847830086e-06, "max_pair_overlap_depth": -2.8002623395084747e-06, "metric_expression": "10.31022", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.31022477468097, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 10.309401076758503, "setup": "domintri", "side": 10.31022477468097, "solution_path": "data/solutions/generated/domintri_019_77c1eb98f0e7fed4.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/77c1eb98f0e7fed4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@20", "density": 0.843501980040664, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_display_metric_value": 10.4641, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/20.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "7+2\u221a3 = 10.46410+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.464101615137755, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@20", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "7+2\u221a3 = 10.46410+", "metric_symbol": "s", "metric_value": 10.4641, "reference_text": "s = 7+2\u221a3 = 10.46410+ | Found by Maurizio Morandi | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/20.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 7+2\u221a3 = 10.46410+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "19214c32485a435f", "improvement": -0.000835535883558336, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8019716271983103e-06, "max_pair_overlap_depth": -2.85508650477162e-06, "metric_expression": "10.46494", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.464937151021314, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 10.464101615137755, "setup": "domintri", "side": 10.464937151021314, "solution_path": "data/solutions/generated/domintri_020_19214c32485a435f.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/19214c32485a435f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@21", "density": 0.8533496545178485, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_display_metric_value": 10.66025, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/21.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "2+5\u221a3 = 10.66025+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.660254037844387, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@21", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "2+5\u221a3 = 10.66025+", "metric_symbol": "s", "metric_value": 10.66025, "reference_text": "s = 2+5\u221a3 = 10.66025+ | Found by Maurizio Morandi | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/21.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 2+5\u221a3 = 10.66025+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "797030ebf0f8c4e4", "improvement": -0.0010620287314413446, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.564559491289197e-06, "max_pair_overlap_depth": -2.4360684990565318e-05, "metric_expression": "10.66132", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.661316066575829, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 10.660254037844387, "setup": "domintri", "side": 10.661316066575829, "solution_path": "data/solutions/generated/domintri_021_797030ebf0f8c4e4.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/797030ebf0f8c4e4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@22", "density": 0.8506833122891716, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_display_metric_value": 10.9282, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/22.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "4(1+\u221a3) = 10.92820+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.928203230275509, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@22", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "4(1+\u221a3) = 10.92820+", "metric_symbol": "s", "metric_value": 10.9282, "reference_text": "s = 4(1+\u221a3) = 10.92820+ | Found by Maurizio Morandi | in April 2026.", "source_image": "22.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/22.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 4(1+\u221a3) = 10.92820+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "90061b49654f08af", "improvement": -0.0010896323453479795, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.631830815268069e-06, "max_pair_overlap_depth": -1.6046632975275088e-05, "metric_expression": "10.92929", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.929292862620857, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 10.928203230275509, "setup": "domintri", "side": 10.929292862620857, "solution_path": "data/solutions/generated/domintri_022_90061b49654f08af.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/90061b49654f08af.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@23", "density": 0.8536884993646849, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_display_metric_value": 11.1547, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/23.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "10+2/\u221a3 = 11.15470+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.154700538379252, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@23", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "10+2/\u221a3 = 11.15470+", "metric_symbol": "s", "metric_value": 11.1547, "reference_text": "s = 10+2/\u221a3 = 11.15470+ | Found by Maurizio Morandi | in April 2026.", "source_image": "23.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/23.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 10+2/\u221a3 = 11.15470+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "8ca8e97a5947c876", "improvement": -0.0005385385946024002, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.068904299595512e-06, "max_pair_overlap_depth": -1.1497281311445562e-05, "metric_expression": "11.15524", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 11.155239076973855, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 11.154700538379252, "setup": "domintri", "side": 11.155239076973855, "solution_path": "data/solutions/generated/domintri_023_8ca8e97a5947c876.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/8ca8e97a5947c876.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@24", "density": 0.8664947344465272, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_display_metric_value": 11.3094, "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/24.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "9+4/\u221a3 = 11.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "domintri@24", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "9+4/\u221a3 = 11.30940+", "metric_symbol": "s", "metric_value": 11.3094, "reference_text": "s = 9+4/\u221a3 = 11.30940+ | Found by Maurizio Morandi | in April 2026.", "source_image": "24.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/24.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 9+4/\u221a3 = 11.30940+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "f8436aa831ae57e5", "improvement": -0.0012430126589055845, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.95572835399557e-06, "max_pair_overlap_depth": -5.492290923159171e-05, "metric_expression": "11.31064", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 11.310644089417409, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 11.309401076758503, "setup": "domintri", "side": 11.310644089417409, "solution_path": "data/solutions/generated/domintri_024_f8436aa831ae57e5.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/f8436aa831ae57e5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@1", "density": 0.826977987261634, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/1.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "r", "friedman_metric_value": 1.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "r", "metric_value": 1.0, "reference_text": "r = 1 | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/1.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 1 | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "48f5aa37c90550c8", "improvement": -9.284285680699611e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.547655283739573e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.0000092842856807, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.0, "setup": "hexincir", "side": 2.0000185685713614, "solution_path": "data/solutions/generated/hexincir_001_48f5aa37c90550c8.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/48f5aa37c90550c8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@2", "density": 0.508894613048892, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.802, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/2.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a13/2 = 1.802+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.8027756377319946, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a13/2 = 1.802+", "metric_symbol": "r", "metric_value": 1.802, "reference_text": "r = \u221a13/2 = 1.802+ | Trivial.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/2.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a13/2 = 1.802+ | Trivial.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "3b6bd2554e997adc", "improvement": -4.316052946373716e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4989872811899119e-06, "max_pair_overlap_depth": -3.954921521903687e-05, "metric_expression": "1.80282", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.8028187982614583, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.8027756377319946, "setup": "hexincir", "side": 3.6056375965229166, "solution_path": "data/solutions/generated/hexincir_002_3b6bd2554e997adc.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/3b6bd2554e997adc.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@3", "density": 0.6202101203168955, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/3.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "r", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "r", "metric_value": 2.0, "reference_text": "r = 2 | Trivial.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/3.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 2 | Trivial.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "194e619a74e29452", "improvement": -5.624955299809997e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.970405754344824e-06, "max_pair_overlap_depth": -7.230141190991447e-05, "metric_expression": "2.00006", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.000056249552998, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "hexincir", "side": 4.000112499105996, "solution_path": "data/solutions/generated/hexincir_003_194e619a74e29452.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/194e619a74e29452.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@4", "density": 0.6594633839026793, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 2.239, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/4.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(21\u2013\u221a145)/4 = 2.239+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.239601355301926, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@4", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "(21\u2013\u221a145)/4 = 2.239+", "metric_symbol": "r", "metric_value": 2.239, "reference_text": "r = (21\u2013\u221a145)/4 = 2.239+ | Found by Maurizio Morandi | in March 2026.", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/4.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = (21\u2013\u221a145)/4 = 2.239+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "355b11dfc363f5ba", "improvement": -7.70321709873123e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.544625404889757e-07, "max_pair_overlap_depth": -5.057462804924917e-05, "metric_expression": "2.23968", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.2396783874729134, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.239601355301926, "setup": "hexincir", "side": 4.479356774945827, "solution_path": "data/solutions/generated/hexincir_004_355b11dfc363f5ba.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/355b11dfc363f5ba.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@5", "density": 0.6766813833384198, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 2.471, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/5.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2.471+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.471, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@5", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "2.471+", "metric_symbol": "r", "metric_value": 2.471, "reference_text": "r = 2.471+ | Found by Maurizio Morandi | in March 2026.", "source_image": "5.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/5.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 2.471+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "9427b00c077aafc3", "improvement": -0.0009739785189006867, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.673907177263573e-06, "max_pair_overlap_depth": -5.983134966366932e-05, "metric_expression": "2.47197", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.4719739785189008, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.471, "setup": "hexincir", "side": 4.9439479570378015, "solution_path": "data/solutions/generated/hexincir_005_9427b00c077aafc3.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/9427b00c077aafc3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@6", "density": 0.7087991567669789, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.645, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/7.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a7 = 2.645+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.6457513110645907, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@6", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a7 = 2.645+", "metric_symbol": "r", "metric_value": 2.645, "reference_text": "r = \u221a7 = 2.645+ | Trivial. |", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/7.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a7 = 2.645+ | Trivial. |", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "d7d900dd0bba32a3", "improvement": -9.757197521187422e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.0221671226394733e-07, "max_pair_overlap_depth": -3.6674166167594e-05, "metric_expression": "2.64585", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.6458488830398026, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.6457513110645907, "setup": "hexincir", "side": 5.291697766079605, "solution_path": "data/solutions/generated/hexincir_006_d7d900dd0bba32a3.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d7d900dd0bba32a3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@7", "density": 0.8269668154291873, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.645, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/7.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a7 = 2.645+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.6457513110645907, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@7", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a7 = 2.645+", "metric_symbol": "r", "metric_value": 2.645, "reference_text": "r = \u221a7 = 2.645+ | Trivial. |", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/7.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a7 = 2.645+ | Trivial. |", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "5cd27a740cc9b2a5", "improvement": -4.2435284075548196e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.370930279076532e-06, "max_pair_overlap_depth": -2.6143388138111234e-05, "metric_expression": "2.64579", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.6457937463486663, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.6457513110645907, "setup": "hexincir", "side": 5.2915874926973325, "solution_path": "data/solutions/generated/hexincir_007_5cd27a740cc9b2a5.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/5cd27a740cc9b2a5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@8", "density": 0.7426247287224678, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 2.984, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/8.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2.984+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.984, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@8", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "2.984+", "metric_symbol": "r", "metric_value": 2.984, "reference_text": "r = 2.984+ | Found by Maurizio Morandi | in March 2026.", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/8.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 2.984+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "7d27528d78a05a43", "improvement": -0.0007729280237529501, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.6889173538057207e-06, "max_pair_overlap_depth": -1.732806256671271e-05, "metric_expression": "2.98477", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.984772928023753, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.984, "setup": "hexincir", "side": 5.969545856047506, "solution_path": "data/solutions/generated/hexincir_008_7d27528d78a05a43.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/7d27528d78a05a43.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@9", "density": 0.682777017123973, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 3.301, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/9.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3.301+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.301, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@9", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "3.301+", "metric_symbol": "r", "metric_value": 3.301, "reference_text": "r = 3.301+ | Found by Maurizio Morandi | in March 2026.", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/9.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 3.301+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "5f9496662ac0b661", "improvement": -0.000663545504778984, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.641836701819614e-06, "max_pair_overlap_depth": -2.219136600895011e-05, "metric_expression": "3.30166", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.301663545504779, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.301, "setup": "hexincir", "side": 6.603327091009558, "solution_path": "data/solutions/generated/hexincir_009_5f9496662ac0b661.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/5f9496662ac0b661.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@10", "density": 0.6804997422869841, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 3.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/10.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "7/2 = 3.5", "friedman_metric_symbol": "r", "friedman_metric_value": 3.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@10", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "7/2 = 3.5", "metric_symbol": "r", "metric_value": 3.5, "reference_text": "r = 7/2 = 3.5 | Found by Maurizio Morandi | in March 2026.", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/10.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 7/2 = 3.5 | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": false, "id": "8fccd3008565aabb", "improvement": 0.013922608209857135, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.016042661651568e-06, "max_pair_overlap_depth": -3.440098626628085e-05, "metric_expression": "3.48608", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.486077391790143, "n": 10, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.", "record_type": "verified", "reference_side": 3.5, "setup": "hexincir", "side": 6.972154783580286, "solution_path": "data/solutions/generated/hexincir_010_8fccd3008565aabb.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/8fccd3008565aabb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@11", "density": 0.7038726397318542, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 3.605, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/12.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a13 = 3.605+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.605551275463989, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@11", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "\u221a13 = 3.605+", "metric_symbol": "r", "metric_value": 3.605, "reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in March 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/12.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": false, "id": "2d2e76ec34c49fb5", "improvement": 0.010539581436358247, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.0630450586220945e-06, "max_pair_overlap_depth": -3.6222629933746475e-05, "metric_expression": "3.59501", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.595011694027631, "n": 11, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.", "record_type": "verified", "reference_side": 3.605551275463989, "setup": "hexincir", "side": 7.190023388055262, "solution_path": "data/solutions/generated/hexincir_011_2d2e76ec34c49fb5.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/2d2e76ec34c49fb5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@12", "density": 0.7629156641677376, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 3.605, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/12.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a13 = 3.605+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.605551275463989, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@12", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "\u221a13 = 3.605+", "metric_symbol": "r", "metric_value": 3.605, "reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in March 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/12.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "5515c10818a71365", "improvement": -0.0010934493506664644, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.2444141653265035e-06, "max_pair_overlap_depth": -3.49998284549164e-05, "metric_expression": "3.60664", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.6066447248146556, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.605551275463989, "setup": "hexincir", "side": 7.213289449629311, "solution_path": "data/solutions/generated/hexincir_012_5515c10818a71365.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/5515c10818a71365.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@13", "density": 0.7347845850822048, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.82298, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/13.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3.82298+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.82298, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@13", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.82298+", "metric_symbol": "r", "metric_value": 3.82298, "reference_text": "r = 3.82298+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/13.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 3.82298+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "defdebc1228b1d63", "improvement": -0.002118865563556671, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3642191814564626e-06, "max_pair_overlap_depth": -3.899276946051078e-05, "metric_expression": "3.82510", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.8250988655635565, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.82298, "setup": "hexincir", "side": 7.650197731127113, "solution_path": "data/solutions/generated/hexincir_013_defdebc1228b1d63.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/defdebc1228b1d63.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@14", "density": 0.7696929179154312, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 3.877, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/14.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a(109\u20139\u221a109) = 3.877+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.877788212345415, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@14", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "\u221a(109\u20139\u221a109) = 3.877+", "metric_symbol": "r", "metric_value": 3.877, "reference_text": "r = \u221a(109\u20139\u221a109) = 3.877+ | Found by Maurizio Morandi | in March 2026.", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/14.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a(109\u20139\u221a109) = 3.877+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "cf6592c7009ff83d", "improvement": -0.0006446628264478171, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.009541618976158e-06, "max_pair_overlap_depth": -5.416099891136783e-05, "metric_expression": "3.87843", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.8784328751718626, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.877788212345415, "setup": "hexincir", "side": 7.756865750343725, "solution_path": "data/solutions/generated/hexincir_014_cf6592c7009ff83d.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/cf6592c7009ff83d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@15", "density": 0.7439908773476231, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.08174, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/15.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.08174+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.08174, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@15", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.08174+", "metric_symbol": "r", "metric_value": 4.08174, "reference_text": "r = 4.08174+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/15.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 4.08174+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "ea523b99f3bf81fb", "improvement": -0.001574502888137097, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.330196611616714e-06, "max_pair_overlap_depth": -5.918641434021765e-05, "metric_expression": "4.08331", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.083314502888137, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.08174, "setup": "hexincir", "side": 8.166629005776274, "solution_path": "data/solutions/generated/hexincir_015_ea523b99f3bf81fb.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/ea523b99f3bf81fb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@16", "density": 0.7714178714001686, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.13966, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/16.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.13966+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.13966, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@16", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.13966+", "metric_symbol": "r", "metric_value": 4.13966, "reference_text": "r = 4.13966+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "16.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/16.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 4.13966+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "928ee7a851bce6e5", "improvement": -0.0019209106018989175, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.8109720468001456e-06, "max_pair_overlap_depth": -4.18854370716204e-05, "metric_expression": "4.14158", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.141580910601899, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.13966, "setup": "hexincir", "side": 8.283161821203798, "solution_path": "data/solutions/generated/hexincir_016_928ee7a851bce6e5.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/928ee7a851bce6e5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@17", "density": 0.7591563034967428, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.3017, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/17.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.30170+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.3017, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@17", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.30170+", "metric_symbol": "r", "metric_value": 4.3017, "reference_text": "r = 4.30170+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/17.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 4.30170+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "e582b760dc061cd3", "improvement": -0.001681676380650643, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.855951803468429e-06, "max_pair_overlap_depth": -4.543663468803416e-05, "metric_expression": "4.30338", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.303381676380651, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.3017, "setup": "hexincir", "side": 8.606763352761302, "solution_path": "data/solutions/generated/hexincir_017_e582b760dc061cd3.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T03:07:58+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/e582b760dc061cd3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@18", "density": 0.7834006630179079, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.35889, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a19 = 4.35889+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.358898943540673, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@18", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a19 = 4.35889+", "metric_symbol": "r", "metric_value": 4.35889, "reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "12eaac899664a007", "improvement": -0.00018559876213242177, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.696366953105269e-06, "max_pair_overlap_depth": -1.0490734119961154e-05, "metric_expression": "4.35908", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.3590845423028055, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.358898943540673, "setup": "hexincir", "side": 8.718169084605611, "solution_path": "data/solutions/generated/hexincir_018_12eaac899664a007.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/12eaac899664a007.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@19", "density": 0.8269599994475847, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.35889, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a19 = 4.35889+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.358898943540673, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@19", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a19 = 4.35889+", "metric_symbol": "r", "metric_value": 4.35889, "reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "b4bf200670caf09c", "improvement": -8.787625086270623e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.636539265552187e-06, "max_pair_overlap_depth": -6.973398227638761e-06, "metric_expression": "4.35899", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.358986819791536, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.358898943540673, "setup": "hexincir", "side": 8.717973639583072, "solution_path": "data/solutions/generated/hexincir_019_b4bf200670caf09c.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/b4bf200670caf09c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@20", "density": 0.7723857667872704, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.62598, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/20.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.62598+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.62598, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.62598+", "metric_symbol": "r", "metric_value": 4.62598, "reference_text": "r = 4.62598+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/20.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 4.62598+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "30108dc5d1ea9a14", "improvement": -0.0015460646281777457, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8288872105642895e-06, "max_pair_overlap_depth": -4.792351042670617e-06, "metric_expression": "4.62753", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.627526064628178, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.62598, "setup": "hexincir", "side": 9.255052129256356, "solution_path": "data/solutions/generated/hexincir_020_30108dc5d1ea9a14.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/30108dc5d1ea9a14.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@21", "density": 0.7917677222663352, "friedman_analytical_or_proved": false, "friedman_credit": "Enea Victor", "friedman_date": "April 2026", "friedman_display_metric_value": 4.68339, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/21.png", "friedman_metric_expression": "4.68339+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.68339, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@21", "credit": "Enea Victor", "date": "April 2026", "family_updated": "", "metric_expression": "4.68339+", "metric_symbol": "r", "metric_value": 4.68339, "reference_text": "r = 4.68339+ | Found by Enea Victor | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/21.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 4.68339+ | Found by Enea Victor | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "49a047c29bb184c3", "improvement": -1.5457789629635954e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.498160996568856e-06, "max_pair_overlap_depth": -3.8704072840012316e-06, "metric_expression": "4.68341", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 4.68340545778963, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.68339, "setup": "hexincir", "side": 9.36681091557926, "solution_path": "data/solutions/generated/hexincir_021_49a047c29bb184c3.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Enea Victor", "svg_path": "data/svg/49a047c29bb184c3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@1", "density": 0.433010701548144, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.73205, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/1.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "\u221a3 = 1.73205+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.7320508075688772, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a3 = 1.73205+", "metric_symbol": "s", "metric_value": 1.73205, "reference_text": "1. | | s = \u221a3 = 1.73205+ | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/1.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "1. | | s = \u221a3 = 1.73205+ | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "899222ca3c83cd8e", "improvement": -4.000702012563195e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0003297862271054e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.73205", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.7320548082708898, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.7320508075688772, "setup": "hexindom", "side": 3.4641096165417795, "solution_path": "data/solutions/generated/hexindom_001_899222ca3c83cd8e.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/899222ca3c83cd8e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@2", "density": 0.7237057542591544, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 1.8946, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/2.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "1.8946+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.8946, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexindom@2", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.8946+", "metric_symbol": "s", "metric_value": 1.8946, "reference_text": "2. | | s = 1.8946+ | Found by Jonathan Viquerat in April 2026.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/2.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "2. | | s = 1.8946+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "419ae881803808e0", "improvement": -0.00011952413629479075, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.154031481298006e-06, "max_pair_overlap_depth": -4.420983116036614e-05, "metric_expression": "1.89472", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.8947195241362949, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.8946, "setup": "hexindom", "side": 3.7894390482725897, "solution_path": "data/solutions/generated/hexindom_002_419ae881803808e0.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/419ae881803808e0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@3", "density": 0.6059845041872388, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.53589, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/3.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "6\u20132\u221a3 = 2.53589+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.5358983848622456, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@3", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6\u20132\u221a3 = 2.53589+", "metric_symbol": "s", "metric_value": 2.53589, "reference_text": "3. | | s = 6\u20132\u221a3 = 2.53589+ | Found by Jonathan Viquerat in April 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/3.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "3. | | s = 6\u20132\u221a3 = 2.53589+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "b8984cccc8c8714d", "improvement": -5.235544974313555e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3815485928603266e-06, "max_pair_overlap_depth": -3.5690372763075295e-05, "metric_expression": "2.53595", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.5359507403119887, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.5358983848622456, "setup": "hexindom", "side": 5.0719014806239775, "solution_path": "data/solutions/generated/hexindom_003_b8984cccc8c8714d.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/b8984cccc8c8714d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@4", "density": 0.5981044188175139, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.94744, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/4.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "22\u201311\u221a3 = 2.94744+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.9474411167423495, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@4", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "22\u201311\u221a3 = 2.94744+", "metric_symbol": "s", "metric_value": 2.94744, "reference_text": "4. | | s = 22\u201311\u221a3 = 2.94744+ | Found by Jonathan Viquerat in April 2026.", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/4.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "4. | | s = 22\u201311\u221a3 = 2.94744+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "de86d3aed3d6a439", "improvement": -4.952939719649052e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.326043343385379e-06, "max_pair_overlap_depth": -1.3607159264461544e-05, "metric_expression": "2.94749", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.947490646139546, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.9474411167423495, "setup": "hexindom", "side": 5.894981292279092, "solution_path": "data/solutions/generated/hexindom_004_de86d3aed3d6a439.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/de86d3aed3d6a439.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@5", "density": 0.6153950410217744, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.24871, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/5.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "7(2\u221a3\u20133) = 3.24871+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.248711305964282, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@5", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "7(2\u221a3\u20133) = 3.24871+", "metric_symbol": "s", "metric_value": 3.24871, "reference_text": "5. | | s = 7(2\u221a3\u20133) = 3.24871+ | Found by Jonathan Viquerat in April 2026.", "source_image": "5.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/5.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "5. | | s = 7(2\u221a3\u20133) = 3.24871+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "6c9e9b8c4daf8e17", "improvement": -5.858397407898508e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.879985772620616e-06, "max_pair_overlap_depth": -1.7392941288552066e-05, "metric_expression": "3.24877", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.248769889938361, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.248711305964282, "setup": "hexindom", "side": 6.497539779876722, "solution_path": "data/solutions/generated/hexindom_005_6c9e9b8c4daf8e17.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/6c9e9b8c4daf8e17.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@6", "density": 0.669460522582725, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.41202, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/6.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "21(15\u20132\u221a3)/71 = 3.41202+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.4120262828465795, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@6", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "21(15\u20132\u221a3)/71 = 3.41202+", "metric_symbol": "s", "metric_value": 3.41202, "reference_text": "6. | | s = 21(15\u20132\u221a3)/71 = 3.41202+ | Found by Jonathan Viquerat in April 2026.", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/6.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "6. | | s = 21(15\u20132\u221a3)/71 = 3.41202+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "3331b621360b9c32", "improvement": -9.205242090626342e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.54326023255247e-06, "max_pair_overlap_depth": -5.983710998713754e-05, "metric_expression": "3.41212", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.4121183352674858, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.4120262828465795, "setup": "hexindom", "side": 6.8242366705349715, "solution_path": "data/solutions/generated/hexindom_006_3331b621360b9c32.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/3331b621360b9c32.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@7", "density": 0.74772405053785, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.4873, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/7.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "3.4873+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.4873, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexindom@7", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.4873+", "metric_symbol": "s", "metric_value": 3.4873, "reference_text": "7. | | s = 3.4873+ | Found by Jonathan Viquerat in April 2026.", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/7.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "7. | | s = 3.4873+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "1cf3d5c48cc9bce3", "improvement": 1.5563940758411832e-07, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.731889618803109e-06, "max_pair_overlap_depth": -2.9943125185782904e-05, "metric_expression": "3.48730", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.4872998443605923, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.4873, "setup": "hexindom", "side": 6.9745996887211845, "solution_path": "data/solutions/generated/hexindom_007_1cf3d5c48cc9bce3.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/1cf3d5c48cc9bce3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@8", "density": 0.7629201456996986, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.6906, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/8.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "3.6906+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.6906, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexindom@8", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.6906+", "metric_symbol": "s", "metric_value": 3.6906, "reference_text": "8. | | s = 3.6906+ | Found by Jonathan Viquerat in April 2026.", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/8.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "8. | | s = 3.6906+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "645a3046b41a06e7", "improvement": -0.00016503281621149668, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.30145200672294e-06, "max_pair_overlap_depth": -4.406733776018967e-05, "metric_expression": "3.69077", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.6907650328162114, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.6906, "setup": "hexindom", "side": 7.381530065632423, "solution_path": "data/solutions/generated/hexindom_008_645a3046b41a06e7.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/645a3046b41a06e7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@9", "density": 0.7092437911682054, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.06002, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/9.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "(36+5\u221a3)/11 = 4.06002+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.060023094349489, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@9", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "(36+5\u221a3)/11 = 4.06002+", "metric_symbol": "s", "metric_value": 4.06002, "reference_text": "9. | | s = (36+5\u221a3)/11 = 4.06002+ | Found by Jonathan Viquerat in April 2026.", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/9.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "9. | | s = (36+5\u221a3)/11 = 4.06002+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "412a5c4dab2378db", "improvement": -5.538905815605233e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.8730699123165095e-06, "max_pair_overlap_depth": -8.397966625661724e-06, "metric_expression": "4.06008", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.060078483407645, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.060023094349489, "setup": "hexindom", "side": 8.12015696681529, "solution_path": "data/solutions/generated/hexindom_009_412a5c4dab2378db.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/412a5c4dab2378db.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@10", "density": 0.7445544573306387, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.17691, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/10.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "9(2\u221a3\u20133) = 4.17691+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.176914536239791, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@10", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "9(2\u221a3\u20133) = 4.17691+", "metric_symbol": "s", "metric_value": 4.17691, "reference_text": "10. | | s = 9(2\u221a3\u20133) = 4.17691+ | Found by Jonathan Viquerat in April 2026.", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/10.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "10. | | s = 9(2\u221a3\u20133) = 4.17691+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "b404bfce93e4b698", "improvement": -6.849932658070657e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.152317509946272e-07, "max_pair_overlap_depth": -2.262161166943777e-05, "metric_expression": "4.17698", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.176983035566372, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.176914536239791, "setup": "hexindom", "side": 8.353966071132744, "solution_path": "data/solutions/generated/hexindom_010_b404bfce93e4b698.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/b404bfce93e4b698.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@11", "density": 0.7041255860017571, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.5036, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/11.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "4.5036+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5036, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexindom@11", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.5036+", "metric_symbol": "s", "metric_value": 4.5036, "reference_text": "11. | | s = 4.5036+ | Found by Jonathan Viquerat in April 2026.", "source_image": "11.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/11.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "11. | | s = 4.5036+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "11.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "de36b527dfa03258", "improvement": -0.0012696093619926074, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.31456043970391e-06, "max_pair_overlap_depth": -1.8725366454197534e-05, "metric_expression": "4.50487", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.504869609361992, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.5036, "setup": "hexindom", "side": 9.009739218723984, "solution_path": "data/solutions/generated/hexindom_011_de36b527dfa03258.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/de36b527dfa03258.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@12", "density": 0.7322405469378734, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.6136, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/12.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "41(18\u20135\u221a3)/83 = 4.6136+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.613609451185303, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@12", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "41(18\u20135\u221a3)/83 = 4.6136+", "metric_symbol": "s", "metric_value": 4.6136, "reference_text": "12. | | s = 41(18\u20135\u221a3)/83 = 4.6136+ | Found by Jonathan Viquerat in April 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/12.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "12. | | s = 41(18\u20135\u221a3)/83 = 4.6136+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "32dafbf1407bbd72", "improvement": -0.0003596469647471068, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.932113721409451e-07, "max_pair_overlap_depth": -3.449528945953517e-05, "metric_expression": "4.61397", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.61396909815005, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.613609451185303, "setup": "hexindom", "side": 9.2279381963001, "solution_path": "data/solutions/generated/hexindom_012_32dafbf1407bbd72.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/32dafbf1407bbd72.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@13", "density": 0.7287142254379715, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.8137, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/13.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "4.8137+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.8137, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexindom@13", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.8137+", "metric_symbol": "s", "metric_value": 4.8137, "reference_text": "13. | | s = 4.8137+ | Found by Jonathan Viquerat in April 2026.", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/13.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "13. | | s = 4.8137+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "4d59f64640558812", "improvement": -0.000276853025948931, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.288235630449776e-07, "max_pair_overlap_depth": -5.701790221179781e-05, "metric_expression": "4.81398", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.813976853025949, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.8137, "setup": "hexindom", "side": 9.627953706051898, "solution_path": "data/solutions/generated/hexindom_013_4d59f64640558812.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/4d59f64640558812.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@14", "density": 0.7731048613358414, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.84994, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/14.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "25(6\u2013\u221a3)/22 = 4.84994+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.849942264126276, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@14", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "25(6\u2013\u221a3)/22 = 4.84994+", "metric_symbol": "s", "metric_value": 4.84994, "reference_text": "14. | | s = 25(6\u2013\u221a3)/22 = 4.84994+ | Found by Jonathan Viquerat in April 2026.", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/14.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "14. | | s = 25(6\u2013\u221a3)/22 = 4.84994+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "1f0ed34d05c35380", "improvement": -0.00021433560638683957, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.312817282834061e-06, "max_pair_overlap_depth": -5.706330400911952e-05, "metric_expression": "4.85016", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.850156599732663, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.849942264126276, "setup": "hexindom", "side": 9.700313199465326, "solution_path": "data/solutions/generated/hexindom_014_1f0ed34d05c35380.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/1f0ed34d05c35380.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@15", "density": 0.7946102881582437, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.95163, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/15.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "56(27\u20134\u221a3)/227 = 4.95163+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.95163268328005, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@15", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "56(27\u20134\u221a3)/227 = 4.95163+", "metric_symbol": "s", "metric_value": 4.95163, "reference_text": "15. | | s = 56(27\u20134\u221a3)/227 = 4.95163+ | Found by Jonathan Viquerat in April 2026.", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/15.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "15. | | s = 56(27\u20134\u221a3)/227 = 4.95163+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "1b00a25adb5cc2e4", "improvement": -0.00035416994814951863, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.185835293301636e-06, "max_pair_overlap_depth": -6.286085527285046e-05, "metric_expression": "4.95199", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.9519868532282, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.95163268328005, "setup": "hexindom", "side": 9.9039737064564, "solution_path": "data/solutions/generated/hexindom_015_1b00a25adb5cc2e4.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/1b00a25adb5cc2e4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@16", "density": 0.7697888241254879, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.19615, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/17.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "3\u221a3 = 5.19615+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.196152422706632, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@16", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3\u221a3 = 5.19615+", "metric_symbol": "s", "metric_value": 5.19615, "reference_text": "16.-17. | | s = 3\u221a3 = 5.19615+ | Trivial.", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/17.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "16.-17. | | s = 3\u221a3 = 5.19615+ | Trivial.", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "f690e0f9c2986401", "improvement": -3.893036729962773e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.00251676779817e-06, "max_pair_overlap_depth": -1.257294679668508e-05, "metric_expression": "5.19619", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.196191353073932, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.196152422706632, "setup": "hexindom", "side": 10.392382706147863, "solution_path": "data/solutions/generated/hexindom_016_f690e0f9c2986401.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/f690e0f9c2986401.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@17", "density": 0.8178722029268405, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.19615, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/17.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "3\u221a3 = 5.19615+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.196152422706632, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@17", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3\u221a3 = 5.19615+", "metric_symbol": "s", "metric_value": 5.19615, "reference_text": "16.-17. | | s = 3\u221a3 = 5.19615+ | Trivial.", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/17.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "16.-17. | | s = 3\u221a3 = 5.19615+ | Trivial.", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "fe395a0426baa674", "improvement": -0.00012921864098114355, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.712543075160227e-06, "max_pair_overlap_depth": -2.5961203853341885e-08, "metric_expression": "5.19628", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.196281641347613, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.196152422706632, "setup": "hexindom", "side": 10.392563282695226, "solution_path": "data/solutions/generated/hexindom_017_fe395a0426baa674.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/fe395a0426baa674.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@18", "density": 0.7993930048940154, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 5.40818, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/18.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "31(4\u2013\u221a3)/13 = 5.40818+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.4081865357972925, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "31(4\u2013\u221a3)/13 = 5.40818+", "metric_symbol": "s", "metric_value": 5.40818, "reference_text": "18. | | s = 31(4\u2013\u221a3)/13 = 5.40818+ | Found by Jonathan Viquerat in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/18.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "18. | | s = 31(4\u2013\u221a3)/13 = 5.40818+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "24be62ab2c11bd5c", "improvement": -0.00019132215573058886, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.006386418315856e-06, "max_pair_overlap_depth": -4.2927090152522496e-05, "metric_expression": "5.40838", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.408377857953023, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.4081865357972925, "setup": "hexindom", "side": 10.816755715906046, "solution_path": "data/solutions/generated/hexindom_018_24be62ab2c11bd5c.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/24be62ab2c11bd5c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@19", "density": 0.7722825822258855, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 5.653, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/19.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "5.6530+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.653, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexindom@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.6530+", "metric_symbol": "s", "metric_value": 5.653, "reference_text": "19. | | s = 5.6530+ | Found by Jonathan Viquerat in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/19.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "19. | | s = 5.6530+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "ca10088586ed125c", "improvement": -0.0002686721147275861, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.885998928396475e-06, "max_pair_overlap_depth": -2.764579666703071e-05, "metric_expression": "5.65327", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.653268672114727, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.653, "setup": "hexindom", "side": 11.306537344229454, "solution_path": "data/solutions/generated/hexindom_019_ca10088586ed125c.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/ca10088586ed125c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexindom@20", "density": 0.7718745532343245, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 5.8012, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/20.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "5.8012+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.8012, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexindom@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.8012+", "metric_symbol": "s", "metric_value": 5.8012, "reference_text": "20. | | s = 5.8012+ | Found by Jonathan Viquerat in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/20.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "20. | | s = 5.8012+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "49ce661db444ec25", "improvement": -0.0004641087628032281, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.575652109486185e-06, "max_pair_overlap_depth": -1.0063478294242145e-05, "metric_expression": "5.80166", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.801664108762803, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.8012, "setup": "hexindom", "side": 11.603328217525606, "solution_path": "data/solutions/generated/hexindom_020_49ce661db444ec25.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/49ce661db444ec25.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@1", "density": 0.9999864500659439, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/1.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "1. | | s = 1 | Trivial.", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/1.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "1. | | s = 1 | Trivial.", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "fd6c6df7b6a9fd4f", "improvement": -6.7750358792029175e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.374323059598708e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0000067750358792, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.0, "setup": "hexinhex", "side": 1.0000067750358792, "solution_path": "data/solutions/generated/hexinhex_001_fd6c6df7b6a9fd4f.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/fd6c6df7b6a9fd4f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@2", "density": 0.49998387949392886, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/2.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "2. | | s = 2 | Trivial.", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/2.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "2. | | s = 2 | Trivial.", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4c0cc36e970c84b1", "improvement": -3.2241791775522444e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.177681809212628e-06, "max_pair_overlap_depth": -3.6384174144801684e-05, "metric_expression": "2.00003", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0000322417917755, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "hexinhex", "side": 2.0000322417917755, "solution_path": "data/solutions/generated/hexinhex_002_4c0cc36e970c84b1.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4c0cc36e970c84b1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@3", "density": 0.7499882422262695, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/3.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "3. | | s = 2 | Trivial.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/3.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "3. | | s = 2 | Trivial.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "2e22e12b6d11de4d", "improvement": -1.5677215970288927e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.457810528986454e-06, "max_pair_overlap_depth": -9.916736621090457e-06, "metric_expression": "2.00002", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0000156772159703, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "hexinhex", "side": 2.0000156772159703, "solution_path": "data/solutions/generated/hexinhex_003_2e22e12b6d11de4d.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/2e22e12b6d11de4d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@4", "density": 0.7346808358825446, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.333, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/4.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "7/3 = 2.333+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.3333333333333335, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@4", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "7/3 = 2.333+", "metric_symbol": "s", "metric_value": 2.333, "reference_text": "4. | | s = 7/3 = 2.333+ | Trivial.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/4.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "4. | | s = 7/3 = 2.333+ | Trivial.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "73ddab3f27a95ffe", "improvement": -2.0709962234466417e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.969618748468479e-06, "max_pair_overlap_depth": -1.5832978702556844e-05, "metric_expression": "2.33335", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.333354043295568, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.3333333333333335, "setup": "hexinhex", "side": 2.333354043295568, "solution_path": "data/solutions/generated/hexinhex_004_73ddab3f27a95ffe.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/73ddab3f27a95ffe.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@5", "density": 0.7031111089487749, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "March 2015", "friedman_display_metric_value": 2.666, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/5.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "8/3 = 2.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.6666666666666665, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@5", "credit": "Erich Friedman", "date": "March 2015", "family_updated": "", "metric_expression": "8/3 = 2.666+", "metric_symbol": "s", "metric_value": 2.666, "reference_text": "5. | | s = 8/3 = 2.666+ | Found by Erich Friedman | in March 2015.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/5.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "5. | | s = 8/3 = 2.666+ | Found by Erich Friedman | in March 2015.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "f45300c86d046ee7", "improvement": -2.6341939302731987e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5309295562371306e-06, "max_pair_overlap_depth": -6.88869177611906e-06, "metric_expression": "2.66669", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.6666930086059693, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.6666666666666665, "setup": "hexinhex", "side": 2.6666930086059693, "solution_path": "data/solutions/generated/hexinhex_005_f45300c86d046ee7.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/f45300c86d046ee7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@6", "density": 0.7199337426480286, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_display_metric_value": 2.886, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/7.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "5/\u221a3 = 2.886+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.8867513459481287, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@6", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "5/\u221a3 = 2.886+", "metric_symbol": "s", "metric_value": 2.886, "reference_text": "6-7. | | s = 5/\u221a3 = 2.886+ | Found by Maurizio Morandi | in April 2015.", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/7.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "6-7. | | s = 5/\u221a3 = 2.886+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "06b9c79146f8c119", "improvement": -0.0001328345152633581, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.09670685382364e-06, "max_pair_overlap_depth": -5.069396536394599e-05, "metric_expression": "2.88688", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.886884180463392, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.8867513459481287, "setup": "hexinhex", "side": 2.886884180463392, "solution_path": "data/solutions/generated/hexinhex_006_06b9c79146f8c119.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/06b9c79146f8c119.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@7", "density": 0.8399730426517898, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_display_metric_value": 2.886, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/7.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "5/\u221a3 = 2.886+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.8867513459481287, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@7", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "5/\u221a3 = 2.886+", "metric_symbol": "s", "metric_value": 2.886, "reference_text": "6-7. | | s = 5/\u221a3 = 2.886+ | Found by Maurizio Morandi | in April 2015.", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/7.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "6-7. | | s = 5/\u221a3 = 2.886+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "d2a43d4ca2836467", "improvement": -4.63220442350476e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.6806989039887556e-06, "max_pair_overlap_depth": -2.9189085207215193e-05, "metric_expression": "2.88680", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.8867976679923637, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.8867513459481287, "setup": "hexinhex", "side": 2.8867976679923637, "solution_path": "data/solutions/generated/hexinhex_007_d2a43d4ca2836467.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/d2a43d4ca2836467.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@8", "density": 0.728171041468435, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_display_metric_value": 3.314, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/8.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "(51+5\u221a3)/18 = 3.314+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.3144585576580217, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@8", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "(51+5\u221a3)/18 = 3.314+", "metric_symbol": "s", "metric_value": 3.314, "reference_text": "8. | | s = (51+5\u221a3)/18 = 3.314+ | Found by Maurizio Morandi | in April 2015.", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/8.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "8. | | s = (51+5\u221a3)/18 = 3.314+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "8d9e02005a596470", "improvement": -0.00011981062760035854, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.71875974277703e-06, "max_pair_overlap_depth": -2.9528072121864923e-05, "metric_expression": "3.31458", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.314578368285622, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.3144585576580217, "setup": "hexinhex", "side": 3.314578368285622, "solution_path": "data/solutions/generated/hexinhex_008_8d9e02005a596470.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/8d9e02005a596470.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@9", "density": 0.683335999337671, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_display_metric_value": 3.628, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/9.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "(24+5\u221a3)/9 = 3.628+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.628917115316043, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@9", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "(24+5\u221a3)/9 = 3.628+", "metric_symbol": "s", "metric_value": 3.628, "reference_text": "9. | | s = (24+5\u221a3)/9 = 3.628+ | Found by Maurizio Morandi | in April 2015.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/9.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "9. | | s = (24+5\u221a3)/9 = 3.628+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "21c530fbe612f27c", "improvement": -0.00022607864944923506, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.454488069704802e-06, "max_pair_overlap_depth": -2.836888994439679e-05, "metric_expression": "3.62914", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.629143193965492, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.628917115316043, "setup": "hexinhex", "side": 3.629143193965492, "solution_path": "data/solutions/generated/hexinhex_009_21c530fbe612f27c.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/21c530fbe612f27c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@10", "density": 0.7179574622038186, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_display_metric_value": 3.732, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/10.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "2 + \u221a3 = 3.732+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.732050807568877, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@10", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "2 + \u221a3 = 3.732+", "metric_symbol": "s", "metric_value": 3.732, "reference_text": "10. | | s = 2 + \u221a3 = 3.732+ | Found by Maurizio Morandi | in April 2015.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/10.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "10. | | s = 2 + \u221a3 = 3.732+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "fd5a10d8a6354174", "improvement": -2.6601546221360906e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.847623197892974e-06, "max_pair_overlap_depth": -2.6880918478910942e-06, "metric_expression": "3.73208", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.7320774091150986, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.732050807568877, "setup": "hexinhex", "side": 3.7320774091150986, "solution_path": "data/solutions/generated/hexinhex_010_fd5a10d8a6354174.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/fd5a10d8a6354174.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@11", "density": 0.7131589068275569, "friedman_analytical_or_proved": true, "friedman_credit": "Johann Schellhorn", "friedman_date": "July 2025", "friedman_display_metric_value": 3.9245, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/11.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "2+10/3\u221a3 = 3.92450+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.9245008972987527, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@11", "credit": "Johann Schellhorn", "date": "July 2025", "family_updated": "", "metric_expression": "2+10/3\u221a3 = 3.92450+", "metric_symbol": "s", "metric_value": 3.9245, "reference_text": "11. | | s = 2+10/3\u221a3 = 3.92450+ | Found by Johann Schellhorn | in July 2025. | | | |", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/11.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "11. | | s = 2+10/3\u221a3 = 3.92450+ | Found by Johann Schellhorn | in July 2025. | | | |", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "cf10a9116bb04a72", "improvement": -0.002881482076440456, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3732870796469545e-06, "max_pair_overlap_depth": -1.938912890975253e-05, "metric_expression": "3.92738", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.927382379375193, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.9245008972987527, "setup": "hexinhex", "side": 3.927382379375193, "solution_path": "data/solutions/generated/hexinhex_011_cf10a9116bb04a72.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Johann Schellhorn", "svg_path": "data/svg/cf10a9116bb04a72.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@12", "density": 0.7723090107470407, "friedman_analytical_or_proved": true, "friedman_credit": "Alexander Novikov et al", "friedman_date": "June 2025", "friedman_display_metric_value": 3.94164, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/12.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "3.94164+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.94164, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@12", "credit": "Alexander Novikov et al", "date": "June 2025", "family_updated": "", "metric_expression": "3.94164+", "metric_symbol": "s", "metric_value": 3.94164, "reference_text": "12. | | s = 3.94164+ | Found by Alexander Novikov et al | in June 2025. | Improved slightly by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/12.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "12. | | s = 3.94164+ | Found by Alexander Novikov et al | in June 2025. | Improved slightly by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "bdc671b076ad0ffe", "improvement": -0.0001644193364005453, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.69077332163481e-06, "max_pair_overlap_depth": -4.133319357890741e-07, "metric_expression": "3.94180", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.9418044193364006, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.94164, "setup": "hexinhex", "side": 3.9418044193364006, "solution_path": "data/solutions/generated/hexinhex_012_bdc671b076ad0ffe.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Alexander Novikov et al", "svg_path": "data/svg/bdc671b076ad0ffe.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@13", "density": 0.8124849152838151, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/13.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@13", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "13 | | s = 4 | Trivial. | | | | |", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/13.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "13 | | s = 4 | Trivial. | | | | |", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "1ac594ff5f07e3d9", "improvement": -3.7132126112560115e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.027960154271181e-06, "max_pair_overlap_depth": -5.440029557712833e-06, "metric_expression": "4.00004", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.000037132126113, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.0, "setup": "hexinhex", "side": 4.000037132126113, "solution_path": "data/solutions/generated/hexinhex_013_1ac594ff5f07e3d9.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/1ac594ff5f07e3d9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@14", "density": 0.7678833113230449, "friedman_analytical_or_proved": false, "friedman_credit": "Dominik Kamp", "friedman_date": "April 2026", "friedman_display_metric_value": 4.26899, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/14.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "4.26899+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.26899, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@14", "credit": "Dominik Kamp", "date": "April 2026", "family_updated": "", "metric_expression": "4.26899+", "metric_symbol": "s", "metric_value": 4.26899, "reference_text": "14. | | s = 4.26899+ | Found by Dominik Kamp | in April 2026.", "source_image": "14.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/14.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "14. | | s = 4.26899+ | Found by Dominik Kamp | in April 2026.", "friedman_source_image": "14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "f86af09d863723a2", "improvement": -0.0008972113481453547, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.52825412539728e-06, "max_pair_overlap_depth": -2.1736642138669993e-05, "metric_expression": "4.26989", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.269887211348145, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.26899, "setup": "hexinhex", "side": 4.269887211348145, "solution_path": "data/solutions/generated/hexinhex_014_f86af09d863723a2.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Dominik Kamp", "svg_path": "data/svg/f86af09d863723a2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@15", "density": 0.7579263950656321, "friedman_analytical_or_proved": true, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_display_metric_value": 4.44727, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/15.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "4.44727+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.44727, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@15", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "4.44727+", "metric_symbol": "s", "metric_value": 4.44727, "reference_text": "15. | | s = 4.44727+ | Found by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/15.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "15. | | s = 4.44727+ | Found by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "536c412ab623afbc", "improvement": -0.0014196922804980971, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.564398033090082e-06, "max_pair_overlap_depth": -2.5468766324809877e-06, "metric_expression": "4.44869", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.448689692280498, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.44727, "setup": "hexinhex", "side": 4.448689692280498, "solution_path": "data/solutions/generated/hexinhex_015_536c412ab623afbc.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/536c412ab623afbc.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@16", "density": 0.7803167098453238, "friedman_analytical_or_proved": true, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_display_metric_value": 4.52746, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/16.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "4.52746+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.52746, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@16", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "4.52746+", "metric_symbol": "s", "metric_value": 4.52746, "reference_text": "16. | | s = 4.52746+ | Found by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/16.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "16. | | s = 4.52746+ | Found by Timo Berthold et al | in January 2026. | Slightly improved by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "17cb432379a18c18", "improvement": -0.0007289208955771898, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.541715273786282e-06, "max_pair_overlap_depth": -2.3206185233659582e-05, "metric_expression": "4.52819", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.528188920895577, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.52746, "setup": "hexinhex", "side": 4.528188920895577, "solution_path": "data/solutions/generated/hexinhex_016_17cb432379a18c18.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/17cb432379a18c18.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@17", "density": 0.7985097849440846, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "February 2026", "friedman_display_metric_value": 4.6136, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/17.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "4.6136+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.6136, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@17", "credit": "Timo Berthold et al", "date": "February 2026", "family_updated": "", "metric_expression": "4.6136+", "metric_symbol": "s", "metric_value": 4.6136, "reference_text": "17. | | s = 4.6136+ | Found by Timo Berthold et al | and Alex Kravatsky et al | in February 2026.", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/17.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "17. | | s = 4.6136+ | Found by Timo Berthold et al | and Alex Kravatsky et al | in February 2026.", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "df809b176b000a6d", "improvement": -0.0004717062665458016, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.290243996089003e-06, "max_pair_overlap_depth": -4.642493336670661e-05, "metric_expression": "4.61407", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.614071706266546, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.6136, "setup": "hexinhex", "side": 4.614071706266546, "solution_path": "data/solutions/generated/hexinhex_017_df809b176b000a6d.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/df809b176b000a6d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@18", "density": 0.8437116836701195, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_display_metric_value": 4.618, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "8/\u221a3 = 4.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.618802153517006, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@18", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "8/\u221a3 = 4.618+", "metric_symbol": "s", "metric_value": 4.618, "reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "e320d39029a817c1", "improvement": -0.00010487797025149348, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 1.0443685916789865e-09, "max_pair_overlap_depth": -3.080790913889686e-05, "metric_expression": "4.61891", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.618907031487257, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.618802153517006, "setup": "hexinhex", "side": 4.618907031487257, "solution_path": "data/solutions/generated/hexinhex_018_e320d39029a817c1.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/e320d39029a817c1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@19", "density": 0.8905854861904853, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_display_metric_value": 4.618, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "8/\u221a3 = 4.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.618802153517006, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@19", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "8/\u221a3 = 4.618+", "metric_symbol": "s", "metric_value": 4.618, "reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4b11a1a09f2a5b70", "improvement": -0.00010246318123208198, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.772589960788204e-06, "max_pair_overlap_depth": -3.612300978728111e-05, "metric_expression": "4.61890", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.618904616698238, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.618802153517006, "setup": "hexinhex", "side": 4.618904616698238, "solution_path": "data/solutions/generated/hexinhex_019_4b11a1a09f2a5b70.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/4b11a1a09f2a5b70.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@20", "density": 0.7999496824068819, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@20", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "20-21. | | s = 5 | Trivial. | |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "20-21. | | s = 5 | Trivial. | |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "2830e2dec38749ef", "improvement": -0.00015724989644283482, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.445035556179186e-06, "max_pair_overlap_depth": -1.6551811964360397e-06, "metric_expression": "5.00016", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.000157249896443, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.0, "setup": "hexinhex", "side": 5.000157249896443, "solution_path": "data/solutions/generated/hexinhex_020_2830e2dec38749ef.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/2830e2dec38749ef.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@21", "density": 0.8399773177134815, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@21", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "20-21. | | s = 5 | Trivial. | |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "20-21. | | s = 5 | Trivial. | |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4a431b677be571c9", "improvement": -6.750817229672634e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5389132812752791e-06, "max_pair_overlap_depth": -3.519050301936666e-06, "metric_expression": "5.00007", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.000067508172297, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.0, "setup": "hexinhex", "side": 5.000067508172297, "solution_path": "data/solutions/generated/hexinhex_021_4a431b677be571c9.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4a431b677be571c9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@22", "density": 0.7873804951730353, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_display_metric_value": 5.285, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/22.gif", "friedman_metric_expression": "(39+8\u221a3)/10 = 5.285+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.285640646055102, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@22", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "(39+8\u221a3)/10 = 5.285+", "metric_symbol": "s", "metric_value": 5.285, "reference_text": "22. | | s = (39+8\u221a3)/10 = 5.285+ | Found by Maurizio Morandi | in April 2015.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/22.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "22. | | s = (39+8\u221a3)/10 = 5.285+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "003a713177cb171c", "improvement": -0.0002602237497804083, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.575542655386671e-06, "max_pair_overlap_depth": -1.0001604064946434e-05, "metric_expression": "5.28590", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.285900869804882, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.285640646055102, "setup": "hexinhex", "side": 5.285900869804882, "solution_path": "data/solutions/generated/hexinhex_022_003a713177cb171c.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/003a713177cb171c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@23", "density": 0.7886255260759908, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_display_metric_value": 5.4, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/23.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "5.400+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.4, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@23", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "", "metric_expression": "5.400+", "metric_symbol": "s", "metric_value": 5.4, "reference_text": "23. | | s = 5.400+ | Found by Alex Kravatsky et al | in February 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/23.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "23. | | s = 5.400+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "e0a82406671652d2", "improvement": -0.00043201188015196124, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4507055603926188e-06, "max_pair_overlap_depth": -1.2502329530761358e-05, "metric_expression": "5.40043", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.400432011880152, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.4, "setup": "hexinhex", "side": 5.400432011880152, "solution_path": "data/solutions/generated/hexinhex_023_e0a82406671652d2.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Alex Kravatsky et al", "svg_path": "data/svg/e0a82406671652d2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@24", "density": 0.797738483588153, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_display_metric_value": 5.484, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/24.gif", "friedman_metric_expression": "19\u221a3/6 = 5.484+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.484827557301445, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@24", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "19\u221a3/6 = 5.484+", "metric_symbol": "s", "metric_value": 5.484, "reference_text": "24. | | s = 19\u221a3/6 = 5.484+ | Found by Maurizio Morandi | in April 2015.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/24.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "24. | | s = 19\u221a3/6 = 5.484+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "c96649ff013a9455", "improvement": -0.0001562426047536647, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.588312731744032e-06, "max_pair_overlap_depth": -4.485524381903083e-05, "metric_expression": "5.48498", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.484983799906199, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.484827557301445, "setup": "hexinhex", "side": 5.484983799906199, "solution_path": "data/solutions/generated/hexinhex_024_c96649ff013a9455.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/c96649ff013a9455.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@25", "density": 0.7898226009433017, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_display_metric_value": 5.6239, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/25.gif", "friedman_metric_expression": "5.62390+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.6239, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@25", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "", "metric_expression": "5.62390+", "metric_symbol": "s", "metric_value": 5.6239, "reference_text": "25. | | s = 5.62390+ | Found by Alex Kravatsky et al | in February 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/25.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "25. | | s = 5.62390+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4ac680367830872b", "improvement": -0.002171223468265815, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8833146044517865e-07, "max_pair_overlap_depth": -2.7316686140865798e-05, "metric_expression": "5.62607", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.626071223468266, "n": 25, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.6239, "setup": "hexinhex", "side": 5.626071223468266, "solution_path": "data/solutions/generated/hexinhex_025_4ac680367830872b.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Alex Kravatsky et al", "svg_path": "data/svg/4ac680367830872b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@26", "density": 0.7965297187067493, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_display_metric_value": 5.70972, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/26.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "5.70972+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.70972, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@26", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "", "metric_expression": "5.70972+", "metric_symbol": "s", "metric_value": 5.70972, "reference_text": "26. | | s = 5.70972+ | Found by Alex Kravatsky et al | in February 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/26.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "26. | | s = 5.70972+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "8ed8c9fb94f18119", "improvement": -0.0035622784284790043, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9624619447323227e-06, "max_pair_overlap_depth": -1.2105377510118753e-05, "metric_expression": "5.71328", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.713282278428479, "n": 26, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.70972, "setup": "hexinhex", "side": 5.713282278428479, "solution_path": "data/solutions/generated/hexinhex_026_8ed8c9fb94f18119.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Alex Kravatsky et al", "svg_path": "data/svg/8ed8c9fb94f18119.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@27", "density": 0.82621496088318, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_display_metric_value": 5.71415, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/27.gif", "friedman_metric_expression": "5.71415+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.71415, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@27", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "", "metric_expression": "5.71415+", "metric_symbol": "s", "metric_value": 5.71415, "reference_text": "27. | | s = 5.71415+ | Found by Alex Kravatsky et al | in February 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/27.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "27. | | s = 5.71415+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4e9628a9f49def85", "improvement": -0.0024177469948583052, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.56387472302006e-06, "max_pair_overlap_depth": -5.6693937127594296e-05, "metric_expression": "5.71657", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.716567746994858, "n": 27, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.71415, "setup": "hexinhex", "side": 5.716567746994858, "solution_path": "data/solutions/generated/hexinhex_027_4e9628a9f49def85.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Alex Kravatsky et al", "svg_path": "data/svg/4e9628a9f49def85.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@28", "density": 0.8011452289129106, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_display_metric_value": 5.90893, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/28.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "5.90893+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.90893, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@28", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "", "metric_expression": "5.90893+", "metric_symbol": "s", "metric_value": 5.90893, "reference_text": "28. | | s = 5.90893+ | Found by Alex Kravatsky et al | in February 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/28.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "28. | | s = 5.90893+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "ba522f97744aed1a", "improvement": -0.002919783094952777, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.424277796084301e-06, "max_pair_overlap_depth": -3.209757705180394e-05, "metric_expression": "5.91185", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.911849783094953, "n": 28, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.90893, "setup": "hexinhex", "side": 5.911849783094953, "solution_path": "data/solutions/generated/hexinhex_028_ba522f97744aed1a.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T02:51:36+00:00", "submitted_by": "Alex Kravatsky et al", "svg_path": "data/svg/ba522f97744aed1a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@29", "density": 0.8055194808067645, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 6.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@29", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "29-31. | | s = 6 | Trivial. |", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "29-31. | | s = 6 | Trivial. |", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "dba25a591b8992bc", "improvement": -0.00013435185279675466, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.231638156342025e-06, "max_pair_overlap_depth": -6.307567709251671e-06, "metric_expression": "6.00013", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.000134351852797, "n": 29, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.0, "setup": "hexinhex", "side": 6.000134351852797, "solution_path": "data/solutions/generated/hexinhex_029_dba25a591b8992bc.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/dba25a591b8992bc.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@30", "density": 0.8333115277207207, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 6.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@30", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "29-31. | | s = 6 | Trivial. |", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "29-31. | | s = 6 | Trivial. |", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "100db5f9f28894cc", "improvement": -7.850174601031767e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7272811687230685e-07, "max_pair_overlap_depth": -4.232627726974414e-06, "metric_expression": "6.00008", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.00007850174601, "n": 30, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.0, "setup": "hexinhex", "side": 6.00007850174601, "solution_path": "data/solutions/generated/hexinhex_030_100db5f9f28894cc.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/100db5f9f28894cc.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@31", "density": 0.8610814974425702, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 6.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@31", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "29-31. | | s = 6 | Trivial. |", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "29-31. | | s = 6 | Trivial. |", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "d503e2b08764a35e", "improvement": -0.0001031728611780025, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0312532034243658e-06, "max_pair_overlap_depth": -8.80446118189937e-06, "metric_expression": "6.00010", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.000103172861178, "n": 31, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.0, "setup": "hexinhex", "side": 6.000103172861178, "solution_path": "data/solutions/generated/hexinhex_031_d503e2b08764a35e.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d503e2b08764a35e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@1", "density": 0.6961402306608654, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.931, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/1.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(1+\u221a3)/\u221a2 = 1.931+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.9318516525781366, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "(1+\u221a3)/\u221a2 = 1.931+", "metric_symbol": "s", "metric_value": 1.931, "reference_text": "s = (1+\u221a3)/\u221a2 = 1.931+ | Trivial. |", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/1.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = (1+\u221a3)/\u221a2 = 1.931+ | Trivial. |", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "1cfff36edc20de72", "improvement": -1.6916936846911312e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8875760125229138e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.93187", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.9318685695149835, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.9318516525781366, "setup": "hexinsqu", "side": 1.9318685695149835, "solution_path": "data/solutions/generated/hexinsqu_001_1cfff36edc20de72.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/1cfff36edc20de72.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@2", "density": 0.5214616218348717, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.156, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/2.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(1+2\u221a3)/\u221a2 = 3.156+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.156596523969726, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "(1+2\u221a3)/\u221a2 = 3.156+", "metric_symbol": "s", "metric_value": 3.156, "reference_text": "s = (1+2\u221a3)/\u221a2 = 3.156+ | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/2.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = (1+2\u221a3)/\u221a2 = 3.156+ | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "ff43d04cda84c856", "improvement": -7.7710926686958e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2405599436706566e-05, "max_pair_overlap_depth": -1.629836664562411e-05, "metric_expression": "3.15667", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.1566742348964127, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.156596523969726, "setup": "hexinsqu", "side": 3.1566742348964127, "solution_path": "data/solutions/generated/hexinsqu_002_ff43d04cda84c856.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/ff43d04cda84c856.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@3", "density": 0.6391474518535116, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 3.491, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/3.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "9(6\u2013\u221a3)/11 = 3.491+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.491958430170919, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@3", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "9(6\u2013\u221a3)/11 = 3.491+", "metric_symbol": "s", "metric_value": 3.491, "reference_text": "s = 9(6\u2013\u221a3)/11 = 3.491+ | Found by Maurizio Morandi | in March 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/3.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 9(6\u2013\u221a3)/11 = 3.491+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "9525d376eafe3c9c", "improvement": -0.00013648770445540137, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.084317521962771e-06, "max_pair_overlap_depth": -8.912711465047796e-05, "metric_expression": "3.49209", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.492094917875374, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.491958430170919, "setup": "hexinsqu", "side": 3.492094917875374, "solution_path": "data/solutions/generated/hexinsqu_003_9525d376eafe3c9c.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/9525d376eafe3c9c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@4", "density": 0.748920266367969, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 3.725, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/4.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(7\u2013\u221a3)/\u221a2 = 3.725+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.7250025969142437, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@4", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "(7\u2013\u221a3)/\u221a2 = 3.725+", "metric_symbol": "s", "metric_value": 3.725, "reference_text": "s = (7\u2013\u221a3)/\u221a2 = 3.725+ | Found by Maurizio Morandi | in March 2026.", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/4.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = (7\u2013\u221a3)/\u221a2 = 3.725+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "33ddf042dd02d191", "improvement": -9.921706716031764e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.577436704193743e-06, "max_pair_overlap_depth": -5.3695636117151446e-05, "metric_expression": "3.72510", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.725101813981404, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.7250025969142437, "setup": "hexinsqu", "side": 3.725101813981404, "solution_path": "data/solutions/generated/hexinsqu_004_33ddf042dd02d191.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/33ddf042dd02d191.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@5", "density": 0.6595778437263831, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 4.437, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/5.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "7(3\u2013\u221a3)/2 = 4.437+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.43782217350893, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@5", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "7(3\u2013\u221a3)/2 = 4.437+", "metric_symbol": "s", "metric_value": 4.437, "reference_text": "s = 7(3\u2013\u221a3)/2 = 4.437+ | Found by Maurizio Morandi | in March 2026.", "source_image": "5.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/5.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 7(3\u2013\u221a3)/2 = 4.437+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "38f2dc66ba941978", "improvement": -8.195604384120259e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.5429089870357805e-06, "max_pair_overlap_depth": -1.5874388830661168e-05, "metric_expression": "4.43790", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.437904129552771, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.43782217350893, "setup": "hexinsqu", "side": 4.437904129552771, "solution_path": "data/solutions/generated/hexinsqu_005_38f2dc66ba941978.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/38f2dc66ba941978.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@6", "density": 0.6726426228424899, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 4.813, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/6.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "20(9\u20132\u221a3)/23 = 4.813+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.813824682488909, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@6", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "20(9\u20132\u221a3)/23 = 4.813+", "metric_symbol": "s", "metric_value": 4.813, "reference_text": "s = 20(9\u20132\u221a3)/23 = 4.813+ | Found by Maurizio Morandi | in March 2026.", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/6.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 20(9\u20132\u221a3)/23 = 4.813+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "31291850c6887128", "improvement": -0.00021179420330419418, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6841191118288626e-06, "max_pair_overlap_depth": -6.696342223433405e-05, "metric_expression": "4.81404", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.8140364766922135, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.813824682488909, "setup": "hexinsqu", "side": 4.8140364766922135, "solution_path": "data/solutions/generated/hexinsqu_006_31291850c6887128.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/31291850c6887128.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@7", "density": 0.6735519886722757, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.196, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/8.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3\u221a3 = 5.196+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.196152422706632, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@7", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3\u221a3 = 5.196+", "metric_symbol": "s", "metric_value": 5.196, "reference_text": "s = 3\u221a3 = 5.196+ | Trivial. |", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/8.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 3\u221a3 = 5.196+ | Trivial. |", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "a4c696c014daab3c", "improvement": -8.99716684248375e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.667089398456013e-06, "max_pair_overlap_depth": -2.5433886154724306e-05, "metric_expression": "5.19624", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.196242394375057, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.196152422706632, "setup": "hexinsqu", "side": 5.196242394375057, "solution_path": "data/solutions/generated/hexinsqu_007_a4c696c014daab3c.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/a4c696c014daab3c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@8", "density": 0.7697897324076285, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.196, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/8.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3\u221a3 = 5.196+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.196152422706632, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@8", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3\u221a3 = 5.196+", "metric_symbol": "s", "metric_value": 5.196, "reference_text": "s = 3\u221a3 = 5.196+ | Trivial. |", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/8.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 3\u221a3 = 5.196+ | Trivial. |", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "b1252a56565d2ec0", "improvement": -3.5864848886291156e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.033193436423119e-06, "max_pair_overlap_depth": -1.0846799477937097e-05, "metric_expression": "5.19619", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.196188287555518, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.196152422706632, "setup": "hexinsqu", "side": 5.196188287555518, "solution_path": "data/solutions/generated/hexinsqu_008_b1252a56565d2ec0.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/b1252a56565d2ec0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@9", "density": 0.7678652278206223, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 5.518, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/9.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(13\u20133\u221a3)/\u221a2 = 5.518+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.518153541250351, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@9", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "(13\u20133\u221a3)/\u221a2 = 5.518+", "metric_symbol": "s", "metric_value": 5.518, "reference_text": "s = (13\u20133\u221a3)/\u221a2 = 5.518+ | Found by Maurizio Morandi | in March 2026.", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/9.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = (13\u20133\u221a3)/\u221a2 = 5.518+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "5b4ef4c36dcfba05", "improvement": -0.00013871088887640326, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.874395903155008e-06, "max_pair_overlap_depth": -4.408050364324012e-05, "metric_expression": "5.51829", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.5182922521392275, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.518153541250351, "setup": "hexinsqu", "side": 5.5182922521392275, "solution_path": "data/solutions/generated/hexinsqu_009_5b4ef4c36dcfba05.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/5b4ef4c36dcfba05.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@10", "density": 0.6970336920701942, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 6.10469, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/10.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.10469+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.10469, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@10", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6.10469+", "metric_symbol": "s", "metric_value": 6.10469, "reference_text": "s = 6.10469+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/10.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 6.10469+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "031f63d864cce10c", "improvement": -0.0004982231227232958, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.5872663706407347e-08, "max_pair_overlap_depth": -2.0702587337384504e-05, "metric_expression": "6.10519", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.105188223122723, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.10469, "setup": "hexinsqu", "side": 6.105188223122723, "solution_path": "data/solutions/generated/hexinsqu_010_031f63d864cce10c.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/031f63d864cce10c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@11", "density": 0.7126826634184014, "friedman_analytical_or_proved": false, "friedman_credit": "Maksymilian Jankowski", "friedman_date": "April 2026", "friedman_display_metric_value": 6.33218, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/11.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.33218+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.33218, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@11", "credit": "Maksymilian Jankowski", "date": "April 2026", "family_updated": "", "metric_expression": "6.33218+", "metric_symbol": "s", "metric_value": 6.33218, "reference_text": "s = 6.33218+ | Found by Maksymilian Jankowski | in April 2026.", "source_image": "11.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/11.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 6.33218+ | Found by Maksymilian Jankowski | in April 2026.", "friedman_source_image": "11.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "f0fe574f6ed3708e", "improvement": -0.0003052751802421483, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.734623780299186e-06, "max_pair_overlap_depth": -4.342994577477555e-05, "metric_expression": "6.33249", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.332485275180242, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.33218, "setup": "hexinsqu", "side": 6.332485275180242, "solution_path": "data/solutions/generated/hexinsqu_011_f0fe574f6ed3708e.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maksymilian Jankowski", "svg_path": "data/svg/f0fe574f6ed3708e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@12", "density": 0.7640646951117188, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 6.387, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/12.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "43(5\u2013\u221a3)/22 = 6.387+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.38735523975174, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@12", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "43(5\u2013\u221a3)/22 = 6.387+", "metric_symbol": "s", "metric_value": 6.387, "reference_text": "s = 43(5\u2013\u221a3)/22 = 6.387+ | Found by Maurizio Morandi | in March 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/12.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 43(5\u2013\u221a3)/22 = 6.387+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "70f372d7c2d3b859", "improvement": -0.00044755123104600614, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.6841159701879252e-07, "max_pair_overlap_depth": -5.12694605685482e-05, "metric_expression": "6.38780", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.387802790982786, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.38735523975174, "setup": "hexinsqu", "side": 6.387802790982786, "solution_path": "data/solutions/generated/hexinsqu_012_70f372d7c2d3b859.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/70f372d7c2d3b859.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@13", "density": 0.7399851108638961, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 6.75558, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/13.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.75558+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.75558, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@13", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6.75558+", "metric_symbol": "s", "metric_value": 6.75558, "reference_text": "s = 6.75558+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/13.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 6.75558+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "96118c364cb8b05d", "improvement": -0.0003653626017898759, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.852098428599495e-06, "max_pair_overlap_depth": -2.731772979069902e-05, "metric_expression": "6.75595", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.75594536260179, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.75558, "setup": "hexinsqu", "side": 6.75594536260179, "solution_path": "data/solutions/generated/hexinsqu_013_96118c364cb8b05d.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/96118c364cb8b05d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@14", "density": 0.7577523835410583, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 6.928, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/14.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4\u221a3 = 6.928+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.928203230275509, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@14", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4\u221a3 = 6.928+", "metric_symbol": "s", "metric_value": 6.928, "reference_text": "s = 4\u221a3 = 6.928+ | Trivial. |", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/14.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 4\u221a3 = 6.928+ | Trivial. |", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "8b7d0912d343dc8b", "improvement": -9.07207319320591e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.277327734003356e-06, "max_pair_overlap_depth": -1.698575172759398e-05, "metric_expression": "6.92829", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.928293951007441, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.928203230275509, "setup": "hexinsqu", "side": 6.928293951007441, "solution_path": "data/solutions/generated/hexinsqu_014_8b7d0912d343dc8b.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/8b7d0912d343dc8b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@15", "density": 0.8035851614122442, "friedman_analytical_or_proved": false, "friedman_credit": "Maksymilian Jankowski", "friedman_date": "April 2026", "friedman_display_metric_value": 6.96367, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/15.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.96367+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.96367, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@15", "credit": "Maksymilian Jankowski", "date": "April 2026", "family_updated": "", "metric_expression": "6.96367+", "metric_symbol": "s", "metric_value": 6.96367, "reference_text": "s = 6.96367+ | Found by Maksymilian Jankowski | in April 2026.", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/15.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 6.96367+ | Found by Maksymilian Jankowski | in April 2026.", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "0691341c684bd112", "improvement": -0.00027958460374311045, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.156990403080692e-07, "max_pair_overlap_depth": -5.813914172492218e-05, "metric_expression": "6.96395", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.963949584603743, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.96367, "setup": "hexinsqu", "side": 6.963949584603743, "solution_path": "data/solutions/generated/hexinsqu_015_0691341c684bd112.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maksymilian Jankowski", "svg_path": "data/svg/0691341c684bd112.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@16", "density": 0.7776171365327941, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_display_metric_value": 7.311, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/16.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(19\u20135\u221a3)/\u221a2 = 7.311+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.311304485586458, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@16", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "(19\u20135\u221a3)/\u221a2 = 7.311+", "metric_symbol": "s", "metric_value": 7.311, "reference_text": "s = (19\u20135\u221a3)/\u221a2 = 7.311+ | Found by Maurizio Morandi | in April 2026.", "source_image": "16.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/16.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = (19\u20135\u221a3)/\u221a2 = 7.311+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "03465bdf660197b5", "improvement": -0.00013724527698588673, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8577837974051795e-06, "max_pair_overlap_depth": -3.069264188360066e-05, "metric_expression": "7.31144", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.311441730863444, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.311304485586458, "setup": "hexinsqu", "side": 7.311441730863444, "solution_path": "data/solutions/generated/hexinsqu_016_03465bdf660197b5.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/03465bdf660197b5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@17", "density": 0.7624212140097384, "friedman_analytical_or_proved": true, "friedman_credit": "Maksymilian Jankowski", "friedman_date": "April 2026", "friedman_display_metric_value": 7.60383, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/17.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6(3\u2013\u221a3) = 7.60383+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.607695154586736, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@17", "credit": "Maksymilian Jankowski", "date": "April 2026", "family_updated": "", "metric_expression": "6(3\u2013\u221a3) = 7.60383+", "metric_symbol": "s", "metric_value": 7.60383, "reference_text": "s = 6(3\u2013\u221a3) = 7.60383+ | Found by Maksymilian Jankowski | in April 2026.", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/17.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 6(3\u2013\u221a3) = 7.60383+ | Found by Maksymilian Jankowski | in April 2026.", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "080714e7afd39346", "improvement": -0.003501058212764363, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.378937853940429e-07, "max_pair_overlap_depth": -2.071443269358042e-05, "metric_expression": "7.61120", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.6111962127995, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.607695154586736, "setup": "hexinsqu", "side": 7.6111962127995, "solution_path": "data/solutions/generated/hexinsqu_017_080714e7afd39346.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maksymilian Jankowski", "svg_path": "data/svg/080714e7afd39346.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@18", "density": 0.7882207738949305, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_display_metric_value": 7.702, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/18.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "32(9\u20132\u221a3)/23 = 7.702+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.702119491982255, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@18", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "32(9\u20132\u221a3)/23 = 7.702+", "metric_symbol": "s", "metric_value": 7.702, "reference_text": "s = 32(9\u20132\u221a3)/23 = 7.702+ | Found by Maurizio Morandi | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/18.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 32(9\u20132\u221a3)/23 = 7.702+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "39a9a99a50ac7cba", "improvement": -0.0004966849623615488, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5800172874233264e-06, "max_pair_overlap_depth": -3.4078889656230515e-05, "metric_expression": "7.70262", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.702616176944616, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.702119491982255, "setup": "hexinsqu", "side": 7.702616176944616, "solution_path": "data/solutions/generated/hexinsqu_018_39a9a99a50ac7cba.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/39a9a99a50ac7cba.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@19", "density": 0.7859807737367643, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_display_metric_value": 7.924, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/19.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "25(3\u2013\u221a3)/4 = 7.924+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.924682452694517, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@19", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "25(3\u2013\u221a3)/4 = 7.924+", "metric_symbol": "s", "metric_value": 7.924, "reference_text": "s = 25(3\u2013\u221a3)/4 = 7.924+ | Found by Maurizio Morandi | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/19.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 25(3\u2013\u221a3)/4 = 7.924+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "10d9f5dde53d25ba", "improvement": -0.0002721365071138848, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.893895229540556e-06, "max_pair_overlap_depth": -3.6221248433054853e-05, "metric_expression": "7.92495", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.924954589201631, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.924682452694517, "setup": "hexinsqu", "side": 7.924954589201631, "solution_path": "data/solutions/generated/hexinsqu_019_10d9f5dde53d25ba.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/10d9f5dde53d25ba.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@20", "density": 0.8222377903171622, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_display_metric_value": 7.948, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/20.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "74(21\u20134\u221a3)/131 = 7.948+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.948953900455056, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@20", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "74(21\u20134\u221a3)/131 = 7.948+", "metric_symbol": "s", "metric_value": 7.948, "reference_text": "s = 74(21\u20134\u221a3)/131 = 7.948+ | Found by Maurizio Morandi | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/20.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 74(21\u20134\u221a3)/131 = 7.948+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "3d530c0ac6e7e3b1", "improvement": -0.0005902270190905057, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.121785608292394e-06, "max_pair_overlap_depth": -4.480534023287852e-05, "metric_expression": "7.94954", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.949544127474146, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.948953900455056, "setup": "hexinsqu", "side": 7.949544127474146, "solution_path": "data/solutions/generated/hexinsqu_020_3d530c0ac6e7e3b1.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/3d530c0ac6e7e3b1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@21", "density": 0.7762795555424945, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 8.381, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/21.png", "friedman_metric_expression": "8.381+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.381, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@21", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "8.381+", "metric_symbol": "s", "metric_value": 8.381, "reference_text": "s = 8.381+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/21.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 8.381+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "5d369a2740fde606", "improvement": -0.002522153681731254, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.85221561134309e-06, "max_pair_overlap_depth": -3.989714052887727e-05, "metric_expression": "8.38352", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.383522153681731, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.381, "setup": "hexinsqu", "side": 8.383522153681731, "solution_path": "data/solutions/generated/hexinsqu_021_5d369a2740fde606.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/5d369a2740fde606.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@22", "density": 0.7770815845496467, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 8.568, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/22.png", "friedman_metric_expression": "8.568+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.568, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@22", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "8.568+", "metric_symbol": "s", "metric_value": 8.568, "reference_text": "s = 8.568+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "22.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/22.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 8.568+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "2f0b0033f0c66708", "improvement": -0.008379204155273712, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.913077650512531e-06, "max_pair_overlap_depth": -1.9097490104869053e-05, "metric_expression": "8.57638", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.576379204155273, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.568, "setup": "hexinsqu", "side": 8.576379204155273, "solution_path": "data/solutions/generated/hexinsqu_022_2f0b0033f0c66708.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/2f0b0033f0c66708.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@23", "density": 0.7967168154089415, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 8.66, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/23.png", "friedman_metric_expression": "5\u221a3 = 8.660+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.660254037844387, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@23", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5\u221a3 = 8.660+", "metric_symbol": "s", "metric_value": 8.66, "reference_text": "s = 5\u221a3 = 8.660+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "23.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/23.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 5\u221a3 = 8.660+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "31cc17034bd25d7b", "improvement": -0.00014433009027925436, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.345963802137002e-06, "max_pair_overlap_depth": -2.1349502021816846e-07, "metric_expression": "8.66040", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.660398367934667, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.660254037844387, "setup": "hexinsqu", "side": 8.660398367934667, "solution_path": "data/solutions/generated/hexinsqu_023_31cc17034bd25d7b.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/31cc17034bd25d7b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@24", "density": 0.8058676683577897, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 8.795, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/24.png", "friedman_metric_expression": "8.795+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.795, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@24", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "8.795+", "metric_symbol": "s", "metric_value": 8.795, "reference_text": "s = 8.795+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "24.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/24.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 8.795+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "941fbce4f50492c6", "improvement": -0.0012932219182459903, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0969884292392119e-07, "max_pair_overlap_depth": -1.611027152126354e-05, "metric_expression": "8.79629", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.796293221918246, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.795, "setup": "hexinsqu", "side": 8.796293221918246, "solution_path": "data/solutions/generated/hexinsqu_024_941fbce4f50492c6.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/941fbce4f50492c6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@25", "density": 0.7898968080720588, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 9.065, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/25.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "30(4\u221a3\u20133)/13 = 9.065+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.065084377558867, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@25", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "30(4\u221a3\u20133)/13 = 9.065+", "metric_symbol": "s", "metric_value": 9.065, "reference_text": "s = 30(4\u221a3\u20133)/13 = 9.065+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "25.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/25.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 30(4\u221a3\u20133)/13 = 9.065+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "25.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "a62e2508884336f7", "improvement": -0.0029001015133136576, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.02442885507961e-06, "max_pair_overlap_depth": -5.091125714784539e-06, "metric_expression": "9.06798", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.06798447907218, "n": 25, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.065084377558867, "setup": "hexinsqu", "side": 9.06798447907218, "solution_path": "data/solutions/generated/hexinsqu_025_a62e2508884336f7.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/a62e2508884336f7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@1", "density": 0.6666490309389511, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/1.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "s = 3 | Trivial.", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/1.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 3 | Trivial.", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "c2fff75544b88239", "improvement": -3.9681174644368156e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.67464904574664e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "3.00004", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0000396811746444, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.0, "setup": "hexintri", "side": 3.0000396811746444, "solution_path": "data/solutions/generated/hexintri_001_c2fff75544b88239.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/c2fff75544b88239.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@2", "density": 0.4799802064426444, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "b77426ecb97f3ce6", "improvement": -0.00010309463302426991, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3591084715906373e-06, "max_pair_overlap_depth": -4.2178351187804886e-05, "metric_expression": "5.00010", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.000103094633024, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.0, "setup": "hexintri", "side": 5.000103094633024, "solution_path": "data/solutions/generated/hexintri_002_b77426ecb97f3ce6.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/b77426ecb97f3ce6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@3", "density": 0.7199659208954582, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "748bfe1ef47ea18c", "improvement": -0.00011833442488207169, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3474135610435156e-06, "max_pair_overlap_depth": -4.4955482604913666e-05, "metric_expression": "5.00012", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.000118334424882, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.0, "setup": "hexintri", "side": 5.000118334424882, "solution_path": "data/solutions/generated/hexintri_003_748bfe1ef47ea18c.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/748bfe1ef47ea18c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@4", "density": 0.6666571046827545, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 6.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/4.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@4", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/4.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 6 | Trivial.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "4bf531bb9fa044b6", "improvement": -4.302939048272947e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.615149234551692e-07, "max_pair_overlap_depth": -1.1132001730862484e-05, "metric_expression": "6.00004", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.000043029390483, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.0, "setup": "hexintri", "side": 6.000043029390483, "solution_path": "data/solutions/generated/hexintri_004_4bf531bb9fa044b6.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4bf531bb9fa044b6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@5", "density": 0.6430466587435534, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_display_metric_value": 6.8301, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/5.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "5(1+\u221a3)/2 = 6.8301+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.830127018922194, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@5", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "", "metric_expression": "5(1+\u221a3)/2 = 6.8301+", "metric_symbol": "s", "metric_value": 6.8301, "reference_text": "s = 5(1+\u221a3)/2 = 6.8301+ | Found by Maurizio Morandi | in April 2015.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/5.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 5(1+\u221a3)/2 = 6.8301+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "92331a16a75cf6c4", "improvement": -0.0001667720995186528, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4626103815685519e-06, "max_pair_overlap_depth": -3.302865088408366e-05, "metric_expression": "6.83029", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.830293791021712, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.830127018922194, "setup": "hexintri", "side": 6.830293791021712, "solution_path": "data/solutions/generated/hexintri_005_92331a16a75cf6c4.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/92331a16a75cf6c4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@6", "density": 0.7560505607557761, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 6.89897, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/6.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "2(1+\u221a6) = 6.89897+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.898979485566356, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@6", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2(1+\u221a6) = 6.89897+", "metric_symbol": "s", "metric_value": 6.89897, "reference_text": "s = 2(1+\u221a6) = 6.89897+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/6.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 2(1+\u221a6) = 6.89897+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "f3621ba5529eef9a", "improvement": -0.001445363900593577, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.849296155859392e-06, "max_pair_overlap_depth": -8.276209533908396e-05, "metric_expression": "6.90042", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.900424849466949, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.898979485566356, "setup": "hexintri", "side": 6.900424849466949, "solution_path": "data/solutions/generated/hexintri_006_f3621ba5529eef9a.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/f3621ba5529eef9a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@7", "density": 0.6562369627570366, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 8.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/7.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "8", "friedman_metric_symbol": "s", "friedman_metric_value": 8.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@7", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "8", "metric_symbol": "s", "metric_value": 8.0, "reference_text": "s = 8 | Trivial. |", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/7.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 8 | Trivial. |", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "635b0cc9d15ec460", "improvement": -7.946628399579936e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.24931067292516e-06, "max_pair_overlap_depth": -1.4685785256318695e-05, "metric_expression": "8.00008", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.000079466283996, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.0, "setup": "hexintri", "side": 8.000079466283996, "solution_path": "data/solutions/generated/hexintri_007_635b0cc9d15ec460.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/635b0cc9d15ec460.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@8", "density": 0.6907428320047944, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2015", "friedman_display_metric_value": 8.3333, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/8.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "25/3 = 8.3333+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.333333333333334, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@8", "credit": "Erich Friedman", "date": "April 2015", "family_updated": "", "metric_expression": "25/3 = 8.3333+", "metric_symbol": "s", "metric_value": 8.3333, "reference_text": "s = 25/3 = 8.3333+ | Found by Erich Friedman | in April 2015.", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/8.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 25/3 = 8.3333+ | Found by Erich Friedman | in April 2015.", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "adf439e6f7b2afb5", "improvement": -0.002757251293548535, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.227185763431761e-07, "max_pair_overlap_depth": -7.882545446008526e-05, "metric_expression": "8.33609", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.336090584626882, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.333333333333334, "setup": "hexintri", "side": 8.336090584626882, "solution_path": "data/solutions/generated/hexintri_008_adf439e6f7b2afb5.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/adf439e6f7b2afb5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@9", "density": 0.7214446032247255, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 8.6602, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/10.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "5\u221a3 = 8.6602+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.660254037844387, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@9", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5\u221a3 = 8.6602+", "metric_symbol": "s", "metric_value": 8.6602, "reference_text": "s = 5\u221a3 = 8.6602+ | Trivial. |", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/10.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 5\u221a3 = 8.6602+ | Trivial. |", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "936a184a58977242", "improvement": 0.008674886386490499, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0939511862432736e-06, "max_pair_overlap_depth": -5.506633970053798e-05, "metric_expression": "8.65158", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.651579151457897, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.660254037844387, "setup": "hexintri", "side": 8.651579151457897, "solution_path": "data/solutions/generated/hexintri_009_936a184a58977242.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/936a184a58977242.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@10", "density": 0.7999538247696885, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 8.6602, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/10.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "5\u221a3 = 8.6602+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.660254037844387, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@10", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5\u221a3 = 8.6602+", "metric_symbol": "s", "metric_value": 8.6602, "reference_text": "s = 5\u221a3 = 8.6602+ | Trivial. |", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/10.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 5\u221a3 = 8.6602+ | Trivial. |", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "5df6cec7a90f52fe", "improvement": -0.0002499415853147724, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2645686941820143e-06, "max_pair_overlap_depth": -4.384611814706174e-05, "metric_expression": "8.66050", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.660503979429702, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.660254037844387, "setup": "hexintri", "side": 8.660503979429702, "solution_path": "data/solutions/generated/hexintri_010_5df6cec7a90f52fe.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/5df6cec7a90f52fe.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@11", "density": 0.7237571814877352, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 9.54823, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/11.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "9.54823+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.54823, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexintri@11", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "9.54823+", "metric_symbol": "s", "metric_value": 9.54823, "reference_text": "s = 9.54823+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/11.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 9.54823+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "d582cb032b9c575f", "improvement": -0.0011576763865779327, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.6199514834868076e-06, "max_pair_overlap_depth": -2.6419225191420814e-05, "metric_expression": "9.54939", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.549387676386578, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.54823, "setup": "hexintri", "side": 9.549387676386578, "solution_path": "data/solutions/generated/hexintri_011_d582cb032b9c575f.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/d582cb032b9c575f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@12", "density": 0.7199169251480841, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 10.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/12.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "10", "friedman_metric_symbol": "s", "friedman_metric_value": 10.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@12", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "10", "metric_symbol": "s", "metric_value": 10.0, "reference_text": "s = 10 | Trivial. |", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/12.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 10 | Trivial. |", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "b6e20361c3af5615", "improvement": -0.0005769586222079681, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.006918638920166e-07, "max_pair_overlap_depth": -2.082412255655086e-05, "metric_expression": "10.00058", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.000576958622208, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 10.0, "setup": "hexintri", "side": 10.000576958622208, "solution_path": "data/solutions/generated/hexintri_012_b6e20361c3af5615.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/b6e20361c3af5615.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@13", "density": 0.7221828032992709, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 10.3923, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "6\u221a3 = 10.3923+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.392304845413264, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@13", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6\u221a3 = 10.3923+", "metric_symbol": "s", "metric_value": 10.3923, "reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "da55bd8ffef5f50e", "improvement": -0.00028361785426156416, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7733151165742505e-06, "max_pair_overlap_depth": -4.4289278687159594e-05, "metric_expression": "10.39259", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.392588463267526, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 10.392304845413264, "setup": "hexintri", "side": 10.392588463267526, "solution_path": "data/solutions/generated/hexintri_013_da55bd8ffef5f50e.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/da55bd8ffef5f50e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@14", "density": 0.7777237680646841, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 10.3923, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "6\u221a3 = 10.3923+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.392304845413264, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@14", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6\u221a3 = 10.3923+", "metric_symbol": "s", "metric_value": 10.3923, "reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "272118e9284c579f", "improvement": -0.00036084512376532984, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.442529134834328e-06, "max_pair_overlap_depth": -4.275788154761706e-05, "metric_expression": "10.39267", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.39266569053703, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 10.392304845413264, "setup": "hexintri", "side": 10.39266569053703, "solution_path": "data/solutions/generated/hexintri_014_272118e9284c579f.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/272118e9284c579f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@15", "density": 0.833304219754554, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 10.3923, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "6\u221a3 = 10.3923+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.392304845413264, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@15", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6\u221a3 = 10.3923+", "metric_symbol": "s", "metric_value": 10.3923, "reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/15.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 6\u221a3 = 10.3923+ | Trivial. |", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "83460d360e93ff66", "improvement": -0.0001815390682331497, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.672744116747984e-07, "max_pair_overlap_depth": -2.8784199847526563e-05, "metric_expression": "10.39249", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.392486384481497, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 10.392304845413264, "setup": "hexintri", "side": 10.392486384481497, "solution_path": "data/solutions/generated/hexintri_015_83460d360e93ff66.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/83460d360e93ff66.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@16", "density": 0.7429369875675369, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 11.36599, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/16.gif", "friedman_metric_expression": "11.36599+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.36599, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexintri@16", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "11.36599+", "metric_symbol": "s", "metric_value": 11.36599, "reference_text": "s = 11.36599+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/16.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 11.36599+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "89d5bef670451c83", "improvement": -0.0013703170956897992, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.657075146936789e-07, "max_pair_overlap_depth": -2.5616124350591463e-06, "metric_expression": "11.36736", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 11.36736031709569, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 11.36599, "setup": "hexintri", "side": 11.36736031709569, "solution_path": "data/solutions/generated/hexintri_16_89d5bef670451c83.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T07:13:53+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/89d5bef670451c83.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@17", "density": 0.7525303158572544, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 11.63457, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/17.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "11.63457+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.63457, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "hexintri@17", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "11.63457+", "metric_symbol": "s", "metric_value": 11.63457, "reference_text": "s = 11.63457+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/17.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 11.63457+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "8137d039fd339f48", "improvement": -0.007711226979866481, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.447216764354318e-05, "max_pair_overlap_depth": -1.3408176938511929e-05, "metric_expression": "11.64228", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 11.642281226979867, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 11.63457, "setup": "hexintri", "side": 11.642281226979867, "solution_path": "data/solutions/generated/hexintri_017_8137d039fd339f48.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T03:07:58+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/8137d039fd339f48.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@18", "density": 0.7507767554452202, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 12.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "12", "friedman_metric_symbol": "s", "friedman_metric_value": 12.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@18", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "12", "metric_symbol": "s", "metric_value": 12.0, "reference_text": "s = 12 | Trivial. |", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 12 | Trivial. |", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "8f10cd5e01be9029", "improvement": 0.0062092209316340075, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.734105056962567e-06, "max_pair_overlap_depth": -5.8920104462956147e-05, "metric_expression": "11.99379", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 11.993790779068366, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 12.0, "setup": "hexintri", "side": 11.993790779068366, "solution_path": "data/solutions/generated/hexintri_018_8f10cd5e01be9029.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/8f10cd5e01be9029.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@19", "density": 0.7866173060867477, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 12.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "12", "friedman_metric_symbol": "s", "friedman_metric_value": 12.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@19", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "12", "metric_symbol": "s", "metric_value": 12.0, "reference_text": "s = 12 | Trivial. |", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 12 | Trivial. |", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "18178ad9efaf7172", "improvement": -0.0384528795380632, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.242681221171444e-06, "max_pair_overlap_depth": -3.13088544121598e-05, "metric_expression": "12.03845", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 12.038452879538063, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "record_type": "verified", "reference_side": 12.0, "setup": "hexintri", "side": 12.038452879538063, "solution_path": "data/solutions/generated/hexintri_019_18178ad9efaf7172.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T03:07:58+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/18178ad9efaf7172.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@19", "density": 0.791614895360766, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 12.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "friedman_metric_expression": "12", "friedman_metric_symbol": "s", "friedman_metric_value": 12.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@19", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "12", "metric_symbol": "s", "metric_value": 12.0, "reference_text": "s = 12 | Trivial. |", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 12 | Trivial. |", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "f5757609f28a7743", "improvement": -0.0003923912481411662, "max_boundary_excess": -6.082421874827662e-06, "max_pair_overlap_depth": -1.8024499229385427e-05, "metric_expression": "12.00039", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 12.000392391248141, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 12.0, "setup": "hexintri", "side": 12.000392391248141, "solution_path": "data/solutions/generated/hexintri_19_f5757609f28a7743.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T16:24:14+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/f5757609f28a7743.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@20", "density": 0.8162942117377381, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 12.1243, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "7\u221a3 = 12.1243+", "friedman_metric_symbol": "s", "friedman_metric_value": 12.12435565298214, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@20", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "7\u221a3 = 12.1243+", "metric_symbol": "s", "metric_value": 12.1243, "reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "f59179c5b6665dc4", "improvement": -0.00024001251311389638, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.116403950810266e-06, "max_pair_overlap_depth": -3.364591626842106e-05, "metric_expression": "12.12460", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 12.124595665495255, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 12.12435565298214, "setup": "hexintri", "side": 12.124595665495255, "solution_path": "data/solutions/generated/hexintri_020_f59179c5b6665dc4.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/f59179c5b6665dc4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@21", "density": 0.8571035425372456, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 12.1243, "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "friedman_metric_expression": "7\u221a3 = 12.1243+", "friedman_metric_symbol": "s", "friedman_metric_value": 12.12435565298214, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@21", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "7\u221a3 = 12.1243+", "metric_symbol": "s", "metric_value": 12.1243, "reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "6cf726ac83ba7d7f", "improvement": -0.000278063717637167, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7607980864287318e-06, "max_pair_overlap_depth": -2.977721456209892e-05, "metric_expression": "12.12463", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 12.124633716699778, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 12.12435565298214, "setup": "hexintri", "side": 12.124633716699778, "solution_path": "data/solutions/generated/hexintri_021_6cf726ac83ba7d7f.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/6cf726ac83ba7d7f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@1", "density": 0.9999940796878448, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/1.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/1.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 1 | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "13c63959e19cfeb5", "improvement": -2.96016922152198e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.1903479056983753e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0000029601692215, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.0, "setup": "octinoct", "side": 1.0000029601692215, "solution_path": "data/solutions/generated/octinoct_001_13c63959e19cfeb5.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/13c63959e19cfeb5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@2", "density": 0.4999889107582135, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/2.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/2.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 2 | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "937fb450c622d9b9", "improvement": -2.2178852493670576e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.909847599495863e-06, "max_pair_overlap_depth": -3.0343321494846753e-05, "metric_expression": "2.00002", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0000221788524937, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "octinoct", "side": 2.0000221788524937, "solution_path": "data/solutions/generated/octinoct_002_937fb450c622d9b9.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/937fb450c622d9b9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@3", "density": 0.6361550822369931, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.17157, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/3.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "5\u20132\u221a2 = 2.17157+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.1715728752538097, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@3", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5\u20132\u221a2 = 2.17157+", "metric_symbol": "s", "metric_value": 2.17157, "reference_text": "s = 5\u20132\u221a2 = 2.17157+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/3.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5\u20132\u221a2 = 2.17157+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "4cb37df94277ed6e", "improvement": -2.3593663045051727e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.359798521217012e-07, "max_pair_overlap_depth": -2.9093807346031175e-05, "metric_expression": "2.17160", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.1715964689168548, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.1715728752538097, "setup": "octinoct", "side": 2.1715964689168548, "solution_path": "data/solutions/generated/octinoct_003_4cb37df94277ed6e.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/4cb37df94277ed6e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@4", "density": 0.7008534259385343, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.38895, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/4.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "\u221a(5+1/\u221a2) = 2.38895+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.3889551651687704, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@4", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "\u221a(5+1/\u221a2) = 2.38895+", "metric_symbol": "s", "metric_value": 2.38895, "reference_text": "s = \u221a(5+1/\u221a2) = 2.38895+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/4.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = \u221a(5+1/\u221a2) = 2.38895+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "8759832408431e84", "improvement": -4.6185877291993194e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.873179406841027e-06, "max_pair_overlap_depth": -4.8382172928693526e-05, "metric_expression": "2.38900", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.3890013510460624, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.3889551651687704, "setup": "octinoct", "side": 2.3890013510460624, "solution_path": "data/solutions/generated/octinoct_004_8759832408431e84.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/8759832408431e84.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@5", "density": 0.6822471038460284, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.7071, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/5.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "2+1/\u221a2 = 2.70710+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.7071067811865475, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@5", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2+1/\u221a2 = 2.70710+", "metric_symbol": "s", "metric_value": 2.7071, "reference_text": "s = 2+1/\u221a2 = 2.70710+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/5.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 2+1/\u221a2 = 2.70710+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "d3468761b0fe9922", "improvement": -5.4636048620437805e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3153662665326975e-06, "max_pair_overlap_depth": -4.586217379215496e-05, "metric_expression": "2.70716", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.707161417235168, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.7071067811865475, "setup": "octinoct", "side": 2.707161417235168, "solution_path": "data/solutions/generated/octinoct_005_d3468761b0fe9922.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/d3468761b0fe9922.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@6", "density": 0.6715848857993428, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.98915, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/6.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "2.98915+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.98915, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@6", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.98915+", "metric_symbol": "s", "metric_value": 2.98915, "reference_text": "s = 2.98915+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/6.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 2.98915+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "3c4b2267adcca69f", "improvement": 0.0001551389501637246, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.973975728535522e-06, "max_pair_overlap_depth": -2.153911208435666e-05, "metric_expression": "2.98899", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.9889948610498362, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.98915, "setup": "octinoct", "side": 2.9889948610498362, "solution_path": "data/solutions/generated/octinoct_006_3c4b2267adcca69f.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/3c4b2267adcca69f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@7", "density": 0.7777522978920184, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/7.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@7", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "s = 3 | Trivial. |", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/7.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 3 | Trivial. |", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "a0053fa5c22778e9", "improvement": -4.914098707065051e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2079023857814054e-06, "max_pair_overlap_depth": -2.6395744560092638e-05, "metric_expression": "3.00005", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0000491409870707, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.0, "setup": "octinoct", "side": 3.0000491409870707, "solution_path": "data/solutions/generated/octinoct_007_a0053fa5c22778e9.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/a0053fa5c22778e9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@8", "density": 0.7457363085593237, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 3.27526, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/8.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "3.27526+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.27526, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@8", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3.27526+", "metric_symbol": "s", "metric_value": 3.27526, "reference_text": "s = 3.27526+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/8.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 3.27526+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "697fa4dfd3dbc6eb", "improvement": -4.953250458550329e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.188513199476399e-06, "max_pair_overlap_depth": -7.758148462100323e-06, "metric_expression": "3.27531", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.2753095325045853, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.27526, "setup": "octinoct", "side": 3.2753095325045853, "solution_path": "data/solutions/generated/octinoct_008_697fa4dfd3dbc6eb.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/697fa4dfd3dbc6eb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@9", "density": 0.7720692797565871, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 3.41421, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/9.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "2+\u221a2 = 3.41421+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.414213562373095, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@9", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2+\u221a2 = 3.41421+", "metric_symbol": "s", "metric_value": 3.41421, "reference_text": "s = 2+\u221a2 = 3.41421+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/9.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 2+\u221a2 = 3.41421+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "7face58a13302eec", "improvement": -1.9145433183265226e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3803938489295472e-05, "max_pair_overlap_depth": -2.6349120965107886e-06, "metric_expression": "3.41423", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.414232707806278, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.414213562373095, "setup": "octinoct", "side": 3.414232707806278, "solution_path": "data/solutions/generated/octinoct_009_7face58a13302eec.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/7face58a13302eec.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@10", "density": 0.7276473732898788, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 3.7071, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/10.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "3+1/\u221a2 = 3.70710+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.7071067811865475, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@10", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3+1/\u221a2 = 3.70710+", "metric_symbol": "s", "metric_value": 3.7071, "reference_text": "s = 3+1/\u221a2 = 3.70710+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/10.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 3+1/\u221a2 = 3.70710+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "bcfc9e294bb15f21", "improvement": -3.773928495354184e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.744023326611903e-06, "max_pair_overlap_depth": -8.094414775450254e-06, "metric_expression": "3.70714", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.707144520471501, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.7071067811865475, "setup": "octinoct", "side": 3.707144520471501, "solution_path": "data/solutions/generated/octinoct_010_bcfc9e294bb15f21.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/bcfc9e294bb15f21.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@11", "density": 0.7111917967389362, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 3.9327, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/11.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "3.93270+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.9327, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@11", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3.93270+", "metric_symbol": "s", "metric_value": 3.9327, "reference_text": "s = 3.93270+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/11.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 3.93270+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "5cff1aa2d330c49e", "improvement": -0.00011007046297972778, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.479089320941585e-06, "max_pair_overlap_depth": -8.811356971838435e-06, "metric_expression": "3.93281", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.93281007046298, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.9327, "setup": "octinoct", "side": 3.93281007046298, "solution_path": "data/solutions/generated/octinoct_011_5cff1aa2d330c49e.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/5cff1aa2d330c49e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@12", "density": 0.7499773041118397, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/12.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@12", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "s = 4 | Trivial. |", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/12.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4 | Trivial. |", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "7bdd4832407bd3be", "improvement": -6.052374207055067e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.082066348113342e-06, "max_pair_overlap_depth": -1.2861422511445397e-05, "metric_expression": "4.00006", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0000605237420706, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.0, "setup": "octinoct", "side": 4.0000605237420706, "solution_path": "data/solutions/generated/octinoct_012_7bdd4832407bd3be.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/7bdd4832407bd3be.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@13", "density": 0.7469920374756177, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 4.17157, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/13.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "7\u20132\u221a2 = 4.17157+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.17157287525381, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@13", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "7\u20132\u221a2 = 4.17157+", "metric_symbol": "s", "metric_value": 4.17157, "reference_text": "s = 7\u20132\u221a2 = 4.17157+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/13.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 7\u20132\u221a2 = 4.17157+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "867ad172957f0ddb", "improvement": -0.000133085095542107, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.683174531654637e-06, "max_pair_overlap_depth": -2.596769201668181e-06, "metric_expression": "4.17171", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.171705960349352, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.17157287525381, "setup": "octinoct", "side": 4.171705960349352, "solution_path": "data/solutions/generated/octinoct_013_867ad172957f0ddb.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/867ad172957f0ddb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@14", "density": 0.7637114154056861, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 4.28155, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/14.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4.28155+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.28155, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@14", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "4.28155+", "metric_symbol": "s", "metric_value": 4.28155, "reference_text": "s = 4.28155+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "14.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/14.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4.28155+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "190d6c8f3f4e37d6", "improvement": 1.6200963535162316e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9636658184049817e-06, "max_pair_overlap_depth": -1.2788583332312697e-05, "metric_expression": "4.28153", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.281533799036465, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.28155, "setup": "octinoct", "side": 4.281533799036465, "solution_path": "data/solutions/generated/octinoct_014_190d6c8f3f4e37d6.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/190d6c8f3f4e37d6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@15", "density": 0.7554665958519668, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 4.45594, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/15.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4.45594+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.45594, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@15", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "4.45594+", "metric_symbol": "s", "metric_value": 4.45594, "reference_text": "s = 4.45594+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/15.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4.45594+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "60843ec4ea56ad88", "improvement": 1.3726756218801484e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.050759161282626e-06, "max_pair_overlap_depth": -3.648956153723404e-05, "metric_expression": "4.45593", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.455926273243781, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.45594, "setup": "octinoct", "side": 4.455926273243781, "solution_path": "data/solutions/generated/octinoct_015_60843ec4ea56ad88.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/60843ec4ea56ad88.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@16", "density": 0.7566625545620705, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 4.59824, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/16.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4.59824+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.59824, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@16", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "4.59824+", "metric_symbol": "s", "metric_value": 4.59824, "reference_text": "s = 4.59824+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/16.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4.59824+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "1178c6831eb46264", "improvement": -0.00018248651533525617, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.297640975948298e-06, "max_pair_overlap_depth": -9.126693151007004e-06, "metric_expression": "4.59842", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.598422486515335, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.59824, "setup": "octinoct", "side": 4.598422486515335, "solution_path": "data/solutions/generated/octinoct_016_1178c6831eb46264.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/1178c6831eb46264.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@17", "density": 0.7511087688524583, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 4.75741, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/17.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4.75741+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.75741, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@17", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "4.75741+", "metric_symbol": "s", "metric_value": 4.75741, "reference_text": "s = 4.75741+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/17.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4.75741+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "ebcfc45448cb8c5f", "improvement": -2.6985802159096295e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.580862819791944e-06, "max_pair_overlap_depth": -2.6446396224955038e-05, "metric_expression": "4.75744", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.757436985802159, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.75741, "setup": "octinoct", "side": 4.757436985802159, "solution_path": "data/solutions/generated/octinoct_017_ebcfc45448cb8c5f.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/ebcfc45448cb8c5f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@18", "density": 0.7629999765077309, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 4.85717, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/18.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4.85717+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.85717, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@18", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "4.85717+", "metric_symbol": "s", "metric_value": 4.85717, "reference_text": "s = 4.85717+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/18.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4.85717+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "46f5ac176d150ffa", "improvement": 0.00010416375427002578, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.225773906749903e-06, "max_pair_overlap_depth": -2.521618462036912e-05, "metric_expression": "4.85707", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.85706583624573, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.85717, "setup": "octinoct", "side": 4.85706583624573, "solution_path": "data/solutions/generated/octinoct_018_46f5ac176d150ffa.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/46f5ac176d150ffa.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@19", "density": 0.7795195170060211, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 4.93586, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/19.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4.93586+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.93586, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "4.93586+", "metric_symbol": "s", "metric_value": 4.93586, "reference_text": "s = 4.93586+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/19.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4.93586+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "4a7169be4bda1825", "improvement": -0.0011420082689239663, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1928573301213418e-05, "max_pair_overlap_depth": -1.491417372267989e-06, "metric_expression": "4.93700", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.937002008268924, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.93586, "setup": "octinoct", "side": 4.937002008268924, "solution_path": "data/solutions/generated/octinoct_019_4a7169be4bda1825.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/4a7169be4bda1825.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@20", "density": 0.778654925537014, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 5.06781, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/20.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "5.06781+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.06781, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@20", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5.06781+", "metric_symbol": "s", "metric_value": 5.06781, "reference_text": "s = 5.06781+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/20.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.06781+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "ef9ffbe57f51321a", "improvement": -0.0002585475900360734, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.202696065204785e-06, "max_pair_overlap_depth": -3.692189855719619e-05, "metric_expression": "5.06807", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.068068547590036, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.06781, "setup": "octinoct", "side": 5.068068547590036, "solution_path": "data/solutions/generated/octinoct_020_ef9ffbe57f51321a.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/ef9ffbe57f51321a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@21", "density": 0.7774838310416734, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 5.19715, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/21.gif", "friedman_metric_expression": "5.19715+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.19715, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@21", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5.19715+", "metric_symbol": "s", "metric_value": 5.19715, "reference_text": "s = 5.19715+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/21.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.19715+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "92c4bcf9428983c2", "improvement": 1.540400287325383e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.1696825424876755e-06, "max_pair_overlap_depth": -2.317393259165801e-05, "metric_expression": "5.19713", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.1971345959971265, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.19715, "setup": "octinoct", "side": 5.1971345959971265, "solution_path": "data/solutions/generated/octinoct_021_92c4bcf9428983c2.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/92c4bcf9428983c2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@22", "density": 0.7663269933124698, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 5.3575, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/22.gif", "friedman_metric_expression": "5.35750+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.3575, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@22", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5.35750+", "metric_symbol": "s", "metric_value": 5.3575, "reference_text": "s = 5.35750+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/22.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.35750+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "b8f2befaa2d4a75e", "improvement": -0.0005193617687213603, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.99203724676962e-06, "max_pair_overlap_depth": -1.57400449714018e-05, "metric_expression": "5.35802", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.358019361768721, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.3575, "setup": "octinoct", "side": 5.358019361768721, "solution_path": "data/solutions/generated/octinoct_022_b8f2befaa2d4a75e.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/b8f2befaa2d4a75e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@23", "density": 0.7845835529808874, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 5.4144, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/23.gif", "friedman_metric_expression": "5.41440+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.4144, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@23", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5.41440+", "metric_symbol": "s", "metric_value": 5.4144, "reference_text": "s = 5.41440+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/23.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.41440+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "d6528e8801e36ce0", "improvement": 7.503853147827755e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3646686331794102e-06, "max_pair_overlap_depth": -4.536567227386712e-05, "metric_expression": "5.41432", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.414324961468521, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.4144, "setup": "octinoct", "side": 5.414324961468521, "solution_path": "data/solutions/generated/octinoct_023_d6528e8801e36ce0.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/d6528e8801e36ce0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@24", "density": 0.777859618157, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 5.55464, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/24.gif", "friedman_metric_expression": "5.55464+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.55464, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@24", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5.55464+", "metric_symbol": "s", "metric_value": 5.55464, "reference_text": "s = 5.55464+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/24.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.55464+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "a34ac6a3c52f70df", "improvement": 1.1631965286973411e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.721783559078116e-06, "max_pair_overlap_depth": -2.4974900467711336e-05, "metric_expression": "5.55463", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.554628368034713, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.55464, "setup": "octinoct", "side": 5.554628368034713, "solution_path": "data/solutions/generated/octinoct_024_a34ac6a3c52f70df.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/a34ac6a3c52f70df.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@25", "density": 0.7805673327264805, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 5.65593, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/25.gif", "friedman_metric_expression": "5.65593+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.65593, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@25", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5.65593+", "metric_symbol": "s", "metric_value": 5.65593, "reference_text": "s = 5.65593+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/25.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.65593+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "113492960b7e7dce", "improvement": -0.003397389940226425, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.281212189125961e-06, "max_pair_overlap_depth": -2.6024797291412938e-05, "metric_expression": "5.65933", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.659327389940226, "n": 25, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.65593, "setup": "octinoct", "side": 5.659327389940226, "solution_path": "data/solutions/generated/octinoct_025_113492960b7e7dce.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/113492960b7e7dce.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@26", "density": 0.7881657239941322, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 5.7394, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/26.gif", "friedman_metric_expression": "5.73940+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.7394, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@26", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5.73940+", "metric_symbol": "s", "metric_value": 5.7394, "reference_text": "s = 5.73940+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/26.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.73940+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "581188c4895e4037", "improvement": -0.004116881359766289, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.43705423351296e-06, "max_pair_overlap_depth": -2.686615288460814e-05, "metric_expression": "5.74352", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.743516881359766, "n": 26, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.7394, "setup": "octinoct", "side": 5.743516881359766, "solution_path": "data/solutions/generated/octinoct_026_581188c4895e4037.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/581188c4895e4037.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@27", "density": 0.7989711846148311, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 5.81238, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/27.gif", "friedman_metric_expression": "5.81238+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.81238, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@27", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "5.81238+", "metric_symbol": "s", "metric_value": 5.81238, "reference_text": "s = 5.81238+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/27.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.81238+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "25c7f85bc0b15209", "improvement": -0.0008341744667159645, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.851030556516347e-06, "max_pair_overlap_depth": -2.4661009629944886e-05, "metric_expression": "5.81321", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.813214174466716, "n": 27, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.81238, "setup": "octinoct", "side": 5.813214174466716, "solution_path": "data/solutions/generated/octinoct_027_25c7f85bc0b15209.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/25c7f85bc0b15209.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@28", "density": 0.8242204012359605, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 5.82842, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/28.gif", "friedman_metric_expression": "3+2\u221a2 = 5.82842+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.82842712474619, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@28", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3+2\u221a2 = 5.82842+", "metric_symbol": "s", "metric_value": 5.82842, "reference_text": "s = 3+2\u221a2 = 5.82842+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/28.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 3+2\u221a2 = 5.82842+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "f8d9c8a9f9a38d45", "improvement": -8.005314316950063e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.739062384519148e-06, "max_pair_overlap_depth": -9.673739088000843e-06, "metric_expression": "5.82851", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.828507177889359, "n": 28, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.82842712474619, "setup": "octinoct", "side": 5.828507177889359, "solution_path": "data/solutions/generated/octinoct_028_f8d9c8a9f9a38d45.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/f8d9c8a9f9a38d45.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@29", "density": 0.7902111886471865, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 6.05746, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/29.gif", "friedman_metric_expression": "6.05746+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.05746, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@29", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "6.05746+", "metric_symbol": "s", "metric_value": 6.05746, "reference_text": "s = 6.05746+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/29.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 6.05746+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "30789c6bb8fd99b7", "improvement": -0.0005140918720876186, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.805265150873157e-06, "max_pair_overlap_depth": -5.6301265520808386e-05, "metric_expression": "6.05797", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.0579740918720875, "n": 29, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.05746, "setup": "octinoct", "side": 6.0579740918720875, "solution_path": "data/solutions/generated/octinoct_029_30789c6bb8fd99b7.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/30789c6bb8fd99b7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@30", "density": 0.7919434557655346, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 6.15432, "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/30.gif", "friedman_metric_expression": "6.15432+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.15432, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@30", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "6.15432+", "metric_symbol": "s", "metric_value": 6.15432, "reference_text": "s = 6.15432+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/30.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 6.15432+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "1a16dc8a4d741008", "improvement": -0.00047426130353134255, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1243912272535679e-05, "max_pair_overlap_depth": -2.8046648627544357e-05, "metric_expression": "6.15479", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.154794261303532, "n": 30, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.15432, "setup": "octinoct", "side": 6.154794261303532, "solution_path": "data/solutions/generated/octinoct_030_1a16dc8a4d741008.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/1a16dc8a4d741008.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@1", "density": 0.7568185573097284, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 0.86065, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/1.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a((5+\u221a5)/10) = .86065+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.8506508083520399, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "penincir@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a((5+\u221a5)/10) = .86065+", "metric_symbol": "r", "metric_value": 0.86065, "reference_text": "r = \u221a((5+\u221a5)/10) = .86065+ | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/1.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = \u221a((5+\u221a5)/10) = .86065+ | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": false, "id": "ca75a5cd7cad481c", "improvement": -4.5922040563528554e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.0926430426282394e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.85066", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 0.8506554005560962, "n": 1, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%. Attribution policy: any @1 packing is credited as Trivial.", "original_submitted_by": "Nathan Roll", "record_type": "verified", "reference_side": 0.8506508083520399, "setup": "penincir", "side": 1.7013108011121925, "solution_path": "data/solutions/generated/penincir_001_ca75a5cd7cad481c.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/ca75a5cd7cad481c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@2", "density": 0.462509898701161, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.53884, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/2.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a(5+2\u221a5)/2 = 1.53884+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.5388417685876268, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "penincir@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a(5+2\u221a5)/2 = 1.53884+", "metric_symbol": "r", "metric_value": 1.53884, "reference_text": "r = \u221a(5+2\u221a5)/2 = 1.53884+ | Trivial.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/2.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = \u221a(5+2\u221a5)/2 = 1.53884+ | Trivial.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "44da10d1d5897aae", "improvement": -3.566683474787169e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.684702690331392e-08, "max_pair_overlap_depth": -5.994543612077171e-05, "metric_expression": "1.53888", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.5388774354223747, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.5388417685876268, "setup": "penincir", "side": 3.0777548708447493, "solution_path": "data/solutions/generated/penincir_002_44da10d1d5897aae.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/44da10d1d5897aae.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@3", "density": 0.6275054691586099, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.61803, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/3.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "(1+\u221a5)/2 = 1.61803+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.618033988749895, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "penincir@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "(1+\u221a5)/2 = 1.61803+", "metric_symbol": "r", "metric_value": 1.61803, "reference_text": "r = (1+\u221a5)/2 = 1.61803+ | Trivial.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/3.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = (1+\u221a5)/2 = 1.61803+ | Trivial.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "350d35e2110a508b", "improvement": -5.133756879227569e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.919906156253262e-06, "max_pair_overlap_depth": -5.073652219536114e-05, "metric_expression": "1.61809", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.6180853263186872, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.618033988749895, "setup": "penincir", "side": 3.2361706526373744, "solution_path": "data/solutions/generated/penincir_003_350d35e2110a508b.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/350d35e2110a508b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@4", "density": 0.6542873961171766, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 1.82971, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/4.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "1.82971+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.82971, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "penincir@4", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.82971+", "metric_symbol": "r", "metric_value": 1.82971, "reference_text": "r = 1.82971+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/4.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 1.82971+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "d03dba2c6efc98dd", "improvement": -5.479863407176211e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.02075710251404e-06, "max_pair_overlap_depth": -3.1570603938990693e-05, "metric_expression": "1.82976", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.8297647986340717, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.82971, "setup": "penincir", "side": 3.6595295972681434, "solution_path": "data/solutions/generated/penincir_004_d03dba2c6efc98dd.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/d03dba2c6efc98dd.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@5", "density": 0.6626607161574516, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.03271, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/5.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.03271+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.03271, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "penincir@5", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.03271+", "metric_symbol": "r", "metric_value": 2.03271, "reference_text": "r = 2.03271+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "5.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/5.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 2.03271+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "97027d267cb23b7f", "improvement": -6.326016348978669e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.209947377376011e-06, "max_pair_overlap_depth": -3.7991648266566536e-05, "metric_expression": "2.03277", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.0327732601634896, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.03271, "setup": "penincir", "side": 4.065546520326979, "solution_path": "data/solutions/generated/penincir_005_97027d267cb23b7f.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/97027d267cb23b7f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@6", "density": 0.6624931586206462, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.22703, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/6.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a((25+11\u221a5)/10) = 2.22703+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.2270327288232137, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "penincir@6", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "\u221a((25+11\u221a5)/10) = 2.22703+", "metric_symbol": "r", "metric_value": 2.22703, "reference_text": "r = \u221a((25+11\u221a5)/10) = 2.22703+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/6.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = \u221a((25+11\u221a5)/10) = 2.22703+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "4b5f96ff666b1595", "improvement": -4.0390809734169864e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3229349565289112e-06, "max_pair_overlap_depth": -2.759876285962637e-05, "metric_expression": "2.22707", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.227073119632948, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.2270327288232137, "setup": "penincir", "side": 4.454146239265896, "solution_path": "data/solutions/generated/penincir_006_4b5f96ff666b1595.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/4b5f96ff666b1595.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@7", "density": 0.7279626259462092, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.29474, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/7.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.29474+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.29474, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "penincir@7", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.29474+", "metric_symbol": "r", "metric_value": 2.29474, "reference_text": "r = 2.29474+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/7.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 2.29474+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "ef28e611d9e22eb0", "improvement": -5.570482584049685e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.717800656082403e-06, "max_pair_overlap_depth": -4.1591260455220436e-05, "metric_expression": "2.29480", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.2947957048258405, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.29474, "setup": "penincir", "side": 4.589591409651681, "solution_path": "data/solutions/generated/penincir_007_ef28e611d9e22eb0.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/ef28e611d9e22eb0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@8", "density": 0.7115852708183573, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.48128, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/8.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.48128+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.48128, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "penincir@8", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.48128+", "metric_symbol": "r", "metric_value": 2.48128, "reference_text": "r = 2.48128+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/8.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 2.48128+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "1a134d3903b2814e", "improvement": -3.0242757913079288e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.375187333127144e-07, "max_pair_overlap_depth": -8.34480700673268e-06, "metric_expression": "2.48131", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.481310242757913, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.48128, "setup": "penincir", "side": 4.962620485515826, "solution_path": "data/solutions/generated/penincir_008_1a134d3903b2814e.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/1a134d3903b2814e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@9", "density": 0.674675474238072, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.70171, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/9.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.70171+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.70171, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "penincir@9", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.70171+", "metric_symbol": "r", "metric_value": 2.70171, "reference_text": "r = 2.70171+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/9.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 2.70171+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "1ca74640a9bafbff", "improvement": -0.0011487048015377255, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.541032137428402e-06, "max_pair_overlap_depth": -3.412963059545859e-05, "metric_expression": "2.70286", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.7028587048015376, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.70171, "setup": "penincir", "side": 5.405717409603075, "solution_path": "data/solutions/generated/penincir_009_1ca74640a9bafbff.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/1ca74640a9bafbff.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@10", "density": 0.6983515169709827, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.79768, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/10.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.79768+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.79768, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "penincir@10", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.79768+", "metric_symbol": "r", "metric_value": 2.79768, "reference_text": "r = 2.79768+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/10.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 2.79768+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "b50c304b68607cc4", "improvement": -0.002671254854186955, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.377527520027513e-06, "max_pair_overlap_depth": -1.3481998292097508e-05, "metric_expression": "2.80035", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.800351254854187, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.79768, "setup": "penincir", "side": 5.600702509708374, "solution_path": "data/solutions/generated/penincir_010_b50c304b68607cc4.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/b50c304b68607cc4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@11", "density": 0.7152777059461288, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.9018, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/11.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.90180+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.9018, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "penincir@11", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.90180+", "metric_symbol": "r", "metric_value": 2.9018, "reference_text": "r = 2.90180+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "11.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/11.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 2.90180+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "11.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "37f9123e1b2153ff", "improvement": -0.0002744381126040807, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.569993058365583e-07, "max_pair_overlap_depth": -3.207817623795961e-05, "metric_expression": "2.90207", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.9020744381126042, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.9018, "setup": "penincir", "side": 5.8041488762252085, "solution_path": "data/solutions/generated/penincir_011_37f9123e1b2153ff.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/37f9123e1b2153ff.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@12", "density": 0.7213016172544706, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.01826, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/12.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.01826+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.01826, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "penincir@12", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.01826+", "metric_symbol": "r", "metric_value": 3.01826, "reference_text": "r = 3.01826+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/12.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.01826+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "a564353850abf267", "improvement": -0.00017424806894128508, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.481723353017998e-06, "max_pair_overlap_depth": -2.751801632361328e-05, "metric_expression": "3.01843", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.0184342480689415, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.01826, "setup": "penincir", "side": 6.036868496137883, "solution_path": "data/solutions/generated/penincir_012_a564353850abf267.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/a564353850abf267.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@13", "density": 0.7515432650569983, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.07769, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/13.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a(5+2\u221a5)/2 =3.07769+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.07769, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "penincir@13", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "\u221a(5+2\u221a5)/2 =3.07769+", "metric_symbol": "r", "metric_value": 3.07769, "reference_text": "r = \u221a(5+2\u221a5)/2 =3.07769+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/13.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = \u221a(5+2\u221a5)/2 =3.07769+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "c39e9475d5bde4a6", "improvement": -0.0001371927275344298, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.94574749318366e-06, "max_pair_overlap_depth": -1.7086792766463077e-05, "metric_expression": "3.07783", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.0778271927275345, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.07769, "setup": "penincir", "side": 6.155654385455069, "solution_path": "data/solutions/generated/penincir_013_c39e9475d5bde4a6.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/c39e9475d5bde4a6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@14", "density": 0.7320837719347534, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.23385, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/14.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.23385+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.23385, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "penincir@14", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.23385+", "metric_symbol": "r", "metric_value": 3.23385, "reference_text": "r = 3.23385+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/14.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.23385+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "4798ec354812edfb", "improvement": -0.0023337860780814346, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.2470094596680497e-07, "max_pair_overlap_depth": -1.086583313658629e-05, "metric_expression": "3.23618", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.2361837860780813, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.23385, "setup": "penincir", "side": 6.472367572156163, "solution_path": "data/solutions/generated/penincir_014_4798ec354812edfb.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/4798ec354812edfb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@15", "density": 0.7364932523686155, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.33911, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/15.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.33911+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.33911, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "penincir@15", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.33911+", "metric_symbol": "r", "metric_value": 3.33911, "reference_text": "r = 3.33911+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/15.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.33911+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "5fb8f24380ed14ba", "improvement": -0.0006156585665682002, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.531307800791922e-07, "max_pair_overlap_depth": -1.652091133119704e-05, "metric_expression": "3.33973", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.339725658566568, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.33911, "setup": "penincir", "side": 6.679451317133136, "solution_path": "data/solutions/generated/penincir_015_5fb8f24380ed14ba.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/5fb8f24380ed14ba.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@16", "density": 0.7415495303728211, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.43657, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/16.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.43657+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.43657, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "penincir@16", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.43657+", "metric_symbol": "r", "metric_value": 3.43657, "reference_text": "r = 3.43657+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "16.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/16.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.43657+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "eb41133064f5f2da", "improvement": -0.0009042932667306935, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3274146969676224e-06, "max_pair_overlap_depth": -1.0162839398697443e-05, "metric_expression": "3.43747", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.437474293266731, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.43657, "setup": "penincir", "side": 6.874948586533462, "solution_path": "data/solutions/generated/penincir_016_eb41133064f5f2da.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/eb41133064f5f2da.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@17", "density": 0.7557819084683968, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.50958, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/17.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.50958+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.50958, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "penincir@17", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.50958+", "metric_symbol": "r", "metric_value": 3.50958, "reference_text": "r = 3.50958+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/17.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.50958+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "9469ef74fc89a75b", "improvement": -0.00016662106909848262, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3042585254605683e-06, "max_pair_overlap_depth": -2.7118152433835974e-05, "metric_expression": "3.50975", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.5097466210690986, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.50958, "setup": "penincir", "side": 7.019493242138197, "solution_path": "data/solutions/generated/penincir_017_9469ef74fc89a75b.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/9469ef74fc89a75b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@18", "density": 0.7533573813986445, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.6208, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/18.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.62080+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.6208, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "penincir@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.62080+", "metric_symbol": "r", "metric_value": 3.6208, "reference_text": "r = 3.62080+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/18.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.62080+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "767a627015948f32", "improvement": 0.00349375267338381, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7774333678797234e-06, "max_pair_overlap_depth": -3.109065453799076e-05, "metric_expression": "3.61731", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.617306247326616, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.6208, "setup": "penincir", "side": 7.234612494653232, "solution_path": "data/solutions/generated/penincir_018_767a627015948f32.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/767a627015948f32.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@19", "density": 0.771366675320165, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.67287, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/19.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.67287+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.67287, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "penincir@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.67287+", "metric_symbol": "r", "metric_value": 3.67287, "reference_text": "r = 3.67287+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/19.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.67287+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "9d482c8012998879", "improvement": 8.154982387598153e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.817340790579493e-06, "max_pair_overlap_depth": -1.6517110137281854e-05, "metric_expression": "3.67279", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.672788450176124, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.67287, "setup": "penincir", "side": 7.345576900352248, "solution_path": "data/solutions/generated/penincir_019_9d482c8012998879.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/9d482c8012998879.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@20", "density": 0.7575056542556782, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.80415, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/20.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.80415+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.80415, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "penincir@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.80415+", "metric_symbol": "r", "metric_value": 3.80415, "reference_text": "r = 3.80415+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/20.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.80415+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "5271226652403829", "improvement": 0.0016291138375779113, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.231424091092009e-06, "max_pair_overlap_depth": -3.071782635011289e-05, "metric_expression": "3.80252", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.802520886162422, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.80415, "setup": "penincir", "side": 7.605041772324844, "solution_path": "data/solutions/generated/penincir_020_5271226652403829.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/5271226652403829.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@21", "density": 0.7521173669587212, "friedman_analytical_or_proved": false, "friedman_credit": "Cyril Summerfield", "friedman_date": "April 2026", "friedman_display_metric_value": 3.90735, "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/21.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.90735+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.90735, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "penincir@21", "credit": "Cyril Summerfield", "date": "April 2026", "family_updated": "", "metric_expression": "3.90735+", "metric_symbol": "r", "metric_value": 3.90735, "reference_text": "r = 3.90735+ | Found by Cyril Summerfield | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/21.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.90735+ | Found by Cyril Summerfield | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "4625f732ad11a859", "improvement": -0.0030068209876064067, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9813425364011437e-06, "max_pair_overlap_depth": -1.4218243721247914e-05, "metric_expression": "3.91036", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.9103568209876065, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.90735, "setup": "penincir", "side": 7.820713641975213, "solution_path": "data/solutions/generated/penincir_021_4625f732ad11a859.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Cyril Summerfield", "svg_path": "data/svg/4625f732ad11a859.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@1", "density": 0.9999780359352667, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/1.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/1.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 1 | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "b3173648630fcdeb", "improvement": -1.0982213277443975e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.256503348572871e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0000109822132774, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.0, "setup": "peninpen", "side": 1.0000109822132774, "solution_path": "data/solutions/generated/peninpen_001_b3173648630fcdeb.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/b3173648630fcdeb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@2", "density": 0.4999891232484648, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/2.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/2.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "edac094186a54129", "improvement": -2.175385798786067e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0537211348702708e-06, "max_pair_overlap_depth": -1.9731507571563167e-05, "metric_expression": "2.00002", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.000021753857988, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "peninpen", "side": 2.000021753857988, "solution_path": "data/solutions/generated/peninpen_002_edac094186a54129.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/edac094186a54129.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@3", "density": 0.599978840427638, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.23606, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/3.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a5 = 2.23606+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.23606797749979, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@3", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "\u221a5 = 2.23606+", "metric_symbol": "s", "metric_value": 2.23606, "reference_text": "s = \u221a5 = 2.23606+ | Found by Jonathan Viquerat in April 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/3.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = \u221a5 = 2.23606+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "bf261a4dce178a90", "improvement": -3.942957804081715e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.7662857614262655e-06, "max_pair_overlap_depth": -2.7755970794667603e-05, "metric_expression": "2.23611", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.2361074070778306, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.23606797749979, "setup": "peninpen", "side": 2.2361074070778306, "solution_path": "data/solutions/generated/peninpen_003_bf261a4dce178a90.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/bf261a4dce178a90.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@4", "density": 0.6678717661629443, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.44719, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/4.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.44719+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.44719, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@4", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.44719+", "metric_symbol": "s", "metric_value": 2.44719, "reference_text": "s = 2.44719+ | Found by Jonathan Viquerat in April 2026.", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/4.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 2.44719+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "85435733af14070a", "improvement": -8.88306059834143e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0634336001709255e-06, "max_pair_overlap_depth": -3.575601486860425e-05, "metric_expression": "2.44728", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.4472788306059834, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.44719, "setup": "peninpen", "side": 2.4472788306059834, "solution_path": "data/solutions/generated/peninpen_004_85435733af14070a.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/85435733af14070a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@5", "density": 0.7294617516267693, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.61803, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/6.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(3+\u221a5)/2 = 2.61803+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.618033988749895, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "(3+\u221a5)/2 = 2.61803+", "metric_symbol": "s", "metric_value": 2.61803, "reference_text": "s = (3+\u221a5)/2 = 2.61803+ | Trivial.", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/6.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = (3+\u221a5)/2 = 2.61803+ | Trivial.", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "28fa9f787595145b", "improvement": -5.099395129359863e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.513169742800457e-06, "max_pair_overlap_depth": -2.4501936757292953e-06, "metric_expression": "2.61808", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.6180849827011885, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.618033988749895, "setup": "peninpen", "side": 2.6180849827011885, "solution_path": "data/solutions/generated/peninpen_005_28fa9f787595145b.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/28fa9f787595145b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@6", "density": 0.8753627744848066, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.61803, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/6.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(3+\u221a5)/2 = 2.61803+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.618033988749895, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@6", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "(3+\u221a5)/2 = 2.61803+", "metric_symbol": "s", "metric_value": 2.61803, "reference_text": "s = (3+\u221a5)/2 = 2.61803+ | Trivial.", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/6.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = (3+\u221a5)/2 = 2.61803+ | Trivial.", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "198bd12691483df1", "improvement": -3.8024766128241794e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4414928963119693e-06, "max_pair_overlap_depth": -1.898562579671914e-05, "metric_expression": "2.61807", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.618072013516023, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.618033988749895, "setup": "peninpen", "side": 2.618072013516023, "solution_path": "data/solutions/generated/peninpen_006_198bd12691483df1.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/198bd12691483df1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@7", "density": 0.7384663216832239, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.07866, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/7.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.07866+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.07866, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@7", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.07866+", "metric_symbol": "s", "metric_value": 3.07866, "reference_text": "s = 3.07866+ | Found by Jonathan Viquerat in April 2026.", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/7.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 3.07866+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "5b6283ab3dc4c3b5", "improvement": -0.00015556249375014986, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.964189962454e-06, "max_pair_overlap_depth": -1.5079265303863387e-05, "metric_expression": "3.07882", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0788155624937503, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.07866, "setup": "peninpen", "side": 3.0788155624937503, "solution_path": "data/solutions/generated/peninpen_007_5b6283ab3dc4c3b5.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/5b6283ab3dc4c3b5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@8", "density": 0.7191427449408644, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.33514, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/8.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.33514+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.33514, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@8", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.33514+", "metric_symbol": "s", "metric_value": 3.33514, "reference_text": "s = 3.33514+ | Found by Jonathan Viquerat in April 2026.", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/8.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 3.33514+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "de5f4ff90a59b8bf", "improvement": -0.00017949381007964504, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.630985964589326e-06, "max_pair_overlap_depth": -3.1607294870367175e-05, "metric_expression": "3.33532", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.3353194938100796, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.33514, "setup": "peninpen", "side": 3.3353194938100796, "solution_path": "data/solutions/generated/peninpen_008_de5f4ff90a59b8bf.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/de5f4ff90a59b8bf.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@9", "density": 0.756208451025979, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.44956, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/9.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.44956+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.44956, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@9", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.44956+", "metric_symbol": "s", "metric_value": 3.44956, "reference_text": "s = 3.44956+ | Found by Jonathan Viquerat in April 2026.", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/9.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 3.44956+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "291eb24a57cfcd61", "improvement": -0.00029221756483766015, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.66255661877786e-06, "max_pair_overlap_depth": -4.9483298464991776e-05, "metric_expression": "3.44985", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.4498522175648376, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.44956, "setup": "peninpen", "side": 3.4498522175648376, "solution_path": "data/solutions/generated/peninpen_009_291eb24a57cfcd61.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/291eb24a57cfcd61.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@10", "density": 0.7370589618267208, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.68324, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/10.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.68324+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.68324, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@10", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.68324+", "metric_symbol": "s", "metric_value": 3.68324, "reference_text": "s = 3.68324+ | Found by Jonathan Viquerat in April 2026.", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/10.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 3.68324+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "90badee8fc213075", "improvement": -0.0001600058005193361, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0386948383243063e-06, "max_pair_overlap_depth": -3.744974033881299e-05, "metric_expression": "3.68340", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.6834000058005194, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.68324, "setup": "peninpen", "side": 3.6834000058005194, "solution_path": "data/solutions/generated/peninpen_010_90badee8fc213075.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/90badee8fc213075.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@11", "density": 0.7628515256681525, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.79704, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/11.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.79704+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.79704, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@11", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.79704+", "metric_symbol": "s", "metric_value": 3.79704, "reference_text": "s = 3.79704+ | Found by Jonathan Viquerat in April 2026.", "source_image": "11.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/11.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 3.79704+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "11.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "e62e9f2d5556f0f5", "improvement": -0.0002724485549276956, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.930866570871943e-06, "max_pair_overlap_depth": -3.185052846443881e-05, "metric_expression": "3.79731", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.7973124485549277, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.79704, "setup": "peninpen", "side": 3.7973124485549277, "solution_path": "data/solutions/generated/peninpen_011_e62e9f2d5556f0f5.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/e62e9f2d5556f0f5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@12", "density": 0.7615744792401016, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.96926, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/12.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.96926+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.96926, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@12", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.96926+", "metric_symbol": "s", "metric_value": 3.96926, "reference_text": "s = 3.96926+ | Found by Jonathan Viquerat in April 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/12.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 3.96926+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "6f961579a76d6be8", "improvement": -0.00022743831780980273, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.8385847579674985e-06, "max_pair_overlap_depth": -3.1875868486519465e-05, "metric_expression": "3.96949", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.9694874383178096, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.96926, "setup": "peninpen", "side": 3.9694874383178096, "solution_path": "data/solutions/generated/peninpen_012_6f961579a76d6be8.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/6f961579a76d6be8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@13", "density": 0.7865963698125578, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.06523, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/13.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.06523+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.06523, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@13", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.06523+", "metric_symbol": "s", "metric_value": 4.06523, "reference_text": "s = 4.06523+ | Found by Jonathan Viquerat in April 2026.", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/13.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 4.06523+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "ce66c878ffee73fc", "improvement": -9.908623501608815e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.805365438846161e-06, "max_pair_overlap_depth": -6.344819103887289e-06, "metric_expression": "4.06533", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.065329086235016, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.06523, "setup": "peninpen", "side": 4.065329086235016, "solution_path": "data/solutions/generated/peninpen_013_ce66c878ffee73fc.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/ce66c878ffee73fc.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@14", "density": 0.7892057892472966, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.2112, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/14.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.21120+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.2112, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@14", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.21120+", "metric_symbol": "s", "metric_value": 4.2112, "reference_text": "s = 4.21120+ | Found by Jonathan Viquerat in April 2026.", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/14.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 4.21120+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "367de42acefe1aa2", "improvement": -0.0006111178171677167, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.1042346422399235e-06, "max_pair_overlap_depth": -2.557915411749434e-05, "metric_expression": "4.21181", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.2118111178171675, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.2112, "setup": "peninpen", "side": 4.2118111178171675, "solution_path": "data/solutions/generated/peninpen_014_367de42acefe1aa2.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/367de42acefe1aa2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@15", "density": 0.8358892308226911, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.23606, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/15.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2+\u221a5 = 4.23606+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.23606797749979, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@15", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2+\u221a5 = 4.23606+", "metric_symbol": "s", "metric_value": 4.23606, "reference_text": "s = 2+\u221a5 = 4.23606+ | Trivial.", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/15.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 2+\u221a5 = 4.23606+ | Trivial.", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "251c50a18682e896", "improvement": -8.138504475141417e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.6294493786472997e-06, "max_pair_overlap_depth": -5.5218241392651635e-06, "metric_expression": "4.23615", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.236149362544541, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.23606797749979, "setup": "peninpen", "side": 4.236149362544541, "solution_path": "data/solutions/generated/peninpen_015_251c50a18682e896.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/251c50a18682e896.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@16", "density": 0.8202808577467057, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.41636, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/16.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.41636+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.41636, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@16", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.41636+", "metric_symbol": "s", "metric_value": 4.41636, "reference_text": "s = 4.41636+ | Found by Jonathan Viquerat in April 2026.", "source_image": "16.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/16.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 4.41636+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "e2bb776d24739328", "improvement": -0.00014476044476463557, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.7250867795500517e-06, "max_pair_overlap_depth": -1.097689597839846e-05, "metric_expression": "4.41650", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.416504760444765, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.41636, "setup": "peninpen", "side": 4.416504760444765, "solution_path": "data/solutions/generated/peninpen_016_e2bb776d24739328.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/e2bb776d24739328.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@17", "density": 0.7834157819221014, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.65561, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/17.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.65561+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.65561, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@17", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.65561+", "metric_symbol": "s", "metric_value": 4.65561, "reference_text": "s = 4.65561+ | Found by Jonathan Viquerat in April 2026.", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/17.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 4.65561+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "54856cb865a77d57", "improvement": -0.0026991003814726966, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9034050721792276e-06, "max_pair_overlap_depth": -2.8148707974851028e-05, "metric_expression": "4.65831", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.658309100381473, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.65561, "setup": "peninpen", "side": 4.658309100381473, "solution_path": "data/solutions/generated/peninpen_017_54856cb865a77d57.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/54856cb865a77d57.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@18", "density": 0.7892194761771266, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.77541, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/18.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.77541+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.77541, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.77541+", "metric_symbol": "s", "metric_value": 4.77541, "reference_text": "s = 4.77541+ | Found by Jonathan Viquerat in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/18.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 4.77541+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "9c442356ca78c3de", "improvement": -0.0002934971525236918, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.1318004154280254e-06, "max_pair_overlap_depth": -1.258487199295999e-05, "metric_expression": "4.77570", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.775703497152524, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.77541, "setup": "peninpen", "side": 4.775703497152524, "solution_path": "data/solutions/generated/peninpen_018_9c442356ca78c3de.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/9c442356ca78c3de.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@19", "density": 0.7735353200149236, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 4.95269, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/19.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.95269+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.95269, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@19", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "4.95269+", "metric_symbol": "s", "metric_value": 4.95269, "reference_text": "s = 4.95269+ | Found by Ian Watson in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/19.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 4.95269+ | Found by Ian Watson in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "b5440311f7b9b10b", "improvement": -0.0033719480383975764, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.8067945532274755e-06, "max_pair_overlap_depth": -5.844604614307913e-06, "metric_expression": "4.95606", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.956061948038397, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.95269, "setup": "peninpen", "side": 4.956061948038397, "solution_path": "data/solutions/generated/peninpen_019_b5440311f7b9b10b.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/b5440311f7b9b10b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@20", "density": 0.7890584950748962, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 5.04154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/20.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "5.04154+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.04154, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.04154+", "metric_symbol": "s", "metric_value": 5.04154, "reference_text": "s = 5.04154+ | Found by Jonathan Viquerat in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/20.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.04154+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "74f61b73dca76fef", "improvement": 0.0069930192193110585, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.063547145356236e-06, "max_pair_overlap_depth": -1.8870971417950244e-05, "metric_expression": "5.03455", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.034546980780689, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.04154, "setup": "peninpen", "side": 5.034546980780689, "solution_path": "data/solutions/generated/peninpen_020_74f61b73dca76fef.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/74f61b73dca76fef.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@21", "density": 0.7887631772097712, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 5.15948, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/21.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "5.15948+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.15948, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@21", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "5.15948+", "metric_symbol": "s", "metric_value": 5.15948, "reference_text": "s = 5.15948+ | Found by Ignacio Vallejo in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/21.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.15948+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "b731ea055eb53ce1", "improvement": -0.00036117133928748046, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.7271978645132776e-06, "max_pair_overlap_depth": -5.857494896677196e-06, "metric_expression": "5.15984", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.159841171339288, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.15948, "setup": "peninpen", "side": 5.159841171339288, "solution_path": "data/solutions/generated/peninpen_021_b731ea055eb53ce1.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/b731ea055eb53ce1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@22", "density": 0.7927891464448104, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 5.2674, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/22.png", "friedman_metric_expression": "5.26740+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.2674, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@22", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "5.26740+", "metric_symbol": "s", "metric_value": 5.2674, "reference_text": "s = 5.26740+ | Found by Ignacio Vallejo in April 2026.", "source_image": "22.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/22.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.26740+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "07e217f200bb677e", "improvement": -0.0004389908125848052, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.647717325013132e-07, "max_pair_overlap_depth": -3.201222129578518e-05, "metric_expression": "5.26784", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.267838990812585, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.2674, "setup": "peninpen", "side": 5.267838990812585, "solution_path": "data/solutions/generated/peninpen_022_07e217f200bb677e.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/07e217f200bb677e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@23", "density": 0.8042579677659262, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 5.34794, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/23.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "5.34794+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.34794, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@23", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "5.34794+", "metric_symbol": "s", "metric_value": 5.34794, "reference_text": "s = 5.34794+ | Found by Ignacio Vallejo in April 2026.", "source_image": "23.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/23.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.34794+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "4286cb7dfd8b00d7", "improvement": 0.00024989883471082663, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.435117490986131e-07, "max_pair_overlap_depth": -1.717758867814112e-05, "metric_expression": "5.34769", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.3476901011652895, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.34794, "setup": "peninpen", "side": 5.3476901011652895, "solution_path": "data/solutions/generated/peninpen_023_4286cb7dfd8b00d7.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/4286cb7dfd8b00d7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@24", "density": 0.7956104957168404, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 5.49241, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/24.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "5.49241+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.49241, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@24", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "5.49241+", "metric_symbol": "s", "metric_value": 5.49241, "reference_text": "s = 5.49241+ | Found by Ignacio Vallejo in April 2026.", "source_image": "24.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/24.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.49241+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "8859e051020078b2", "improvement": 9.586393159466411e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.446346359580623e-06, "max_pair_overlap_depth": -9.458275242596459e-07, "metric_expression": "5.49231", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.492314136068405, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.49241, "setup": "peninpen", "side": 5.492314136068405, "solution_path": "data/solutions/generated/peninpen_024_8859e051020078b2.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/8859e051020078b2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@25", "density": 0.8019460079699491, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 5.5837, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/25.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "5.58370+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.5837, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@25", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "5.58370+", "metric_symbol": "s", "metric_value": 5.5837, "reference_text": "s = 5.58370+ | Found by Ignacio Vallejo in April 2026.", "source_image": "25.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/25.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.58370+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "25.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "0f0645180a7be991", "improvement": 0.00031674927347591364, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.618192580437412e-06, "max_pair_overlap_depth": -2.8739793660470525e-06, "metric_expression": "5.58338", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.583383250726524, "n": 25, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.5837, "setup": "peninpen", "side": 5.583383250726524, "solution_path": "data/solutions/generated/peninpen_025_0f0645180a7be991.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/0f0645180a7be991.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@1", "density": 0.6736263863631768, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.59811, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/1.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.5981133053749155, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "peninsqu@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "(3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+", "metric_symbol": "s", "metric_value": 1.59811, "reference_text": "s = (3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+ | Trivial. |", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/1.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = (3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+ | Trivial. |", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "ec216f3e37e16785", "improvement": -2.713365417239544e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.733207856432108e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.59814", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.5981404390290879, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.5981133053749155, "setup": "peninsqu", "side": 1.5981404390290879, "solution_path": "data/solutions/generated/peninsqu_001_ec216f3e37e16785.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/ec216f3e37e16785.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@2", "density": 0.5669967061443146, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.46345, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/2.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2.46345+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.46345, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "peninsqu@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2.46345+", "metric_symbol": "s", "metric_value": 2.46345, "reference_text": "s = 2.46345+ | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/2.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 2.46345+ | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "bb5e10eb4917963f", "improvement": -3.0994037563569776e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.416866607183818e-07, "max_pair_overlap_depth": -1.473425980974552e-05, "metric_expression": "2.46348", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.4634809940375635, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.46345, "setup": "peninsqu", "side": 2.4634809940375635, "solution_path": "data/solutions/generated/peninsqu_002_bb5e10eb4917963f.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/bb5e10eb4917963f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@3", "density": 0.6102674136126431, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.90812, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/3.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2.90812+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.90812, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@3", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.90812+", "metric_symbol": "s", "metric_value": 2.90812, "reference_text": "s = 2.90812+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/3.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 2.90812+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "52b96ec8c7f6b741", "improvement": -8.50430757179943e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.362613813108376e-06, "max_pair_overlap_depth": -5.5799797820554886e-05, "metric_expression": "2.90821", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.908205043075718, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.90812, "setup": "peninsqu", "side": 2.908205043075718, "solution_path": "data/solutions/generated/peninsqu_003_52b96ec8c7f6b741.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/52b96ec8c7f6b741.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@4", "density": 0.7148924907955395, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.10252, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/4.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3.10252+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.10252, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@4", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.10252+", "metric_symbol": "s", "metric_value": 3.10252, "reference_text": "s = 3.10252+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/4.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 3.10252+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "a2fcd0b0beef7a6f", "improvement": -0.00013948165686938907, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2690386136380924e-06, "max_pair_overlap_depth": -3.0975557991252956e-05, "metric_expression": "3.10266", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.1026594816568696, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.10252, "setup": "peninsqu", "side": 3.1026594816568696, "solution_path": "data/solutions/generated/peninsqu_004_a2fcd0b0beef7a6f.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/a2fcd0b0beef7a6f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@5", "density": 0.6829538263136812, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.54903, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/5.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3.54903+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.54903, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@5", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.54903+", "metric_symbol": "s", "metric_value": 3.54903, "reference_text": "s = 3.54903+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "5.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/5.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 3.54903+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "bda3fbac20c8a756", "improvement": -3.388580996466217e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.104606408908601e-07, "max_pair_overlap_depth": -5.251218256785428e-06, "metric_expression": "3.54906", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.549063885809965, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.54903, "setup": "peninsqu", "side": 3.549063885809965, "solution_path": "data/solutions/generated/peninsqu_005_bda3fbac20c8a756.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/bda3fbac20c8a756.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@6", "density": 0.6845927654826146, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.883, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/6.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3.88300+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.883, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@6", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.88300+", "metric_symbol": "s", "metric_value": 3.883, "reference_text": "s = 3.88300+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/6.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 3.88300+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "a267ec5809e79964", "improvement": -0.00014813728762552714, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0190677678703185e-06, "max_pair_overlap_depth": -5.678337215275775e-05, "metric_expression": "3.88315", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.8831481372876255, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.883, "setup": "peninsqu", "side": 3.8831481372876255, "solution_path": "data/solutions/generated/peninsqu_006_a267ec5809e79964.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/a267ec5809e79964.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@7", "density": 0.6891282499986281, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.18038, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/7.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.18038+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.18038, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@7", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.18038+", "metric_symbol": "s", "metric_value": 4.18038, "reference_text": "s = 4.18038+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/7.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 4.18038+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "b5565b951637dc85", "improvement": -7.429190517971307e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4725627916323898e-06, "max_pair_overlap_depth": -1.919059115845778e-05, "metric_expression": "4.18045", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.18045429190518, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.18038, "setup": "peninsqu", "side": 4.18045429190518, "solution_path": "data/solutions/generated/peninsqu_007_b5565b951637dc85.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/b5565b951637dc85.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@8", "density": 0.7167004559270932, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.38191, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/8.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.38191+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.38191, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@8", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.38191+", "metric_symbol": "s", "metric_value": 4.38191, "reference_text": "s = 4.38191+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/8.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 4.38191+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "eac74e93d82a54dd", "improvement": -0.00037521167052823046, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2846178652549832e-06, "max_pair_overlap_depth": -2.0945039418324152e-05, "metric_expression": "4.38229", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.382285211670529, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.38191, "setup": "peninsqu", "side": 4.382285211670529, "solution_path": "data/solutions/generated/peninsqu_008_eac74e93d82a54dd.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/eac74e93d82a54dd.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@9", "density": 0.7314097601583741, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.60033, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/9.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.60033+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.60033, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@9", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.60033+", "metric_symbol": "s", "metric_value": 4.60033, "reference_text": "s = 4.60033+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/9.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 4.60033+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "0270d827693b6f8d", "improvement": -0.0008091240419938472, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.8644555136003204e-06, "max_pair_overlap_depth": -1.0559011279553943e-05, "metric_expression": "4.60114", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.601139124041993, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.60033, "setup": "peninsqu", "side": 4.601139124041993, "solution_path": "data/solutions/generated/peninsqu_009_0270d827693b6f8d.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/0270d827693b6f8d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@10", "density": 0.7142869465585481, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 4.90584, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/10.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.90584+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.90584, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@10", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "4.90584+", "metric_symbol": "s", "metric_value": 4.90584, "reference_text": "s = 4.90584+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/10.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 4.90584+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "fba502b92276222e", "improvement": -0.0019743867107484547, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.710048632437797e-06, "max_pair_overlap_depth": -3.5387419318078095e-05, "metric_expression": "4.90781", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.907814386710749, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.90584, "setup": "peninsqu", "side": 4.907814386710749, "solution_path": "data/solutions/generated/peninsqu_010_fba502b92276222e.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/fba502b92276222e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@11", "density": 0.7230188560400136, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 5.11557, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/11.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5.11557+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.11557, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@11", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.11557+", "metric_symbol": "s", "metric_value": 5.11557, "reference_text": "s = 5.11557+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "11.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/11.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 5.11557+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "11.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "3596998e61e47a27", "improvement": -0.0006123708648555493, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.520631561500943e-07, "max_pair_overlap_depth": -2.3531878005744744e-05, "metric_expression": "5.11618", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.1161823708648555, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.11557, "setup": "peninsqu", "side": 5.1161823708648555, "solution_path": "data/solutions/generated/peninsqu_011_3596998e61e47a27.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/3596998e61e47a27.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@12", "density": 0.7539256100231233, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 5.2325, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/12.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5.23250+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.2325, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@12", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.23250+", "metric_symbol": "s", "metric_value": 5.2325, "reference_text": "s = 5.23250+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/12.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 5.23250+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "72fe010d0104fc76", "improvement": -0.0005015230417875216, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6940168948787563e-07, "max_pair_overlap_depth": -3.660774509528508e-05, "metric_expression": "5.23300", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.2330015230417875, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.2325, "setup": "peninsqu", "side": 5.2330015230417875, "solution_path": "data/solutions/generated/peninsqu_012_72fe010d0104fc76.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/72fe010d0104fc76.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@13", "density": 0.7325239130137876, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 5.52183, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/13.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5.52183+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.52183, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@13", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.52183+", "metric_symbol": "s", "metric_value": 5.52183, "reference_text": "s = 5.52183+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/13.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 5.52183+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "b54e12045e01b08b", "improvement": -0.0038439980668076856, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7653030405329436e-07, "max_pair_overlap_depth": -2.666929117722816e-05, "metric_expression": "5.52567", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.525673998066807, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.52183, "setup": "peninsqu", "side": 5.525673998066807, "solution_path": "data/solutions/generated/peninsqu_013_b54e12045e01b08b.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/b54e12045e01b08b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@14", "density": 0.7420924387932526, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 5.69775, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/14.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5.69775+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.69775, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@14", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.69775+", "metric_symbol": "s", "metric_value": 5.69775, "reference_text": "s = 5.69775+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/14.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 5.69775+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "70191e649c0c34a4", "improvement": 0.0005757762276479284, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.376635005869759e-06, "max_pair_overlap_depth": -1.761308907194392e-05, "metric_expression": "5.69717", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.697174223772352, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.69775, "setup": "peninsqu", "side": 5.697174223772352, "solution_path": "data/solutions/generated/peninsqu_014_70191e649c0c34a4.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/70191e649c0c34a4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@15", "density": 0.737588729235034, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 5.91106, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/15.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5.91106+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.91106, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@15", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "5.91106+", "metric_symbol": "s", "metric_value": 5.91106, "reference_text": "s = 5.91106+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/15.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 5.91106+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "f5d70026e15060e9", "improvement": -0.004052102776268995, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.031797802365455e-06, "max_pair_overlap_depth": -3.458627910934986e-05, "metric_expression": "5.91511", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.915112102776269, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.91106, "setup": "peninsqu", "side": 5.915112102776269, "solution_path": "data/solutions/generated/peninsqu_015_f5d70026e15060e9.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/f5d70026e15060e9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@16", "density": 0.7479800847585042, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 6.11021, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/16.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.11021+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.11021, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@16", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6.11021+", "metric_symbol": "s", "metric_value": 6.11021, "reference_text": "s = 6.11021+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "16.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/16.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 6.11021+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": false, "id": "4644b3e97f0bdea2", "improvement": 0.04369242522759276, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5325677563252472e-06, "max_pair_overlap_depth": -5.091262792966678e-06, "metric_expression": "6.06652", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.066517574772408, "n": 16, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.", "record_type": "verified", "reference_side": 6.11021, "setup": "peninsqu", "side": 6.066517574772408, "solution_path": "data/solutions/generated/peninsqu_016_4644b3e97f0bdea2.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/4644b3e97f0bdea2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@17", "density": 0.7514950307673967, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 6.26466, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/17.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.26466+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.26466, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@17", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6.26466+", "metric_symbol": "s", "metric_value": 6.26466, "reference_text": "s = 6.26466+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/17.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 6.26466+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": false, "id": "a6cd0104bc26d2a0", "improvement": 0.026077965234885703, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.35268853525978e-06, "max_pair_overlap_depth": -1.565351530530279e-05, "metric_expression": "6.23858", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.238582034765114, "n": 17, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.", "record_type": "verified", "reference_side": 6.26466, "setup": "peninsqu", "side": 6.238582034765114, "solution_path": "data/solutions/generated/peninsqu_017_a6cd0104bc26d2a0.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/a6cd0104bc26d2a0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@18", "density": 0.7710926756280118, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 6.33632, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/18.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.33632+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.33632, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6.33632+", "metric_symbol": "s", "metric_value": 6.33632, "reference_text": "s = 6.33632+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/18.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 6.33632+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "9705d17615c32308", "improvement": -0.0010264494540361824, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.1888526227077803e-06, "max_pair_overlap_depth": -2.3019703547788595e-06, "metric_expression": "6.33735", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.337346449454036, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.33632, "setup": "peninsqu", "side": 6.337346449454036, "solution_path": "data/solutions/generated/peninsqu_018_9705d17615c32308.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/9705d17615c32308.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@19", "density": 0.759469213458349, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 6.55939, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/19.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.55939+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.55939, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6.55939+", "metric_symbol": "s", "metric_value": 6.55939, "reference_text": "s = 6.55939+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/19.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 6.55939+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "3b1113745987c1d6", "improvement": -0.0012498840705594816, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9916513391919655e-06, "max_pair_overlap_depth": -2.545361094719034e-05, "metric_expression": "6.56064", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.560639884070559, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.55939, "setup": "peninsqu", "side": 6.560639884070559, "solution_path": "data/solutions/generated/peninsqu_019_3b1113745987c1d6.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/3b1113745987c1d6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@20", "density": 0.7723902783602073, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 6.69588, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/20.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.69588+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.69588, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "6.69588+", "metric_symbol": "s", "metric_value": 6.69588, "reference_text": "s = 6.69588+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/20.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 6.69588+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": false, "id": "eafd28d28fb8e254", "improvement": 0.021343927884186265, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.197045603091071e-06, "max_pair_overlap_depth": -2.9426570577584243e-05, "metric_expression": "6.67454", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.674536072115814, "n": 20, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.", "record_type": "verified", "reference_side": 6.69588, "setup": "peninsqu", "side": 6.674536072115814, "solution_path": "data/solutions/generated/peninsqu_020_eafd28d28fb8e254.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/eafd28d28fb8e254.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@21", "density": 0.7688621226676746, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 6.8554, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/21.png", "friedman_metric_expression": "6.85540+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.8554, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@21", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "6.85540+", "metric_symbol": "s", "metric_value": 6.8554, "reference_text": "s = 6.85540+ | Found by Emerson Connelly | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/21.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 6.85540+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "9d320f91f05e2f0e", "improvement": 0.0003614666962281632, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5104768148309566e-06, "max_pair_overlap_depth": -4.3073173047414315e-05, "metric_expression": "6.85504", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.855038533303772, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.8554, "setup": "peninsqu", "side": 6.855038533303772, "solution_path": "data/solutions/generated/peninsqu_21_9d320f91f05e2f0e.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T13:47:12+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/9d320f91f05e2f0e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@22", "density": 0.7625061251104759, "friedman_analytical_or_proved": false, "friedman_credit": "Teodors Smith", "friedman_date": "April 2026", "friedman_display_metric_value": 7.04532, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/22.png", "friedman_metric_expression": "7.04532+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.04532, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@22", "credit": "Teodors Smith", "date": "April 2026", "family_updated": "", "metric_expression": "7.04532+", "metric_symbol": "s", "metric_value": 7.04532, "reference_text": "s = 7.04532+ | Found by Teodors Smith | in April 2026.", "source_image": "22.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/22.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 7.04532+ | Found by Teodors Smith | in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "70964f50e662283c", "improvement": -0.0002179452221122702, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.550099486392989e-07, "max_pair_overlap_depth": -3.276547527986118e-05, "metric_expression": "7.04554", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.0455379452221125, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.04532, "setup": "peninsqu", "side": 7.0455379452221125, "solution_path": "data/solutions/generated/peninsqu_22_70964f50e662283c.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T13:47:12+00:00", "submitted_by": "Teodors Smith", "svg_path": "data/svg/70964f50e662283c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@23", "density": 0.7617923823536098, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 7.20731, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/23.png", "friedman_metric_expression": "7.20731+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.20731, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@23", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "7.20731+", "metric_symbol": "s", "metric_value": 7.20731, "reference_text": "s = 7.20731+ | Found by Emerson Connelly | in April 2026.", "source_image": "23.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/23.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 7.20731+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "5b526f4bb0fda83c", "improvement": 5.162671385594564e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.635959726042516e-06, "max_pair_overlap_depth": -3.224520897293637e-05, "metric_expression": "7.20726", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.207258373286144, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.20731, "setup": "peninsqu", "side": 7.207258373286144, "solution_path": "data/solutions/generated/peninsqu_23_5b526f4bb0fda83c.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T13:47:12+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/5b526f4bb0fda83c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninsqu@24", "density": 0.766901141845129, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 7.33823, "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/24.png", "friedman_metric_expression": "7.33823+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.33823, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@24", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "7.33823+", "metric_symbol": "s", "metric_value": 7.33823, "reference_text": "s = 7.33823+ | Found by Emerson Connelly | in April 2026.", "source_image": "24.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/24.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 7.33823+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "3e42e9e085ed4c16", "improvement": 0.0005221765418985669, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.294217705264547e-06, "max_pair_overlap_depth": -1.6096651148655994e-05, "metric_expression": "7.33771", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.337707823458102, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.33823, "setup": "peninsqu", "side": 7.337707823458102, "solution_path": "data/solutions/generated/peninsqu_24_3e42e9e085ed4c16.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T13:47:12+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/3e42e9e085ed4c16.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@1", "density": 0.6366152339868586, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 0.707, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/1.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a2 / 2 = .707+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.7071067811865476, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a2 / 2 = .707+", "metric_symbol": "r", "metric_value": 0.707, "reference_text": "r = \u221a2 / 2 = .707+ | Trivial.", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/1.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a2 / 2 = .707+ | Trivial.", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "e1e16b7d18b1243e", "improvement": -2.520450261056517e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.331866965270656e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.70711", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 0.7071093016368086, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.7071067811865476, "setup": "squincir", "side": 1.4142186032736173, "solution_path": "data/solutions/generated/squincir_001_e1e16b7d18b1243e.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/e1e16b7d18b1243e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@2", "density": 0.5092878238610891, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.118, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/2.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a5 / 2 = 1.118+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.118033988749895, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a5 / 2 = 1.118+", "metric_symbol": "r", "metric_value": 1.118, "reference_text": "r = \u221a5 / 2 = 1.118+ | Trivial.", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/2.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a5 / 2 = 1.118+ | Trivial.", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "e0e32383f27cd27d", "improvement": -8.774572141545534e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.769902571588602e-06, "max_pair_overlap_depth": -3.18210820038356e-06, "metric_expression": "1.11804", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.1180427633220364, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.118033988749895, "setup": "squincir", "side": 2.236085526644073, "solution_path": "data/solutions/generated/squincir_002_e0e32383f27cd27d.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/e0e32383f27cd27d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@3", "density": 0.5751857401746373, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 1.288, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/3.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "5 \u221a17 / 16 = 1.288+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.288470508005519, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@3", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "5 \u221a17 / 16 = 1.288+", "metric_symbol": "r", "metric_value": 1.288, "reference_text": "r = 5 \u221a17 / 16 = 1.288+ | Found by Erich Friedman | in 1997.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/3.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 5 \u221a17 / 16 = 1.288+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "226172dcb69c3daf", "improvement": -2.1222784961860697e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4552703365164916e-07, "max_pair_overlap_depth": -2.6483206490832134e-05, "metric_expression": "1.28849", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.2884917307904808, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.288470508005519, "setup": "squincir", "side": 2.5769834615809617, "solution_path": "data/solutions/generated/squincir_003_226172dcb69c3daf.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/226172dcb69c3daf.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@4", "density": 0.6365934661039774, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 1.414, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/4.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a2 = 1.414+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.4142135623730951, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@4", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a2 = 1.414+", "metric_symbol": "r", "metric_value": 1.414, "reference_text": "r = \u221a2 = 1.414+ | Found by Erich Friedman | in 1997.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/4.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a2 = 1.414+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "59645297dac888b6", "improvement": -2.921981799763884e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.7659081458272254e-06, "max_pair_overlap_depth": -2.7879728913877792e-05, "metric_expression": "1.41424", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.4142427821910928, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.4142135623730951, "setup": "squincir", "side": 2.8284855643821856, "solution_path": "data/solutions/generated/squincir_004_59645297dac888b6.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/59645297dac888b6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@5", "density": 0.6366006254695611, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 1.581, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/5.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a10 / 2 = 1.581+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.5811388300841898, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@5", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a10 / 2 = 1.581+", "metric_symbol": "r", "metric_value": 1.581, "reference_text": "r = \u221a10 / 2 = 1.581+ | Found by Erich Friedman | in 1997.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/5.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a10 / 2 = 1.581+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "ee29f4bb5ac19bc4", "improvement": -2.3777604900576677e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.383463508896625e-07, "max_pair_overlap_depth": -1.4376414261496606e-05, "metric_expression": "1.58116", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.5811626076890903, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.5811388300841898, "setup": "squincir", "side": 3.1623252153781807, "solution_path": "data/solutions/generated/squincir_005_ee29f4bb5ac19bc4.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/ee29f4bb5ac19bc4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@6", "density": 0.6697921489003816, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 1.688, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/6.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "1.688+ *", "friedman_metric_symbol": "r", "friedman_metric_value": 1.688, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@6", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "1.688+ *", "metric_symbol": "r", "metric_value": 1.688, "reference_text": "r = 1.688+ * | Found by Erich Friedman | in 1997.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/6.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 1.688+ * | Found by Erich Friedman | in 1997.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "00816b044d90c514", "improvement": -0.0006150768345383195, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.526575301033731e-06, "max_pair_overlap_depth": -2.575413327610132e-05, "metric_expression": "1.68862", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.6886150768345383, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.688, "setup": "squincir", "side": 3.3772301536690765, "solution_path": "data/solutions/generated/squincir_006_00816b044d90c514.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/00816b044d90c514.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@7", "density": 0.685554128713642, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 1.802, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/7.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a13 / 2 = 1.802+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.8027756377319946, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@7", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a13 / 2 = 1.802+", "metric_symbol": "r", "metric_value": 1.802, "reference_text": "r = \u221a13 / 2 = 1.802+ | Found by Erich Friedman | in 1997.", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/7.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a13 / 2 = 1.802+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "f533c6ece1865b92", "improvement": -4.785313147648296e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3338190876808227e-06, "max_pair_overlap_depth": -2.5625121306882548e-05, "metric_expression": "1.80282", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.802823490863471, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.8027756377319946, "setup": "squincir", "side": 3.605646981726942, "solution_path": "data/solutions/generated/squincir_007_f533c6ece1865b92.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/f533c6ece1865b92.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@8", "density": 0.6501060351379704, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "March 2002", "friedman_display_metric_value": 1.978, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/8.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "1.978+ *", "friedman_metric_symbol": "r", "friedman_metric_value": 1.978, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@8", "credit": "David W. Cantrell", "date": "March 2002", "family_updated": "", "metric_expression": "1.978+ *", "metric_symbol": "r", "metric_value": 1.978, "reference_text": "r = 1.978+ * | Found by David W. Cantrell | in March 2002.", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/8.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 1.978+ * | Found by David W. Cantrell | in March 2002.", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "056dfca89502965a", "improvement": -0.0011465711618996455, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7255803199667241e-06, "max_pair_overlap_depth": -1.3772848531545812e-05, "metric_expression": "1.97915", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.9791465711618996, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.978, "setup": "squincir", "side": 3.9582931423237993, "solution_path": "data/solutions/generated/squincir_008_056dfca89502965a.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/056dfca89502965a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@9", "density": 0.6635107369929176, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 2.077, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/9.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a1105 / 16 = 2.077+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.0775962673243327, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@9", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a1105 / 16 = 2.077+", "metric_symbol": "r", "metric_value": 2.077, "reference_text": "r = \u221a1105 / 16 = 2.077+ | Found by Erich Friedman | in 1997.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/9.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a1105 / 16 = 2.077+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "a0eb38ed275fd3c7", "improvement": -0.00029271757480131555, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.939578609861826e-06, "max_pair_overlap_depth": -1.5145046883935365e-05, "metric_expression": "2.07789", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.077888984899134, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0775962673243327, "setup": "squincir", "side": 4.155777969798268, "solution_path": "data/solutions/generated/squincir_009_a0eb38ed275fd3c7.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/a0eb38ed275fd3c7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@10", "density": 0.7072738827790132, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 2.121, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/10.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3 \u221a2 / 2 = 2.121+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.1213203435596424, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@10", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 \u221a2 / 2 = 2.121+", "metric_symbol": "r", "metric_value": 2.121, "reference_text": "r = 3 \u221a2 / 2 = 2.121+ | Found by Erich Friedman | in 1997.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/10.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3 \u221a2 / 2 = 2.121+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "eacd7cf43d9f9c99", "improvement": -0.00012209740908764033, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.093937328557672e-07, "max_pair_overlap_depth": -1.6684797704336063e-05, "metric_expression": "2.12144", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.12144244096873, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.1213203435596424, "setup": "squincir", "side": 4.24288488193746, "solution_path": "data/solutions/generated/squincir_010_eacd7cf43d9f9c99.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/eacd7cf43d9f9c99.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@11", "density": 0.7141684249475255, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "March 2002", "friedman_display_metric_value": 2.214, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/11.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.214+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.214, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@11", "credit": "David W. Cantrell", "date": "March 2002", "family_updated": "", "metric_expression": "2.214+", "metric_symbol": "r", "metric_value": 2.214, "reference_text": "r = 2.214+ | Found by David W. Cantrell | in March 2002.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/11.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.214+ | Found by David W. Cantrell | in March 2002.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "ed2b520c292f3457", "improvement": -0.00022160321374320446, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.710372663145449e-07, "max_pair_overlap_depth": -1.7996528127950384e-05, "metric_expression": "2.21422", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.214221603213743, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.214, "setup": "squincir", "side": 4.428443206427486, "solution_path": "data/solutions/generated/squincir_011_ed2b520c292f3457.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/ed2b520c292f3457.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@12", "density": 0.7638630053365897, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 2.236, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/12.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a5 = 2.236+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.23606797749979, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@12", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a5 = 2.236+", "metric_symbol": "r", "metric_value": 2.236, "reference_text": "r = \u221a5 = 2.236+ | Found by Erich Friedman | in 1997.", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/12.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a5 = 2.236+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "064666a02cb4bcc6", "improvement": -0.00011814553247679882, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.505810228203842e-06, "max_pair_overlap_depth": -1.897198109612752e-05, "metric_expression": "2.23619", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.2361861230322666, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.23606797749979, "setup": "squincir", "side": 4.472372246064533, "solution_path": "data/solutions/generated/squincir_012_064666a02cb4bcc6.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/064666a02cb4bcc6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@13", "density": 0.7419440056386433, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "November 2010", "friedman_display_metric_value": 2.3607, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/13.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.3607+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.3607, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@13", "credit": "David W. Cantrell", "date": "November 2010", "family_updated": "", "metric_expression": "2.3607+", "metric_symbol": "r", "metric_value": 2.3607, "reference_text": "r = 2.3607+ | Found by David W. Cantrell | in November 2010.", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/13.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.3607+ | Found by David W. Cantrell | in November 2010.", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "1ff894504e55415a", "improvement": -0.0009262889169745492, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0049576295578788e-06, "max_pair_overlap_depth": -2.3549111853871096e-05, "metric_expression": "2.36163", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.3616262889169746, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.3607, "setup": "squincir", "side": 4.723252577833949, "solution_path": "data/solutions/generated/squincir_013_1ff894504e55415a.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/1ff894504e55415a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@14", "density": 0.7129258170438343, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 2.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/14.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.5", "friedman_metric_symbol": "r", "friedman_metric_value": 2.5, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@14", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "2.5", "metric_symbol": "r", "metric_value": 2.5, "reference_text": "r = 2.5 | Found by Erich Friedman | in 1997.", "source_image": "14.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/14.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.5 | Found by Erich Friedman | in 1997.", "friedman_source_image": "14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "16de07d86777c846", "improvement": -0.0001548640652071498, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.318191377805647e-07, "max_pair_overlap_depth": -1.9980447390599565e-05, "metric_expression": "2.50015", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.500154864065207, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.5, "setup": "squincir", "side": 5.000309728130414, "solution_path": "data/solutions/generated/squincir_014_16de07d86777c846.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/16de07d86777c846.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@15", "density": 0.7434807535174716, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "June 2002", "friedman_display_metric_value": 2.533, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/15.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.533+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.533, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@15", "credit": "David W. Cantrell", "date": "June 2002", "family_updated": "", "metric_expression": "2.533+", "metric_symbol": "r", "metric_value": 2.533, "reference_text": "r = 2.533+ | Found by by David W. Cantrell | in June 2002.", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/15.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.533+ | Found by by David W. Cantrell | in June 2002.", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "4a2ad28ea2097ba3", "improvement": -0.001170482100864234, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.5068887214985125e-06, "max_pair_overlap_depth": -8.103900655004326e-06, "metric_expression": "2.53417", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.534170482100864, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.533, "setup": "squincir", "side": 5.068340964201728, "solution_path": "data/solutions/generated/squincir_015_4a2ad28ea2097ba3.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/4a2ad28ea2097ba3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@16", "density": 0.7401412241351131, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 2.623, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/16.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a11009 / 40 = 2.623+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.623094546523247, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@16", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a11009 / 40 = 2.623+", "metric_symbol": "r", "metric_value": 2.623, "reference_text": "r = \u221a11009 / 40 = 2.623+ | Found by Erich Friedman | in 1997.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/16.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a11009 / 40 = 2.623+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "94d0a09f4c75dcc4", "improvement": -8.343293336743329e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.109474628753105e-06, "max_pair_overlap_depth": -5.84557896199378e-06, "metric_expression": "2.62318", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.6231779794566146, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.623094546523247, "setup": "squincir", "side": 5.246355958913229, "solution_path": "data/solutions/generated/squincir_016_94d0a09f4c75dcc4.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/94d0a09f4c75dcc4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@17", "density": 0.7544956917261334, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2010", "friedman_display_metric_value": 2.677, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/17.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.677+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.677, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@17", "credit": "Maurizio Morandi", "date": "December 2010", "family_updated": "", "metric_expression": "2.677+", "metric_symbol": "r", "metric_value": 2.677, "reference_text": "r = 2.677+ | Found by Maurizio Morandi | in December 2010.", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/17.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.677+ | Found by Maurizio Morandi | in December 2010.", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "036910f6c0550e2f", "improvement": -0.0010651760341882088, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2297138575488873e-06, "max_pair_overlap_depth": -2.14353819976143e-05, "metric_expression": "2.67807", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.6780651760341883, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.677, "setup": "squincir", "side": 5.3561303520683765, "solution_path": "data/solutions/generated/squincir_017_036910f6c0550e2f.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/036910f6c0550e2f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@18", "density": 0.7617085472368383, "friedman_analytical_or_proved": true, "friedman_credit": "David W. Cantrell", "friedman_date": "March 2002", "friedman_display_metric_value": 2.741, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/18.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a481 / 8 = 2.741+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.7414640249326636, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@18", "credit": "David W. Cantrell", "date": "March 2002", "family_updated": "", "metric_expression": "\u221a481 / 8 = 2.741+", "metric_symbol": "r", "metric_value": 2.741, "reference_text": "r = \u221a481 / 8 = 2.741+ | Found by David W. Cantrell | in March 2002.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/18.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a481 / 8 = 2.741+ | Found by David W. Cantrell | in March 2002.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "d726e310dc0e9eaa", "improvement": -0.0011639514877832546, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.727763966399067e-06, "max_pair_overlap_depth": -2.573974201414142e-05, "metric_expression": "2.74263", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.742627976420447, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.7414640249326636, "setup": "squincir", "side": 5.485255952840894, "solution_path": "data/solutions/generated/squincir_018_d726e310dc0e9eaa.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d726e310dc0e9eaa.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@19", "density": 0.76918194004105, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.802, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/19.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.802+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.802, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.802+", "metric_symbol": "r", "metric_value": 2.802, "reference_text": "r = 2.802+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/19.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.802+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "1966e8e14b94f055", "improvement": -0.002060145605657926, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.987997947874078e-06, "max_pair_overlap_depth": -1.7618196217927817e-05, "metric_expression": "2.80406", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.804060145605658, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.802, "setup": "squincir", "side": 5.608120291211316, "solution_path": "data/solutions/generated/squincir_019_1966e8e14b94f055.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:51:36+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/1966e8e14b94f055.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@20", "density": 0.7600583693203081, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "June 2002", "friedman_display_metric_value": 2.893, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/20.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.893+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.893, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@20", "credit": "David W. Cantrell", "date": "June 2002", "family_updated": "", "metric_expression": "2.893+", "metric_symbol": "r", "metric_value": 2.893, "reference_text": "r = 2.893+ | Found by David W. Cantrell | in June 2002.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/20.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.893+ | Found by David W. Cantrell | in June 2002.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "d2a3e673398d1cd8", "improvement": -0.001120361357695998, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.0691232615918125e-06, "max_pair_overlap_depth": -2.4937171242911393e-05, "metric_expression": "2.89412", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.894120361357696, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.893, "setup": "squincir", "side": 5.788240722715392, "solution_path": "data/solutions/generated/squincir_020_d2a3e673398d1cd8.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d2a3e673398d1cd8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@21", "density": 0.7859297816487661, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 2.915, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/21.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a34 / 2 = 2.915+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.9154759474226504, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@21", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a34 / 2 = 2.915+", "metric_symbol": "r", "metric_value": 2.915, "reference_text": "r = \u221a34 / 2 = 2.915+ | Found by Erich Friedman | in 1997.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/21.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a34 / 2 = 2.915+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "af376e36d9f212b7", "improvement": -0.0008955023890897529, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.2933372016152873e-06, "max_pair_overlap_depth": -5.039957310160048e-06, "metric_expression": "2.91637", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.91637144981174, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.9154759474226504, "setup": "squincir", "side": 5.83274289962348, "solution_path": "data/solutions/generated/squincir_021_af376e36d9f212b7.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/af376e36d9f212b7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@22", "density": 0.7599553171633651, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.033, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/22.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.033+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.033, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@22", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.033+", "metric_symbol": "r", "metric_value": 3.033, "reference_text": "r = 3.033+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/22.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.033+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "d08f4c9050539106", "improvement": -0.002584838809432277, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.8140931262198308e-06, "max_pair_overlap_depth": -1.4316626561150514e-05, "metric_expression": "3.03558", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.035584838809432, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.033, "setup": "squincir", "side": 6.071169677618864, "solution_path": "data/solutions/generated/squincir_022_d08f4c9050539106.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:51:36+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/d08f4c9050539106.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@23", "density": 0.7743799032674085, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "June 2002", "friedman_display_metric_value": 3.073, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/23.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.073+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.073, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@23", "credit": "David W. Cantrell", "date": "June 2002", "family_updated": "", "metric_expression": "3.073+", "metric_symbol": "r", "metric_value": 3.073, "reference_text": "r = 3.073+ | Found by David W. Cantrell | in June 2002.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/23.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.073+ | Found by David W. Cantrell | in June 2002.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "3cacab4fa2a4614f", "improvement": -0.0017651132247276102, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.255819924494972e-06, "max_pair_overlap_depth": -2.255301194975523e-05, "metric_expression": "3.07477", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.0747651132247276, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.073, "setup": "squincir", "side": 6.149530226449455, "solution_path": "data/solutions/generated/squincir_023_3cacab4fa2a4614f.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/3cacab4fa2a4614f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@24", "density": 0.7887737589513796, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "October 2010", "friedman_display_metric_value": 3.11, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/24.gif", "friedman_metric_expression": "3.110+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.11, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@24", "credit": "Maurizio Morandi", "date": "October 2010", "family_updated": "", "metric_expression": "3.110+", "metric_symbol": "r", "metric_value": 3.11, "reference_text": "r = 3.110+ | Found by Maurizio Morandi | in October 2010.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/24.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.110+ | Found by Maurizio Morandi | in October 2010.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "35e22c7b35c718bd", "improvement": -0.0021065491772924716, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.225275177878075e-06, "max_pair_overlap_depth": -2.5024692080766187e-05, "metric_expression": "3.11211", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.1121065491772923, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.11, "setup": "squincir", "side": 6.224213098354585, "solution_path": "data/solutions/generated/squincir_024_35e22c7b35c718bd.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/35e22c7b35c718bd.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@25", "density": 0.7888590017487276, "friedman_analytical_or_proved": true, "friedman_credit": "David W. Cantrell", "friedman_date": "April 2002", "friedman_display_metric_value": 3.175, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/25.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a5809 / 24 = 3.175+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.175699835381871, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@25", "credit": "David W. Cantrell", "date": "April 2002", "family_updated": "", "metric_expression": "\u221a5809 / 24 = 3.175+", "metric_symbol": "r", "metric_value": 3.175, "reference_text": "r = \u221a5809 / 24 = 3.175+ | Found by David W. Cantrell | in April 2002.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/25.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a5809 / 24 = 3.175+ | Found by David W. Cantrell | in April 2002.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "0cabb86031dba8fd", "improvement": -0.00040899428692897644, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4103138832897173e-06, "max_pair_overlap_depth": -3.0578471952869e-05, "metric_expression": "3.17611", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.1761088296688, "n": 25, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.175699835381871, "setup": "squincir", "side": 6.3522176593376, "solution_path": "data/solutions/generated/squincir_025_0cabb86031dba8fd.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/0cabb86031dba8fd.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@26", "density": 0.806871444276765, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 3.201, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/26.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a41 / 2 = 3.201+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.2015621187164243, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@26", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a41 / 2 = 3.201+", "metric_symbol": "r", "metric_value": 3.201, "reference_text": "r = \u221a41 / 2 = 3.201+ | Found by Erich Friedman | in 1997.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/26.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a41 / 2 = 3.201+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "d3c528742ca2afa0", "improvement": -0.0010885092393086993, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.80804369340504e-06, "max_pair_overlap_depth": -4.195014817909293e-06, "metric_expression": "3.20265", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.202650627955733, "n": 26, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.2015621187164243, "setup": "squincir", "side": 6.405301255911466, "solution_path": "data/solutions/generated/squincir_026_d3c528742ca2afa0.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/d3c528742ca2afa0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@27", "density": 0.8080261870592086, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "September 2010", "friedman_display_metric_value": 3.261, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/27.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "13\u221a145/48 = 3.261+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.2612651984229135, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@27", "credit": "Maurizio Morandi", "date": "September 2010", "family_updated": "", "metric_expression": "13\u221a145/48 = 3.261+", "metric_symbol": "r", "metric_value": 3.261, "reference_text": "r = 13\u221a145/48 = 3.261+ | Found by Maurizio Morandi | in September 2010.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/27.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 13\u221a145/48 = 3.261+ | Found by Maurizio Morandi | in September 2010.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "24101c6f5ef6d134", "improvement": -6.091429524834879e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.239249729032224e-06, "max_pair_overlap_depth": -1.3019517370316258e-05, "metric_expression": "3.26133", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.261326112718162, "n": 27, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.2612651984229135, "setup": "squincir", "side": 6.522652225436324, "solution_path": "data/solutions/generated/squincir_027_24101c6f5ef6d134.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/24101c6f5ef6d134.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@28", "density": 0.8008141779745183, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.333, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/28.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.333+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.333, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@28", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.333+", "metric_symbol": "r", "metric_value": 3.333, "reference_text": "r = 3.333+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/28.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.333+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "33c1007b5e868482", "improvement": -0.0030934121555343808, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.8010138785924426e-06, "max_pair_overlap_depth": -3.2305275887267726e-05, "metric_expression": "3.33609", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.3360934121555346, "n": 28, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.333, "setup": "squincir", "side": 6.672186824311069, "solution_path": "data/solutions/generated/squincir_028_33c1007b5e868482.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T03:19:00+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/33c1007b5e868482.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@29", "density": 0.7983676158390189, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.401, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/29.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.401+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.401, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@29", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.401+", "metric_symbol": "r", "metric_value": 3.401, "reference_text": "r = 3.401+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/29.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.401+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "ab533ab0ad8e3eeb", "improvement": 0.000657947854124874, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.686355668135576e-06, "max_pair_overlap_depth": -1.5593607360919748e-05, "metric_expression": "3.40034", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.400342052145875, "n": 29, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.401, "setup": "squincir", "side": 6.80068410429175, "solution_path": "data/solutions/generated/squincir_029_ab533ab0ad8e3eeb.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:51:36+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/ab533ab0ad8e3eeb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@30", "density": 0.7941259454921153, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.472, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/30.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.472+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.472, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@30", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.472+", "metric_symbol": "r", "metric_value": 3.472, "reference_text": "r = 3.472+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/30.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.472+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "d6d4b17471528bfa", "improvement": 0.004304153213534612, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2997799895563276e-06, "max_pair_overlap_depth": -1.7959424514213396e-05, "metric_expression": "3.46770", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.4676958467864654, "n": 30, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.472, "setup": "squincir", "side": 6.935391693572931, "solution_path": "data/solutions/generated/squincir_030_d6d4b17471528bfa.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:51:36+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/d6d4b17471528bfa.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@31", "density": 0.7887915525098625, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 3.535, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/31.gif", "friedman_metric_expression": "5 \u221a2 / 2 = 3.535+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.5355339059327378, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@31", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "5 \u221a2 / 2 = 3.535+", "metric_symbol": "r", "metric_value": 3.535, "reference_text": "r = 5 \u221a2 / 2 = 3.535+ | Found by Erich Friedman | in 1997.", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/31.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 5 \u221a2 / 2 = 3.535+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "fdf9170d30584f4f", "improvement": -0.001382415354477029, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.62119976746078e-06, "max_pair_overlap_depth": -1.7231292489316985e-05, "metric_expression": "3.53692", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.536916321287215, "n": 31, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.5355339059327378, "setup": "squincir", "side": 7.07383264257443, "solution_path": "data/solutions/generated/squincir_031_fdf9170d30584f4f.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/fdf9170d30584f4f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@32", "density": 0.7916012707303632, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 3.584, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/32.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.584+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.584, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@32", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3.584+", "metric_symbol": "r", "metric_value": 3.584, "reference_text": "r = 3.584+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/32.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.584+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "b8bda371acb2b492", "improvement": -0.0031274839526354015, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.2509087862826505e-06, "max_pair_overlap_depth": -6.52310694349012e-09, "metric_expression": "3.58713", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.5871274839526355, "n": 32, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.584, "setup": "squincir", "side": 7.174254967905271, "solution_path": "data/solutions/generated/squincir_032_b8bda371acb2b492.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/b8bda371acb2b492.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@33", "density": 0.8076634866746639, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2010", "friedman_display_metric_value": 3.605, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/33.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a13 = 3.605+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.605551275463989, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@33", "credit": "Maurizio Morandi", "date": "June 2010", "family_updated": "", "metric_expression": "\u221a13 = 3.605+", "metric_symbol": "r", "metric_value": 3.605, "reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in June 2010.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/33.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in June 2010.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "e5a9fc9a4b7235a0", "improvement": -0.0007898865816988732, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.493268955270025e-06, "max_pair_overlap_depth": -1.6481229587750335e-06, "metric_expression": "3.60634", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.606341162045688, "n": 33, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.605551275463989, "setup": "squincir", "side": 7.212682324091376, "solution_path": "data/solutions/generated/squincir_033_e5a9fc9a4b7235a0.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/e5a9fc9a4b7235a0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@34", "density": 0.8197136332658641, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2010", "friedman_display_metric_value": 3.629, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif", "friedman_metric_expression": "3.629+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.629, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@34", "credit": "Maurizio Morandi", "date": "December 2010", "family_updated": "", "metric_expression": "3.629+", "metric_symbol": "r", "metric_value": 3.629, "reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "8e846defa45411b2", "improvement": -0.004569262546602282, "max_boundary_excess": -4.951833559641017e-06, "max_pair_overlap_depth": -2.1724087376329138e-05, "metric_expression": "3.63357", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.6335692625466023, "n": 34, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 3.629, "setup": "squincir", "side": 7.267138525093205, "solution_path": "data/solutions/generated/squincir_34_8e846defa45411b2.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T16:24:14+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/8e846defa45411b2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@34", "density": 0.819454861319337, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2010", "friedman_display_metric_value": 3.629, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif", "friedman_metric_expression": "3.629+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.629, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@34", "credit": "Maurizio Morandi", "date": "December 2010", "family_updated": "", "metric_expression": "3.629+", "metric_symbol": "r", "metric_value": 3.629, "reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "9214fdf4034b8f9a", "improvement": -0.005142931467513545, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0151594769247652e-06, "max_pair_overlap_depth": -1.71712946250846e-07, "metric_expression": "3.63414", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.6341429314675135, "n": 34, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "record_type": "verified", "reference_side": 3.629, "setup": "squincir", "side": 7.268285862935027, "solution_path": "data/solutions/generated/squincir_34_9214fdf4034b8f9a.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T14:34:18+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/9214fdf4034b8f9a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@34", "density": 0.8206376457817698, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2010", "friedman_display_metric_value": 3.629, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif", "friedman_metric_expression": "3.629+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.629, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squincir@34", "credit": "Maurizio Morandi", "date": "December 2010", "family_updated": "", "metric_expression": "3.629+", "metric_symbol": "r", "metric_value": 3.629, "reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "aa2ddbda942a0ffd", "improvement": -0.0025230432891554244, "max_boundary_excess": -1.1187926634015355e-06, "max_pair_overlap_depth": -1.3727466190216475e-05, "metric_expression": "3.63152", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.6315230432891554, "n": 34, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 3.629, "setup": "squincir", "side": 7.263046086578311, "solution_path": "data/solutions/generated/squincir_34_aa2ddbda942a0ffd.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T17:13:54+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/aa2ddbda942a0ffd.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@35", "density": 0.8405414638481816, "friedman_analytical_or_proved": true, "friedman_credit": "David Eppstein", "friedman_date": "March 2002", "friedman_display_metric_value": 3.64, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/35.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a53 / 2 = 3.640+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.640054944640259, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squincir@35", "credit": "David Eppstein", "date": "March 2002", "family_updated": "", "metric_expression": "\u221a53 / 2 = 3.640+", "metric_symbol": "r", "metric_value": 3.64, "reference_text": "r = \u221a53 / 2 = 3.640+ | Found by David Eppstein | in March 2002.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/35.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a53 / 2 = 3.640+ | Found by David Eppstein | in March 2002.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "f2d91d98b4c2ee39", "improvement": -0.0005999636150639809, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.121617296348745e-07, "max_pair_overlap_depth": -2.1344301219083928e-05, "metric_expression": "3.64065", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 3.640654908255323, "n": 35, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.640054944640259, "setup": "squincir", "side": 7.281309816510646, "solution_path": "data/solutions/generated/squincir_035_f2d91d98b4c2ee39.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David Eppstein", "svg_path": "data/svg/f2d91d98b4c2ee39.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@1", "density": 0.499990679660235, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "1-2. | | s = 1 | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "1-2. | | s = 1 | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "557f8de873a17a8e", "improvement": -9.320470070184328e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7525252651882113e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0000093204700702, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.0, "setup": "squindom", "side": 2.0000186409401404, "solution_path": "data/solutions/generated/squindom_001_557f8de873a17a8e.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/557f8de873a17a8e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@2", "density": 0.9999882998008334, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "1-2. | | s = 1 | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "1-2. | | s = 1 | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "7684110dce2e5290", "improvement": -5.850150919473052e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.463373909884382e-07, "max_pair_overlap_depth": -9.41881114351023e-06, "metric_expression": "1.00001", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0000058501509195, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.0, "setup": "squindom", "side": 2.000011700301839, "solution_path": "data/solutions/generated/squindom_002_7684110dce2e5290.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/7684110dce2e5290.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@3", "density": 0.6666417193387711, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/3.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3/2 = 1.5", "friedman_metric_symbol": "s", "friedman_metric_value": 1.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3/2 = 1.5", "metric_symbol": "s", "metric_value": 1.5, "reference_text": "3. | | s = 3/2 = 1.5 | Trivial. |", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/3.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "3. | | s = 3/2 = 1.5 | Trivial. |", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "3047ca63de76a853", "improvement": -2.8066531593262667e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.0617527398680835e-06, "max_pair_overlap_depth": -1.9554412996725112e-05, "metric_expression": "1.50003", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.5000280665315933, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.5, "setup": "squindom", "side": 3.0000561330631865, "solution_path": "data/solutions/generated/squindom_003_3047ca63de76a853.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/3047ca63de76a853.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@4", "density": 0.5367260778952853, "friedman_analytical_or_proved": false, "friedman_credit": "Evert Stenlund", "friedman_date": "June 2010", "friedman_display_metric_value": 1.93, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/4.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "1.930+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.93, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squindom@4", "credit": "Evert Stenlund", "date": "June 2010", "family_updated": "", "metric_expression": "1.930+", "metric_symbol": "s", "metric_value": 1.93, "reference_text": "4. | | s = 1.930+ | Found by Evert Stenlund | in June 2010.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/4.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "4. | | s = 1.930+ | Found by Evert Stenlund | in June 2010.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "8d067d60c7138964", "improvement": -0.00036150970269521743, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.561542731343124e-06, "max_pair_overlap_depth": -3.757775137364083e-05, "metric_expression": "1.93036", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.9303615097026952, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.93, "setup": "squindom", "side": 3.8607230194053903, "solution_path": "data/solutions/generated/squindom_004_8d067d60c7138964.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Evert Stenlund", "svg_path": "data/svg/8d067d60c7138964.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@5", "density": 0.6249853765160349, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "5-8. | | s = 2 | Trivial. |", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "5-8. | | s = 2 | Trivial. |", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "05f6000ecc64a077", "improvement": -2.3397984937112426e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3736510935966635e-06, "max_pair_overlap_depth": -1.2206465427119814e-05, "metric_expression": "2.00002", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.000023397984937, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "squindom", "side": 4.000046795969874, "solution_path": "data/solutions/generated/squindom_005_05f6000ecc64a077.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/05f6000ecc64a077.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@6", "density": 0.749983975114432, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@6", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "5-8. | | s = 2 | Trivial. |", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "5-8. | | s = 2 | Trivial. |", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "095d951ace7a918a", "improvement": -2.136685649301029e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.707507375492412e-07, "max_pair_overlap_depth": -1.170836956105551e-05, "metric_expression": "2.00002", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.000021366856493, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "squindom", "side": 4.000042733712986, "solution_path": "data/solutions/generated/squindom_006_095d951ace7a918a.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/095d951ace7a918a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@7", "density": 0.8749639011598754, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@7", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "5-8. | | s = 2 | Trivial. |", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "5-8. | | s = 2 | Trivial. |", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "50aa0817a0117c40", "improvement": -4.1257093861268856e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4800520663781356e-06, "max_pair_overlap_depth": -1.885899157594295e-05, "metric_expression": "2.00004", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0000412570938613, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "squindom", "side": 4.0000825141877225, "solution_path": "data/solutions/generated/squindom_007_50aa0817a0117c40.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/50aa0817a0117c40.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@8", "density": 0.9999722279382355, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@8", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "5-8. | | s = 2 | Trivial. |", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/8.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "5-8. | | s = 2 | Trivial. |", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "0b83841ee591689c", "improvement": -2.7772640243561852e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.0495464614356251e-07, "max_pair_overlap_depth": -1.777420024382249e-07, "metric_expression": "2.00003", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0000277726402436, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "squindom", "side": 4.000055545280487, "solution_path": "data/solutions/generated/squindom_008_0b83841ee591689c.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/0b83841ee591689c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@9", "density": 0.7367411181657051, "friedman_analytical_or_proved": true, "friedman_credit": "Evert Stenlund", "friedman_date": "June 2010", "friedman_display_metric_value": 2.471, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/9.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "2 + \u221a2/3 = 2.471+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.471404520791032, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@9", "credit": "Evert Stenlund", "date": "June 2010", "family_updated": "", "metric_expression": "2 + \u221a2/3 = 2.471+", "metric_symbol": "s", "metric_value": 2.471, "reference_text": "9. | | s = 2 + \u221a2/3 = 2.471+ | Found by Evert Stenlund | in June 2010.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/9.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "9. | | s = 2 + \u221a2/3 = 2.471+ | Found by Evert Stenlund | in June 2010.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "2963ae62200cf2c5", "improvement": -2.8257928626818085e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.8492494266174617e-06, "max_pair_overlap_depth": -7.2416104319739105e-06, "metric_expression": "2.47143", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.4714327787196586, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.471404520791032, "setup": "squindom", "side": 4.942865557439317, "solution_path": "data/solutions/generated/squindom_009_2963ae62200cf2c5.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Evert Stenlund", "svg_path": "data/svg/2963ae62200cf2c5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@10", "density": 0.7999865137938963, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/10.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "5/2 = 2.5", "friedman_metric_symbol": "s", "friedman_metric_value": 2.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@10", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5/2 = 2.5", "metric_symbol": "s", "metric_value": 2.5, "reference_text": "10. | | s = 5/2 = 2.5 | Trivial. |", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/10.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "10. | | s = 5/2 = 2.5 | Trivial. |", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "7d3cb25d7577069f", "improvement": -2.1072463463500668e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5655128748903735e-06, "max_pair_overlap_depth": -9.554543500822632e-07, "metric_expression": "2.50002", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.5000210724634635, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.5, "setup": "squindom", "side": 5.000042144926927, "solution_path": "data/solutions/generated/squindom_010_7d3cb25d7577069f.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/7d3cb25d7577069f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@11", "density": 0.7109112928838592, "friedman_analytical_or_proved": false, "friedman_credit": "Evert Stenlund", "friedman_date": "June 2010", "friedman_display_metric_value": 2.779, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/11.gif", "friedman_metric_expression": "2.779+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.779, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squindom@11", "credit": "Evert Stenlund", "date": "June 2010", "family_updated": "", "metric_expression": "2.779+", "metric_symbol": "s", "metric_value": 2.779, "reference_text": "11. | | s = 2.779+ | Found by Evert Stenlund | in June 2010. |", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/11.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "11. | | s = 2.779+ | Found by Evert Stenlund | in June 2010. |", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "eadb11fb534aa6a1", "improvement": -0.0024652481713771657, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.886034921991467e-06, "max_pair_overlap_depth": -3.432035104045106e-05, "metric_expression": "2.78147", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.781465248171377, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.779, "setup": "squindom", "side": 5.562930496342754, "solution_path": "data/solutions/generated/squindom_11_eadb11fb534aa6a1.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T07:13:53+00:00", "submitted_by": "Evert Stenlund", "svg_path": "data/svg/eadb11fb534aa6a1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@12", "density": 0.7147860825866693, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2010", "friedman_display_metric_value": 2.897, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/12.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "6 (1 + \u221a2) / 5 = 2.897+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.897056274847714, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@12", "credit": "Maurizio Morandi", "date": "June 2010", "family_updated": "", "metric_expression": "6 (1 + \u221a2) / 5 = 2.897+", "metric_symbol": "s", "metric_value": 2.897, "reference_text": "12. | | s = 6 (1 + \u221a2) / 5 = 2.897+ | Found by Maurizio Morandi | in June 2010. |", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/12.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "12. | | s = 6 (1 + \u221a2) / 5 = 2.897+ | Found by Maurizio Morandi | in June 2010. |", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "4c82fd3f736a139f", "improvement": -0.00020446384343131285, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.382389093311346e-06, "max_pair_overlap_depth": -2.837543626332817e-05, "metric_expression": "2.89726", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.8972607386911453, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.897056274847714, "setup": "squindom", "side": 5.794521477382291, "solution_path": "data/solutions/generated/squindom_012_4c82fd3f736a139f.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/4c82fd3f736a139f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@13", "density": 0.7330751854461901, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 2.976, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/13.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "2.976+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.976, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squindom@13", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "2.976+", "metric_symbol": "s", "metric_value": 2.976, "reference_text": "13. | | s = 2.976+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/13.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "13. | | s = 2.976+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d738dfc349a8c940", "improvement": -0.0017101333567786092, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.7694174018241284e-06, "max_pair_overlap_depth": -2.048132261660285e-05, "metric_expression": "2.97771", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.9777101333567786, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.976, "setup": "squindom", "side": 5.955420266713557, "solution_path": "data/solutions/generated/squindom_013_d738dfc349a8c940.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d738dfc349a8c940.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@14", "density": 0.7777474504876777, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@14", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "14-18. | | s = 3 | Trivial. |", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "14-18. | | s = 3 | Trivial. |", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "167b47d5e39e076d", "improvement": -5.849005569213972e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0369016045785884e-06, "max_pair_overlap_depth": -1.5707310774493166e-05, "metric_expression": "3.00006", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.000058490055692, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.0, "setup": "squindom", "side": 6.000116980111384, "solution_path": "data/solutions/generated/squindom_014_167b47d5e39e076d.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/167b47d5e39e076d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@15", "density": 0.8333077568349537, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@15", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "14-18. | | s = 3 | Trivial. |", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "14-18. | | s = 3 | Trivial. |", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "6d686963e9ef0ece", "improvement": -4.603875684550118e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0382270816400307e-06, "max_pair_overlap_depth": -3.605764309855264e-06, "metric_expression": "3.00005", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0000460387568455, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.0, "setup": "squindom", "side": 6.000092077513691, "solution_path": "data/solutions/generated/squindom_015_6d686963e9ef0ece.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/6d686963e9ef0ece.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@16", "density": 0.888839182217615, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@16", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "14-18. | | s = 3 | Trivial. |", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "14-18. | | s = 3 | Trivial. |", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "0f551306e71d2ff0", "improvement": -8.388352586674586e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4593433725073055e-06, "max_pair_overlap_depth": -5.7555123290642385e-06, "metric_expression": "3.00008", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0000838835258667, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.0, "setup": "squindom", "side": 6.0001677670517335, "solution_path": "data/solutions/generated/squindom_016_0f551306e71d2ff0.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/0f551306e71d2ff0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@17", "density": 0.9444002665800334, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@17", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "14-18. | | s = 3 | Trivial. |", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "14-18. | | s = 3 | Trivial. |", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "52c5d2070c49c79c", "improvement": -7.016730512532376e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.650126292496168e-06, "max_pair_overlap_depth": -3.2807804517531736e-07, "metric_expression": "3.00007", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0000701673051253, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.0, "setup": "squindom", "side": 6.000140334610251, "solution_path": "data/solutions/generated/squindom_017_52c5d2070c49c79c.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/52c5d2070c49c79c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@18", "density": 0.9999599238999353, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@18", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "14-18. | | s = 3 | Trivial. |", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "14-18. | | s = 3 | Trivial. |", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "a6900e1fd3f925c6", "improvement": -6.011595701327366e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.408701424045262e-07, "max_pair_overlap_depth": -1.079909316636929e-06, "metric_expression": "3.00006", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0000601159570133, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.0, "setup": "squindom", "side": 6.0001202319140265, "solution_path": "data/solutions/generated/squindom_018_a6900e1fd3f925c6.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/a6900e1fd3f925c6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@19", "density": 0.7988013748197259, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2010", "friedman_display_metric_value": 3.447, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/19.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3 + 1/\u221a5 = 3.447+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.447213595499958, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@19", "credit": "Maurizio Morandi", "date": "June 2010", "family_updated": "", "metric_expression": "3 + 1/\u221a5 = 3.447+", "metric_symbol": "s", "metric_value": 3.447, "reference_text": "19. | | s = 3 + 1/\u221a5 = 3.447+ | Found by Maurizio Morandi | in June 2010.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/19.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "19. | | s = 3 + 1/\u221a5 = 3.447+ | Found by Maurizio Morandi | in June 2010.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "cddf920bff527727", "improvement": -0.0013830451761869256, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.98512899937964e-06, "max_pair_overlap_depth": -1.3782300862574814e-05, "metric_expression": "3.44860", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.448596640676145, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.447213595499958, "setup": "squindom", "side": 6.89719328135229, "solution_path": "data/solutions/generated/squindom_019_cddf920bff527727.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/cddf920bff527727.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@20", "density": 0.8162860196976518, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "7/2 = 3.5", "friedman_metric_symbol": "s", "friedman_metric_value": 3.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@20", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "7/2 = 3.5", "metric_symbol": "s", "metric_value": 3.5, "reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "4a48c58d60a1f36b", "improvement": -8.6848505622239e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.863306484192975e-06, "max_pair_overlap_depth": -2.3696014737728532e-05, "metric_expression": "3.50009", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.5000868485056222, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.5, "setup": "squindom", "side": 7.0001736970112445, "solution_path": "data/solutions/generated/squindom_020_4a48c58d60a1f36b.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4a48c58d60a1f36b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@21", "density": 0.8571139620178546, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "friedman_metric_expression": "7/2 = 3.5", "friedman_metric_symbol": "s", "friedman_metric_value": 3.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@21", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "7/2 = 3.5", "metric_symbol": "s", "metric_value": 3.5, "reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "f91a28177536f6d3", "improvement": -5.899570515355279e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8534056853702905e-06, "max_pair_overlap_depth": -1.3464050134803784e-06, "metric_expression": "3.50006", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.5000589957051536, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.5, "setup": "squindom", "side": 7.000117991410307, "solution_path": "data/solutions/generated/squindom_021_f91a28177536f6d3.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/f91a28177536f6d3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@22", "density": 0.783535190077589, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 3.745, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/22.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3.745+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.745, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squindom@22", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "3.745+", "metric_symbol": "s", "metric_value": 3.745, "reference_text": "22. | | s = 3.745+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/22.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "22. | | s = 3.745+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d2d5380917cfe7ce", "improvement": -0.0018567500999222553, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.72695736733975e-06, "max_pair_overlap_depth": -9.08031145729904e-06, "metric_expression": "3.74686", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.7468567500999224, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.745, "setup": "squindom", "side": 7.493713500199845, "solution_path": "data/solutions/generated/squindom_022_d2d5380917cfe7ce.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d2d5380917cfe7ce.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@23", "density": 0.7750857674093591, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2010", "friedman_display_metric_value": 3.849, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/23.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3.849+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.849, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squindom@23", "credit": "Maurizio Morandi", "date": "June 2010", "family_updated": "", "metric_expression": "3.849+", "metric_symbol": "s", "metric_value": 3.849, "reference_text": "23. | | s = 3.849+ | Found by Maurizio Morandi | in June 2010. |", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/23.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "23. | | s = 3.849+ | Found by Maurizio Morandi | in June 2010. |", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d12d3a9a87ba3b11", "improvement": -0.002891443742406352, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.707858897694649e-06, "max_pair_overlap_depth": -2.3445235071584136e-05, "metric_expression": "3.85189", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.8518914437424066, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.849, "setup": "squindom", "side": 7.703782887484813, "solution_path": "data/solutions/generated/squindom_023_d12d3a9a87ba3b11.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/d12d3a9a87ba3b11.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@24", "density": 0.7961447064751783, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell after Maurizio Morandi", "friedman_date": "August 2012", "friedman_display_metric_value": 3.882, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/24.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3.882+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.882, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squindom@24", "credit": "David W. Cantrell after Maurizio Morandi", "date": "August 2012", "family_updated": "", "metric_expression": "3.882+", "metric_symbol": "s", "metric_value": 3.882, "reference_text": "24. | | s = 3.882+ | Found by DC after MM | in August 2012. |", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/24.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "24. | | s = 3.882+ | Found by DC after MM | in August 2012. |", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "f954e5304808181f", "improvement": -0.0003493916461954072, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7445287290307476e-06, "max_pair_overlap_depth": -1.9183513864096113e-05, "metric_expression": "3.88235", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.8823493916461955, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.882, "setup": "squindom", "side": 7.764698783292391, "solution_path": "data/solutions/generated/squindom_024_f954e5304808181f.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "David W. Cantrell after Maurizio Morandi", "svg_path": "data/svg/f954e5304808181f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@25", "density": 0.8043920132931294, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell after Maurizio Morandi", "friedman_date": "August 2012", "friedman_display_metric_value": 3.939, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/25.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3.939+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.939, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squindom@25", "credit": "David W. Cantrell after Maurizio Morandi", "date": "August 2012", "family_updated": "", "metric_expression": "3.939+", "metric_symbol": "s", "metric_value": 3.939, "reference_text": "25. | | s = 3.939+ | Found by DC after MM | in August 2012. |", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/25.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "25. | | s = 3.939+ | Found by DC after MM | in August 2012. |", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "26273cb13b41bf72", "improvement": -0.003040951197706754, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.269696070480222e-06, "max_pair_overlap_depth": -2.5070959039568547e-05, "metric_expression": "3.94204", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.942040951197707, "n": 25, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.939, "setup": "squindom", "side": 7.884081902395414, "solution_path": "data/solutions/generated/squindom_025_26273cb13b41bf72.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "David W. Cantrell after Maurizio Morandi", "svg_path": "data/svg/26273cb13b41bf72.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@26", "density": 0.8201428647660397, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 3.981, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/26.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3.981+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.981, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squindom@26", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "3.981+", "metric_symbol": "s", "metric_value": 3.981, "reference_text": "26. | | s = 3.981+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in July 2012.)", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/26.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "26. | | s = 3.981+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in July 2012.)", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "a46204eea3d7f9fe", "improvement": -0.00031848875831208545, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.947984543621445e-06, "max_pair_overlap_depth": -8.516034391559124e-06, "metric_expression": "3.98132", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.981318488758312, "n": 26, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.981, "setup": "squindom", "side": 7.962636977516624, "solution_path": "data/solutions/generated/squindom_026_a46204eea3d7f9fe.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/a46204eea3d7f9fe.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@27", "density": 0.8436994977206457, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@27", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "c68e03cc8f5005db", "improvement": -0.00011971448073744284, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.175631390130775e-07, "max_pair_overlap_depth": -1.4466911184563003e-06, "metric_expression": "4.00012", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.000119714480737, "n": 27, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.000239428961475, "solution_path": "data/solutions/generated/squindom_027_c68e03cc8f5005db.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/c68e03cc8f5005db.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@28", "density": 0.8749068629130922, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@28", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "2c8c79126d60cdac", "improvement": -0.00021290176655508475, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.243746303256302e-06, "max_pair_overlap_depth": -1.6386799395987463e-05, "metric_expression": "4.00021", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.000212901766555, "n": 28, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.00042580353311, "solution_path": "data/solutions/generated/squindom_028_2c8c79126d60cdac.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/2c8c79126d60cdac.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@29", "density": 0.9062096331295707, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@29", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d2548471aff7d9f5", "improvement": -8.908848335043018e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.8156140130519702e-06, "max_pair_overlap_depth": -2.026030487822794e-06, "metric_expression": "4.00009", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.00008908848335, "n": 29, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.0001781769667, "solution_path": "data/solutions/generated/squindom_029_d2548471aff7d9f5.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d2548471aff7d9f5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@30", "density": 0.9374597146255952, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@30", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d67a491f7b4498c0", "improvement": -8.594490193214455e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.188605266186585e-06, "max_pair_overlap_depth": -1.644068809536492e-06, "metric_expression": "4.00009", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.000085944901932, "n": 30, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.000171889803864, "solution_path": "data/solutions/generated/squindom_030_d67a491f7b4498c0.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d67a491f7b4498c0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@31", "density": 0.9683879031627185, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@31", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "86ec622f54cecf7c", "improvement": -0.000747764390431449, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.872732694063188e-07, "max_pair_overlap_depth": -2.9208615389531944e-06, "metric_expression": "4.00075", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0007477643904314, "n": 31, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.001495528780863, "solution_path": "data/solutions/generated/squindom_031_86ec622f54cecf7c.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/86ec622f54cecf7c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@32", "density": 0.9989694769831047, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@32", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "2873ac78de186b97", "improvement": -0.0020626403695489515, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0386280700511747e-06, "max_pair_overlap_depth": -2.476940408779882e-06, "metric_expression": "4.00206", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.002062640369549, "n": 32, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.004125280739098, "solution_path": "data/solutions/generated/squindom_032_2873ac78de186b97.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/2873ac78de186b97.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@33", "density": 0.8455857799388354, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2012", "friedman_display_metric_value": 4.414, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/33.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3 + \u221a2 = 4.414+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.414213562373095, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@33", "credit": "Maurizio Morandi", "date": "July 2012", "family_updated": "", "metric_expression": "3 + \u221a2 = 4.414+", "metric_symbol": "s", "metric_value": 4.414, "reference_text": "33. | | s = 3 + \u221a2 = 4.414+ | Found by Maurizio Morandi | in July 2012.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/33.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "33. | | s = 3 + \u221a2 = 4.414+ | Found by Maurizio Morandi | in July 2012.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "167e5e2a52e9b5fe", "improvement": -0.0031499203989495683, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.856211927670387e-06, "max_pair_overlap_depth": -6.591285420576298e-06, "metric_expression": "4.41736", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.4173634827720445, "n": 33, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.414213562373095, "setup": "squindom", "side": 8.834726965544089, "solution_path": "data/solutions/generated/squindom_033_167e5e2a52e9b5fe.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/167e5e2a52e9b5fe.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@34", "density": 0.8499062715939519, "friedman_analytical_or_proved": true, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 4.471, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/34.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "4 + \u221a2/3 = 4.471+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.471404520791031, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@34", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "4 + \u221a2/3 = 4.471+", "metric_symbol": "s", "metric_value": 4.471, "reference_text": "34. | | s = 4 + \u221a2/3 = 4.471+ | Found by David W. Cantrell | in July 2012.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/34.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "34. | | s = 4 + \u221a2/3 = 4.471+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "b631e5a58c1517e1", "improvement": -0.0009780229400568885, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.603876101403557e-07, "max_pair_overlap_depth": -3.616786977911346e-06, "metric_expression": "4.47238", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.472382543731088, "n": 34, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.471404520791031, "setup": "squindom", "side": 8.944765087462176, "solution_path": "data/solutions/generated/squindom_034_b631e5a58c1517e1.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/b631e5a58c1517e1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@35", "density": 0.8625827503428114, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "9/2 = 4.5", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@35", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "9/2 = 4.5", "metric_symbol": "s", "metric_value": 4.5, "reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "dcd4cfae3ff101a2", "improvement": -0.004210097373901434, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9606355010637344e-06, "max_pair_overlap_depth": -1.1537592481902781e-05, "metric_expression": "4.50421", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.504210097373901, "n": 35, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.5, "setup": "squindom", "side": 9.008420194747803, "solution_path": "data/solutions/generated/squindom_035_dcd4cfae3ff101a2.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/dcd4cfae3ff101a2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@36", "density": 0.8873457711540725, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "9/2 = 4.5", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@36", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "9/2 = 4.5", "metric_symbol": "s", "metric_value": 4.5, "reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "e0fc61bd01777ea3", "improvement": -0.003911109790387002, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.310647293148122e-07, "max_pair_overlap_depth": -3.943598063660403e-06, "metric_expression": "4.50391", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.503911109790387, "n": 36, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.5, "setup": "squindom", "side": 9.007822219580774, "solution_path": "data/solutions/generated/squindom_036_e0fc61bd01777ea3.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/e0fc61bd01777ea3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@37", "density": 0.8199742411033116, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2012", "friedman_display_metric_value": 4.747, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/37.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "10 / 3 + \u221a2 = 4.747+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.747546895706428, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@37", "credit": "Maurizio Morandi", "date": "August 2012", "family_updated": "", "metric_expression": "10 / 3 + \u221a2 = 4.747+", "metric_symbol": "s", "metric_value": 4.747, "reference_text": "37. | | s = 10 / 3 + \u221a2 = 4.747+ | Found by Maurizio Morandi | in August 2012.", "source_image": "37.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/37.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "37. | | s = 10 / 3 + \u221a2 = 4.747+ | Found by Maurizio Morandi | in August 2012.", "friedman_source_image": "37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "09a846134d0a3602", "improvement": -0.002367245250098904, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.702594714522945e-06, "max_pair_overlap_depth": -1.6080659807293785e-05, "metric_expression": "4.74991", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.749914140956527, "n": 37, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.747546895706428, "setup": "squindom", "side": 9.499828281913054, "solution_path": "data/solutions/generated/squindom_037_09a846134d0a3602.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/09a846134d0a3602.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@38", "density": 0.8220103806251009, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2012", "friedman_display_metric_value": 4.804, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/38.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "(13 + \u221a2) / 3 = 4.804+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.804737854124365, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@38", "credit": "Maurizio Morandi", "date": "August 2012", "family_updated": "", "metric_expression": "(13 + \u221a2) / 3 = 4.804+", "metric_symbol": "s", "metric_value": 4.804, "reference_text": "38. | | s = (13 + \u221a2) / 3 = 4.804+ | Found by Maurizio Morandi | in August 2012.", "source_image": "38.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/38.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "38. | | s = (13 + \u221a2) / 3 = 4.804+ | Found by Maurizio Morandi | in August 2012.", "friedman_source_image": "38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d4d1cf6ab169d8aa", "improvement": -0.0029708865595097222, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.518216488058613e-06, "max_pair_overlap_depth": -2.290026661011524e-05, "metric_expression": "4.80771", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.807708740683875, "n": 38, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.804737854124365, "setup": "squindom", "side": 9.61541748136775, "solution_path": "data/solutions/generated/squindom_038_d4d1cf6ab169d8aa.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/d4d1cf6ab169d8aa.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@39", "density": 0.8326335013079162, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "August 2012", "friedman_display_metric_value": 4.839, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/39.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "4.839+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.839, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squindom@39", "credit": "David W. Cantrell", "date": "August 2012", "family_updated": "", "metric_expression": "4.839+", "metric_symbol": "s", "metric_value": 4.839, "reference_text": "39. | | s = 4.839+ | Found by David W. Cantrell | in August 2012.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/39.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "39. | | s = 4.839+ | Found by David W. Cantrell | in August 2012.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "a606e4f52500fa01", "improvement": -0.00038713064593576263, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.790990827618913e-06, "max_pair_overlap_depth": -1.236762303413741e-05, "metric_expression": "4.83939", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.839387130645936, "n": 39, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.839, "setup": "squindom", "side": 9.678774261291872, "solution_path": "data/solutions/generated/squindom_039_a606e4f52500fa01.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/a606e4f52500fa01.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@40", "density": 0.8345719865483486, "friedman_analytical_or_proved": false, "friedman_credit": "Sigvart Brendberg", "friedman_date": "June 2023", "friedman_display_metric_value": 4.895, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/40.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "4.895+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.895, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squindom@40", "credit": "Sigvart Brendberg", "date": "June 2023", "family_updated": "", "metric_expression": "4.895+", "metric_symbol": "s", "metric_value": 4.895, "reference_text": "40. | | s = 4.895+ | Found by Sigvart Brendberg | in June 2023.", "source_image": "40.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/40.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "40. | | s = 4.895+ | Found by Sigvart Brendberg | in June 2023.", "friedman_source_image": "40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "bb2811be04efb5ee", "improvement": -0.0003426573425642232, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.37233266706005e-06, "max_pair_overlap_depth": -3.9677918853286975e-06, "metric_expression": "4.89534", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.895342657342564, "n": 40, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.895, "setup": "squindom", "side": 9.790685314685128, "solution_path": "data/solutions/generated/squindom_040_bb2811be04efb5ee.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Sigvart Brendberg", "svg_path": "data/svg/bb2811be04efb5ee.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@41", "density": 0.8199858015324071, "friedman_analytical_or_proved": false, "friedman_credit": "Sigvart Brendberg", "friedman_date": "June 2023", "friedman_display_metric_value": 4.927, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif", "friedman_metric_expression": "4.927+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.927, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squindom@41", "credit": "Sigvart Brendberg", "date": "June 2023", "family_updated": "", "metric_expression": "4.927+", "metric_symbol": "s", "metric_value": 4.927, "reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.", "source_image": "41.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.", "friedman_source_image": "41.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "5bbf9f2ba5ab11a2", "improvement": -0.07304328857311848, "max_boundary_excess": -2.2531322496632813e-07, "max_pair_overlap_depth": -9.877316924367108e-07, "metric_expression": "5.00004", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.000043288573118, "n": 41, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 4.927, "setup": "squindom", "side": 10.000086577146236, "solution_path": "data/solutions/generated/squindom_41_5bbf9f2ba5ab11a2.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T16:24:14+00:00", "submitted_by": "Sigvart Brendberg", "svg_path": "data/svg/5bbf9f2ba5ab11a2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@41", "density": 0.8440618888942375, "friedman_analytical_or_proved": false, "friedman_credit": "Sigvart Brendberg", "friedman_date": "June 2023", "friedman_display_metric_value": 4.927, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif", "friedman_metric_expression": "4.927+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.927, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squindom@41", "credit": "Sigvart Brendberg", "date": "June 2023", "family_updated": "", "metric_expression": "4.927+", "metric_symbol": "s", "metric_value": 4.927, "reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.", "source_image": "41.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.", "friedman_source_image": "41.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "9ed000ff11bd8b55", "improvement": -0.0012165723290076258, "max_boundary_excess": -1.8525221028298233e-06, "max_pair_overlap_depth": -8.594557442787032e-06, "metric_expression": "4.92822", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.928216572329007, "n": 41, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "recovery_tag": "20260501_squindom41_fresh_cg", "reference_side": 4.927, "setup": "squindom", "side": 9.856433144658014, "solution_path": "data/solutions/generated/squindom_41_9ed000ff11bd8b55.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T18:06:20+00:00", "submitted_by": "Sigvart Brendberg", "svg_path": "data/svg/9ed000ff11bd8b55.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@41", "density": 0.8199798328031639, "friedman_analytical_or_proved": false, "friedman_credit": "Sigvart Brendberg", "friedman_date": "June 2023", "friedman_display_metric_value": 4.927, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif", "friedman_metric_expression": "4.927+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.927, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squindom@41", "credit": "Sigvart Brendberg", "date": "June 2023", "family_updated": "", "metric_expression": "4.927+", "metric_symbol": "s", "metric_value": 4.927, "reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.", "source_image": "41.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.", "friedman_source_image": "41.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "cb1462995bd3b2c0", "improvement": -0.07306148649036626, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.465020711057036e-07, "max_pair_overlap_depth": -6.131910444850952e-06, "metric_expression": "5.00006", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.000061486490366, "n": 41, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "record_type": "verified", "reference_side": 4.927, "setup": "squindom", "side": 10.000122972980732, "solution_path": "data/solutions/generated/squindom_41_cb1462995bd3b2c0.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T13:47:12+00:00", "submitted_by": "Sigvart Brendberg", "svg_path": "data/svg/cb1462995bd3b2c0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@42", "density": 0.8472590848618945, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "August 2012", "friedman_display_metric_value": 4.989, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/42.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "4.989+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.989, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squindom@42", "credit": "David W. Cantrell", "date": "August 2012", "family_updated": "", "metric_expression": "4.989+", "metric_symbol": "s", "metric_value": 4.989, "reference_text": "42. | | s = 4.989+ | Found by David W. Cantrell | in August 2012.", "source_image": "42.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/42.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "42. | | s = 4.989+ | Found by David W. Cantrell | in August 2012.", "friedman_source_image": "42.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": false, "id": "7faea8ae450b67a1", "improvement": 0.010465394774865189, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.54667148005916e-06, "max_pair_overlap_depth": -1.5216861767419765e-05, "metric_expression": "4.97853", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.978534605225135, "n": 42, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.", "record_type": "verified", "reference_side": 4.989, "setup": "squindom", "side": 9.95706921045027, "solution_path": "data/solutions/generated/squindom_042_7faea8ae450b67a1.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/7faea8ae450b67a1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@43", "density": 0.859888117316887, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@43", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "7f9527ccddc9d648", "improvement": -0.00032527209571497906, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.1461540806485566e-08, "max_pair_overlap_depth": -2.005039219099558e-06, "metric_expression": "5.00033", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.000325272095715, "n": 43, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.00065054419143, "solution_path": "data/solutions/generated/squindom_043_7f9527ccddc9d648.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/7f9527ccddc9d648.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@44", "density": 0.8799631966546829, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@44", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "1ffd758f1f058de5", "improvement": -0.00010455823792376862, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.245467354557775e-06, "max_pair_overlap_depth": -3.962242465904708e-06, "metric_expression": "5.00010", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.000104558237924, "n": 44, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000209116475848, "solution_path": "data/solutions/generated/squindom_044_1ffd758f1f058de5.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/1ffd758f1f058de5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@45", "density": 0.8999501217119913, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@45", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d085ed9682ca2968", "improvement": -0.00013855655918781906, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0485935568738114e-06, "max_pair_overlap_depth": -1.361329106774889e-06, "metric_expression": "5.00014", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.000138556559188, "n": 45, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000277113118376, "solution_path": "data/solutions/generated/squindom_045_d085ed9682ca2968.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d085ed9682ca2968.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@46", "density": 0.9198953665582859, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@46", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "3b408e84cd206068", "improvement": -0.00028435426002282327, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1757865436834436e-06, "max_pair_overlap_depth": -7.423155479191479e-07, "metric_expression": "5.00028", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.000284354260023, "n": 46, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000568708520046, "solution_path": "data/solutions/generated/squindom_046_3b408e84cd206068.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/3b408e84cd206068.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@47", "density": 0.9398436614252309, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@47", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "2525e331a392c6b9", "improvement": -0.00041584595443833194, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3105818880431173e-06, "max_pair_overlap_depth": -3.7244704524930228e-06, "metric_expression": "5.00042", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.000415845954438, "n": 47, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000831691908877, "solution_path": "data/solutions/generated/squindom_047_2525e331a392c6b9.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/2525e331a392c6b9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@48", "density": 0.9599518570950978, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@48", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "0433c6294c4f3fe7", "improvement": -0.00012537686383318203, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0555756748686917e-06, "max_pair_overlap_depth": -4.3576353303542703e-07, "metric_expression": "5.00013", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.000125376863833, "n": 48, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000250753727666, "solution_path": "data/solutions/generated/squindom_048_0433c6294c4f3fe7.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/0433c6294c4f3fe7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@49", "density": 0.9798599360041962, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@49", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "c84a987ae840ebe3", "improvement": -0.0003573444166047324, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.316744310450815e-06, "max_pair_overlap_depth": -1.1644813818767474e-06, "metric_expression": "5.00036", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.000357344416605, "n": 49, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.00071468883321, "solution_path": "data/solutions/generated/squindom_049_c84a987ae840ebe3.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/c84a987ae840ebe3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@50", "density": 0.9999308512263965, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squindom@50", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "df0259815cc5320a", "improvement": -0.00017288089993794387, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.912590304139712e-09, "max_pair_overlap_depth": -7.234911549747203e-06, "metric_expression": "5.00017", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.000172880899938, "n": 50, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000345761799876, "solution_path": "data/solutions/generated/squindom_050_df0259815cc5320a.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/df0259815cc5320a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@1", "density": 0.6187919623349352, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 0.778, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/1.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(3+\u221a3)/6 = 0.778+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.7886751345948129, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "(3+\u221a3)/6 = 0.778+", "metric_symbol": "s", "metric_value": 0.778, "reference_text": "s = (3+\u221a3)/6 = 0.778+ | Trivial. |", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/1.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = (3+\u221a3)/6 = 0.778+ | Trivial. |", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "7a4ae27d520be7d9", "improvement": -6.494508079879502e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.500249687614274e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.78868", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.7886816291028927, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.7886751345948129, "setup": "squinhex", "side": 0.7886816291028927, "solution_path": "data/solutions/generated/squinhex_001_7a4ae27d520be7d9.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T03:07:58+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/7a4ae27d520be7d9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@2", "density": 0.5773349997096187, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/2.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2/\u221a3 = 1.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.1547005383792515, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2/\u221a3 = 1.154+", "metric_symbol": "s", "metric_value": 1.154, "reference_text": "s = 2/\u221a3 = 1.154+ | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/2.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2/\u221a3 = 1.154+ | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "21fb35b9b51e59c5", "improvement": -1.526978289367875e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.964730208767781e-07, "max_pair_overlap_depth": -4.154668371614267e-06, "metric_expression": "1.15472", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.1547158081621451, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.1547005383792515, "setup": "squinhex", "side": 1.1547158081621451, "solution_path": "data/solutions/generated/squinhex_002_21fb35b9b51e59c5.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/21fb35b9b51e59c5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@3", "density": 0.6187647598988664, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 1.366, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/3.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(1+\u221a3)/2 = 1.366+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.3660254037844386, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@3", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "(1+\u221a3)/2 = 1.366+", "metric_symbol": "s", "metric_value": 1.366, "reference_text": "s = (1+\u221a3)/2 = 1.366+ | Found by Maurizio Morandi | in March 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/3.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = (1+\u221a3)/2 = 1.366+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "a5c3dc7083e49634", "improvement": -4.1275670430218625e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5592677317674368e-06, "max_pair_overlap_depth": -3.548280330942233e-05, "metric_expression": "1.36607", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.3660666794548688, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.3660254037844386, "setup": "squinhex", "side": 1.3660666794548688, "solution_path": "data/solutions/generated/squinhex_003_a5c3dc7083e49634.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/a5c3dc7083e49634.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@4", "density": 0.6666229789487077, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 1.519, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/4.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2/3 1/4 = 1.519+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.519, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@4", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "2/3 1/4 = 1.519+", "metric_symbol": "s", "metric_value": 1.519, "reference_text": "s = 2/3 1/4 = 1.519+ | Found by Maurizio Morandi | in March 2026.", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/4.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2/3 1/4 = 1.519+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "49c10fcc6144044b", "improvement": -0.0007211669812854371, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.944520361455586e-06, "max_pair_overlap_depth": -3.91225282254104e-05, "metric_expression": "1.51972", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.5197211669812853, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.519, "setup": "squinhex", "side": 1.5197211669812853, "solution_path": "data/solutions/generated/squinhex_004_49c10fcc6144044b.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/49c10fcc6144044b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@5", "density": 0.6414868196410884, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.732, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/5.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a3 = 1.732+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.7320508075688772, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a3 = 1.732+", "metric_symbol": "s", "metric_value": 1.732, "reference_text": "s = \u221a3 = 1.732+ | Trivial. |", "source_image": "5.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/5.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = \u221a3 = 1.732+ | Trivial. |", "friedman_source_image": "5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "1d1f44767245ecd6", "improvement": -1.819755575049875e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.1790980134561805e-06, "max_pair_overlap_depth": -6.972508607594463e-06, "metric_expression": "1.73207", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.7320690051246277, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.7320508075688772, "setup": "squinhex", "side": 1.7320690051246277, "solution_path": "data/solutions/generated/squinhex_005_1d1f44767245ecd6.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/1d1f44767245ecd6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@6", "density": 0.6953530967749227, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 1.821, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/6.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.821+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.821, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@6", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "1.821+", "metric_symbol": "s", "metric_value": 1.821, "reference_text": "s = 1.821+ | Found by Maurizio Morandi | in March 2026.", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/6.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 1.821+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "974baf9dad527270", "improvement": -0.001413758154348077, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6930873179275063e-06, "max_pair_overlap_depth": -8.425702388847878e-06, "metric_expression": "1.82241", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.822413758154348, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.821, "setup": "squinhex", "side": 1.822413758154348, "solution_path": "data/solutions/generated/squinhex_006_974baf9dad527270.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/974baf9dad527270.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@7", "density": 0.777727236784812, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 1.861, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/7.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(\u221a2)3 1/4 = 1.861+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.861, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@7", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "(\u221a2)3 1/4 = 1.861+", "metric_symbol": "s", "metric_value": 1.861, "reference_text": "s = (\u221a2)3 1/4 = 1.861+ | Found by Maurizio Morandi | in March 2026.", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/7.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = (\u221a2)3 1/4 = 1.861+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "3877067eb2c9921c", "improvement": -0.0002701930433344213, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.58302978193184e-06, "max_pair_overlap_depth": -6.096494394869367e-07, "metric_expression": "1.86127", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.8612701930433344, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.861, "setup": "squinhex", "side": 1.8612701930433344, "solution_path": "data/solutions/generated/squinhex_007_3877067eb2c9921c.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/3877067eb2c9921c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@8", "density": 0.6631734535885272, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.15378, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/8.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.15378+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.15378, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@8", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.15378+", "metric_symbol": "s", "metric_value": 2.15378, "reference_text": "s = 2.15378+ | Found by Ian Watson | in April 2026.", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/8.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.15378+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "15b61ced9a55fd6e", "improvement": -0.0010126406302717328, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9874417895385996e-06, "max_pair_overlap_depth": -2.4862858205326743e-05, "metric_expression": "2.15479", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.1547926406302715, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.15378, "setup": "squinhex", "side": 2.1547926406302715, "solution_path": "data/solutions/generated/squinhex_008_15b61ced9a55fd6e.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/15b61ced9a55fd6e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@9", "density": 0.6952132004138262, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.23205, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/9.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1/2+\u221a3 = 2.23205+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.232050807568877, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@9", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1/2+\u221a3 = 2.23205+", "metric_symbol": "s", "metric_value": 2.23205, "reference_text": "s = 1/2+\u221a3 = 2.23205+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/9.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 1/2+\u221a3 = 2.23205+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "55005bb44a4d74d4", "improvement": -0.00016565461997997133, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6345465208580115e-06, "max_pair_overlap_depth": -3.4334606535568746e-05, "metric_expression": "2.23222", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.232216462188857, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.232050807568877, "setup": "squinhex", "side": 2.232216462188857, "solution_path": "data/solutions/generated/squinhex_009_55005bb44a4d74d4.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/55005bb44a4d74d4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@10", "density": 0.721657360923786, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.309, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/10.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4/\u221a3 = 2.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@10", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4/\u221a3 = 2.309+", "metric_symbol": "s", "metric_value": 2.309, "reference_text": "s = 4/\u221a3 = 2.309+ | Trivial. |", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/10.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 4/\u221a3 = 2.309+ | Trivial. |", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "1dc9bb5dff8e4212", "improvement": -4.876244556140108e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.82433796662779e-07, "max_pair_overlap_depth": -1.056245311698012e-05, "metric_expression": "2.30945", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.3094498392040643, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.309401076758503, "setup": "squinhex", "side": 2.3094498392040643, "solution_path": "data/solutions/generated/squinhex_010_1dc9bb5dff8e4212.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/1dc9bb5dff8e4212.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@11", "density": 0.7291333157228544, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.40944, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/11.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.40944+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.40944, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@11", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.40944+", "metric_symbol": "s", "metric_value": 2.40944, "reference_text": "s = 2.40944+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "11.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/11.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.40944+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "11.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "705689a83f76dc66", "improvement": -0.00028191921915876605, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.56887695052102e-06, "max_pair_overlap_depth": -2.8090377436340574e-05, "metric_expression": "2.40972", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.409721919219159, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.40944, "setup": "squinhex", "side": 2.409721919219159, "solution_path": "data/solutions/generated/squinhex_011_705689a83f76dc66.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/705689a83f76dc66.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@12", "density": 0.7736310958293992, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_display_metric_value": 2.443, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/12.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1+5\u221a3/6 = 2.443+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.4433756729740645, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@12", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "", "metric_expression": "1+5\u221a3/6 = 2.443+", "metric_symbol": "s", "metric_value": 2.443, "reference_text": "s = 1+5\u221a3/6 = 2.443+ | Found by Maurizio Morandi | in March 2026.", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/12.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 1+5\u221a3/6 = 2.443+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "2605d29267e364f4", "improvement": -4.205732621720415e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4756288282540256e-06, "max_pair_overlap_depth": -2.0709990555811686e-06, "metric_expression": "2.44342", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.4434177303002818, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.4433756729740645, "setup": "squinhex", "side": 2.4434177303002818, "solution_path": "data/solutions/generated/squinhex_012_2605d29267e364f4.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/2605d29267e364f4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@13", "density": 0.7555572001975633, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_display_metric_value": 2.572, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/13.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.572+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.572, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@13", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "", "metric_expression": "2.572+", "metric_symbol": "s", "metric_value": 2.572, "reference_text": "s = 2.572+ | Found by Maurizio Morandi | in April 2026.", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/13.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.572+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "051502d315bb277c", "improvement": -0.001428217365099016, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2709109889167893e-06, "max_pair_overlap_depth": -2.7796124429491087e-05, "metric_expression": "2.57343", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.573428217365099, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.572, "setup": "squinhex", "side": 2.573428217365099, "solution_path": "data/solutions/generated/squinhex_013_051502d315bb277c.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/051502d315bb277c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@14", "density": 0.7839123498532168, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.62126, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/14.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.62126+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.62126, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@14", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.62126+", "metric_symbol": "s", "metric_value": 2.62126, "reference_text": "s = 2.62126+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/14.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.62126+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "525e7cc585bd027c", "improvement": -0.000568749699766613, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5893267782285044e-06, "max_pair_overlap_depth": -1.4910539989809735e-05, "metric_expression": "2.62183", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.6218287496997665, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.62126, "setup": "squinhex", "side": 2.6218287496997665, "solution_path": "data/solutions/generated/squinhex_014_525e7cc585bd027c.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/525e7cc585bd027c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@15", "density": 0.7612787773180276, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.75365, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/15.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.75365+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.75365, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@15", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.75365+", "metric_symbol": "s", "metric_value": 2.75365, "reference_text": "s = 2.75365+ | Found by Ian Watson | in April 2026.", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/15.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.75365+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "b68c71af3475ffed", "improvement": -0.00024783676108830477, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.513954837939443e-06, "max_pair_overlap_depth": -3.0296502803062175e-05, "metric_expression": "2.75390", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.7538978367610882, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.75365, "setup": "squinhex", "side": 2.7538978367610882, "solution_path": "data/solutions/generated/squinhex_015_b68c71af3475ffed.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/b68c71af3475ffed.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@16", "density": 0.7742958402345232, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.82004, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/16.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.82004+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.82004, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@16", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.82004+", "metric_symbol": "s", "metric_value": 2.82004, "reference_text": "s = 2.82004+ | Found by Ian Watson | in April 2026.", "source_image": "16.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/16.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.82004+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "89a68dd125601a79", "improvement": -0.0001643950752789891, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.5133109066385543e-06, "max_pair_overlap_depth": -7.772490123292286e-06, "metric_expression": "2.82020", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.820204395075279, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.82004, "setup": "squinhex", "side": 2.820204395075279, "solution_path": "data/solutions/generated/squinhex_016_89a68dd125601a79.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/89a68dd125601a79.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@17", "density": 0.7850485918652831, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.88675, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/17.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "5/\u221a3 = 2.88675+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.8867513459481287, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@17", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5/\u221a3 = 2.88675+", "metric_symbol": "s", "metric_value": 2.88675, "reference_text": "s = 5/\u221a3 = 2.88675+ | Trivial. |", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/17.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 5/\u221a3 = 2.88675+ | Trivial. |", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "68ba30b81c3844a7", "improvement": -0.000271682158551112, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9250177449939015e-07, "max_pair_overlap_depth": -5.409854801341485e-05, "metric_expression": "2.88702", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.8870230281066798, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.8867513459481287, "setup": "squinhex", "side": 2.8870230281066798, "solution_path": "data/solutions/generated/squinhex_017_68ba30b81c3844a7.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/68ba30b81c3844a7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@18", "density": 0.8107158050212577, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.92111, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/18.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.92111+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.92111, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@18", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.92111+", "metric_symbol": "s", "metric_value": 2.92111, "reference_text": "s = 2.92111+ | Found by Ian Watson | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/18.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.92111+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "e136eeec3de765c3", "improvement": -0.0022075205933282938, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.264526989622803e-06, "max_pair_overlap_depth": -7.64695502597501e-06, "metric_expression": "2.92332", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.9233175205933284, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.92111, "setup": "squinhex", "side": 2.9233175205933284, "solution_path": "data/solutions/generated/squinhex_018_e136eeec3de765c3.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/e136eeec3de765c3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@19", "density": 0.8472470384096148, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.93511, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/19.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.93511+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.93511, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@19", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.93511+", "metric_symbol": "s", "metric_value": 2.93511, "reference_text": "s = 2.93511+ | Found by Ian Watson | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/19.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.93511+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "ae3850bdb0ac1880", "improvement": -0.0028496545666087947, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.965076151420116e-06, "max_pair_overlap_depth": -7.201359447650546e-06, "metric_expression": "2.93796", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.9379596545666087, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.93511, "setup": "squinhex", "side": 2.9379596545666087, "solution_path": "data/solutions/generated/squinhex_019_ae3850bdb0ac1880.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/ae3850bdb0ac1880.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@20", "density": 0.7690325218237841, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.16123, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/20.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.16123+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.16123, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@20", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.16123+", "metric_symbol": "s", "metric_value": 3.16123, "reference_text": "s = 3.16123+ | Found by Ian Watson | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/20.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.16123+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "79028917ac70723d", "improvement": -0.0026259473298471114, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.697008230249216e-06, "max_pair_overlap_depth": -2.836652900617409e-05, "metric_expression": "3.16386", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.1638559473298473, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.16123, "setup": "squinhex", "side": 3.1638559473298473, "solution_path": "data/solutions/generated/squinhex_020_79028917ac70723d.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/79028917ac70723d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@21", "density": 0.7707944086673769, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.23496, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png", "friedman_metric_expression": "3.23496+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.23496, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@21", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.23496+", "metric_symbol": "s", "metric_value": 3.23496, "reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "1d2ec517035658cd", "improvement": -0.0033202143530659534, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4830527974218215e-06, "max_pair_overlap_depth": -2.662964935497389e-05, "metric_expression": "3.23828", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.238280214353066, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "record_type": "verified", "reference_side": 3.23496, "setup": "squinhex", "side": 3.238280214353066, "solution_path": "data/solutions/generated/squinhex_21_1d2ec517035658cd.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T13:47:12+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/1d2ec517035658cd.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@21", "density": 0.7708011334148378, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.23496, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png", "friedman_metric_expression": "3.23496+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.23496, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@21", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.23496+", "metric_symbol": "s", "metric_value": 3.23496, "reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "3fb669c73e695ac9", "improvement": -0.0033060883592122003, "max_boundary_excess": -5.301769191883493e-06, "max_pair_overlap_depth": -1.6683459818422897e-05, "metric_expression": "3.23827", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.2382660883592123, "n": 21, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 3.23496, "setup": "squinhex", "side": 3.2382660883592123, "solution_path": "data/solutions/generated/squinhex_21_3fb669c73e695ac9.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T17:13:54+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/3fb669c73e695ac9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@21", "density": 0.7715986824430026, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.23496, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png", "friedman_metric_expression": "3.23496+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.23496, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@21", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.23496+", "metric_symbol": "s", "metric_value": 3.23496, "reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "c6682411cb8007fa", "improvement": -0.001632068068800674, "max_boundary_excess": -2.8602915252841952e-06, "max_pair_overlap_depth": -2.8463485488683382e-05, "metric_expression": "3.23659", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.2365920680688007, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "recovery_tag": "20260501_squinhex21_fresh", "reference_side": 3.23496, "setup": "squinhex", "side": 3.2365920680688007, "solution_path": "data/solutions/generated/squinhex_21_c6682411cb8007fa.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T17:21:04+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/c6682411cb8007fa.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@22", "density": 0.770525380181529, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.31573, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/22.png", "friedman_metric_expression": "3.31573+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.31573, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@22", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.31573+", "metric_symbol": "s", "metric_value": 3.31573, "reference_text": "s = 3.31573+ | Found by Ian Watson | in April 2026.", "source_image": "22.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/22.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.31573+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "a1e7eaf12003fa2e", "improvement": 0.0006659560348909466, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.169977234601665e-06, "max_pair_overlap_depth": -1.9814540655582746e-05, "metric_expression": "3.31506", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.315064043965109, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.31573, "setup": "squinhex", "side": 3.315064043965109, "solution_path": "data/solutions/generated/squinhex_022_a1e7eaf12003fa2e.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/a1e7eaf12003fa2e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@23", "density": 0.7808954728618008, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.36437, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/23.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.36437+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.36437, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@23", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.36437+", "metric_symbol": "s", "metric_value": 3.36437, "reference_text": "s = 3.36437+ | Found by Ian Watson | in April 2026.", "source_image": "23.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/23.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.36437+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "de78b89055181fd4", "improvement": -0.00261764110148599, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.240294795076849e-06, "max_pair_overlap_depth": -2.4390771091731267e-07, "metric_expression": "3.36699", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.366987641101486, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.36437, "setup": "squinhex", "side": 3.366987641101486, "solution_path": "data/solutions/generated/squinhex_023_de78b89055181fd4.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/de78b89055181fd4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@24", "density": 0.7904120022571139, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.41524, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/24.png", "friedman_metric_expression": "3.41524+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.41524, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@24", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.41524+", "metric_symbol": "s", "metric_value": 3.41524, "reference_text": "s = 3.41524+ | Found by Ian Watson | in April 2026.", "source_image": "24.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/24.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.41524+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "73f1ceeaee97d32f", "improvement": -0.0033964158861361504, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0115328209217065e-06, "max_pair_overlap_depth": -2.5222031625055097e-05, "metric_expression": "3.41864", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.418636415886136, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.41524, "setup": "squinhex", "side": 3.418636415886136, "solution_path": "data/solutions/generated/squinhex_24_73f1ceeaee97d32f.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T14:34:18+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/73f1ceeaee97d32f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@25", "density": 0.8017157641998289, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.4641, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/25.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2\u221a3 = 3.46410+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.4641016151377544, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@25", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2\u221a3 = 3.46410+", "metric_symbol": "s", "metric_value": 3.4641, "reference_text": "s = 2\u221a3 = 3.46410+ | Trivial. |", "source_image": "25.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/25.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2\u221a3 = 3.46410+ | Trivial. |", "friedman_source_image": "25.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "803edc96e272ee7a", "improvement": -0.00034480837251393837, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4684956309553432e-06, "max_pair_overlap_depth": -2.379294205911986e-05, "metric_expression": "3.46445", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.4644464235102683, "n": 25, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.4641016151377544, "setup": "squinhex", "side": 3.4644464235102683, "solution_path": "data/solutions/generated/squinhex_025_803edc96e272ee7a.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/803edc96e272ee7a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@26", "density": 0.8183272598135501, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.4939927, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/26.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.4939927+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.4939927, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@26", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.4939927+", "metric_symbol": "s", "metric_value": 3.4939927, "reference_text": "s = 3.4939927+ | Found by Ian Watson | in April 2026.", "source_image": "26.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/26.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.4939927+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "26.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "5fb7804364b5caaf", "improvement": -0.003020096739570377, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.392756549893556e-06, "max_pair_overlap_depth": -2.620566831379456e-05, "metric_expression": "3.49701", "metric_recovery_tolerance_abs": 1e-07, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.4970127967395706, "n": 26, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.4939927, "setup": "squinhex", "side": 3.4970127967395706, "solution_path": "data/solutions/generated/squinhex_026_5fb7804364b5caaf.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/5fb7804364b5caaf.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@27", "density": 0.8382703933092833, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_display_metric_value": 3.52072, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/27.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(9+7\u221a3)/6 = 3.52072+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.5207259421636903, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@27", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "", "metric_expression": "(9+7\u221a3)/6 = 3.52072+", "metric_symbol": "s", "metric_value": 3.52072, "reference_text": "s = (9+7\u221a3)/6 = 3.52072+ | Found by Erich Friedman | in April 2026.", "source_image": "27.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/27.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = (9+7\u221a3)/6 = 3.52072+ | Found by Erich Friedman | in April 2026.", "friedman_source_image": "27.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "9cebbb5918ba8e81", "improvement": -0.00025662666655756894, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.315485793993667e-06, "max_pair_overlap_depth": -2.3466684225592616e-05, "metric_expression": "3.52098", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.520982568830248, "n": 27, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.5207259421636903, "setup": "squinhex", "side": 3.520982568830248, "solution_path": "data/solutions/generated/squinhex_027_9cebbb5918ba8e81.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/9cebbb5918ba8e81.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@28", "density": 0.8183465665432688, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.62565, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/28.png", "friedman_metric_expression": "3.62565+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.62565, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@28", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.62565+", "metric_symbol": "s", "metric_value": 3.62565, "reference_text": "s = 3.62565+ | Found by Ian Watson | in April 2026.", "source_image": "28.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/28.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.62565+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "28.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "184baa4d16ce7f9e", "improvement": -0.00332887546169669, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.700161000518847e-07, "max_pair_overlap_depth": -3.0973746406592895e-06, "metric_expression": "3.62898", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.6289788754616965, "n": 28, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.62565, "setup": "squinhex", "side": 3.6289788754616965, "solution_path": "data/solutions/generated/squinhex_28_184baa4d16ce7f9e.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T14:34:18+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/184baa4d16ce7f9e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@29", "density": 0.829741145219895, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.66437, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/29.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.66437+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.66437, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@29", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.66437+", "metric_symbol": "s", "metric_value": 3.66437, "reference_text": "s = 3.66437+ | Found by Ian Watson | in April 2026.", "source_image": "29.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/29.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.66437+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "29.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "3b329ff6f7babb15", "improvement": -0.0033970322125265184, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.61123003800209e-07, "max_pair_overlap_depth": -5.962934573305878e-06, "metric_expression": "3.66777", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.6677670322125264, "n": 29, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.66437, "setup": "squinhex", "side": 3.6677670322125264, "solution_path": "data/solutions/generated/squinhex_029_3b329ff6f7babb15.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/3b329ff6f7babb15.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@30", "density": 0.8440944212011869, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.69554, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/30.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.69554+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.69554, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@30", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.69554+", "metric_symbol": "s", "metric_value": 3.69554, "reference_text": "s = 3.69554+ | Found by Ian Watson | in April 2026.", "source_image": "30.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/30.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.69554+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "30.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "0b645f27b41cbed7", "improvement": -0.0030753622873653796, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7116676711139033e-06, "max_pair_overlap_depth": -4.452216716410717e-06, "metric_expression": "3.69862", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.698615362287365, "n": 30, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.69554, "setup": "squinhex", "side": 3.698615362287365, "solution_path": "data/solutions/generated/squinhex_030_0b645f27b41cbed7.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/0b645f27b41cbed7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@31", "density": 0.83334567619728, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 3.7841, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/31.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.78410+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.7841, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.78410+", "metric_symbol": "s", "metric_value": 3.7841, "reference_text": "s = 3.78410+ | Found by Emerson Connelly | in April 2026.", "source_image": "31.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/31.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.78410+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "31.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "83b47696242e2320", "improvement": 0.00017682363310500548, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.0307084382837186e-06, "max_pair_overlap_depth": -2.9858800666679453e-05, "metric_expression": "3.78392", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.783923176366895, "n": 31, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.7841, "setup": "squinhex", "side": 3.783923176366895, "solution_path": "data/solutions/generated/squinhex_031_83b47696242e2320.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/83b47696242e2320.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@32", "density": 0.8302114212681493, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 3.84795, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/32.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.84795+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.84795, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.84795+", "metric_symbol": "s", "metric_value": 3.84795, "reference_text": "s = 3.84795+ | Found by Emerson Connelly | in April 2026.", "source_image": "32.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/32.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.84795+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "32.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "b233eac9bd8cc0d8", "improvement": -0.003769870972095468, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1351534734416697e-07, "max_pair_overlap_depth": -1.2013295066060081e-05, "metric_expression": "3.85172", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.8517198709720954, "n": 32, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.84795, "setup": "squinhex", "side": 3.8517198709720954, "solution_path": "data/solutions/generated/squinhex_032_b233eac9bd8cc0d8.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/b233eac9bd8cc0d8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@33", "density": 0.8381951703957873, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 3.88897, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/33.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.88897+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.88897, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.88897+", "metric_symbol": "s", "metric_value": 3.88897, "reference_text": "s = 3.88897+ | Found by Emerson Connelly | in April 2026.", "source_image": "33.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/33.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.88897+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "33.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "b14228e93eb45276", "improvement": -0.003797355726243623, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.797125554432215e-06, "max_pair_overlap_depth": -8.18730119578337e-06, "metric_expression": "3.89277", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.8927673557262437, "n": 33, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.88897, "setup": "squinhex", "side": 3.8927673557262437, "solution_path": "data/solutions/generated/squinhex_033_b14228e93eb45276.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/b14228e93eb45276.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@34", "density": 0.8486832973249016, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 3.92704, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/34.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.92704+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.92704, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.92704+", "metric_symbol": "s", "metric_value": 3.92704, "reference_text": "s = 3.92704+ | Found by Emerson Connelly | in April 2026.", "source_image": "34.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/34.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.92704+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "34.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "fc2f6f3b6cabd5ed", "improvement": 0.0002227711135822652, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.30656742709778e-06, "max_pair_overlap_depth": -1.5057714820798651e-05, "metric_expression": "3.92682", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.9268172288864176, "n": 34, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.92704, "setup": "squinhex", "side": 3.9268172288864176, "solution_path": "data/solutions/generated/squinhex_034_fc2f6f3b6cabd5ed.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/fc2f6f3b6cabd5ed.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@35", "density": 0.8429987640989463, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 3.99833, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/35.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.99833+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.99833, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@35", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.99833+", "metric_symbol": "s", "metric_value": 3.99833, "reference_text": "s = 3.99833+ | Found by Emerson Connelly | in April 2026.", "source_image": "35.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/35.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.99833+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "1ea058e93fb408a4", "improvement": 0.0007735056288105113, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.597269939847931e-06, "max_pair_overlap_depth": -1.4652234902046146e-05, "metric_expression": "3.99756", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.9975564943711897, "n": 35, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.99833, "setup": "squinhex", "side": 3.9975564943711897, "solution_path": "data/solutions/generated/squinhex_035_1ea058e93fb408a4.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/1ea058e93fb408a4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@36", "density": 0.8532492984675044, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2026", "friedman_display_metric_value": 4.02072, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png", "friedman_metric_expression": "2+7\u221a3/6 = 4.02072+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.02072594216369, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@36", "credit": "Maurizio Morandi", "date": "May 2026", "family_updated": "", "metric_expression": "2+7\u221a3/6 = 4.02072+", "metric_symbol": "s", "metric_value": 4.02072594216369, "reference_text": "s = 2+7\u221a3/6 = 4.02072+ | Found by Maurizio Morandi | in May 2026.", "source_image": "36.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2+7\u221a3/6 = 4.02072+ | Found by Maurizio Morandi | in May 2026.", "friedman_source_image": "36.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "8da86e16a42a7ee1", "improvement": -0.009109732860929753, "max_boundary_excess": -2.1577223076817982e-06, "max_pair_overlap_depth": -9.723761702495892e-07, "metric_expression": "4.02984", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.02983567502462, "n": 36, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 4.02072594216369, "setup": "squinhex", "side": 4.02983567502462, "solution_path": "data/solutions/generated/squinhex_36_8da86e16a42a7ee1.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T17:13:54+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/8da86e16a42a7ee1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@36", "density": 0.8531956067904081, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2026", "friedman_display_metric_value": 4.02072, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png", "friedman_metric_expression": "2+7\u221a3/6 = 4.02072+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.02072594216369, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@36", "credit": "Maurizio Morandi", "date": "May 2026", "family_updated": "", "metric_expression": "2+7\u221a3/6 = 4.02072+", "metric_symbol": "s", "metric_value": 4.02072, "reference_text": "s = 2+7\u221a3/6 = 4.02072+ | Found by Maurizio Morandi | in May 2026.", "source_image": "36.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2+7\u221a3/6 = 4.02072+ | Found by Maurizio Morandi | in May 2026.", "friedman_source_image": "36.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "b7083884dfb200c3", "improvement": -0.009236529828808848, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.100230231840266e-07, "max_pair_overlap_depth": -2.2076071326537772e-07, "metric_expression": "4.02996", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.029962471992499, "n": 36, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "record_type": "verified", "reference_side": 4.02072594216369, "setup": "squinhex", "side": 4.029962471992499, "solution_path": "data/solutions/record_hunt/squinhex_36_b7083884dfb200c3.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/b7083884dfb200c3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@36", "density": 0.8571629708269735, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2026", "friedman_display_metric_value": 4.02072, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png", "friedman_metric_expression": "2+7\u221a3/6 = 4.02072+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.02072594216369, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@36", "credit": "Maurizio Morandi", "date": "May 2026", "family_updated": "", "metric_expression": "2+7\u221a3/6 = 4.02072+", "metric_symbol": "s", "metric_value": 4.02072594216369, "reference_text": "s = 2+7\u221a3/6 = 4.02072+ | Found by Maurizio Morandi | in May 2026.", "source_image": "36.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2+7\u221a3/6 = 4.02072+ | Found by Maurizio Morandi | in May 2026.", "friedman_source_image": "36.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "cbc24f56627bdbaa", "improvement": 0.00010059280068741572, "max_boundary_excess": -9.204501591489719e-07, "max_pair_overlap_depth": -4.634554187088469e-07, "metric_expression": "4.02063", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.020625349363002, "n": 36, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "recovery_tag": "20260501_squinhex36_linecell", "reference_side": 4.02072594216369, "setup": "squinhex", "side": 4.020625349363002, "solution_path": "data/solutions/generated/squinhex_36_cbc24f56627bdbaa.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T18:08:26+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/cbc24f56627bdbaa.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@37", "density": 0.8718839158050435, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.04145, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/37.png", "friedman_metric_expression": "7/\u221a3 = 4.04145+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.041451884327381, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@37", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "7/\u221a3 = 4.04145+", "metric_symbol": "s", "metric_value": 4.04145, "reference_text": "s = 7/\u221a3 = 4.04145+ | Trivial. |", "source_image": "37.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/37.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 7/\u221a3 = 4.04145+ | Trivial. |", "friedman_source_image": "37.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "a455ecb05be301ad", "improvement": -7.60583571324247e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1637259667017477e-06, "max_pair_overlap_depth": -1.0162747484221413e-05, "metric_expression": "4.04153", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.041527942684513, "n": 37, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.041451884327381, "setup": "squinhex", "side": 4.041527942684513, "solution_path": "data/solutions/generated/squinhex_037_a455ecb05be301ad.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/a455ecb05be301ad.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@38", "density": 0.8354467372021385, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.18476, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/38.png", "friedman_metric_expression": "4.18476+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.18476, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.18476+", "metric_symbol": "s", "metric_value": 4.18476, "reference_text": "s = 4.18476+ | Found by Emerson Connelly | in April 2026.", "source_image": "38.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/38.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 4.18476+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "38.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "657f5bc54656101d", "improvement": 0.0006174563357541629, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.3358638004937594e-07, "max_pair_overlap_depth": -2.4459335521420655e-06, "metric_expression": "4.18414", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.184142543664246, "n": 38, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.18476, "setup": "squinhex", "side": 4.184142543664246, "solution_path": "data/solutions/record_hunt/squinhex_38_657f5bc54656101d.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/657f5bc54656101d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@39", "density": 0.8275155837189719, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.25744, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/39.png", "friedman_metric_expression": "4.25744+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.25744, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.25744+", "metric_symbol": "s", "metric_value": 4.25744, "reference_text": "s = 4.25744+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/39.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 4.25744+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "85e7e9eb3b3b7f5f", "improvement": -0.001664243334674076, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.204496689819836e-06, "max_pair_overlap_depth": -1.602842749781619e-05, "metric_expression": "4.25910", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.259104243334674, "n": 39, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.25744, "setup": "squinhex", "side": 4.259104243334674, "solution_path": "data/solutions/generated/squinhex_039_85e7e9eb3b3b7f5f.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/85e7e9eb3b3b7f5f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@40", "density": 0.8288203735668404, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.31157, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/40.png", "friedman_metric_expression": "4.31157+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.31157, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.31157+", "metric_symbol": "s", "metric_value": 4.31157, "reference_text": "s = 4.31157+ | Found by Emerson Connelly | in April 2026.", "source_image": "40.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/40.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 4.31157+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "40.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "9859865bba74b499", "improvement": 0.001604007461533108, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.921136271031391e-07, "max_pair_overlap_depth": -1.8467799072219293e-06, "metric_expression": "4.30997", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.309965992538467, "n": 40, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.31157, "setup": "squinhex", "side": 4.309965992538467, "solution_path": "data/solutions/record_hunt/squinhex_40_9859865bba74b499.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/9859865bba74b499.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@1", "density": 0.7071036297921394, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 0.54119, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/1.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "1/\u221a(2+\u221a2) = .54119+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.541196100146197, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1/\u221a(2+\u221a2) = .54119+", "metric_symbol": "s", "metric_value": 0.54119, "reference_text": "s = 1/\u221a(2+\u221a2) = .54119+ | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/1.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 1/\u221a(2+\u221a2) = .54119+ | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "b63c90f60717ba08", "improvement": -1.2059904600514315e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1705346114441018e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.54120", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.5411973061366571, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.541196100146197, "setup": "squinoct", "side": 0.5411973061366571, "solution_path": "data/solutions/generated/squinoct_001_b63c90f60717ba08.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/b63c90f60717ba08.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@2", "density": 0.5389047922692529, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2013", "friedman_display_metric_value": 0.87667, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/2.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": ".87667+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.87667, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@2", "credit": "Maurizio Morandi", "date": "December 2013", "family_updated": "", "metric_expression": ".87667+", "metric_symbol": "s", "metric_value": 0.87667, "reference_text": "s = .87667+ | Found by Maurizio Morandi | in December 2013.", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/2.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = .87667+ | Found by Maurizio Morandi | in December 2013.", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "7194ac58cba12fa7", "improvement": -4.0351762315649076e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.607981571160174e-06, "max_pair_overlap_depth": -1.1896285956325414e-06, "metric_expression": "0.87671", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.8767103517623156, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.87667, "setup": "squinoct", "side": 0.8767103517623156, "solution_path": "data/solutions/generated/squinoct_002_7194ac58cba12fa7.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/7194ac58cba12fa7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@3", "density": 0.5862650280603752, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "December 2013", "friedman_display_metric_value": 1.0294, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/3.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "18 \u2013 12\u221a2 = 1.02940+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0294372515228594, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@3", "credit": "Erich Friedman", "date": "December 2013", "family_updated": "", "metric_expression": "18 \u2013 12\u221a2 = 1.02940+", "metric_symbol": "s", "metric_value": 1.0294, "reference_text": "s = 18 \u2013 12\u221a2 = 1.02940+ | Found by Erich Friedman | in December 2013.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/3.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 18 \u2013 12\u221a2 = 1.02940+ | Found by Erich Friedman | in December 2013.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "3d85991afac60053", "improvement": -2.5868046270138834e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.835100684478856e-06, "max_pair_overlap_depth": -3.4409461626638826e-05, "metric_expression": "1.02946", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0294631195691295, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.0294372515228594, "setup": "squinoct", "side": 1.0294631195691295, "solution_path": "data/solutions/generated/squinoct_003_3d85991afac60053.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/3d85991afac60053.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@4", "density": 0.7070860385519216, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.08239, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/4.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "\u221a(4\u20132\u221a2) = 1.08239+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.082392200292394, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@4", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a(4\u20132\u221a2) = 1.08239+", "metric_symbol": "s", "metric_value": 1.08239, "reference_text": "s = \u221a(4\u20132\u221a2) = 1.08239+ | Trivial. |", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/4.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = \u221a(4\u20132\u221a2) = 1.08239+ | Trivial. |", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "30bfa7c46cf6dd87", "improvement": -1.587607451858375e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.1007450963540665e-06, "max_pair_overlap_depth": -1.5610612916431253e-05, "metric_expression": "1.08241", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0824080763669126, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.082392200292394, "setup": "squinoct", "side": 1.0824080763669126, "solution_path": "data/solutions/generated/squinoct_004_30bfa7c46cf6dd87.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/30bfa7c46cf6dd87.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@5", "density": 0.6705984373456575, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.24261, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/5.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "3\u221a2 \u2013 3 = 1.24261+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.2426406871192852, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3\u221a2 \u2013 3 = 1.24261+", "metric_symbol": "s", "metric_value": 1.24261, "reference_text": "s = 3\u221a2 \u2013 3 = 1.24261+ | Trivial. |", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/5.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 3\u221a2 \u2013 3 = 1.24261+ | Trivial. |", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "3bf97518bf42702c", "improvement": -1.5232844760237896e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2899385621933342e-06, "max_pair_overlap_depth": -9.75715015771872e-06, "metric_expression": "1.24266", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.2426559199640455, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.2426406871192852, "setup": "squinoct", "side": 1.2426559199640455, "solution_path": "data/solutions/generated/squinoct_005_3bf97518bf42702c.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/3bf97518bf42702c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@6", "density": 0.6887710971991018, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2013", "friedman_display_metric_value": 1.34314, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/6.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "7 \u2013 4\u221a2 = 1.34314+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.3431457505076199, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@6", "credit": "Maurizio Morandi", "date": "December 2013", "family_updated": "", "metric_expression": "7 \u2013 4\u221a2 = 1.34314+", "metric_symbol": "s", "metric_value": 1.34314, "reference_text": "s = 7 \u2013 4\u221a2 = 1.34314+ | Found by Maurizio Morandi | in December 2013.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/6.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 7 \u2013 4\u221a2 = 1.34314+ | Found by Maurizio Morandi | in December 2013.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "6368fdc8880da7e0", "improvement": -3.768520392477548e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.645757686457117e-06, "max_pair_overlap_depth": -2.457675057909725e-05, "metric_expression": "1.34318", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.3431834357115446, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.3431457505076199, "setup": "squinoct", "side": 1.3431834357115446, "solution_path": "data/solutions/generated/squinoct_006_6368fdc8880da7e0.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/6368fdc8880da7e0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@7", "density": 0.702115846733366, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2013", "friedman_display_metric_value": 1.43691, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/7.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "1.43691+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.43691, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@7", "credit": "Maurizio Morandi", "date": "December 2013", "family_updated": "", "metric_expression": "1.43691+", "metric_symbol": "s", "metric_value": 1.43691, "reference_text": "s = 1.43691+ | Found by Maurizio Morandi | in December 2013.", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/7.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 1.43691+ | Found by Maurizio Morandi | in December 2013.", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "35d0c06f5c122826", "improvement": -4.0447358323758564e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.691262438170272e-07, "max_pair_overlap_depth": -1.2495412028745712e-05, "metric_expression": "1.43695", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.4369504473583237, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.43691, "setup": "squinoct", "side": 1.4369504473583237, "solution_path": "data/solutions/generated/squinoct_007_35d0c06f5c122826.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/35d0c06f5c122826.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@8", "density": 0.6722160358662614, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.56967, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/8.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "1.56967+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.56967, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@8", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.56967+", "metric_symbol": "s", "metric_value": 1.56967, "reference_text": "s = 1.56967+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/8.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 1.56967+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "ecaef16600354c9f", "improvement": -0.00028685978676801227, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.463017743294653e-07, "max_pair_overlap_depth": -1.4183990756477804e-05, "metric_expression": "1.56996", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.569956859786768, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.56967, "setup": "squinoct", "side": 1.569956859786768, "solution_path": "data/solutions/generated/squinoct_008_ecaef16600354c9f.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/ecaef16600354c9f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@9", "density": 0.707064805820287, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.62358, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/9.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "3/\u221a(2+\u221a2) = 1.62358+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.623588300438591, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@9", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3/\u221a(2+\u221a2) = 1.62358+", "metric_symbol": "s", "metric_value": 1.62358, "reference_text": "s = 3/\u221a(2+\u221a2) = 1.62358+ | Trivial. |", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/9.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 3/\u221a(2+\u221a2) = 1.62358+ | Trivial. |", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "703059104a2b70f8", "improvement": -4.819197730077107e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6691071523245226e-06, "max_pair_overlap_depth": -7.928509179855325e-06, "metric_expression": "1.62364", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.6236364924158917, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.623588300438591, "setup": "squinoct", "side": 1.6236364924158917, "solution_path": "data/solutions/generated/squinoct_009_703059104a2b70f8.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/703059104a2b70f8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@10", "density": 0.732083417533705, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2013", "friedman_display_metric_value": 1.68179, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/10.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2^(3/4) = 1.68179+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.681792830507429, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@10", "credit": "Maurizio Morandi", "date": "December 2013", "family_updated": "", "metric_expression": "2^(3/4) = 1.68179+", "metric_symbol": "s", "metric_value": 1.68179, "reference_text": "s = 2^(3/4) = 1.68179+ | Found by Maurizio Morandi | in December 2013.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/10.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2^(3/4) = 1.68179+ | Found by Maurizio Morandi | in December 2013.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "03facc71923f1148", "improvement": -0.00017186085431797338, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.2978224497762506e-06, "max_pair_overlap_depth": -2.3560442145575955e-05, "metric_expression": "1.68196", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.681964691361747, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.681792830507429, "setup": "squinoct", "side": 1.681964691361747, "solution_path": "data/solutions/generated/squinoct_010_03facc71923f1148.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/03facc71923f1148.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@11", "density": 0.7597329550134904, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.7318, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/11.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "1.73180+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.7318, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@11", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.73180+", "metric_symbol": "s", "metric_value": 1.7318, "reference_text": "s = 1.73180+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/11.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 1.73180+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "78c32afdb2263b2d", "improvement": 0.00013842799014240903, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.409684401929808e-09, "max_pair_overlap_depth": -1.1021961062729346e-05, "metric_expression": "1.73166", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.7316615720098576, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.7318, "setup": "squinoct", "side": 1.7316615720098576, "solution_path": "data/solutions/generated/squinoct_011_78c32afdb2263b2d.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/78c32afdb2263b2d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@12", "density": 0.8083084838512736, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2013", "friedman_display_metric_value": 1.7533, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/12.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "1.7533+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.7533, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@12", "credit": "Maurizio Morandi", "date": "December 2013", "family_updated": "", "metric_expression": "1.7533+", "metric_symbol": "s", "metric_value": 1.7533, "reference_text": "s = 1.7533+ | Found by Maurizio Morandi | in December 2013.", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/12.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 1.7533+ | Found by Maurizio Morandi | in December 2013.", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "7a9451cae59dbb40", "improvement": -0.00017352882969978722, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.088823188597466e-06, "max_pair_overlap_depth": -2.0797652260817756e-05, "metric_expression": "1.75347", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.7534735288296999, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.7533, "setup": "squinoct", "side": 1.7534735288296999, "solution_path": "data/solutions/generated/squinoct_012_7a9451cae59dbb40.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/7a9451cae59dbb40.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@13", "density": 0.7475846505942733, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.8976, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/13.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "1.89760+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.8976, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@13", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.89760+", "metric_symbol": "s", "metric_value": 1.8976, "reference_text": "s = 1.89760+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/13.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 1.89760+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "c5bdcacf094e428e", "improvement": -0.00014846020367564883, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.439964464558682e-06, "max_pair_overlap_depth": -2.7883136850093138e-05, "metric_expression": "1.89775", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.8977484602036756, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.8976, "setup": "squinoct", "side": 1.8977484602036756, "solution_path": "data/solutions/generated/squinoct_013_c5bdcacf094e428e.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/c5bdcacf094e428e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@14", "density": 0.7369251630765782, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.9835, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/14.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "1.98350+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.9835, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@14", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.98350+", "metric_symbol": "s", "metric_value": 1.9835, "reference_text": "s = 1.98350+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "14.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/14.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 1.98350+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "994e0dd57a80d4a3", "improvement": -7.891975572338339e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.49261632156563e-06, "max_pair_overlap_depth": -2.894591689805992e-05, "metric_expression": "1.98358", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.9835789197557234, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.9835, "setup": "squinoct", "side": 1.9835789197557234, "solution_path": "data/solutions/generated/squinoct_014_994e0dd57a80d4a3.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/994e0dd57a80d4a3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@15", "density": 0.7515649396279209, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.03259, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/15.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.03259+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.03259, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@15", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.03259+", "metric_symbol": "s", "metric_value": 2.03259, "reference_text": "s = 2.03259+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/15.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.03259+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "c898d8b3cd2b55db", "improvement": -0.0005137104569299389, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7983161874182644e-07, "max_pair_overlap_depth": -1.9704810269915995e-05, "metric_expression": "2.03310", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.03310371045693, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.03259, "setup": "squinoct", "side": 2.03310371045693, "solution_path": "data/solutions/generated/squinoct_015_c898d8b3cd2b55db.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/c898d8b3cd2b55db.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@16", "density": 0.7725175260502497, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.07106, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/16.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "5\u221a2 \u2013 5 = 2.07106+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.071067811865475, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@16", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5\u221a2 \u2013 5 = 2.07106+", "metric_symbol": "s", "metric_value": 2.07106, "reference_text": "s = 5\u221a2 \u2013 5 = 2.07106+ | Trivial. |", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/16.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 5\u221a2 \u2013 5 = 2.07106+ | Trivial. |", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "3a2e6d99239355fd", "improvement": -4.130460271545289e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5220970331887e-06, "max_pair_overlap_depth": -8.060079695892952e-07, "metric_expression": "2.07111", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0711091164681905, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.071067811865475, "setup": "squinoct", "side": 2.0711091164681905, "solution_path": "data/solutions/generated/squinoct_016_3a2e6d99239355fd.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/3a2e6d99239355fd.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@17", "density": 0.8208079603816107, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.07106, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/17.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "5\u221a2 \u2013 5 = 2.07106+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.071067811865475, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@17", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5\u221a2 \u2013 5 = 2.07106+", "metric_symbol": "s", "metric_value": 2.07106, "reference_text": "s = 5\u221a2 \u2013 5 = 2.07106+ | Trivial. |", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/17.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 5\u221a2 \u2013 5 = 2.07106+ | Trivial. |", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "ab660f0510a3dd1c", "improvement": -3.109932520750647e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 1.368661750365744e-09, "max_pair_overlap_depth": -1.0480566122961221e-05, "metric_expression": "2.07110", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0710989111906826, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.071067811865475, "setup": "squinoct", "side": 2.0710989111906826, "solution_path": "data/solutions/generated/squinoct_017_ab660f0510a3dd1c.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/ab660f0510a3dd1c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@18", "density": 0.7934296897658486, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.16778, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/18.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.16778+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.16778, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@18", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.16778+", "metric_symbol": "s", "metric_value": 2.16778, "reference_text": "s = 2.16778+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/18.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.16778+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "a7275e2ab7024187", "improvement": 0.00017977070139485463, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9711774532196686e-06, "max_pair_overlap_depth": -1.4522556675777842e-05, "metric_expression": "2.16760", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.167600229298605, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.16778, "setup": "squinoct", "side": 2.167600229298605, "solution_path": "data/solutions/generated/squinoct_018_a7275e2ab7024187.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/a7275e2ab7024187.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@19", "density": 0.793469906795261, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.22823, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/19.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.22823+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.22823, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.22823+", "metric_symbol": "s", "metric_value": 2.22823, "reference_text": "s = 2.22823+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/19.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.22823+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "330906f1db929cdb", "improvement": 0.0012889040224068893, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0543459428412958e-06, "max_pair_overlap_depth": -1.4850274468458657e-05, "metric_expression": "2.22694", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.226941095977593, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.22823, "setup": "squinoct", "side": 2.226941095977593, "solution_path": "data/solutions/generated/squinoct_019_330906f1db929cdb.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/330906f1db929cdb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@20", "density": 0.7912106699597153, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.2873, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/20.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.28730+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.2873, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@20", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.28730+", "metric_symbol": "s", "metric_value": 2.2873, "reference_text": "s = 2.28730+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/20.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.28730+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "d1597d2fdf3beee1", "improvement": -0.0007530500807275686, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.367182536359887e-05, "max_pair_overlap_depth": -8.661317408398261e-06, "metric_expression": "2.28805", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.2880530500807277, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.2873, "setup": "squinoct", "side": 2.2880530500807277, "solution_path": "data/solutions/generated/squinoct_020_d1597d2fdf3beee1.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/d1597d2fdf3beee1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@21", "density": 0.8091484006744551, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.32167, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/21.gif", "friedman_metric_expression": "2.32167+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.32167, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@21", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.32167+", "metric_symbol": "s", "metric_value": 2.32167, "reference_text": "s = 2.32167+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/21.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.32167+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "a3759fa0325bb184", "improvement": 0.0032467851108277657, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.288437924896875e-06, "max_pair_overlap_depth": -7.589979277911052e-06, "metric_expression": "2.31842", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.3184232148891724, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.32167, "setup": "squinoct", "side": 2.3184232148891724, "solution_path": "data/solutions/generated/squinoct_021_a3759fa0325bb184.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/a3759fa0325bb184.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@22", "density": 0.779088370401765, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.41811, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/22.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.41811+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.41811, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@22", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.41811+", "metric_symbol": "s", "metric_value": 2.41811, "reference_text": "s = 2.41811+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/22.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.41811+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "c01cc63fb6a654c8", "improvement": -0.00021763715445111131, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4586625716053672e-06, "max_pair_overlap_depth": -2.804598842454098e-05, "metric_expression": "2.41833", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.418327637154451, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.41811, "setup": "squinoct", "side": 2.418327637154451, "solution_path": "data/solutions/generated/squinoct_022_c01cc63fb6a654c8.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/c01cc63fb6a654c8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@23", "density": 0.7777209980912639, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.47329, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/23.gif", "friedman_metric_expression": "2.47329+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.47329, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@23", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.47329+", "metric_symbol": "s", "metric_value": 2.47329, "reference_text": "s = 2.47329+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/23.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.47329+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "004d1c5d4d7bca47", "improvement": -0.0015616154620987643, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.985478608046375e-06, "max_pair_overlap_depth": -1.4996046389881279e-05, "metric_expression": "2.47485", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.4748516154620988, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.47329, "setup": "squinoct", "side": 2.4748516154620988, "solution_path": "data/solutions/generated/squinoct_023_004d1c5d4d7bca47.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/004d1c5d4d7bca47.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@24", "density": 0.804709078453695, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.48528, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/24.gif", "friedman_metric_expression": "6\u221a2 \u2013 6 = 2.48528+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.4852813742385704, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@24", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6\u221a2 \u2013 6 = 2.48528+", "metric_symbol": "s", "metric_value": 2.48528, "reference_text": "s = 6\u221a2 \u2013 6 = 2.48528+ | Trivial.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/24.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 6\u221a2 \u2013 6 = 2.48528+ | Trivial.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "4f255616aca5e547", "improvement": -4.443531267428469e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.67146332394231e-06, "max_pair_overlap_depth": -9.95881463161652e-06, "metric_expression": "2.48533", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.4853258095512447, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.4852813742385704, "setup": "squinoct", "side": 2.4853258095512447, "solution_path": "data/solutions/generated/squinoct_024_4f255616aca5e547.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4f255616aca5e547.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@25", "density": 0.8352526418920933, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.49195, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/25.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "11/(3+\u221a2) = 2.49195+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.491950116270851, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@25", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "11/(3+\u221a2) = 2.49195+", "metric_symbol": "s", "metric_value": 2.49195, "reference_text": "s = 11/(3+\u221a2) = 2.49195+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/25.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 11/(3+\u221a2) = 2.49195+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "0d3ca23da8f19da7", "improvement": 0.0021858196070967395, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.3164106628379786e-06, "max_pair_overlap_depth": -1.12459370678053e-05, "metric_expression": "2.48976", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.489764296663754, "n": 25, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.491950116270851, "setup": "squinoct", "side": 2.489764296663754, "solution_path": "data/solutions/generated/squinoct_025_0d3ca23da8f19da7.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/0d3ca23da8f19da7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@26", "density": 0.8421766228224283, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.52841, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/26.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.52841+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.52841, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@26", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.52841+", "metric_symbol": "s", "metric_value": 2.52841, "reference_text": "s = 2.52841+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/26.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.52841+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "6c0cffa2ebc39455", "improvement": -0.00020227836257324938, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3125873649857306e-07, "max_pair_overlap_depth": -6.684300461579085e-06, "metric_expression": "2.52861", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.5286122783625733, "n": 26, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.52841, "setup": "squinoct", "side": 2.5286122783625733, "solution_path": "data/solutions/generated/squinoct_026_6c0cffa2ebc39455.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/6c0cffa2ebc39455.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@27", "density": 0.8354347334144809, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.58695, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/27.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.58695+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.58695, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@27", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.58695+", "metric_symbol": "s", "metric_value": 2.58695, "reference_text": "s = 2.58695+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/27.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.58695+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "9243c0031663b10e", "improvement": -0.0002069616913620287, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1228507689492215e-06, "max_pair_overlap_depth": -1.654834709174935e-05, "metric_expression": "2.58716", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.587156961691362, "n": 27, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.58695, "setup": "squinoct", "side": 2.587156961691362, "solution_path": "data/solutions/generated/squinoct_027_9243c0031663b10e.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/9243c0031663b10e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@28", "density": 0.8375235613860185, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.63116, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/28.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.63116+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.63116, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@28", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.63116+", "metric_symbol": "s", "metric_value": 2.63116, "reference_text": "s = 2.63116+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/28.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.63116+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "f74e0430c683aaa0", "improvement": -0.0001841851467743183, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.686366302485504e-06, "max_pair_overlap_depth": -8.053108887406957e-06, "metric_expression": "2.63134", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.6313441851467743, "n": 28, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.63116, "setup": "squinoct", "side": 2.6313441851467743, "solution_path": "data/solutions/generated/squinoct_028_f74e0430c683aaa0.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/f74e0430c683aaa0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@29", "density": 0.8192713469622411, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.70811, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/29.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.70811+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.70811, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@29", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.70811+", "metric_symbol": "s", "metric_value": 2.70811, "reference_text": "s = 2.70811+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/29.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.70811+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "7d4fefbdad04f318", "improvement": 0.0005239033117416803, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.8746413323634285e-06, "max_pair_overlap_depth": -4.299633667326219e-06, "metric_expression": "2.70759", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.7075860966882583, "n": 29, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.70811, "setup": "squinoct", "side": 2.7075860966882583, "solution_path": "data/solutions/generated/squinoct_029_7d4fefbdad04f318.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/7d4fefbdad04f318.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@30", "density": 0.8256466842229233, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.7422, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/30.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.74220+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.7422, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@30", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.74220+", "metric_symbol": "s", "metric_value": 2.7422, "reference_text": "s = 2.74220+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/30.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.74220+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "e6809975fe4af696", "improvement": -0.0010201760226595802, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.275653162265926e-06, "max_pair_overlap_depth": -1.2928136431611392e-05, "metric_expression": "2.74322", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.7432201760226596, "n": 30, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.7422, "setup": "squinoct", "side": 2.7432201760226596, "solution_path": "data/solutions/generated/squinoct_030_e6809975fe4af696.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/e6809975fe4af696.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@1", "density": 0.6621920830904189, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 0.936, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/1.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": ".936+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.936, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "squinpen@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": ".936+", "metric_symbol": "s", "metric_value": 0.936, "reference_text": "s = cos(27\u00b0) / cos(18\u00b0) | s = .936+ | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/1.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = cos(27\u00b0) / cos(18\u00b0) | s = .936+ | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "7c4deaf46828e45f", "improvement": -0.0008790374068264883, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1116494686738636e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.93688", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.9368790374068265, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.936, "setup": "squinpen", "side": 0.9368790374068265, "solution_path": "data/solutions/generated/squinpen_001_7c4deaf46828e45f.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/7c4deaf46828e45f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@2", "density": 0.49287502021209156, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "March 2012", "friedman_display_metric_value": 1.535, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/2.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "1.535+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.535, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@2", "credit": "Erich Friedman", "date": "March 2012", "family_updated": "", "metric_expression": "1.535+", "metric_symbol": "s", "metric_value": 1.535, "reference_text": "s = 4\u221a(1\u20132/\u221a5)+\u221a5\u20132 | s = 1.535+ | Found by Erich Friedman | in March 2012.", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/2.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4\u221a(1\u20132/\u221a5)+\u221a5\u20132 | s = 1.535+ | Found by Erich Friedman | in March 2012.", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "e0d70422bfa035f2", "improvement": -0.0007556004426736429, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.603512178169518e-07, "max_pair_overlap_depth": -4.1992473865937185e-06, "metric_expression": "1.53576", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.5357556004426736, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.535, "setup": "squinpen", "side": 1.5357556004426736, "solution_path": "data/solutions/generated/squinpen_002_e0d70422bfa035f2.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/e0d70422bfa035f2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@3", "density": 0.6064545372240481, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 1.695, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/3.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "1.695+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.695, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@3", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "1.695+", "metric_symbol": "s", "metric_value": 1.695, "reference_text": "s = 1.695+ | Found by David W. Cantrell | in July 2012. |", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/3.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 1.695+ | Found by David W. Cantrell | in July 2012. |", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "20345bd1acea07ee", "improvement": -0.0006531320538840646, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.096669049020619e-07, "max_pair_overlap_depth": -2.3507012493845236e-05, "metric_expression": "1.69565", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.6956531320538841, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.695, "setup": "squinpen", "side": 1.6956531320538841, "solution_path": "data/solutions/generated/squinpen_003_20345bd1acea07ee.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/20345bd1acea07ee.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@4", "density": 0.6707731008924028, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2012", "friedman_display_metric_value": 1.861, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/4.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "1.861+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.861, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@4", "credit": "Maurizio Morandi", "date": "July 2012", "family_updated": "", "metric_expression": "1.861+", "metric_symbol": "s", "metric_value": 1.861, "reference_text": "s = 1.861+ | Found by Maurizio Morandi | in July 2012. |", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/4.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 1.861+ | Found by Maurizio Morandi | in July 2012. |", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "3b3728a72d1e463a", "improvement": -0.0007342580262259535, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8617284829398191e-06, "max_pair_overlap_depth": -1.61527471932571e-05, "metric_expression": "1.86173", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.861734258026226, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.861, "setup": "squinpen", "side": 1.861734258026226, "solution_path": "data/solutions/generated/squinpen_004_3b3728a72d1e463a.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/3b3728a72d1e463a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@5", "density": 0.7633756933560932, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "March 2012", "friedman_display_metric_value": 1.951, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/5.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "1.951+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.951, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@5", "credit": "Erich Friedman", "date": "March 2012", "family_updated": "", "metric_expression": "1.951+", "metric_symbol": "s", "metric_value": 1.951, "reference_text": "s = 1 + cos(18\u00b0) | s = 1.951+ | Found by Erich Friedman | in March 2012.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/5.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 1 + cos(18\u00b0) | s = 1.951+ | Found by Erich Friedman | in March 2012.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "dfdcf10f7cfe5f16", "improvement": -0.00015311806809270578, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.72748390891526e-06, "max_pair_overlap_depth": -2.251588894827683e-05, "metric_expression": "1.95115", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.9511531180680928, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.951, "setup": "squinpen", "side": 1.9511531180680928, "solution_path": "data/solutions/generated/squinpen_005_dfdcf10f7cfe5f16.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/dfdcf10f7cfe5f16.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@6", "density": 0.7300382566069571, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "March 2012", "friedman_display_metric_value": 2.185, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/6.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "2.185+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.185, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@6", "credit": "Erich Friedman", "date": "March 2012", "family_updated": "", "metric_expression": "2.185+", "metric_symbol": "s", "metric_value": 2.185, "reference_text": "s = 6\u221a(1\u20132/\u221a5)+\u221a5\u20132 | s = 2.185+ | Found by Erich Friedman | in March 2012.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/6.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 6\u221a(1\u20132/\u221a5)+\u221a5\u20132 | s = 2.185+ | Found by Erich Friedman | in March 2012.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "fbc8fa063fa8154f", "improvement": -0.0006384860733987807, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.046305607470139e-06, "max_pair_overlap_depth": -1.535481943848449e-05, "metric_expression": "2.18564", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.185638486073399, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.185, "setup": "squinpen", "side": 2.185638486073399, "solution_path": "data/solutions/generated/squinpen_006_fbc8fa063fa8154f.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/fbc8fa063fa8154f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@7", "density": 0.6937337333431398, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "July 2012", "friedman_display_metric_value": 2.421, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/7.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "2.421+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.421, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@7", "credit": "Erich Friedman", "date": "July 2012", "family_updated": "", "metric_expression": "2.421+", "metric_symbol": "s", "metric_value": 2.421, "reference_text": "s = 6\u221a(1\u20132/\u221a5)+2\u221a5\u20134 | s = 2.421+ | Found by Erich Friedman | in July 2012.", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/7.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 6\u221a(1\u20132/\u221a5)+2\u221a5\u20134 | s = 2.421+ | Found by Erich Friedman | in July 2012.", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "a9079c85f43f1608", "improvement": -0.0007434143519042813, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.2537276094194668e-06, "max_pair_overlap_depth": -4.1098373515402464e-05, "metric_expression": "2.42174", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.421743414351904, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.421, "setup": "squinpen", "side": 2.421743414351904, "solution_path": "data/solutions/generated/squinpen_007_a9079c85f43f1608.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/a9079c85f43f1608.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@8", "density": 0.7064703560745587, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 2.565, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/8.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "2.565+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.565, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@8", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "2.565+", "metric_symbol": "s", "metric_value": 2.565, "reference_text": "s = 2.565+ | Found by David W. Cantrell | in July 2012. |", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/8.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 2.565+ | Found by David W. Cantrell | in July 2012. |", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "eedfd38786ce3d06", "improvement": -0.0005089596009386632, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2839977085297321e-06, "max_pair_overlap_depth": -2.052513031336467e-05, "metric_expression": "2.56551", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.5655089596009386, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.565, "setup": "squinpen", "side": 2.5655089596009386, "solution_path": "data/solutions/generated/squinpen_008_eedfd38786ce3d06.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/eedfd38786ce3d06.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@9", "density": 0.7204851744660768, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_display_metric_value": 2.693, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/9.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "2.693+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.693, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@9", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "2.693+", "metric_symbol": "s", "metric_value": 2.693, "reference_text": "s = 2.693+ | Found by Timo Berthold et al | in January 2026. |", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/9.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 2.693+ | Found by Timo Berthold et al | in January 2026. |", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "b050939c544c8091", "improvement": -0.0015375753912136858, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.502705162025631e-06, "max_pair_overlap_depth": -2.4857642315079254e-05, "metric_expression": "2.69454", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.6945375753912137, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.693, "setup": "squinpen", "side": 2.6945375753912137, "solution_path": "data/solutions/generated/squinpen_009_b050939c544c8091.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/b050939c544c8091.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@10", "density": 0.7436124164686567, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_display_metric_value": 2.793, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/10.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "2.793+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.793, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@10", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "2.793+", "metric_symbol": "s", "metric_value": 2.793, "reference_text": "s = 2.793+ | Found by Timo Berthold et al | in January 2026.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/10.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 2.793+ | Found by Timo Berthold et al | in January 2026.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "5e3ff0fc92953694", "improvement": -0.0027748736770187854, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.695299675143831e-07, "max_pair_overlap_depth": -2.06179882833446e-05, "metric_expression": "2.79577", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.795774873677019, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.793, "setup": "squinpen", "side": 2.795774873677019, "solution_path": "data/solutions/generated/squinpen_010_5e3ff0fc92953694.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/5e3ff0fc92953694.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@11", "density": 0.7644165493663143, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_display_metric_value": 2.89, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/11.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "2.890+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.89, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@11", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "2.890+", "metric_symbol": "s", "metric_value": 2.89, "reference_text": "s = 2.890+ | Found by Timo Berthold et al | in January 2026.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/11.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 2.890+ | Found by Timo Berthold et al | in January 2026.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "eed6c273a2c34445", "improvement": -0.002056785153238039, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.157725543754771e-07, "max_pair_overlap_depth": -2.6396452143861993e-05, "metric_expression": "2.89206", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.892056785153238, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.89, "setup": "squinpen", "side": 2.892056785153238, "solution_path": "data/solutions/generated/squinpen_011_eed6c273a2c34445.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/eed6c273a2c34445.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@12", "density": 0.7899142461050866, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_display_metric_value": 2.969, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/12.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "2.969+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.969, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@12", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "2.969+", "metric_symbol": "s", "metric_value": 2.969, "reference_text": "s = 2.969+ | Found by Timo Berthold et al | in January 2026.", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/12.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 2.969+ | Found by Timo Berthold et al | in January 2026.", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "0dc0d2750d6b1986", "improvement": -0.0025029358297610216, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.6525891073399466e-06, "max_pair_overlap_depth": -2.2708088333933674e-05, "metric_expression": "2.97150", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.971502935829761, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.969, "setup": "squinpen", "side": 2.971502935829761, "solution_path": "data/solutions/generated/squinpen_012_0dc0d2750d6b1986.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/0dc0d2750d6b1986.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@13", "density": 0.7748259330672266, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 3.121, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/13.gif", "friedman_metric_expression": "3.121+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.121, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@13", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "3.121+", "metric_symbol": "s", "metric_value": 3.121, "reference_text": "s = 2\u221a(1\u20132/\u221a5)+2\u221a5\u20132 | s = 3.121+ | Found by David W. Cantrell | in July 2012.", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/13.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 2\u221a(1\u20132/\u221a5)+2\u221a5\u20132 | s = 3.121+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "13449338c659bacc", "improvement": -0.0018067975436526496, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.882913072523962e-06, "max_pair_overlap_depth": -3.6524180263897144e-05, "metric_expression": "3.12281", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.1228067975436526, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.121, "setup": "squinpen", "side": 3.1228067975436526, "solution_path": "data/solutions/generated/squinpen_13_13449338c659bacc.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T07:13:53+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/13449338c659bacc.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@14", "density": 0.8005863693145643, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 3.187, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/14.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.187+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.187, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@14", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "3.187+", "metric_symbol": "s", "metric_value": 3.187, "reference_text": "s = 3.187+ | Found by David W. Cantrell | in July 2012. |", "source_image": "14.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/14.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.187+ | Found by David W. Cantrell | in July 2012. |", "friedman_source_image": "14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "c910e2e69c5e952c", "improvement": -0.0011256975399334124, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.345127969056754e-07, "max_pair_overlap_depth": -6.672013015962541e-06, "metric_expression": "3.18813", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.1881256975399332, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.187, "setup": "squinpen", "side": 3.1881256975399332, "solution_path": "data/solutions/generated/squinpen_014_c910e2e69c5e952c.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/c910e2e69c5e952c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@15", "density": 0.8079241717093747, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 3.284, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/15.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.284+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.284, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@15", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "3.284+", "metric_symbol": "s", "metric_value": 3.284, "reference_text": "s = (\u221a(125\u201338\u221a5)+8\u20132\u221a5)/3 | s = 3.284+ | Found by David W. Cantrell | in July 2012.", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/15.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = (\u221a(125\u201338\u221a5)+8\u20132\u221a5)/3 | s = 3.284+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "d5cf3c3cc0980b70", "improvement": -0.001003544834322856, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.349360852435288e-06, "max_pair_overlap_depth": -2.4505079251779804e-05, "metric_expression": "3.28500", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.2850035448343227, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.284, "setup": "squinpen", "side": 3.2850035448343227, "solution_path": "data/solutions/generated/squinpen_015_d5cf3c3cc0980b70.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d5cf3c3cc0980b70.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@16", "density": 0.7674551673762713, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 3.48, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/16.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.480+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.48, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@16", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3.480+", "metric_symbol": "s", "metric_value": 3.48, "reference_text": "s = 3.480+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/16.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.480+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "9ca0c9eddf5257a6", "improvement": -0.0010398730905230025, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 5.610061847707955e-09, "max_pair_overlap_depth": -2.0020049716018562e-05, "metric_expression": "3.48104", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.481039873090523, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.48, "setup": "squinpen", "side": 3.481039873090523, "solution_path": "data/solutions/generated/squinpen_016_9ca0c9eddf5257a6.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/9ca0c9eddf5257a6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@17", "density": 0.7871473019367167, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 3.541, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/17.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.541+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.541, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@17", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3.541+", "metric_symbol": "s", "metric_value": 3.541, "reference_text": "s = 3.541+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/17.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.541+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "c1324401d6fef4ff", "improvement": -0.0020066620107224153, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3581595293550302e-06, "max_pair_overlap_depth": -1.9942519651539037e-05, "metric_expression": "3.54301", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.5430066620107223, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.541, "setup": "squinpen", "side": 3.5430066620107223, "solution_path": "data/solutions/generated/squinpen_017_c1324401d6fef4ff.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/c1324401d6fef4ff.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@18", "density": 0.7949963635829483, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 3.626, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/18.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.626+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.626, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@18", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3.626+", "metric_symbol": "s", "metric_value": 3.626, "reference_text": "s = 3.626+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/18.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.626+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "521e6ed1020d53e6", "improvement": -0.001681876520355896, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.132718950610418e-06, "max_pair_overlap_depth": -5.952134619235938e-06, "metric_expression": "3.62768", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.627681876520356, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.626, "setup": "squinpen", "side": 3.627681876520356, "solution_path": "data/solutions/generated/squinpen_018_521e6ed1020d53e6.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/521e6ed1020d53e6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@19", "density": 0.8016091392666894, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 3.71, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/19.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.710+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.71, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3.710+", "metric_symbol": "s", "metric_value": 3.71, "reference_text": "s = 3.710+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/19.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.710+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "66aeca1af6b9bf65", "improvement": -0.001683910599032501, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.240508232322902e-06, "max_pair_overlap_depth": -2.033383687716217e-05, "metric_expression": "3.71168", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.7116839105990325, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.71, "setup": "squinpen", "side": 3.7116839105990325, "solution_path": "data/solutions/generated/squinpen_019_66aeca1af6b9bf65.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/66aeca1af6b9bf65.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@20", "density": 0.8030009751844291, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 3.802, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/20.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.802+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.802, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@20", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "3.802+", "metric_symbol": "s", "metric_value": 3.802, "reference_text": "s = 3.802+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/20.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.802+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "8424f972564f51a8", "improvement": -0.00280562795003636, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.488842199203112e-06, "max_pair_overlap_depth": -3.2279665458823104e-05, "metric_expression": "3.80481", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.8048056279500364, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.802, "setup": "squinpen", "side": 3.8048056279500364, "solution_path": "data/solutions/generated/squinpen_020_8424f972564f51a8.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/8424f972564f51a8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@21", "density": 0.8168349282229689, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 3.864, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/21.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.864+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.864, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@21", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "3.864+", "metric_symbol": "s", "metric_value": 3.864, "reference_text": "s = 3.864+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/21.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.864+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "7f1bf6bbe100ca6c", "improvement": -0.0016097781764203845, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0975793470973527e-06, "max_pair_overlap_depth": -2.933142426009283e-05, "metric_expression": "3.86561", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.8656097781764203, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.864, "setup": "squinpen", "side": 3.8656097781764203, "solution_path": "data/solutions/generated/squinpen_021_7f1bf6bbe100ca6c.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/7f1bf6bbe100ca6c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@22", "density": 0.8236901899623935, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 3.937, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/22.gif", "friedman_metric_expression": "3.937+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.937, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@22", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "3.937+", "metric_symbol": "s", "metric_value": 3.937, "reference_text": "s = 3.937+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/22.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.937+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "33b95c59890c6cd7", "improvement": -0.0030787983666398233, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.1912141987053604e-06, "max_pair_overlap_depth": -2.2837560550437175e-06, "metric_expression": "3.94008", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.9400787983666397, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.937, "setup": "squinpen", "side": 3.9400787983666397, "solution_path": "data/solutions/generated/squinpen_022_33b95c59890c6cd7.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/33b95c59890c6cd7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@23", "density": 0.8342850114016098, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 4.002, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/23.gif", "friedman_metric_expression": "4.002+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.002, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@23", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.002+", "metric_symbol": "s", "metric_value": 4.002, "reference_text": "s = 4.002+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/23.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.002+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "125d15e1f42d4cc7", "improvement": -0.000968856434470311, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.142206802972531e-06, "max_pair_overlap_depth": -1.3381668518996914e-05, "metric_expression": "4.00297", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.00296885643447, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.002, "setup": "squinpen", "side": 4.00296885643447, "solution_path": "data/solutions/generated/squinpen_023_125d15e1f42d4cc7.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/125d15e1f42d4cc7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@24", "density": 0.8254992867774645, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 4.107, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/24.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.107+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.107, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@24", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.107+", "metric_symbol": "s", "metric_value": 4.107, "reference_text": "s = 4.107+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/24.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.107+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "7b6bed1452ec8f75", "improvement": -0.003766262034448964, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.187233974203672e-07, "max_pair_overlap_depth": -1.4055675707780324e-06, "metric_expression": "4.11077", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.110766262034449, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.107, "setup": "squinpen", "side": 4.110766262034449, "solution_path": "data/solutions/generated/squinpen_024_7b6bed1452ec8f75.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/7b6bed1452ec8f75.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@25", "density": 0.8346264431391957, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 4.169, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/25.gif", "friedman_metric_expression": "4.169+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.169, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@25", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.169+", "metric_symbol": "s", "metric_value": 4.169, "reference_text": "s = 4.169+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/25.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.169+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "965f543dd3a1a5b2", "improvement": -0.003529809873594303, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.8760801669609005e-06, "max_pair_overlap_depth": -9.22783607931743e-06, "metric_expression": "4.17253", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.172529809873594, "n": 25, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.169, "setup": "squinpen", "side": 4.172529809873594, "solution_path": "data/solutions/generated/squinpen_025_965f543dd3a1a5b2.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/965f543dd3a1a5b2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@26", "density": 0.846720772454187, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 4.223, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/26.gif", "friedman_metric_expression": "4.223+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.223, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@26", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.223+", "metric_symbol": "s", "metric_value": 4.223, "reference_text": "s = 4.223+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/26.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.223+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "12ea954c92ca25d9", "improvement": -0.0016630925283189768, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.329734777233707e-07, "max_pair_overlap_depth": -5.080948892621784e-06, "metric_expression": "4.22466", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.224663092528319, "n": 26, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.223, "setup": "squinpen", "side": 4.224663092528319, "solution_path": "data/solutions/generated/squinpen_026_12ea954c92ca25d9.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/12ea954c92ca25d9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@27", "density": 0.8284208480685643, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 4.35, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/27.gif", "friedman_metric_expression": "4.350+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.35, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@27", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.350+", "metric_symbol": "s", "metric_value": 4.35, "reference_text": "s = 4.350+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/27.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.350+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "0b33929541015a68", "improvement": -0.0024309111336107136, "max_boundary_excess": -5.563644238076049e-06, "max_pair_overlap_depth": -1.2401213729695826e-05, "metric_expression": "4.35243", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.35243091113361, "n": 27, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 4.35, "setup": "squinpen", "side": 4.35243091113361, "solution_path": "data/solutions/generated/squinpen_27_0b33929541015a68.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T16:24:14+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/0b33929541015a68.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@27", "density": 0.8275684076653715, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 4.35, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/27.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.350+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.35, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@27", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.350+", "metric_symbol": "s", "metric_value": 4.35, "reference_text": "s = 4.350+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/27.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.350+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "fc7fa66fe1928440", "improvement": -0.0046719542874926745, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1174449550978842e-06, "max_pair_overlap_depth": -1.176344423625686e-05, "metric_expression": "4.35467", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.354671954287492, "n": 27, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "record_type": "verified", "reference_side": 4.35, "setup": "squinpen", "side": 4.354671954287492, "solution_path": "data/solutions/generated/squinpen_027_fc7fa66fe1928440.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/fc7fa66fe1928440.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@28", "density": 0.8327551046015365, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 4.421, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/28.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.421+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.421, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@28", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.421+", "metric_symbol": "s", "metric_value": 4.421, "reference_text": "s = 4.421+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/28.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.421+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "81b95a9d0915b9b0", "improvement": 0.0002507922234444848, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3068707244667255e-06, "max_pair_overlap_depth": -1.2232567722092469e-05, "metric_expression": "4.42075", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.420749207776556, "n": 28, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.421, "setup": "squinpen", "side": 4.420749207776556, "solution_path": "data/solutions/generated/squinpen_028_81b95a9d0915b9b0.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/81b95a9d0915b9b0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@29", "density": 0.8326213695314967, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 4.499, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/29.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.499+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.499, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@29", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.499+", "metric_symbol": "s", "metric_value": 4.499, "reference_text": "s = 4.499+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/29.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.499+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "7cc5c6e51420a8c4", "improvement": -0.0003599298979271026, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.900416840645271e-06, "max_pair_overlap_depth": -1.3857736228028994e-05, "metric_expression": "4.49936", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.499359929897927, "n": 29, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.499, "setup": "squinpen", "side": 4.499359929897927, "solution_path": "data/solutions/generated/squinpen_029_7cc5c6e51420a8c4.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/7cc5c6e51420a8c4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@30", "density": 0.8380230132738162, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 4.55, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif", "friedman_metric_expression": "4.550+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.55, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@30", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.550+", "metric_symbol": "s", "metric_value": 4.55, "reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "45dff6d0a270c6c5", "improvement": -0.011505140806147729, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.226407328203014e-06, "max_pair_overlap_depth": -5.655700288098586e-07, "metric_expression": "4.56151", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.5615051408061476, "n": 30, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "record_type": "verified", "reference_side": 4.55, "setup": "squinpen", "side": 4.5615051408061476, "solution_path": "data/solutions/generated/squinpen_30_45dff6d0a270c6c5.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T14:34:18+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/45dff6d0a270c6c5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@30", "density": 0.8400050623992149, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 4.55, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif", "friedman_metric_expression": "4.550+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.55, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@30", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.550+", "metric_symbol": "s", "metric_value": 4.55, "reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "6d45a6352a0ed4b0", "improvement": -0.006120371552951198, "max_boundary_excess": -3.665422902102479e-06, "max_pair_overlap_depth": -2.26166097641034e-05, "metric_expression": "4.55612", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.556120371552951, "n": 30, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 4.55, "setup": "squinpen", "side": 4.556120371552951, "solution_path": "data/solutions/generated/squinpen_30_6d45a6352a0ed4b0.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T17:13:54+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/6d45a6352a0ed4b0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@30", "density": 0.8399251030020208, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 4.55, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif", "friedman_metric_expression": "4.550+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.55, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@30", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.550+", "metric_symbol": "s", "metric_value": 4.55, "reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "abcbdd03f9f27f35", "improvement": -0.006337233727490954, "max_boundary_excess": -2.6577244583856583e-06, "max_pair_overlap_depth": -1.8093080493608582e-05, "metric_expression": "4.55634", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.556337233727491, "n": 30, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 4.55, "setup": "squinpen", "side": 4.556337233727491, "solution_path": "data/solutions/generated/squinpen_30_abcbdd03f9f27f35.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T16:24:14+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/abcbdd03f9f27f35.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@30", "density": 0.841773778692945, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 4.55, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif", "friedman_metric_expression": "4.550+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.55, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@30", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "4.550+", "metric_symbol": "s", "metric_value": 4.55, "reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "c7e14ee67108e002", "improvement": -0.0013312452630751537, "max_boundary_excess": -9.300402051962128e-07, "max_pair_overlap_depth": -1.6239474948775978e-05, "metric_expression": "4.55133", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.551331245263075, "n": 30, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "recovery_tag": "20260501_squinpen30_fresh", "reference_side": 4.55, "setup": "squinpen", "side": 4.551331245263075, "solution_path": "data/solutions/generated/squinpen_30_c7e14ee67108e002.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T17:22:49+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/c7e14ee67108e002.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@31", "density": 0.8407016075258085, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.63041, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/31.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.63041+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.63041, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.63041+", "metric_symbol": "s", "metric_value": 4.63041, "reference_text": "s = 4.63041+ | Found by Emerson Connelly | in April 2026.", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/31.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.63041+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "8b17df7ad9586809", "improvement": 0.0008957860403464579, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9662880539345523e-06, "max_pair_overlap_depth": -1.825266620247845e-05, "metric_expression": "4.62951", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.629514213959654, "n": 31, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.63041, "setup": "squinpen", "side": 4.629514213959654, "solution_path": "data/solutions/generated/squinpen_031_8b17df7ad9586809.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/8b17df7ad9586809.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@32", "density": 0.839043760254319, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.70774, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/32.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.70774+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.70774, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.70774+", "metric_symbol": "s", "metric_value": 4.70774, "reference_text": "s = 4.70774+ | Found by Emerson Connelly | in April 2026.", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/32.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.70774+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "ded24abc59c82646", "improvement": -0.000495710626569057, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.910425347385825e-07, "max_pair_overlap_depth": -1.0586072088480947e-05, "metric_expression": "4.70824", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.708235710626569, "n": 32, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.70774, "setup": "squinpen", "side": 4.708235710626569, "solution_path": "data/solutions/generated/squinpen_032_ded24abc59c82646.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/ded24abc59c82646.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@33", "density": 0.8454321018371573, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.75774, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/33.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.75774+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.75774, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.75774+", "metric_symbol": "s", "metric_value": 4.75774, "reference_text": "s = 4.75774+ | Found by Emerson Connelly | in April 2026.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/33.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.75774+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "a9622b0aeea26f74", "improvement": -0.00539747702354898, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.5906514265382727e-06, "max_pair_overlap_depth": -5.445984948337923e-06, "metric_expression": "4.76314", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.763137477023549, "n": 33, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "record_type": "verified", "reference_side": 4.75774, "setup": "squinpen", "side": 4.763137477023549, "solution_path": "data/solutions/generated/squinpen_033_a9622b0aeea26f74.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T03:19:00+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/a9622b0aeea26f74.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@33", "density": 0.8460150186653703, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.75774, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/33.gif", "friedman_metric_expression": "4.75774+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.75774, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.75774+", "metric_symbol": "s", "metric_value": 4.75774, "reference_text": "s = 4.75774+ | Found by Emerson Connelly | in April 2026.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/33.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.75774+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "d93824a50e5c0a99", "improvement": -0.00375625827528836, "max_boundary_excess": -9.018172200219921e-07, "max_pair_overlap_depth": -7.073955850867009e-06, "metric_expression": "4.76150", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.761496258275288, "n": 33, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 4.75774, "setup": "squinpen", "side": 4.761496258275288, "solution_path": "data/solutions/generated/squinpen_33_d93824a50e5c0a99.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T17:13:54+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/d93824a50e5c0a99.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@34", "density": 0.8474289841167177, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.81817, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif", "friedman_metric_expression": "4.81817+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.81817, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.81817+", "metric_symbol": "s", "metric_value": 4.81817, "reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "7dafd61dbd636b00", "improvement": -0.010897939266756751, "max_boundary_excess": -3.4941000501213588e-06, "max_pair_overlap_depth": -2.3754649831841945e-05, "metric_expression": "4.82907", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.829067939266757, "n": 34, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 4.81817, "setup": "squinpen", "side": 4.829067939266757, "solution_path": "data/solutions/generated/squinpen_34_7dafd61dbd636b00.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T17:13:54+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/7dafd61dbd636b00.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@34", "density": 0.8513759101343428, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.81817, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif", "friedman_metric_expression": "4.81817+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.81817, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.81817+", "metric_symbol": "s", "metric_value": 4.81817, "reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "a3f4dd7d0b94e803", "improvement": 0.0003086941552625788, "max_boundary_excess": -3.6641444865908995e-06, "max_pair_overlap_depth": -7.393521151310978e-06, "metric_expression": "4.81786", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.817861305844738, "n": 34, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "recovery_tag": "20260501_squinpen34_fresh_cg", "reference_side": 4.81817, "setup": "squinpen", "side": 4.817861305844738, "solution_path": "data/solutions/generated/squinpen_34_a3f4dd7d0b94e803.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T17:42:33+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/a3f4dd7d0b94e803.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@34", "density": 0.8467800838831615, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.81817, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.81817+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.81817, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.81817+", "metric_symbol": "s", "metric_value": 4.81817, "reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "d7af1c3ed90603fd", "improvement": -0.012747878392191048, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.414710391441419e-07, "max_pair_overlap_depth": -6.11976491438071e-06, "metric_expression": "4.83092", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.830917878392191, "n": 34, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "record_type": "verified", "reference_side": 4.81817, "setup": "squinpen", "side": 4.830917878392191, "solution_path": "data/solutions/generated/squinpen_034_d7af1c3ed90603fd.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/d7af1c3ed90603fd.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@35", "density": 0.8578692979479161, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.86994, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/35.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.86994+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.86994, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@35", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.86994+", "metric_symbol": "s", "metric_value": 4.86994, "reference_text": "s = 4.86994+ | Found by Emerson Connelly | in April 2026.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/35.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.86994+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "d0212c88c498f951", "improvement": 0.0002762594618035408, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.74898699366526e-06, "max_pair_overlap_depth": -8.959642868955342e-06, "metric_expression": "4.86966", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.869663740538196, "n": 35, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.86994, "setup": "squinpen", "side": 4.869663740538196, "solution_path": "data/solutions/generated/squinpen_035_d0212c88c498f951.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/d0212c88c498f951.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@36", "density": 0.8582852742974874, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.93902, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/36.gif", "friedman_metric_expression": "4.93902+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.93902, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@36", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.93902+", "metric_symbol": "s", "metric_value": 4.93902, "reference_text": "s = 4.93902+ | Found by Emerson Connelly | in April 2026.", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/36.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.93902+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "e43d96c031faf38c", "improvement": 0.0014765141690524786, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.258589189166597e-07, "max_pair_overlap_depth": -1.4614402910062552e-07, "metric_expression": "4.93754", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.937543485830948, "n": 36, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.93902, "setup": "squinpen", "side": 4.937543485830948, "solution_path": "data/solutions/record_hunt/squinpen_36_e43d96c031faf38c.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/e43d96c031faf38c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@37", "density": 0.8661967376016183, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.98234, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/37.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "4.98234+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.98234, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@37", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.98234+", "metric_symbol": "s", "metric_value": 4.98234, "reference_text": "s = 4.98234+ | Found by Emerson Connelly | in April 2026.", "source_image": "37.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/37.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.98234+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "dba281681536eecb", "improvement": -0.00039859816128817727, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.161377353190805e-07, "max_pair_overlap_depth": -4.181534561720213e-06, "metric_expression": "4.98274", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.982738598161288, "n": 37, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.98234, "setup": "squinpen", "side": 4.982738598161288, "solution_path": "data/solutions/generated/squinpen_037_dba281681536eecb.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/dba281681536eecb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@38", "density": 0.8656682257376033, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 5.05233, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/38.gif", "friedman_metric_expression": "5.05233+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.05233, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "5.05233+", "metric_symbol": "s", "metric_value": 5.05233, "reference_text": "s = 5.05233+ | Found by Emerson Connelly | in April 2026.", "source_image": "38.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/38.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 5.05233+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "00496638a2011285", "improvement": 0.001164786809802365, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.776103493630765e-07, "max_pair_overlap_depth": -5.692587072836375e-07, "metric_expression": "5.05117", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.051165213190198, "n": 38, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.05233, "setup": "squinpen", "side": 5.051165213190198, "solution_path": "data/solutions/record_hunt/squinpen_38_00496638a2011285.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/00496638a2011285.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@39", "density": 0.8585952949364365, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_display_metric_value": 5.13846, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/39.gif", "friedman_metric_expression": "5.13846+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.13846, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@39", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "5.13846+", "metric_symbol": "s", "metric_value": 5.13846, "reference_text": "s = 5.13846+ | Found by Nathan Roll | in April 2026.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/39.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 5.13846+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "b01313a4744f0eda", "improvement": 0.00022970687679979562, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2716746597467209e-07, "max_pair_overlap_depth": -7.26967224418118e-07, "metric_expression": "5.13823", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.1382302931232005, "n": 39, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.13846, "setup": "squinpen", "side": 5.1382302931232005, "solution_path": "data/solutions/record_hunt/squinpen_39_b01313a4744f0eda.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/b01313a4744f0eda.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@40", "density": 0.8691683896670805, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 5.1725, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/40.gif", "friedman_metric_expression": "5.17250+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.1725, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "5.17250+", "metric_symbol": "s", "metric_value": 5.1725, "reference_text": "s = 5.17250+ | Found by Emerson Connelly | in April 2026.", "source_image": "40.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/40.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 5.17250+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "153dbd88227e7083", "improvement": 0.0005591675539955432, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.137577186347585e-07, "max_pair_overlap_depth": -4.818340240131391e-07, "metric_expression": "5.17194", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.171940832446005, "n": 40, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.1725, "setup": "squinpen", "side": 5.171940832446005, "solution_path": "data/solutions/record_hunt/squinpen_40_153dbd88227e7083.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/153dbd88227e7083.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@1", "density": 0.49741240626661626, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts1.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "1 + 2 / \u221a3 = 2.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.1547005383792515, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1 + 2 / \u221a3 = 2.154+", "metric_symbol": "s", "metric_value": 2.154, "reference_text": "s = 1 + 2 / \u221a3 = 2.154+ | Trivial.", "source_image": "ts1.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts1.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 1 + 2 / \u221a3 = 2.154+ | Trivial.", "friedman_source_image": "ts1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "bc8215883b0d29fa", "improvement": -2.2104427053193376e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.189638991319711e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "2.15472", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.1547226428063047, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.1547005383792515, "setup": "squintri", "side": 2.1547226428063047, "solution_path": "data/solutions/generated/squintri_001_bc8215883b0d29fa.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/bc8215883b0d29fa.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@2", "density": 0.4640775964340414, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts2.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2 + 2 / \u221a3 = 3.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.1547005383792515, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2 + 2 / \u221a3 = 3.154+", "metric_symbol": "s", "metric_value": 3.154, "reference_text": "s = 2 + 2 / \u221a3 = 3.154+ | Trivial.", "source_image": "ts2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts2.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 2 + 2 / \u221a3 = 3.154+ | Trivial.", "friedman_source_image": "ts2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "9fcb7fc91bdb6f8d", "improvement": -8.163595671861756e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.2952441585539525e-06, "max_pair_overlap_depth": -3.4919698730116744e-05, "metric_expression": "3.15478", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.15478217433597, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.1547005383792515, "setup": "squintri", "side": 3.15478217433597, "solution_path": "data/solutions/generated/squintri_002_9fcb7fc91bdb6f8d.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/9fcb7fc91bdb6f8d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@3", "density": 0.6632023535454387, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 3.232, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts3.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3 / 2 + \u221a3 = 3.232+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.232050807568877, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@3", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 / 2 + \u221a3 = 3.232+", "metric_symbol": "s", "metric_value": 3.232, "reference_text": "s = 3 / 2 + \u221a3 = 3.232+ | Found by Erich Friedman | in 1997.", "source_image": "ts3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts3.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 / 2 + \u221a3 = 3.232+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "6a0fd09e2fb037d5", "improvement": -6.772906422058966e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.0862631378148764e-06, "max_pair_overlap_depth": -4.0896047962125925e-05, "metric_expression": "3.23212", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.232118536633098, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.232050807568877, "setup": "squintri", "side": 3.232118536633098, "solution_path": "data/solutions/generated/squintri_003_6a0fd09e2fb037d5.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/6a0fd09e2fb037d5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@4", "density": 0.5351297741951115, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 4.154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts4.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3 + 2 / \u221a3 = 4.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.1547005383792515, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@4", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 + 2 / \u221a3 = 4.154+", "metric_symbol": "s", "metric_value": 4.154, "reference_text": "s = 3 + 2 / \u221a3 = 4.154+ | Found by Erich Friedman | in 1997.", "source_image": "ts4.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts4.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 2 / \u221a3 = 4.154+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "a14dd3a45e182f53", "improvement": -9.943269259693466e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3541096500101422e-06, "max_pair_overlap_depth": -2.3979848717270436e-05, "metric_expression": "4.15480", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.154799971071848, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.1547005383792515, "setup": "squintri", "side": 4.154799971071848, "solution_path": "data/solutions/generated/squintri_004_a14dd3a45e182f53.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/a14dd3a45e182f53.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@5", "density": 0.6217402820027407, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 4.309, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts6.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2 + 4 / \u221a3 = 4.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@5", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "2 + 4 / \u221a3 = 4.309+", "metric_symbol": "s", "metric_value": 4.309, "reference_text": "s = 2 + 4 / \u221a3 = 4.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts6.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts6.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 2 + 4 / \u221a3 = 4.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "b7ec125fb5317da3", "improvement": -0.0001316313976955641, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.818148398440643e-06, "max_pair_overlap_depth": -2.4242157156018074e-05, "metric_expression": "4.30953", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.3095327081561985, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.309401076758503, "setup": "squintri", "side": 4.3095327081561985, "solution_path": "data/solutions/generated/squintri_005_b7ec125fb5317da3.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/b7ec125fb5317da3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@6", "density": 0.7460914321932061, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 4.309, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts6.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2 + 4 / \u221a3 = 4.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@6", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "2 + 4 / \u221a3 = 4.309+", "metric_symbol": "s", "metric_value": 4.309, "reference_text": "s = 2 + 4 / \u221a3 = 4.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts6.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts6.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 2 + 4 / \u221a3 = 4.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "cafd65072dcc4c6f", "improvement": -0.0001226962979972157, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6885485560193324e-06, "max_pair_overlap_depth": -3.2625800104213454e-05, "metric_expression": "4.30952", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.3095237730565, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.309401076758503, "setup": "squintri", "side": 4.3095237730565, "solution_path": "data/solutions/generated/squintri_006_cafd65072dcc4c6f.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/cafd65072dcc4c6f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@7", "density": 0.6083690864087284, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 5.154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts7.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4 + 2 / \u221a3 = 5.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.1547005383792515, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@7", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "4 + 2 / \u221a3 = 5.154+", "metric_symbol": "s", "metric_value": 5.154, "reference_text": "s = 4 + 2 / \u221a3 = 5.154+ | Found by Erich Friedman | in 1997.", "source_image": "ts7.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts7.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 2 / \u221a3 = 5.154+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "b90420d34e1bd6e3", "improvement": -0.0001387881494867571, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.7967605582714725e-06, "max_pair_overlap_depth": -3.132565940933141e-05, "metric_expression": "5.15484", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.154839326528738, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.1547005383792515, "setup": "squintri", "side": 5.154839326528738, "solution_path": "data/solutions/generated/squintri_007_b90420d34e1bd6e3.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/b90420d34e1bd6e3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@8", "density": 0.6568042680930309, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_display_metric_value": 5.301, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts8.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5.301+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.301, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squintri@8", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "5.301+", "metric_symbol": "s", "metric_value": 5.301, "reference_text": "s = 5.301+ | Found by David W. Cantrell | in July 2002.", "source_image": "ts8.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts8.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5.301+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "ts8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "9523798d0eb30de3", "improvement": -0.0026724224763796656, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4466353188141736e-06, "max_pair_overlap_depth": -2.591508822799571e-05, "metric_expression": "5.30367", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.30367242247638, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.301, "setup": "squintri", "side": 5.30367242247638, "solution_path": "data/solutions/generated/squintri_008_9523798d0eb30de3.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/9523798d0eb30de3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@9", "density": 0.7370953908179042, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 5.309, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts9.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3 + 4 / \u221a3 = 5.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@9", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 + 4 / \u221a3 = 5.309+", "metric_symbol": "s", "metric_value": 5.309, "reference_text": "s = 3 + 4 / \u221a3 = 5.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts9.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts9.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 4 / \u221a3 = 5.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "221ec438e9e78bec", "improvement": -0.0007770436761855848, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.476651564783165e-07, "max_pair_overlap_depth": -2.048243915964143e-05, "metric_expression": "5.31018", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.3101781204346885, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.309401076758503, "setup": "squintri", "side": 5.3101781204346885, "solution_path": "data/solutions/generated/squintri_009_221ec438e9e78bec.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/221ec438e9e78bec.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@10", "density": 0.773471405329893, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 5.464, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts10.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2 + 2 \u221a3 = 5.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.464101615137754, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@10", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "2 + 2 \u221a3 = 5.464+", "metric_symbol": "s", "metric_value": 5.464, "reference_text": "s = 2 + 2 \u221a3 = 5.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts10.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts10.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 2 + 2 \u221a3 = 5.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "4b92d4f5e6704540", "improvement": -0.0001105090944024667, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1415169103720102e-06, "max_pair_overlap_depth": -1.0706995126841257e-05, "metric_expression": "5.46421", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.464212124232157, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.464101615137754, "setup": "squintri", "side": 5.464212124232157, "solution_path": "data/solutions/generated/squintri_010_4b92d4f5e6704540.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/4b92d4f5e6704540.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@11", "density": 0.6705894339586221, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 6.154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts11.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5 + 2 / \u221a3 = 6.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.1547005383792515, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@11", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "5 + 2 / \u221a3 = 6.154+", "metric_symbol": "s", "metric_value": 6.154, "reference_text": "s = 5 + 2 / \u221a3 = 6.154+ | Found by Erich Friedman | in 1997.", "source_image": "ts11.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts11.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 2 / \u221a3 = 6.154+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "c18f0f7b3b1e0227", "improvement": -0.0001522711306831681, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.062945956811758e-06, "max_pair_overlap_depth": -2.0039414804218225e-05, "metric_expression": "6.15485", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.154852809509935, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.1547005383792515, "setup": "squintri", "side": 6.154852809509935, "solution_path": "data/solutions/generated/squintri_011_c18f0f7b3b1e0227.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/c18f0f7b3b1e0227.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@12", "density": 0.6970880090801083, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_display_metric_value": 6.301, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts12.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6.301+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.301, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squintri@12", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "6.301+", "metric_symbol": "s", "metric_value": 6.301, "reference_text": "s = 6.301+ | Found by David W. Cantrell | in July 2002.", "source_image": "ts12.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts12.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 6.301+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "ts12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "d248ead86c97d2e6", "improvement": -0.004165620418586258, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6132876791233732e-06, "max_pair_overlap_depth": -5.9825433180948906e-05, "metric_expression": "6.30517", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.305165620418586, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.301, "setup": "squintri", "side": 6.305165620418586, "solution_path": "data/solutions/generated/squintri_012_d248ead86c97d2e6.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d248ead86c97d2e6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@13", "density": 0.7541442288903037, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 6.309, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts13.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4 + 4 / \u221a3 = 6.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@13", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "4 + 4 / \u221a3 = 6.309+", "metric_symbol": "s", "metric_value": 6.309, "reference_text": "s = 4 + 4 / \u221a3 = 6.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts13.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts13.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 4 / \u221a3 = 6.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "3b7ab78f832490ed", "improvement": -8.740933612205737e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1403459653225352e-06, "max_pair_overlap_depth": -1.2003638542146255e-05, "metric_expression": "6.30949", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.309488486094625, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.309401076758503, "setup": "squintri", "side": 6.309488486094625, "solution_path": "data/solutions/generated/squintri_013_3b7ab78f832490ed.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/3b7ab78f832490ed.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@14", "density": 0.7737221641470288, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 6.464, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts15.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3 + 2 \u221a3 = 6.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.464101615137754, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@14", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 + 2 \u221a3 = 6.464+", "metric_symbol": "s", "metric_value": 6.464, "reference_text": "s = 3 + 2 \u221a3 = 6.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts15.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts15.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 2 \u221a3 = 6.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "ffc152ae79167d33", "improvement": -0.00019358583212980562, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.958378324017974e-07, "max_pair_overlap_depth": -1.6732970481436737e-05, "metric_expression": "6.46430", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.464295200969884, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.464101615137754, "setup": "squintri", "side": 6.464295200969884, "solution_path": "data/solutions/generated/squintri_014_ffc152ae79167d33.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/ffc152ae79167d33.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@15", "density": 0.8289675963035161, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 6.464, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts15.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3 + 2 \u221a3 = 6.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.464101615137754, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@15", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 + 2 \u221a3 = 6.464+", "metric_symbol": "s", "metric_value": 6.464, "reference_text": "s = 3 + 2 \u221a3 = 6.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts15.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts15.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 2 \u221a3 = 6.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "37ace9570dd5c15b", "improvement": -0.00027326815037209684, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.039916977622108e-06, "max_pair_overlap_depth": -1.0702944550522453e-05, "metric_expression": "6.46437", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.4643748832881265, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.464101615137754, "setup": "squintri", "side": 6.4643748832881265, "solution_path": "data/solutions/generated/squintri_015_37ace9570dd5c15b.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/37ace9570dd5c15b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@16", "density": 0.7217958800018128, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 7.154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts16.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6 + 2 / \u221a3 = 7.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.1547005383792515, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@16", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "6 + 2 / \u221a3 = 7.154+", "metric_symbol": "s", "metric_value": 7.154, "reference_text": "s = 6 + 2 / \u221a3 = 7.154+ | Found by Erich Friedman | in 1997.", "source_image": "ts16.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts16.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 6 + 2 / \u221a3 = 7.154+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "36afe756f11f62d6", "improvement": -0.00018143281400995193, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.5571215058068575e-06, "max_pair_overlap_depth": -2.4408532427300234e-05, "metric_expression": "7.15488", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.154881971193261, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.1547005383792515, "setup": "squintri", "side": 7.154881971193261, "solution_path": "data/solutions/generated/squintri_016_36afe756f11f62d6.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/36afe756f11f62d6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@17", "density": 0.7357616143895036, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_display_metric_value": 7.301, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts17.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "7.301+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.301, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squintri@17", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "7.301+", "metric_symbol": "s", "metric_value": 7.301, "reference_text": "s = 7.301+ | Found by David W. Cantrell | in July 2002.", "source_image": "ts17.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts17.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 7.301+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "ts17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "3a2c987432da5f1d", "improvement": -0.0037537403553287163, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 2.4850519352755694e-10, "max_pair_overlap_depth": -2.8059876787889237e-05, "metric_expression": "7.30475", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.304753740355329, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.301, "setup": "squintri", "side": 7.304753740355329, "solution_path": "data/solutions/generated/squintri_017_3a2c987432da5f1d.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/3a2c987432da5f1d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@18", "density": 0.7780278532013658, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 7.309, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts18.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5 + 4 / \u221a3 = 7.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@18", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "5 + 4 / \u221a3 = 7.309+", "metric_symbol": "s", "metric_value": 7.309, "reference_text": "s = 5 + 4 / \u221a3 = 7.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts18.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 4 / \u221a3 = 7.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "e729e13f2fcc5856", "improvement": -0.00011056420509358844, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1021248752761939e-06, "max_pair_overlap_depth": -8.579145527987109e-06, "metric_expression": "7.30951", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.3095116409635965, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.309401076758503, "setup": "squintri", "side": 7.3095116409635965, "solution_path": "data/solutions/generated/squintri_018_e729e13f2fcc5856.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/e729e13f2fcc5856.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@19", "density": 0.787537700321716, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 7.464, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts19.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4 + 2 \u221a3 = 7.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.464101615137754, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@19", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "4 + 2 \u221a3 = 7.464+", "metric_symbol": "s", "metric_value": 7.464, "reference_text": "s = 4 + 2 \u221a3 = 7.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts19.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 2 \u221a3 = 7.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "805d1e50c1db2842", "improvement": -0.00022794589769237206, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0609380559736765e-06, "max_pair_overlap_depth": -1.836020690809681e-05, "metric_expression": "7.46433", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.464329561035447, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.464101615137754, "setup": "squintri", "side": 7.464329561035447, "solution_path": "data/solutions/generated/squintri_019_805d1e50c1db2842.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/805d1e50c1db2842.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@20", "density": 0.795657127614163, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 7.618, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3 + 8 / \u221a3 = 7.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.618802153517006, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@20", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 + 8 / \u221a3 = 7.618+", "metric_symbol": "s", "metric_value": 7.618, "reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "f4d21a73470ce742", "improvement": -0.00026323872093936274, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.382631857088383e-07, "max_pair_overlap_depth": -1.1470843414018717e-05, "metric_expression": "7.61907", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.619065392237945, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.618802153517006, "setup": "squintri", "side": 7.619065392237945, "solution_path": "data/solutions/generated/squintri_020_f4d21a73470ce742.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/f4d21a73470ce742.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@21", "density": 0.8354483980307021, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 7.618, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "friedman_metric_expression": "3 + 8 / \u221a3 = 7.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.618802153517006, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@21", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 + 8 / \u221a3 = 7.618+", "metric_symbol": "s", "metric_value": 7.618, "reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "a2e24601c2557198", "improvement": -0.00022487174892038553, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.8035391721895233e-06, "max_pair_overlap_depth": -9.7266150509423e-06, "metric_expression": "7.61903", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 7.619027025265926, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 7.618802153517006, "setup": "squintri", "side": 7.619027025265926, "solution_path": "data/solutions/generated/squintri_021_a2e24601c2557198.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/a2e24601c2557198.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@22", "density": 0.7639711289147475, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 8.154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts22.gif", "friedman_metric_expression": "7 + 2 / \u221a3 = 8.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.154700538379252, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@22", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "7 + 2 / \u221a3 = 8.154+", "metric_symbol": "s", "metric_value": 8.154, "reference_text": "s = 7 + 2 / \u221a3 = 8.154+ | Found by Erich Friedman | in 1997.", "source_image": "ts22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts22.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 7 + 2 / \u221a3 = 8.154+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "bbb028380d997350", "improvement": -0.0002728678276717744, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4334644744109685e-07, "max_pair_overlap_depth": -2.16343036094635e-05, "metric_expression": "8.15497", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.154973406206924, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.154700538379252, "setup": "squintri", "side": 8.154973406206924, "solution_path": "data/solutions/generated/squintri_022_bbb028380d997350.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/bbb028380d997350.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@23", "density": 0.7697946105392801, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_display_metric_value": 8.301, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts23.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "8.301+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.301, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squintri@23", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "8.301+", "metric_symbol": "s", "metric_value": 8.301, "reference_text": "s = 8.301+ | Found by David W. Cantrell | in July 2002.", "source_image": "ts23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts23.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 8.301+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "ts23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "b1534ea73e00f283", "improvement": -0.005654877387726742, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7355116411507935e-05, "max_pair_overlap_depth": 9.193993899536679e-09, "metric_expression": "8.30665", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.306654877387727, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.301, "setup": "squintri", "side": 8.306654877387727, "solution_path": "data/solutions/generated/squintri_023_b1534ea73e00f283.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/b1534ea73e00f283.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@24", "density": 0.8026821430235043, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 8.309, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts24.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6 + 4 / \u221a3 = 8.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@24", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "6 + 4 / \u221a3 = 8.309+", "metric_symbol": "s", "metric_value": 8.309, "reference_text": "s = 6 + 4 / \u221a3 = 8.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts24.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 6 + 4 / \u221a3 = 8.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "648f7ef8ee4a197f", "improvement": -0.0002636615215294569, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.518509956206752e-06, "max_pair_overlap_depth": -1.764131142900638e-05, "metric_expression": "8.30966", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.309664738280032, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.309401076758503, "setup": "squintri", "side": 8.309664738280032, "solution_path": "data/solutions/generated/squintri_024_648f7ef8ee4a197f.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/648f7ef8ee4a197f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@25", "density": 0.8057999996349686, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 8.464, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts25.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5 + 2 \u221a3 = 8.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.464101615137755, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@25", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "5 + 2 \u221a3 = 8.464+", "metric_symbol": "s", "metric_value": 8.464, "reference_text": "s = 5 + 2 \u221a3 = 8.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts25.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 2 \u221a3 = 8.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "a868d8af97a256ad", "improvement": -0.0004908775583540859, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7884356498379287e-06, "max_pair_overlap_depth": -2.4212693654490636e-06, "metric_expression": "8.46459", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.46459249269611, "n": 25, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.464101615137755, "setup": "squintri", "side": 8.46459249269611, "solution_path": "data/solutions/generated/squintri_025_a868d8af97a256ad.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/a868d8af97a256ad.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@26", "density": 0.8076243715506172, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 8.618, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4 + 8 / \u221a3 = 8.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.618802153517006, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@26", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "4 + 8 / \u221a3 = 8.618+", "metric_symbol": "s", "metric_value": 8.618, "reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "249af47eefa3a74b", "improvement": -0.0036669710848595827, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.4769017068652995e-06, "max_pair_overlap_depth": -2.5879119370686432e-05, "metric_expression": "8.62247", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.622469124601865, "n": 26, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.618802153517006, "setup": "squintri", "side": 8.622469124601865, "solution_path": "data/solutions/generated/squintri_026_249af47eefa3a74b.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/249af47eefa3a74b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@27", "density": 0.8380226358442442, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 8.618, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4 + 8 / \u221a3 = 8.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.618802153517006, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@27", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "4 + 8 / \u221a3 = 8.618+", "metric_symbol": "s", "metric_value": 8.618, "reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "3c62cd2126467cec", "improvement": -0.007083352000387677, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.235025861662866e-06, "max_pair_overlap_depth": -2.0721793894562524e-05, "metric_expression": "8.62589", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.625885505517394, "n": 27, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.618802153517006, "setup": "squintri", "side": 8.625885505517394, "solution_path": "data/solutions/generated/squintri_027_3c62cd2126467cec.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/3c62cd2126467cec.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@28", "density": 0.8400113660191094, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 8.773, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts28.gif", "friedman_metric_expression": "3 + 10 / \u221a3 = 8.773+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.773502691896258, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@28", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3 + 10 / \u221a3 = 8.773+", "metric_symbol": "s", "metric_value": 8.773, "reference_text": "s = 3 + 10 / \u221a3 = 8.773+ | Found by Erich Friedman | in 1997.", "source_image": "ts28.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts28.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 10 / \u221a3 = 8.773+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "0d20b359435ed501", "improvement": -0.0002647025069464348, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0145694937175628e-06, "max_pair_overlap_depth": -1.3941973455278145e-05, "metric_expression": "8.77377", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 8.773767394403205, "n": 28, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 8.773502691896258, "setup": "squintri", "side": 8.773767394403205, "solution_path": "data/solutions/generated/squintri_028_0d20b359435ed501.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/0d20b359435ed501.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@29", "density": 0.7990846545133872, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 9.154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts29.gif", "friedman_metric_expression": "8 + 2 / \u221a3 = 9.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.154700538379252, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@29", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "8 + 2 / \u221a3 = 9.154+", "metric_symbol": "s", "metric_value": 9.154, "reference_text": "s = 8 + 2 / \u221a3 = 9.154+ | Found by Erich Friedman | in 1997.", "source_image": "ts29.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts29.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 8 + 2 / \u221a3 = 9.154+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "3947aab39c0a1a92", "improvement": -0.00017165307172639643, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2628787428294703e-06, "max_pair_overlap_depth": -1.875431036468811e-05, "metric_expression": "9.15487", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.154872191450979, "n": 29, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.154700538379252, "setup": "squintri", "side": 9.154872191450979, "solution_path": "data/solutions/generated/squintri_029_3947aab39c0a1a92.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/3947aab39c0a1a92.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@30", "density": 0.7992784153759376, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_display_metric_value": 9.301, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts30.gif", "friedman_metric_expression": "9.301+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.301, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squintri@30", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "9.301+", "metric_symbol": "s", "metric_value": 9.301, "reference_text": "s = 9.301+ | Found by David W. Cantrell | in July 2002.", "source_image": "ts30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts30.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 9.301+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "ts30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "e0b7505d8b6b1d46", "improvement": -0.009248370808917272, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.5690858985090003e-06, "max_pair_overlap_depth": -2.654303096472077e-05, "metric_expression": "9.31025", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.310248370808917, "n": 30, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.301, "setup": "squintri", "side": 9.310248370808917, "solution_path": "data/solutions/generated/squintri_030_e0b7505d8b6b1d46.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/e0b7505d8b6b1d46.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@31", "density": 0.825993871568094, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 9.309, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts31.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "7 + 4 / \u221a3 = 9.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.309401076758503, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@31", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "7 + 4 / \u221a3 = 9.309+", "metric_symbol": "s", "metric_value": 9.309, "reference_text": "s = 7 + 4 / \u221a3 = 9.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts31.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts31.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 7 + 4 / \u221a3 = 9.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "22b5f5f5707858bb", "improvement": -0.0004367611689630735, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6472234336534766e-06, "max_pair_overlap_depth": -3.090204228461957e-05, "metric_expression": "9.30984", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.309837837927466, "n": 31, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.309401076758503, "setup": "squintri", "side": 9.309837837927466, "solution_path": "data/solutions/generated/squintri_031_22b5f5f5707858bb.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/22b5f5f5707858bb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@32", "density": 0.8249717531277396, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 9.464, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts32.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "6 + 2 \u221a3 = 9.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.464101615137755, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@32", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "6 + 2 \u221a3 = 9.464+", "metric_symbol": "s", "metric_value": 9.464, "reference_text": "s = 6 + 2 \u221a3 = 9.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts32.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 6 + 2 \u221a3 = 9.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "a44fbd99145b1ab3", "improvement": -0.0005608790583710999, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.1832282131171085e-07, "max_pair_overlap_depth": -1.699280632205813e-06, "metric_expression": "9.46466", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.464662494196126, "n": 32, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.464101615137755, "setup": "squintri", "side": 9.464662494196126, "solution_path": "data/solutions/generated/squintri_032_a44fbd99145b1ab3.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/a44fbd99145b1ab3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@33", "density": 0.8228028312642216, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 9.618, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5 + 8 / \u221a3 = 9.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.618802153517006, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@33", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "5 + 8 / \u221a3 = 9.618+", "metric_symbol": "s", "metric_value": 9.618, "reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "67de1e08be2d150c", "improvement": -0.005267626054981989, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.226435414550563e-06, "max_pair_overlap_depth": -3.0944328952564604e-06, "metric_expression": "9.62407", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.624069779571988, "n": 33, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.618802153517006, "setup": "squintri", "side": 9.624069779571988, "solution_path": "data/solutions/generated/squintri_033_67de1e08be2d150c.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/67de1e08be2d150c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@34", "density": 0.8485900582279403, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 9.618, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "friedman_metric_expression": "5 + 8 / \u221a3 = 9.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.618802153517006, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@34", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "5 + 8 / \u221a3 = 9.618+", "metric_symbol": "s", "metric_value": 9.618, "reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "3661302cdd9d0eb0", "improvement": -0.0004247846581613146, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.159334309452278e-06, "max_pair_overlap_depth": -1.741303470170763e-05, "metric_expression": "9.61923", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.619226938175167, "n": 34, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.618802153517006, "setup": "squintri", "side": 9.619226938175167, "solution_path": "data/solutions/generated/squintri_034_3661302cdd9d0eb0.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/3661302cdd9d0eb0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@35", "density": 0.8451911560111607, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 9.773, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4 + 10 / \u221a3 = 9.773+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.773502691896258, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@35", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "4 + 10 / \u221a3 = 9.773+", "metric_symbol": "s", "metric_value": 9.773, "reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "source_image": "ts36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "39d52a823b632afe", "improvement": -0.005762697591846333, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.195518233524095e-06, "max_pair_overlap_depth": -2.612964804571405e-05, "metric_expression": "9.77927", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.779265389488105, "n": 35, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.773502691896258, "setup": "squintri", "side": 9.779265389488105, "solution_path": "data/solutions/generated/squintri_035_39d52a823b632afe.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/39d52a823b632afe.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@36", "density": 0.8698156108347095, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 9.773, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4 + 10 / \u221a3 = 9.773+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.773502691896258, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "squintri@36", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "4 + 10 / \u221a3 = 9.773+", "metric_symbol": "s", "metric_value": 9.773, "reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "source_image": "ts36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "f0473aaa767ebe98", "improvement": -0.0030857518024500763, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9270562690497914e-06, "max_pair_overlap_depth": -7.45737725771356e-06, "metric_expression": "9.77659", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 9.776588443698708, "n": 36, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 9.773502691896258, "setup": "squintri", "side": 9.776588443698708, "solution_path": "data/solutions/generated/squintri_036_f0473aaa767ebe98.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/f0473aaa767ebe98.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@37", "density": 0.8285699034870297, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 10.154, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts37.gif", "friedman_metric_expression": "10.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.154, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squintri@37", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "10.154+", "metric_symbol": "s", "metric_value": 10.154, "reference_text": "s = 10.154+ | Found by Emerson Connelly | in April 2026.", "source_image": "ts37.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts37.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 10.154+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "ts37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "8530be000ac2e9ed", "improvement": -0.0011412138177444575, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3566887422690367e-06, "max_pair_overlap_depth": -1.2239987045248313e-05, "metric_expression": "10.15514", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.155141213817744, "n": 37, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 10.154, "setup": "squintri", "side": 10.155141213817744, "solution_path": "data/solutions/generated/squintri_037_8530be000ac2e9ed.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/8530be000ac2e9ed.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@38", "density": 0.8256293316995508, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 10.309, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts38.gif", "friedman_metric_expression": "10.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.309, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squintri@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "10.309+", "metric_symbol": "s", "metric_value": 10.309, "reference_text": "s = 10.309+ | Found by Emerson Connelly | in April 2026.", "source_image": "ts38.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts38.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 10.309+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "ts38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "896b636f9d899bf5", "improvement": -0.0007687369401132571, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.231911901047403e-06, "max_pair_overlap_depth": -1.6045122417374102e-05, "metric_expression": "10.30977", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.309768736940113, "n": 38, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 10.309, "setup": "squintri", "side": 10.309768736940113, "solution_path": "data/solutions/generated/squintri_038_896b636f9d899bf5.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/896b636f9d899bf5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@39", "density": 0.8473534790778084, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 10.31, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts39.gif", "friedman_metric_expression": "10.310+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.31, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squintri@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "10.310+", "metric_symbol": "s", "metric_value": 10.31, "reference_text": "s = 10.310+ | Found by Emerson Connelly | in April 2026.", "source_image": "ts39.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts39.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 10.310+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "ts39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "c0988e1f3bf189d9", "improvement": 0.00021337573935120702, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.79079015949438e-07, "max_pair_overlap_depth": -3.1188368032619707e-06, "metric_expression": "10.30979", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.30978662426065, "n": 39, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 10.31, "setup": "squintri", "side": 10.30978662426065, "solution_path": "data/solutions/record_hunt/squintri_39_c0988e1f3bf189d9.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/c0988e1f3bf189d9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@40", "density": 0.8436138407048179, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_display_metric_value": 10.46426, "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts40.gif", "friedman_metric_expression": "10.46426+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.46426, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "squintri@40", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "10.46426+", "metric_symbol": "s", "metric_value": 10.46426, "reference_text": "s = 10.46426+ | Found by Nathan Roll | in April 2026.", "source_image": "ts40.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts40.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 10.46426+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "ts40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "13b03f25af76ce87", "improvement": 1.6681613434599285e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.839061064144293e-07, "max_pair_overlap_depth": -1.4626365829606414e-06, "metric_expression": "10.46424", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 10.464243318386565, "n": 40, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 10.46426, "setup": "squintri", "side": 10.464243318386565, "solution_path": "data/solutions/record_hunt/squintri_40_13b03f25af76ce87.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/13b03f25af76ce87.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@1", "density": 0.41349293224745, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 0.577, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc1.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1/\u221a3 = .577+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.5773502691896257, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triincir@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1/\u221a3 = .577+", "metric_symbol": "r", "metric_value": 0.577, "reference_text": "r = 1/\u221a3 = .577+ | Trivial.", "source_image": "tc1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc1.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1/\u221a3 = .577+ | Trivial.", "friedman_source_image": "tc1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "49954bfbb560620d", "improvement": -2.6105547652477412e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.775275519510515e-07, "max_pair_overlap_depth": 0.0, "metric_expression": "0.57735", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 0.577352879744391, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.5773502691896257, "setup": "triincir", "side": 1.154705759488782, "solution_path": "data/solutions/generated/triincir_001_49954bfbb560620d.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/49954bfbb560620d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@2", "density": 0.3675414068402789, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 0.866, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc2.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "\u221a3/2 = .866+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.8660254037844386, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triincir@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a3/2 = .866+", "metric_symbol": "r", "metric_value": 0.866, "reference_text": "r = \u221a3/2 = .866+ | Trivial.", "source_image": "tc2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc2.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = \u221a3/2 = .866+ | Trivial.", "friedman_source_image": "tc2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "92f5511b689fe041", "improvement": -1.3183335940358809e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.072458078845486e-06, "max_pair_overlap_depth": -1.0890566688626091e-05, "metric_expression": "0.86604", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 0.866038587120379, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.8660254037844386, "setup": "triincir", "side": 1.732077174240758, "solution_path": "data/solutions/generated/triincir_002_92f5511b689fe041.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/92f5511b689fe041.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@3", "density": 0.45476420302551357, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 0.953, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc3.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "3\u221a3 - 3\u221a2 = .953+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.9535117355873467, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triincir@3", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "3\u221a3 - 3\u221a2 = .953+", "metric_symbol": "r", "metric_value": 0.953, "reference_text": "r = 3\u221a3 - 3\u221a2 = .953+ | Found by Erich Friedman | in 1997.", "source_image": "tc3.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc3.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 3\u221a3 - 3\u221a2 = .953+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tc3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "6ede8225b5939550", "improvement": -3.6952980157156645e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4231654198736408e-06, "max_pair_overlap_depth": -2.0408752807413166e-05, "metric_expression": "0.95355", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 0.9535486885675039, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.9535117355873467, "setup": "triincir", "side": 1.9070973771350077, "solution_path": "data/solutions/generated/triincir_003_6ede8225b5939550.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/6ede8225b5939550.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@4", "density": 0.5732690550709103, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 0.98, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc4.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": ".980+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.98, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@4", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": ".980+", "metric_symbol": "r", "metric_value": 0.98, "reference_text": "r = .980+ | Found by Erich Friedman | in 1997.", "source_image": "tc4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc4.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = .980+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tc4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "7f9481f33de5ecda", "improvement": -0.0006773112916812485, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.642177417024662e-06, "max_pair_overlap_depth": -2.677155749965807e-05, "metric_expression": "0.98068", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 0.9806773112916812, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.98, "setup": "triincir", "side": 1.9613546225833625, "solution_path": "data/solutions/generated/triincir_004_7f9481f33de5ecda.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/7f9481f33de5ecda.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@5", "density": 0.6891272508887964, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc5.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1", "friedman_metric_symbol": "r", "friedman_metric_value": 1.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triincir@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "r", "metric_value": 1.0, "reference_text": "r = 1 | Trivial.", "source_image": "tc5.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc5.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1 | Trivial.", "friedman_source_image": "tc5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "cf17d061ebfe392b", "improvement": -2.4573090296353683e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.800898255106432e-06, "max_pair_overlap_depth": -9.00554050570603e-06, "metric_expression": "1.00002", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.0000245730902964, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.0, "setup": "triincir", "side": 2.0000491461805927, "solution_path": "data/solutions/generated/triincir_005_cf17d061ebfe392b.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/cf17d061ebfe392b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@6", "density": 0.826963635452614, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc6.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1", "friedman_metric_symbol": "r", "friedman_metric_value": 1.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triincir@6", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "r", "metric_value": 1.0, "reference_text": "r = 1 | Trivial.", "source_image": "tc6.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc6.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1 | Trivial.", "friedman_source_image": "tc6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "fe93ba87f23c6c01", "improvement": -1.7961741001881748e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.861140867618019e-08, "max_pair_overlap_depth": -9.037179045745058e-06, "metric_expression": "1.00002", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.0000179617410019, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.0, "setup": "triincir", "side": 2.0000359234820038, "solution_path": "data/solutions/generated/triincir_006_fe93ba87f23c6c01.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/fe93ba87f23c6c01.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@7", "density": 0.7265087780749782, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 1.152, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc7.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.152+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.152, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@7", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "1.152+", "metric_symbol": "r", "metric_value": 1.152, "reference_text": "r = 1.152+ | Found by Erich Friedman | in 1997.", "source_image": "tc7.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc7.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.152+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tc7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "4d32cb6092e127b9", "improvement": -0.0004019079826915739, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.469968968942808e-06, "max_pair_overlap_depth": -4.662019983989185e-06, "metric_expression": "1.15240", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.1524019079826915, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.152, "setup": "triincir", "side": 2.304803815965383, "solution_path": "data/solutions/generated/triincir_007_4d32cb6092e127b9.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/4d32cb6092e127b9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@8", "density": 0.6908236123299982, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2008", "friedman_display_metric_value": 1.263, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc8.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.263+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.263, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@8", "credit": "Maurizio Morandi", "date": "April 2008", "family_updated": "", "metric_expression": "1.263+", "metric_symbol": "r", "metric_value": 1.263, "reference_text": "r = 1.263+ | Found by Maurizio Morandi | in April 2008.", "source_image": "tc8.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc8.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.263+ | Found by Maurizio Morandi | in April 2008.", "friedman_source_image": "tc8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "33389e3c966a2171", "improvement": -0.0003881191911174753, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.08502399998045e-06, "max_pair_overlap_depth": -2.667573266001977e-06, "metric_expression": "1.26339", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.2633881191911174, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.263, "setup": "triincir", "side": 2.5267762383822348, "solution_path": "data/solutions/generated/triincir_008_33389e3c966a2171.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/33389e3c966a2171.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@9", "density": 0.7175995300521633, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_display_metric_value": 1.314, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc9.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.314+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.314, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@9", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "1.314+", "metric_symbol": "r", "metric_value": 1.314, "reference_text": "r = 1.314+ | Found by David W. Cantrell | in July 2002.", "source_image": "tc9.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc9.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.314+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "tc9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "68692b6dc093b182", "improvement": -0.0007874911911363025, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.28479338054899e-06, "max_pair_overlap_depth": -4.021549232235966e-06, "metric_expression": "1.31479", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.3147874911911364, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.314, "setup": "triincir", "side": 2.6295749823822727, "solution_path": "data/solutions/generated/triincir_009_68692b6dc093b182.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/68692b6dc093b182.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@10", "density": 0.7187883776258066, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_display_metric_value": 1.385, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc10.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.385+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.385, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@10", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "1.385+", "metric_symbol": "r", "metric_value": 1.385, "reference_text": "r = 1.385+ | Found by David W. Cantrell | in July 2002.", "source_image": "tc10.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc10.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.385+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "tc10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "676585e5c31a1d2f", "improvement": 0.0002388888356295027, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.405400112705848e-06, "max_pair_overlap_depth": -1.0902511275390214e-05, "metric_expression": "1.38476", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.3847611111643705, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.385, "setup": "triincir", "side": 2.769522222328741, "solution_path": "data/solutions/generated/triincir_010_676585e5c31a1d2f.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/676585e5c31a1d2f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@11", "density": 0.7044397586610418, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell after Maurizio Morandi", "friedman_date": "August 2012", "friedman_display_metric_value": 1.466, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc11.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.466+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.466, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@11", "credit": "David W. Cantrell after Maurizio Morandi", "date": "August 2012", "family_updated": "", "metric_expression": "1.466+", "metric_symbol": "r", "metric_value": 1.466, "reference_text": "r = 1.466+ | Found by DC after MM | in August 2012.", "source_image": "tc11.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc11.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.466+ | Found by DC after MM | in August 2012.", "friedman_source_image": "tc11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "27341d9b331a210b", "improvement": -0.0010664804404059147, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5710045151440255e-06, "max_pair_overlap_depth": -1.3965597729533735e-05, "metric_expression": "1.46707", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.4670664804404059, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.466, "setup": "triincir", "side": 2.9341329608808118, "solution_path": "data/solutions/generated/triincir_011_27341d9b331a210b.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell after Maurizio Morandi", "svg_path": "data/svg/27341d9b331a210b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@12", "density": 0.7276318026083056, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "October 2005", "friedman_display_metric_value": 1.507, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc12.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.507+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.507, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@12", "credit": "David W. Cantrell", "date": "October 2005", "family_updated": "", "metric_expression": "1.507+", "metric_symbol": "r", "metric_value": 1.507, "reference_text": "r = 1.507+ | Found by David W. Cantrell | in October 2005.", "source_image": "tc12.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc12.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.507+ | Found by David W. Cantrell | in October 2005.", "friedman_source_image": "tc12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "0430950ce5a6ad65", "improvement": -0.0006834530254535842, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.988712507651542e-07, "max_pair_overlap_depth": -1.4096456774082e-06, "metric_expression": "1.50768", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.5076834530254535, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.507, "setup": "triincir", "side": 3.015366906050907, "solution_path": "data/solutions/generated/triincir_012_0430950ce5a6ad65.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/0430950ce5a6ad65.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@13", "density": 0.7678670311765523, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 1.527, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc13.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "\u221a(7/3) = 1.527+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.5275252316519468, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triincir@13", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a(7/3) = 1.527+", "metric_symbol": "r", "metric_value": 1.527, "reference_text": "r = \u221a(7/3) = 1.527+ | Found by Erich Friedman | in 1997.", "source_image": "tc13.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc13.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = \u221a(7/3) = 1.527+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tc13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "2b014eeead965100", "improvement": -5.50619776724659e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.995535488687807e-06, "max_pair_overlap_depth": -6.278738689302621e-06, "metric_expression": "1.52758", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.5275802936296192, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.5275252316519468, "setup": "triincir", "side": 3.0551605872592384, "solution_path": "data/solutions/generated/triincir_013_2b014eeead965100.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/2b014eeead965100.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@14", "density": 0.7492543391037492, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell after Maurizio Morandi", "friedman_date": "August 2012", "friedman_display_metric_value": 1.609, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc14.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.609+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.609, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@14", "credit": "David W. Cantrell after Maurizio Morandi", "date": "August 2012", "family_updated": "", "metric_expression": "1.609+", "metric_symbol": "r", "metric_value": 1.609, "reference_text": "r = 1.609+ | Found by DC after MM | in August 2012.", "source_image": "tc14.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc14.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.609+ | Found by DC after MM | in August 2012.", "friedman_source_image": "tc14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": false, "id": "da4114b8f6b7e383", "improvement": 0.0041857717254343285, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4204418656849072e-06, "max_pair_overlap_depth": -6.9567849071972e-06, "metric_expression": "1.60481", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.6048142282745657, "n": 14, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.", "record_type": "verified", "reference_side": 1.609, "setup": "triincir", "side": 3.2096284565491313, "solution_path": "data/solutions/generated/triincir_014_da4114b8f6b7e383.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/da4114b8f6b7e383.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@15", "density": 0.7710002838935242, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_display_metric_value": 1.636, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc15.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.636+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.636, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@15", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "1.636+", "metric_symbol": "r", "metric_value": 1.636, "reference_text": "r = 1.636+ | Found by David W. Cantrell | in July 2002.", "source_image": "tc15.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc15.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.636+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "tc15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "e8f573cc9f431ed8", "improvement": -0.001546881163444036, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.392157777674768e-06, "max_pair_overlap_depth": -3.2056821285264547e-06, "metric_expression": "1.63755", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.637546881163444, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.636, "setup": "triincir", "side": 3.275093762326888, "solution_path": "data/solutions/generated/triincir_015_e8f573cc9f431ed8.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/e8f573cc9f431ed8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@16", "density": 0.7739404139048575, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2008", "friedman_display_metric_value": 1.687, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc16.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.687+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.687, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@16", "credit": "Maurizio Morandi", "date": "April 2008", "family_updated": "", "metric_expression": "1.687+", "metric_symbol": "r", "metric_value": 1.687, "reference_text": "r = 1.687+ | Found by Maurizio Morandi | in April 2008.", "source_image": "tc16.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc16.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.687+ | Found by Maurizio Morandi | in April 2008.", "friedman_source_image": "tc16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "8bb5531a7df45934", "improvement": -0.0010356342518775818, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.068784430077415e-07, "max_pair_overlap_depth": -9.622687440202782e-07, "metric_expression": "1.68804", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.6880356342518776, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.687, "setup": "triincir", "side": 3.3760712685037553, "solution_path": "data/solutions/generated/triincir_16_8bb5531a7df45934.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/8bb5531a7df45934.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@17", "density": 0.7824875965148136, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2005", "friedman_display_metric_value": 1.73, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc17.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.730+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.73, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@17", "credit": "David W. Cantrell", "date": "July 2005", "family_updated": "", "metric_expression": "1.730+", "metric_symbol": "r", "metric_value": 1.73, "reference_text": "r = 1.730+ | Found by David W. Cantrell | in July 2005.", "source_image": "tc17.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc17.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.730+ | Found by David W. Cantrell | in July 2005.", "friedman_source_image": "tc17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "47c836632f7377eb", "improvement": -0.00045819251380652126, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3405989713065622e-06, "max_pair_overlap_depth": -3.2207400054717894e-06, "metric_expression": "1.73046", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.7304581925138065, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.73, "setup": "triincir", "side": 3.460916385027613, "solution_path": "data/solutions/generated/triincir_017_47c836632f7377eb.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/47c836632f7377eb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@18", "density": 0.763334042584198, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 1.802, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc18.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "\u221a13/2 = 1.802+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.8027756377319946, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triincir@18", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "\u221a13/2 = 1.802+", "metric_symbol": "r", "metric_value": 1.802, "reference_text": "r = \u221a13/2 = 1.802+ | Found by Erich Friedman | in 1997.", "source_image": "tc18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc18.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = \u221a13/2 = 1.802+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tc18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "8d495d33c78cce38", "improvement": -5.246232046740573e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0688499290090192e-06, "max_pair_overlap_depth": -2.7547144944017887e-06, "metric_expression": "1.80283", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.802828100052462, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.8027756377319946, "setup": "triincir", "side": 3.605656200104924, "solution_path": "data/solutions/generated/triincir_018_8d495d33c78cce38.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/8d495d33c78cce38.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@19", "density": 0.7847061820967525, "friedman_analytical_or_proved": true, "friedman_credit": "Haym Hirsh", "friedman_date": "August 2019", "friedman_display_metric_value": 1.825, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc19.gif", "friedman_metric_expression": "\u221a(10/3) = 1.825+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.8257418583505538, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triincir@19", "credit": "Haym Hirsh", "date": "August 2019", "family_updated": "", "metric_expression": "\u221a(10/3) = 1.825+", "metric_symbol": "r", "metric_value": 1.825, "reference_text": "r = \u221a(10/3) = 1.825+ | Found by Haym Hirsh | in August 2019.", "source_image": "tc19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc19.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = \u221a(10/3) = 1.825+ | Found by Haym Hirsh | in August 2019.", "friedman_source_image": "tc19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "975121af758119a3", "improvement": -0.0010902876388556582, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1422789436554837e-06, "max_pair_overlap_depth": -1.3515939734642934e-06, "metric_expression": "1.82683", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.8268321459894095, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.8257418583505538, "setup": "triincir", "side": 3.653664291978819, "solution_path": "data/solutions/generated/triincir_19_975121af758119a3.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T14:34:18+00:00", "submitted_by": "Haym Hirsh", "svg_path": "data/svg/975121af758119a3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@20", "density": 0.7838286390350678, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 1.874, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc20.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.874+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.874, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@20", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "1.874+", "metric_symbol": "r", "metric_value": 1.874, "reference_text": "r = 1.874+ | Found by Erich Friedman | in 1997.", "source_image": "tc20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc20.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.874+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tc20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "1217493f9010e655", "improvement": -0.0013391312177313264, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.256942872007727e-07, "max_pair_overlap_depth": -1.3401476308239069e-05, "metric_expression": "1.87534", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.8753391312177314, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.874, "setup": "triincir", "side": 3.750678262435463, "solution_path": "data/solutions/generated/triincir_020_1217493f9010e655.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/1217493f9010e655.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@21", "density": 0.7923995336773865, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_display_metric_value": 1.91, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc21.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.910+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.91, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@21", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "", "metric_expression": "1.910+", "metric_symbol": "r", "metric_value": 1.91, "reference_text": "r = 1.910+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tc21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc21.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.910+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tc21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "46b1371ff82573dd", "improvement": -0.001229866251050593, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3922552147160872e-05, "max_pair_overlap_depth": -4.454706840822942e-06, "metric_expression": "1.91123", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.9112298662510505, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.91, "setup": "triincir", "side": 3.822459732502101, "solution_path": "data/solutions/generated/triincir_021_46b1371ff82573dd.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/46b1371ff82573dd.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@22", "density": 0.8017796736685735, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2008", "friedman_display_metric_value": 1.943, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc22.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.943+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.943, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@22", "credit": "Maurizio Morandi", "date": "June 2008", "family_updated": "", "metric_expression": "1.943+", "metric_symbol": "r", "metric_value": 1.943, "reference_text": "r = 1.943+ | Found by Maurizio Morandi | in June 2008.", "source_image": "tc22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc22.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.943+ | Found by Maurizio Morandi | in June 2008.", "friedman_source_image": "tc22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "69faaab68dcae114", "improvement": -0.0017294951342150533, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.28347034731047e-06, "max_pair_overlap_depth": -4.770520652064292e-06, "metric_expression": "1.94473", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.9447294951342151, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.943, "setup": "triincir", "side": 3.8894589902684302, "solution_path": "data/solutions/generated/triincir_022_69faaab68dcae114.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/69faaab68dcae114.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@23", "density": 0.8020036651008373, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2008", "friedman_display_metric_value": 1.988, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc23.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.988+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.988, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@23", "credit": "Maurizio Morandi", "date": "June 2008", "family_updated": "", "metric_expression": "1.988+", "metric_symbol": "r", "metric_value": 1.988, "reference_text": "r = 1.988+ | Found by Maurizio Morandi | in June 2008.", "source_image": "tc23.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc23.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.988+ | Found by Maurizio Morandi | in June 2008.", "friedman_source_image": "tc23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "bc03a535bc1be813", "improvement": -0.0001590443736558811, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0403434641002036e-06, "max_pair_overlap_depth": -2.2042403398092603e-06, "metric_expression": "1.98816", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 1.9881590443736559, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.988, "setup": "triincir", "side": 3.9763180887473117, "solution_path": "data/solutions/generated/triincir_023_bc03a535bc1be813.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/bc03a535bc1be813.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@24", "density": 0.82672890671807, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc24.gif", "friedman_metric_expression": "2", "friedman_metric_symbol": "r", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triincir@24", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "r", "metric_value": 2.0, "reference_text": "r = 2 | Trivial.", "source_image": "tc24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc24.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2 | Trivial.", "friedman_source_image": "tc24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "e1de703df3a339d6", "improvement": -0.00031983310403260745, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.886123831735148e-06, "max_pair_overlap_depth": -6.330279525013083e-07, "metric_expression": "2.00032", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.0003198331040326, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "triincir", "side": 4.000639666208065, "solution_path": "data/solutions/generated/triincir_24_e1de703df3a339d6.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/e1de703df3a339d6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@25", "density": 0.814798554480224, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2005", "friedman_display_metric_value": 2.055, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc25.gif", "friedman_metric_expression": "2.055+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.055, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@25", "credit": "David W. Cantrell", "date": "July 2005", "family_updated": "", "metric_expression": "2.055+", "metric_symbol": "r", "metric_value": 2.055, "reference_text": "r = 2.055+ | Found by David W. Cantrell | in July 2005.", "source_image": "tc25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc25.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.055+ | Found by David W. Cantrell | in July 2005.", "friedman_source_image": "tc25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "460bfc63493e0a99", "improvement": -0.0014599742843675045, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.499842621325968e-07, "max_pair_overlap_depth": -5.533591762807433e-06, "metric_expression": "2.05646", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.0564599742843677, "n": 25, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.055, "setup": "triincir", "side": 4.112919948568735, "solution_path": "data/solutions/generated/triincir_025_460bfc63493e0a99.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/460bfc63493e0a99.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@26", "density": 0.8055666262709128, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2008", "friedman_display_metric_value": 2.109, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc26.gif", "friedman_metric_expression": "2.109+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.109, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@26", "credit": "Maurizio Morandi", "date": "April 2008", "family_updated": "", "metric_expression": "2.109+", "metric_symbol": "r", "metric_value": 2.109, "reference_text": "r = 2.109+ | Found by Maurizio Morandi | in April 2008.", "source_image": "tc26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc26.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.109+ | Found by Maurizio Morandi | in April 2008.", "friedman_source_image": "tc26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "8245fa6b2a472124", "improvement": -0.00016872463985961872, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.221408735321063e-06, "max_pair_overlap_depth": -3.3631357487795555e-07, "metric_expression": "2.10917", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.1091687246398596, "n": 26, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.109, "setup": "triincir", "side": 4.218337449279719, "solution_path": "data/solutions/generated/triincir_26_8245fa6b2a472124.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/8245fa6b2a472124.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@27", "density": 0.8132267625810148, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2005", "friedman_display_metric_value": 2.138, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc27.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "2.138+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.138, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@27", "credit": "David W. Cantrell", "date": "July 2005", "family_updated": "", "metric_expression": "2.138+", "metric_symbol": "r", "metric_value": 2.138, "reference_text": "r = 2.138+ | Found by David W. Cantrell | in July 2005.", "source_image": "tc27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc27.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.138+ | Found by David W. Cantrell | in July 2005.", "friedman_source_image": "tc27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "6af16151fd4089a6", "improvement": -0.0012002098551513463, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.142316272914286e-07, "max_pair_overlap_depth": -2.7141719629586447e-06, "metric_expression": "2.13920", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.1392002098551512, "n": 27, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.138, "setup": "triincir", "side": 4.2784004197103025, "solution_path": "data/solutions/generated/triincir_027_6af16151fd4089a6.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/6af16151fd4089a6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@28", "density": 0.8029867070046219, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2005", "friedman_display_metric_value": 2.191, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc28.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "2.191+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.191, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@28", "credit": "David W. Cantrell", "date": "July 2005", "family_updated": "", "metric_expression": "2.191+", "metric_symbol": "r", "metric_value": 2.191, "reference_text": "r = 2.191+ | Found by David W. Cantrell | in July 2005.", "source_image": "tc28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc28.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.191+ | Found by David W. Cantrell | in July 2005.", "friedman_source_image": "tc28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "b8a030f48c690095", "improvement": -0.0013011891131600173, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3556564240069235e-06, "max_pair_overlap_depth": -5.7499508869796045e-06, "metric_expression": "2.19230", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.19230118911316, "n": 28, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.191, "setup": "triincir", "side": 4.38460237822632, "solution_path": "data/solutions/generated/triincir_028_b8a030f48c690095.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/b8a030f48c690095.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@29", "density": 0.8182348688742829, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2008", "friedman_display_metric_value": 2.215, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc29.gif", "friedman_metric_expression": "2.215+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.215, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@29", "credit": "Maurizio Morandi", "date": "June 2008", "family_updated": "", "metric_expression": "2.215+", "metric_symbol": "r", "metric_value": 2.215, "reference_text": "r = 2.215+ | Found by Maurizio Morandi | in June 2008.", "source_image": "tc29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc29.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.215+ | Found by Maurizio Morandi | in June 2008.", "friedman_source_image": "tc29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": false, "id": "73bcaf90b9fd2226", "improvement": 0.004780586805306797, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.1271053040349273e-06, "max_pair_overlap_depth": -1.2019034158372577e-05, "metric_expression": "2.21022", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.210219413194693, "n": 29, "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.", "record_type": "verified", "reference_side": 2.215, "setup": "triincir", "side": 4.420438826389386, "solution_path": "data/solutions/generated/triincir_029_73bcaf90b9fd2226.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/73bcaf90b9fd2226.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@30", "density": 0.8110819400631206, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2008", "friedman_display_metric_value": 2.258, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc30.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "2.258+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.258, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@30", "credit": "Maurizio Morandi", "date": "July 2008", "family_updated": "", "metric_expression": "2.258+", "metric_symbol": "r", "metric_value": 2.258, "reference_text": "r = 2.258+ | Found by Maurizio Morandi | in July 2008.", "source_image": "tc30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc30.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.258+ | Found by Maurizio Morandi | in July 2008.", "friedman_source_image": "tc30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "f720ec98817b9983", "improvement": 0.00010551194829711008, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9289733554094255e-06, "max_pair_overlap_depth": -4.657725350298847e-06, "metric_expression": "2.25789", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.257894488051703, "n": 30, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.258, "setup": "triincir", "side": 4.515788976103406, "solution_path": "data/solutions/generated/triincir_030_f720ec98817b9983.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/f720ec98817b9983.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@31", "density": 0.8263348764897189, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2008", "friedman_display_metric_value": 2.272, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc31.gif", "friedman_metric_expression": "2.272+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.272, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triincir@31", "credit": "Maurizio Morandi", "date": "July 2008", "family_updated": "", "metric_expression": "2.272+", "metric_symbol": "r", "metric_value": 2.272, "reference_text": "r = 2.272+ | Found by Maurizio Morandi | in July 2008.", "source_image": "tc31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc31.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.272+ | Found by Maurizio Morandi | in July 2008.", "friedman_source_image": "tc31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "ed4a5072cc8d0adf", "improvement": -0.0019357369126002943, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3803713964376527e-06, "max_pair_overlap_depth": -5.497010580973738e-06, "metric_expression": "2.27394", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "r", "metric_value": 2.2739357369126, "n": 31, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.272, "setup": "triincir", "side": 4.5478714738252, "solution_path": "data/solutions/generated/triincir_31_ed4a5072cc8d0adf.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T07:13:53+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/ed4a5072cc8d0adf.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@1", "density": 0.2886702903701934, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 0.8660254037844386, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "\u221a3/2", "friedman_metric_symbol": "s", "friedman_metric_value": 0.8660254037844386, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triindom@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a3/2", "metric_symbol": "s", "metric_value": 0.8660254037844386, "reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "37b1dca676a779e3", "improvement": -7.266428382335377e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4019537994690587e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.86603", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.8660326702128209, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.8660254037844386, "setup": "triindom", "side": 1.7320653404256419, "solution_path": "data/solutions/generated/triindom_001_37b1dca676a779e3.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/37b1dca676a779e3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@2", "density": 0.5773351362696808, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 0.8660254037844386, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "\u221a3/2", "friedman_metric_symbol": "s", "friedman_metric_value": 0.8660254037844386, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triindom@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a3/2", "metric_symbol": "s", "metric_value": 0.8660254037844386, "reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "31518429031d2b51", "improvement": -1.1349913078717577e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.727531273176268e-07, "max_pair_overlap_depth": -0.13184728443338464, "metric_expression": "0.86604", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.8660367536975173, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.8660254037844386, "setup": "triindom", "side": 1.7320735073950346, "solution_path": "data/solutions/generated/triindom_002_31518429031d2b51.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/31518429031d2b51.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@3", "density": 0.6931800833949334, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 0.96796, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/3.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": ".96796+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.96796, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triindom@3", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": ".96796+", "metric_symbol": "s", "metric_value": 0.96796, "reference_text": "3. | | s = .96796+ | Found by Jonathan Viquerat | in April 2026", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/3.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "3. | | s = .96796+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "b10402bd10926cd1", "improvement": -3.454421484250236e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.601436348197538e-06, "max_pair_overlap_depth": -2.0206571078401625e-05, "metric_expression": "0.96799", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.9679945442148425, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.96796, "setup": "triindom", "side": 1.935989088429685, "solution_path": "data/solutions/generated/triindom_003_b10402bd10926cd1.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/b10402bd10926cd1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@4", "density": 0.6899032945238053, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 1.12036, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/4.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.12036+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.12036, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triindom@4", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.12036+", "metric_symbol": "s", "metric_value": 1.12036, "reference_text": "4. | | s = 1.12036+ | Found by Jonathan Viquerat | in April 2026", "source_image": "4.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/4.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "4. | | s = 1.12036+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "4.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "daed4fc0474960d9", "improvement": -3.511453092652772e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.5154853256512695e-07, "max_pair_overlap_depth": -1.4193770285886309e-05, "metric_expression": "1.12040", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.1203951145309266, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.12036, "setup": "triindom", "side": 2.240790229061853, "solution_path": "data/solutions/generated/triindom_004_daed4fc0474960d9.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/daed4fc0474960d9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@5", "density": 0.6784100035927487, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 1.26315, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/5.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.26315+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.26315, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triindom@5", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.26315+", "metric_symbol": "s", "metric_value": 1.26315, "reference_text": "5. | | s = 1.26315+ | Found by Jonathan Viquerat | in April 2026", "source_image": "5.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/5.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "5. | | s = 1.26315+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "5.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "5f00d1fbe39c88e1", "improvement": -5.606079820497101e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.863453948036664e-06, "max_pair_overlap_depth": -2.090220821476807e-05, "metric_expression": "1.26321", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.263206060798205, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.26315, "setup": "triindom", "side": 2.52641212159641, "solution_path": "data/solutions/generated/triindom_005_5f00d1fbe39c88e1.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/5f00d1fbe39c88e1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@6", "density": 0.6857340379834939, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 1.37629, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/6.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.37629+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.37629, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triindom@6", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.37629+", "metric_symbol": "s", "metric_value": 1.37629, "reference_text": "6. | | s = 1.37629+ | Found by Jonathan Viquerat | in April 2026", "source_image": "6.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/6.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "6. | | s = 1.37629+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "6.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "cd22df1373fe40ae", "improvement": -7.332504683676966e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4791971315062398e-06, "max_pair_overlap_depth": -2.311431619983484e-05, "metric_expression": "1.37636", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.3763633250468368, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.37629, "setup": "triindom", "side": 2.7527266500936736, "solution_path": "data/solutions/generated/triindom_006_cd22df1373fe40ae.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/cd22df1373fe40ae.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@7", "density": 0.6816978937448389, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 1.49076, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/7.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.49076+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.49076, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triindom@7", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.49076+", "metric_symbol": "s", "metric_value": 1.49076, "reference_text": "7. | | s = 1.49076+ | Found by Jonathan Viquerat | in April 2026", "source_image": "7.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/7.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "7. | | s = 1.49076+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "7.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "070c4bf393378882", "improvement": -0.0002768061413715994, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.6376140599128062e-06, "max_pair_overlap_depth": -1.7596834968304498e-05, "metric_expression": "1.49104", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.4910368061413717, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.49076, "setup": "triindom", "side": 2.9820736122827434, "solution_path": "data/solutions/generated/triindom_007_070c4bf393378882.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/070c4bf393378882.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@8", "density": 0.7089538292098625, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 1.56293, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/8.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.56293+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.56293, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triindom@8", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.56293+", "metric_symbol": "s", "metric_value": 1.56293, "reference_text": "8. | | s = 1.56293+ | Found by Jonathan Viquerat | in April 2026", "source_image": "8.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/8.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "8. | | s = 1.56293+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "8.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "dc89b8abdea24aaa", "improvement": -0.00011448128988833517, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.119934312653896e-07, "max_pair_overlap_depth": -2.4977335194534267e-05, "metric_expression": "1.56304", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.5630444812898883, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.56293, "setup": "triindom", "side": 3.1260889625797765, "solution_path": "data/solutions/generated/triindom_008_dc89b8abdea24aaa.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/dc89b8abdea24aaa.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@9", "density": 0.7166974833845204, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 1.64908, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/9.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.64908+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.64908, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triindom@9", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.64908+", "metric_symbol": "s", "metric_value": 1.64908, "reference_text": "9. | | s = 1.64908+ | Found by Jonathan Viquerat | in April 2026", "source_image": "9.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/9.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "9. | | s = 1.64908+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "9.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "9817bdf32d5c0df3", "improvement": 0.00020157610904458778, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.318788145301177e-06, "max_pair_overlap_depth": -1.0913014285005018e-05, "metric_expression": "1.64888", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.6488784238909555, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.64908, "setup": "triindom", "side": 3.297756847781911, "solution_path": "data/solutions/generated/triindom_009_9817bdf32d5c0df3.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/9817bdf32d5c0df3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@10", "density": 0.7634583385020529, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 1.68303, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/10.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.68303+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.68303, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triindom@10", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.68303+", "metric_symbol": "s", "metric_value": 1.68303, "reference_text": "10. | | s = 1.68303+ | Found by Jonathan Viquerat | in April 2026", "source_image": "10.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/10.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "10. | | s = 1.68303+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "10.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "d60b37ee7b5fe8bb", "improvement": -0.0009721776557043427, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.2406370054083306e-07, "max_pair_overlap_depth": -6.360676094274709e-06, "metric_expression": "1.68400", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.6840021776557044, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.68303, "setup": "triindom", "side": 3.3680043553114087, "solution_path": "data/solutions/generated/triindom_010_d60b37ee7b5fe8bb.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/d60b37ee7b5fe8bb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@11", "density": 0.7938130122561631, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 1.73127, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/11.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.73127+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.73127, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triindom@11", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.73127+", "metric_symbol": "s", "metric_value": 1.73127, "reference_text": "11. | | s = 1.73127+ | Found by Jonathan Viquerat | in April 2026", "source_image": "11.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/11.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "11. | | s = 1.73127+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "11.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "92f51b49b50f6469", "improvement": -0.0008283817611449695, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.752164488808219e-06, "max_pair_overlap_depth": -9.417608768792381e-06, "metric_expression": "1.73210", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.732098381761145, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.73127, "setup": "triindom", "side": 3.46419676352229, "solution_path": "data/solutions/generated/triindom_011_92f51b49b50f6469.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/92f51b49b50f6469.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@12", "density": 0.8578074620402373, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 1.7404, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/12.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.74040+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.7404, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triindom@12", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.74040+", "metric_symbol": "s", "metric_value": 1.7404, "reference_text": "12. | | s = 1.74040+ | Found by Jonathan Viquerat | in April 2026", "source_image": "12.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/12.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "12. | | s = 1.74040+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "12.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "d4d97a50d19ba7f9", "improvement": 7.229766750849187e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6179955143756928e-06, "max_pair_overlap_depth": -3.432318619178698e-05, "metric_expression": "1.74033", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.7403277023324915, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.7404, "setup": "triindom", "side": 3.480655404664983, "solution_path": "data/solutions/generated/triindom_012_d4d97a50d19ba7f9.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/d4d97a50d19ba7f9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@13", "density": 0.819430202315155, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 1.85319, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/13.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.85319+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.85319, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triindom@13", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.85319+", "metric_symbol": "s", "metric_value": 1.85319, "reference_text": "13. | | s = 1.85319+ | Found by Jonathan Viquerat | in April 2026", "source_image": "13.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/13.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "13. | | s = 1.85319+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "13.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "734b8b487f97f149", "improvement": -0.00013256217488510913, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3279304722789718e-06, "max_pair_overlap_depth": -3.056740874492897e-05, "metric_expression": "1.85332", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.853322562174885, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.85319, "setup": "triindom", "side": 3.70664512434977, "solution_path": "data/solutions/generated/triindom_013_734b8b487f97f149.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/734b8b487f97f149.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@14", "density": 0.837880420446461, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 1.90192, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/14.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "3(3\u2013\u221a3)/2 = 1.90192+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.901923788646684, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triindom@14", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "3(3\u2013\u221a3)/2 = 1.90192+", "metric_symbol": "s", "metric_value": 1.90192, "reference_text": "14. | | s = 3(3\u2013\u221a3)/2 = 1.90192+ | Found by Jonathan Viquerat | in April 2026", "source_image": "14.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/14.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "14. | | s = 3(3\u2013\u221a3)/2 = 1.90192+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "14.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "050249738efebc30", "improvement": -6.659588303392638e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.8171942911825454e-06, "max_pair_overlap_depth": -1.6337035744662387e-05, "metric_expression": "1.90199", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.901990384529718, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.901923788646684, "setup": "triindom", "side": 3.803980769059436, "solution_path": "data/solutions/generated/triindom_014_050249738efebc30.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/050249738efebc30.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@15", "density": 0.827720714535801, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 1.9795, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/15.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "1.97950+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.9795, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triindom@15", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "1.97950+", "metric_symbol": "s", "metric_value": 1.9795, "reference_text": "15. | | s = 1.97950+ | Found by Jonathan Viquerat | in April 2026", "source_image": "15.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/15.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "15. | | s = 1.97950+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "15.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "a012f18849dc81a9", "improvement": -0.001292749811030447, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.8417244084533166e-06, "max_pair_overlap_depth": -2.1063364326057155e-05, "metric_expression": "1.98079", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.9807927498110305, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.9795, "setup": "triindom", "side": 3.961585499622061, "solution_path": "data/solutions/generated/triindom_015_a012f18849dc81a9.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/a012f18849dc81a9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@16", "density": 0.8658669941172707, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/16.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triindom@16", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "16. | | s = 2 | Found by Jonathan Viquerat | in April 2026", "source_image": "16.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/16.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "16. | | s = 2 | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "16.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "97ac1b8d90281e30", "improvement": -0.0001829408254119258, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4402032156322093e-07, "max_pair_overlap_depth": -8.654468217628164e-06, "metric_expression": "2.00018", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.000182940825412, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "triindom", "side": 4.000365881650824, "solution_path": "data/solutions/generated/triindom_016_97ac1b8d90281e30.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/97ac1b8d90281e30.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@17", "density": 0.8312856464398565, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.10306, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/17.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "2.10306+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.10306, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triindom@17", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.10306+", "metric_symbol": "s", "metric_value": 2.10306, "reference_text": "17. | | s = 2.10306+ | Found by Jonathan Viquerat | in April 2026", "source_image": "17.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/17.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "17. | | s = 2.10306+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "17.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "3b35e95b5dec0d61", "improvement": -0.001128486819858221, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9321384165115205e-07, "max_pair_overlap_depth": -4.175356206781444e-05, "metric_expression": "2.10419", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.1041884868198584, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.10306, "setup": "triindom", "side": 4.208376973639717, "solution_path": "data/solutions/generated/triindom_017_3b35e95b5dec0d61.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/3b35e95b5dec0d61.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@18", "density": 0.8436836711045761, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.14913, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/18.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "2.14913.+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.14913, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triindom@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.14913.+", "metric_symbol": "s", "metric_value": 2.14913, "reference_text": "18. | | s = 2.14913.+ | Found by Jonathan Viquerat | in April 2026", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/18.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "18. | | s = 2.14913.+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "c7d745720c03d379", "improvement": -9.434274541320065e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.205887803834571e-06, "max_pair_overlap_depth": -1.5204184911299379e-05, "metric_expression": "2.14922", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.149224342745413, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.14913, "setup": "triindom", "side": 4.298448685490826, "solution_path": "data/solutions/generated/triindom_018_c7d745720c03d379.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/c7d745720c03d379.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@19", "density": 0.815605476746989, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.24848, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/19.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "2.24848+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.24848, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triindom@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.24848+", "metric_symbol": "s", "metric_value": 2.24848, "reference_text": "19. | | s = 2.24848+ | Found by Jonathan Viquerat | in April 2026", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/19.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "19. | | s = 2.24848+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "ccdcfac9f05e2d80", "improvement": 0.002674950513982033, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.889707633764061e-07, "max_pair_overlap_depth": -1.2330676740557323e-05, "metric_expression": "2.24581", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.245805049486018, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.24848, "setup": "triindom", "side": 4.491610098972036, "solution_path": "data/solutions/generated/triindom_019_ccdcfac9f05e2d80.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/ccdcfac9f05e2d80.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triindom@20", "density": 0.820310655560819, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_display_metric_value": 2.2973, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/20.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "2.29730+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.2973, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triindom@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "", "metric_expression": "2.29730+", "metric_symbol": "s", "metric_value": 2.2973, "reference_text": "20. | | s = 2.29730+ | Found by Jonathan Viquerat | in April 2026", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/20.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "20. | | s = 2.29730+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "b651b20201d5daf5", "improvement": -0.00022973895965483493, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.6504306361575516e-06, "max_pair_overlap_depth": -2.6692790362048413e-05, "metric_expression": "2.29753", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.2975297389596547, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.2973, "setup": "triindom", "side": 4.5950594779193095, "solution_path": "data/solutions/generated/triindom_020_b651b20201d5daf5.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T02:49:16+00:00", "submitted_by": "Jonathan Viquerat", "svg_path": "data/svg/b651b20201d5daf5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@1", "density": 0.4999941032613389, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 0.577, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/1.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1/\u221a3 = .577+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.5773502691896257, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1/\u221a3 = .577+", "metric_symbol": "s", "metric_value": 0.577, "reference_text": "s = 1/\u221a3 = .577+ | Trivial.", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/1.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1/\u221a3 = .577+ | Trivial.", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "e9bcdcd079c1c3b7", "improvement": -3.4045137666804948e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.663290249487904e-07, "max_pair_overlap_depth": 0.0, "metric_expression": "0.57735", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.5773536737033924, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.5773502691896257, "setup": "triinhex", "side": 0.5773536737033924, "solution_path": "data/solutions/generated/triinhex_001_e9bcdcd079c1c3b7.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/e9bcdcd079c1c3b7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@2", "density": 0.4444266358884555, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 0.866, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/2.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a3/2 = .866+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.8660254037844386, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a3/2 = .866+", "metric_symbol": "s", "metric_value": 0.866, "reference_text": "s = \u221a3/2 = .866+ | Trivial.", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/2.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = \u221a3/2 = .866+ | Trivial.", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "132c3ed1fad59f87", "improvement": -1.735101606104017e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.75428637420658e-06, "max_pair_overlap_depth": -4.36783093215443e-06, "metric_expression": "0.86604", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.8660427548004996, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.8660254037844386, "setup": "triinhex", "side": 0.8660427548004996, "solution_path": "data/solutions/generated/triinhex_002_132c3ed1fad59f87.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/132c3ed1fad59f87.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@3", "density": 0.5108536175549566, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2005", "friedman_display_metric_value": 0.989, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/3.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a((6+\u221a33)/12) = .989+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.9892995268765516, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@3", "credit": "Erich Friedman", "date": "April 2005", "family_updated": "", "metric_expression": "\u221a((6+\u221a33)/12) = .989+", "metric_symbol": "s", "metric_value": 0.989, "reference_text": "s = \u221a((6+\u221a33)/12) = .989+ | Found by Erich Friedman | in April 2005.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/3.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = \u221a((6+\u221a33)/12) = .989+ | Found by Erich Friedman | in April 2005.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "3f19c46d9d07a54d", "improvement": -2.0420220901540276e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.001855317125196e-07, "max_pair_overlap_depth": -5.956334362088034e-06, "metric_expression": "0.98932", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.9893199470974532, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.9892995268765516, "setup": "triinhex", "side": 0.9893199470974532, "solution_path": "data/solutions/generated/triinhex_003_3f19c46d9d07a54d.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/3f19c46d9d07a54d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@4", "density": 0.6666347131299533, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/4.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@4", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/4.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1 | Trivial.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "9a8f72cbad0da23e", "improvement": -2.396601406218224e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.5130077190296347e-08, "max_pair_overlap_depth": -1.1324383645797624e-05, "metric_expression": "1.00002", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0000239660140622, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.0, "setup": "triinhex", "side": 1.0000239660140622, "solution_path": "data/solutions/generated/triinhex_004_9a8f72cbad0da23e.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/9a8f72cbad0da23e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@5", "density": 0.8333022730508762, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/5.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@5", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/5.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1 | Trivial.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "0d61e48787b7d5d1", "improvement": -1.863669045065741e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0710555572355552e-06, "max_pair_overlap_depth": -2.545819687190834e-06, "metric_expression": "1.00002", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0000186366904507, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.0, "setup": "triinhex", "side": 1.0000186366904507, "solution_path": "data/solutions/generated/triinhex_005_0d61e48787b7d5d1.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/0d61e48787b7d5d1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@6", "density": 0.9999558832137269, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/6.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@6", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/6.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1 | Trivial.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "163de15143701be8", "improvement": -2.2059123022444282e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.751347439371281e-07, "max_pair_overlap_depth": -4.053173147537176e-06, "metric_expression": "1.00002", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0000220591230224, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.0, "setup": "triinhex", "side": 1.0000220591230224, "solution_path": "data/solutions/generated/triinhex_006_163de15143701be8.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/163de15143701be8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@7", "density": 0.7149966699512036, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "May 2005", "friedman_display_metric_value": 1.277, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/7.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.277+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.277, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@7", "credit": "David W. Cantrell", "date": "May 2005", "family_updated": "", "metric_expression": "1.277+", "metric_symbol": "s", "metric_value": 1.277, "reference_text": "s = 1.277+ | Found by David W. Cantrell | in May 2005.", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/7.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.277+ | Found by David W. Cantrell | in May 2005.", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "af96c8dfd69688ff", "improvement": -0.0003837447071250999, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8980834118002716e-06, "max_pair_overlap_depth": -1.0312174508100846e-05, "metric_expression": "1.27738", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.277383744707125, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.277, "setup": "triinhex", "side": 1.277383744707125, "solution_path": "data/solutions/generated/triinhex_007_af96c8dfd69688ff.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/af96c8dfd69688ff.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@8", "density": 0.724469693124155, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 1.356, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/8.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.356+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.356, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@8", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "1.356+", "metric_symbol": "s", "metric_value": 1.356, "reference_text": "s = 1.356+ | Found by David W. Cantrell | in July 2012.", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/8.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.356+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "d557994d1935d6fb", "improvement": -0.0006232543073974028, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6958384610035216e-07, "max_pair_overlap_depth": -6.193690244168937e-06, "metric_expression": "1.35662", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.3566232543073975, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.356, "setup": "triinhex", "side": 1.3566232543073975, "solution_path": "data/solutions/generated/triinhex_008_d557994d1935d6fb.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d557994d1935d6fb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@9", "density": 0.7288897241647109, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "April 2005", "friedman_display_metric_value": 1.434, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/9.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.434+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.434, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@9", "credit": "Erich Friedman", "date": "April 2005", "family_updated": "", "metric_expression": "1.434+", "metric_symbol": "s", "metric_value": 1.434, "reference_text": "s = 1.434+ | Found by Erich Friedman | in April 2005.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/9.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.434+ | Found by Erich Friedman | in April 2005.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "e1592cc41ab92d4d", "improvement": -0.0005467824277936018, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.288341076546003e-06, "max_pair_overlap_depth": -3.69502244107478e-06, "metric_expression": "1.43455", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.4345467824277935, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.434, "setup": "triinhex", "side": 1.4345467824277935, "solution_path": "data/solutions/generated/triinhex_009_e1592cc41ab92d4d.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/e1592cc41ab92d4d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@10", "density": 0.7432082873431878, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_display_metric_value": 1.497, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/10.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.497+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.497, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@10", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "1.497+", "metric_symbol": "s", "metric_value": 1.497, "reference_text": "s = 1.497+ | Found by Timo Berthold et al | in January 2026.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/10.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.497+ | Found by Timo Berthold et al | in January 2026.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "27f77a1826f41a7d", "improvement": -0.0005078337450310499, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4736979206377467e-06, "max_pair_overlap_depth": -5.4498855950879665e-06, "metric_expression": "1.49751", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.4975078337450312, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.497, "setup": "triinhex", "side": 1.4975078337450312, "solution_path": "data/solutions/generated/triinhex_010_27f77a1826f41a7d.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/27f77a1826f41a7d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@11", "density": 0.8147753094192889, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2005", "friedman_display_metric_value": 1.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/11.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3/2 = 1.500", "friedman_metric_symbol": "s", "friedman_metric_value": 1.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@11", "credit": "Erich Friedman", "date": "April 2005", "family_updated": "", "metric_expression": "3/2 = 1.500", "metric_symbol": "s", "metric_value": 1.5, "reference_text": "s = 3/2 = 1.500 | Found by Erich Friedman | in April 2005.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/11.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 3/2 = 1.500 | Found by Erich Friedman | in April 2005.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "a4d7af61e2935a14", "improvement": -3.636424319730658e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0384668058064728e-06, "max_pair_overlap_depth": -9.97710385775008e-06, "metric_expression": "1.50004", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.5000363642431973, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.5, "setup": "triinhex", "side": 1.5000363642431973, "solution_path": "data/solutions/generated/triinhex_011_a4d7af61e2935a14.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/a4d7af61e2935a14.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@12", "density": 0.7583806241339298, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_display_metric_value": 1.623, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/12.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.623+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.623, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@12", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "1.623+", "metric_symbol": "s", "metric_value": 1.623, "reference_text": "s = 1.623+ | Found by Timo Berthold et al | in January 2026.", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/12.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.623+ | Found by Timo Berthold et al | in January 2026.", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "9de540041e59931a", "improvement": -0.0009452508446496921, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.928415721340796e-06, "max_pair_overlap_depth": -1.3315156502324843e-05, "metric_expression": "1.62395", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.6239452508446497, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.623, "setup": "triinhex", "side": 1.6239452508446497, "solution_path": "data/solutions/generated/triinhex_012_9de540041e59931a.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/9de540041e59931a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@13", "density": 0.7821155301010267, "friedman_analytical_or_proved": true, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 1.663829, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/13.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a(587+51\u221a17)/12\u221a2 = 1.663829+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.663829237726708, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@13", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "\u221a(587+51\u221a17)/12\u221a2 = 1.663829+", "metric_symbol": "s", "metric_value": 1.663829, "reference_text": "s = \u221a(587+51\u221a17)/12\u221a2 = 1.663829+ | Found by Ian Watson | in April 2026.", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/13.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = \u221a(587+51\u221a17)/12\u221a2 = 1.663829+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "efc43a6cbf81ae24", "improvement": -0.0005818344206434123, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.9742574580490386e-06, "max_pair_overlap_depth": -2.1993638058326326e-05, "metric_expression": "1.66441", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.6644110721473515, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.663829237726708, "setup": "triinhex", "side": 1.6644110721473515, "solution_path": "data/solutions/generated/triinhex_013_efc43a6cbf81ae24.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/efc43a6cbf81ae24.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@14", "density": 0.7828804179520853, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "August 2012", "friedman_display_metric_value": 1.725, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/14.gif", "friedman_metric_expression": "1.725+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.725, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@14", "credit": "David W. Cantrell", "date": "August 2012", "family_updated": "", "metric_expression": "1.725+", "metric_symbol": "s", "metric_value": 1.725, "reference_text": "s = 1.725+ | Found by David W. Cantrell | in August 2012.", "source_image": "14.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/14.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.725+ | Found by David W. Cantrell | in August 2012.", "friedman_source_image": "14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "dbfe389f1c3777d5", "improvement": -0.0013970193042536216, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.5600740703080906e-07, "max_pair_overlap_depth": -1.248505498985253e-07, "metric_expression": "1.72640", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.7263970193042537, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.725, "setup": "triinhex", "side": 1.7263970193042537, "solution_path": "data/solutions/generated/triinhex_14_dbfe389f1c3777d5.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T07:13:53+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/dbfe389f1c3777d5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@15", "density": 0.8162509918871499, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2005", "friedman_display_metric_value": 1.75, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/15.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "7/4 = 1.750", "friedman_metric_symbol": "s", "friedman_metric_value": 1.75, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@15", "credit": "Erich Friedman", "date": "April 2005", "family_updated": "", "metric_expression": "7/4 = 1.750", "metric_symbol": "s", "metric_value": 1.75, "reference_text": "s = 7/4 = 1.750 | Found by Erich Friedman | in April 2005.", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/15.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 7/4 = 1.750 | Found by Erich Friedman | in April 2005.", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "20b1a0e905211ce9", "improvement": -8.097369067638915e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.758472784251539e-06, "max_pair_overlap_depth": -9.75502017092067e-06, "metric_expression": "1.75008", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.7500809736906764, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.75, "setup": "triinhex", "side": 1.7500809736906764, "solution_path": "data/solutions/generated/triinhex_015_20b1a0e905211ce9.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/20b1a0e905211ce9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@16", "density": 0.8229668363309378, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2008", "friedman_display_metric_value": 1.8, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/16.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "9/5 = 1.800", "friedman_metric_symbol": "s", "friedman_metric_value": 1.8, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@16", "credit": "Maurizio Morandi", "date": "April 2008", "family_updated": "", "metric_expression": "9/5 = 1.800", "metric_symbol": "s", "metric_value": 1.8, "reference_text": "s = 9/5 = 1.800 | Found by Maurizio Morandi | in April 2008.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/16.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 9/5 = 1.800 | Found by Maurizio Morandi | in April 2008.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "a0b20d24de5f00ac", "improvement": -8.577060222680899e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.740972449159294e-06, "max_pair_overlap_depth": -2.3139042383268915e-06, "metric_expression": "1.80009", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.8000857706022269, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.8, "setup": "triinhex", "side": 1.8000857706022269, "solution_path": "data/solutions/generated/triinhex_016_a0b20d24de5f00ac.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/a0b20d24de5f00ac.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@17", "density": 0.842931104392013, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2008", "friedman_display_metric_value": 1.833, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/17.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "11/6 = 1.833+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.8333333333333333, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@17", "credit": "Maurizio Morandi", "date": "April 2008", "family_updated": "", "metric_expression": "11/6 = 1.833+", "metric_symbol": "s", "metric_value": 1.833, "reference_text": "s = 11/6 = 1.833+ | Found by Maurizio Morandi | in April 2008.", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/17.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 11/6 = 1.833+ | Found by Maurizio Morandi | in April 2008.", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "b8b9e4b4d61ec96c", "improvement": -4.7959442487144344e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4990722513823532e-07, "max_pair_overlap_depth": -1.1854387088505725e-05, "metric_expression": "1.83338", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.8333812927758204, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.8333333333333333, "setup": "triinhex", "side": 1.8333812927758204, "solution_path": "data/solutions/generated/triinhex_017_b8b9e4b4d61ec96c.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/b8b9e4b4d61ec96c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@18", "density": 0.8400311467465807, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2008", "friedman_display_metric_value": 1.888, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/18.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "17/9 = 1.888+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.8888888888888888, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@18", "credit": "Maurizio Morandi", "date": "April 2008", "family_updated": "", "metric_expression": "17/9 = 1.888+", "metric_symbol": "s", "metric_value": 1.888, "reference_text": "s = 17/9 = 1.888+ | Found by Maurizio Morandi | in April 2008.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/18.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 17/9 = 1.888+ | Found by Maurizio Morandi | in April 2008.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "7671cfd644a7af24", "improvement": -0.000898440334977213, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.484924045151217e-06, "max_pair_overlap_depth": -8.796062168636709e-06, "metric_expression": "1.88979", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.889787329223866, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.8888888888888888, "setup": "triinhex", "side": 1.889787329223866, "solution_path": "data/solutions/generated/triinhex_018_7671cfd644a7af24.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/7671cfd644a7af24.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@19", "density": 0.8283361930438612, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Adri\u00e1n Nieto", "friedman_date": "April 2026", "friedman_display_metric_value": 1.953, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/19.gif", "friedman_metric_expression": "1.953+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.953, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@19", "credit": "Alex Adri\u00e1n Nieto", "date": "April 2026", "family_updated": "", "metric_expression": "1.953+", "metric_symbol": "s", "metric_value": 1.953, "reference_text": "s = 1.953+ | Found by Alex Adri\u00e1n Nieto | in April 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/19.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.953+ | Found by Alex Adri\u00e1n Nieto | in April 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "451018f1291a5791", "improvement": -0.0022300191069650754, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7079807782201595e-06, "max_pair_overlap_depth": -1.3478523960663846e-05, "metric_expression": "1.95523", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.9552300191069651, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "record_type": "verified", "reference_side": 1.953, "setup": "triinhex", "side": 1.9552300191069651, "solution_path": "data/solutions/generated/triinhex_19_451018f1291a5791.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T07:13:53+00:00", "submitted_by": "Alex Adri\u00e1n Nieto", "svg_path": "data/svg/451018f1291a5791.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@19", "density": 0.828872982650555, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Adri\u00e1n Nieto", "friedman_date": "April 2026", "friedman_display_metric_value": 1.953, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/19.gif", "friedman_metric_expression": "1.953+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.953, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@19", "credit": "Alex Adri\u00e1n Nieto", "date": "April 2026", "family_updated": "", "metric_expression": "1.953+", "metric_symbol": "s", "metric_value": 1.953, "reference_text": "s = 1.953+ | Found by Alex Adri\u00e1n Nieto | in April 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/19.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.953+ | Found by Alex Adri\u00e1n Nieto | in April 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "545ef4899aee40a3", "improvement": -0.0015967995695436166, "max_boundary_excess": -2.527824635230551e-06, "max_pair_overlap_depth": -1.5640219825363566e-05, "metric_expression": "1.95460", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.9545967995695437, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 1.953, "setup": "triinhex", "side": 1.9545967995695437, "solution_path": "data/solutions/generated/triinhex_19_545ef4899aee40a3.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T16:53:45+00:00", "submitted_by": "Alex Adri\u00e1n Nieto", "svg_path": "data/svg/545ef4899aee40a3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@20", "density": 0.8524037354438128, "friedman_analytical_or_proved": false, "friedman_credit": "Aaden Abraham", "friedman_date": "April 2026", "friedman_display_metric_value": 1.97591, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/20.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.97591+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.97591, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@20", "credit": "Aaden Abraham", "date": "April 2026", "family_updated": "", "metric_expression": "1.97591+", "metric_symbol": "s", "metric_value": 1.97591, "reference_text": "s = 1.97591+ | Found by Aaden Abraham | in April 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/20.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.97591+ | Found by Aaden Abraham | in April 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "388fc73ef451e99b", "improvement": -0.0015909487133152211, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7558573966506123e-06, "max_pair_overlap_depth": -5.2993150605473716e-06, "metric_expression": "1.97750", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.9775009487133153, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.97591, "setup": "triinhex", "side": 1.9775009487133153, "solution_path": "data/solutions/generated/triinhex_020_388fc73ef451e99b.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:51:36+00:00", "submitted_by": "Aaden Abraham", "svg_path": "data/svg/388fc73ef451e99b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@21", "density": 0.8749527320468723, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 1.99878, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/21.gif", "friedman_metric_expression": "1.99878+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.99878, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@21", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "1.99878+", "metric_symbol": "s", "metric_value": 1.99878, "reference_text": "s = 1.99878+ | Found by Ian Watson | in April 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/21.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.99878+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "96f74df50573bb81", "improvement": -0.0012740227066210252, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.545179480294009e-07, "max_pair_overlap_depth": -6.765642482919887e-06, "metric_expression": "2.00005", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.000054022706621, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.99878, "setup": "triinhex", "side": 2.000054022706621, "solution_path": "data/solutions/generated/triinhex_021_96f74df50573bb81.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/96f74df50573bb81.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@22", "density": 0.9166150664792877, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@22", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial. |", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2 | Trivial. |", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "38182a59461da74e", "improvement": -5.629349013291929e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.91184500961419e-07, "max_pair_overlap_depth": -9.942352799940934e-07, "metric_expression": "2.00006", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.000056293490133, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "triinhex", "side": 2.000056293490133, "solution_path": "data/solutions/generated/triinhex_022_38182a59461da74e.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/38182a59461da74e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@23", "density": 0.958278890368788, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@23", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial. |", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2 | Trivial. |", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "dcd331994270a997", "improvement": -5.681247061106731e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0734329507489061e-06, "max_pair_overlap_depth": -9.41664729126046e-06, "metric_expression": "2.00006", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.000056812470611, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "triinhex", "side": 2.000056812470611, "solution_path": "data/solutions/generated/triinhex_023_dcd331994270a997.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/dcd331994270a997.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@24", "density": 0.9999420291406096, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@24", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial. |", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2 | Trivial. |", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "13936a08bfd4d152", "improvement": -5.7973379977482864e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3635152509087512e-06, "max_pair_overlap_depth": -3.8859579855957235e-06, "metric_expression": "2.00006", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0000579733799775, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "triinhex", "side": 2.0000579733799775, "solution_path": "data/solutions/generated/triinhex_024_13936a08bfd4d152.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/13936a08bfd4d152.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@25", "density": 0.8871759236838516, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 2.166, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/25.gif", "friedman_metric_expression": "13/6 = 2.166+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.1666666666666665, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@25", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "13/6 = 2.166+", "metric_symbol": "s", "metric_value": 2.166, "reference_text": "s = 13/6 = 2.166+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/25.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 13/6 = 2.166+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "71a7801cfb4a8d31", "improvement": -0.0004859943935220379, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.780494307380179e-07, "max_pair_overlap_depth": -1.3308976067882838e-06, "metric_expression": "2.16715", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.1671526610601886, "n": 25, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.1666666666666665, "setup": "triinhex", "side": 2.1671526610601886, "solution_path": "data/solutions/generated/triinhex_025_71a7801cfb4a8d31.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/71a7801cfb4a8d31.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@26", "density": 0.878430458154361, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.21991, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/26.gif", "friedman_metric_expression": "2.21991+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.21991, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@26", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.21991+", "metric_symbol": "s", "metric_value": 2.21991, "reference_text": "s = 2.21991+ | Found by Ian Watson | in April 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/26.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.21991+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "658d7f93b604b663", "improvement": -0.0011349903788469007, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.149641376243232e-07, "max_pair_overlap_depth": -5.41804289733161e-06, "metric_expression": "2.22104", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.221044990378847, "n": 26, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.21991, "setup": "triinhex", "side": 2.221044990378847, "solution_path": "data/solutions/generated/triinhex_026_658d7f93b604b663.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/658d7f93b604b663.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@27", "density": 0.8525233088554102, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.29541, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/27.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.29541+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.29541, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@27", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.29541+", "metric_symbol": "s", "metric_value": 2.29541, "reference_text": "s = 2.29541+ | Found by Ian Watson | in April 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/27.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.29541+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "ace1d8ac458c5bc4", "improvement": -0.0020773347367342154, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.449964623966915e-06, "max_pair_overlap_depth": -5.244956223338093e-06, "metric_expression": "2.29749", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.297487334736734, "n": 27, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.29541, "setup": "triinhex", "side": 2.297487334736734, "solution_path": "data/solutions/generated/triinhex_027_ace1d8ac458c5bc4.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/ace1d8ac458c5bc4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@28", "density": 0.8636324031387004, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.32289, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/28.gif", "friedman_metric_expression": "2.32289+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.32289, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@28", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.32289+", "metric_symbol": "s", "metric_value": 2.32289, "reference_text": "s = 2.32289+ | Found by Ian Watson | in April 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/28.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.32289+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "3435500023858121", "improvement": -0.0016601826518787277, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.60736131059532e-06, "max_pair_overlap_depth": -1.0038160656700157e-05, "metric_expression": "2.32455", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.324550182651879, "n": 28, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.32289, "setup": "triinhex", "side": 2.324550182651879, "solution_path": "data/solutions/generated/triinhex_28_3435500023858121.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/3435500023858121.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@29", "density": 0.8876189549602443, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 2.333, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/29.gif", "friedman_metric_expression": "7/3 = 2.333+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.3333333333333335, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@29", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "7/3 = 2.333+", "metric_symbol": "s", "metric_value": 2.333, "reference_text": "s = 7/3 = 2.333+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/29.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 7/3 = 2.333+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "4339d1ebd3160f94", "improvement": -0.00017894184144084946, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.371335525980428e-06, "max_pair_overlap_depth": -4.303492490143057e-07, "metric_expression": "2.33351", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.3335122751747743, "n": 29, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.3333333333333335, "setup": "triinhex", "side": 2.3335122751747743, "solution_path": "data/solutions/generated/triinhex_29_4339d1ebd3160f94.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/4339d1ebd3160f94.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@30", "density": 0.8862493271562808, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 2.375, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/30.gif", "friedman_metric_expression": "19/8 = 2.375", "friedman_metric_symbol": "s", "friedman_metric_value": 2.375, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@30", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "19/8 = 2.375", "metric_symbol": "s", "metric_value": 2.375, "reference_text": "s = 19/8 = 2.375 | Found by Ignacio Vallejo | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/30.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 19/8 = 2.375 | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "7274d354e73d8050", "improvement": -0.00023750926269094919, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.946881910542413e-07, "max_pair_overlap_depth": -3.1129912760885503e-06, "metric_expression": "2.37524", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.375237509262691, "n": 30, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.375, "setup": "triinhex", "side": 2.375237509262691, "solution_path": "data/solutions/generated/triinhex_30_7274d354e73d8050.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/7274d354e73d8050.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@31", "density": 0.896119877899338, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 2.4, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/31.gif", "friedman_metric_expression": "12/5 = 2.400", "friedman_metric_symbol": "s", "friedman_metric_value": 2.4, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "12/5 = 2.400", "metric_symbol": "s", "metric_value": 2.4, "reference_text": "s = 12/5 = 2.400 | Found by Emerson Connelly | in April 2026.", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/31.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 12/5 = 2.400 | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "cae7087451040120", "improvement": -0.0011658949471424762, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9409739826535097e-07, "max_pair_overlap_depth": -2.8541100203227643e-06, "metric_expression": "2.40117", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.4011658949471424, "n": 31, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.4, "setup": "triinhex", "side": 2.4011658949471424, "solution_path": "data/solutions/generated/triinhex_31_cae7087451040120.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/cae7087451040120.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@32", "density": 0.8767870241121234, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 2.465, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/32.gif", "friedman_metric_expression": "2.465+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.465, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "2.465+", "metric_symbol": "s", "metric_value": 2.465, "reference_text": "s = 2.465+ | Found by Emerson Connelly | in April 2026.", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/32.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.465+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "8674581436e5e74d", "improvement": -0.0013363682337788063, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.925122041572899e-07, "max_pair_overlap_depth": -1.2807310418028184e-06, "metric_expression": "2.46634", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.4663363682337787, "n": 32, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.465, "setup": "triinhex", "side": 2.4663363682337787, "solution_path": "data/solutions/generated/triinhex_032_8674581436e5e74d.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/8674581436e5e74d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@33", "density": 0.8799443949567897, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 2.498, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/33.gif", "friedman_metric_expression": "2.498+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.498, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "2.498+", "metric_symbol": "s", "metric_value": 2.498, "reference_text": "s = 2.498+ | Found by Emerson Connelly | in April 2026.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/33.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.498+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "5b836a27d2bb958c", "improvement": -0.00207898817969987, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.8634496562140136e-06, "max_pair_overlap_depth": -5.829272115620565e-06, "metric_expression": "2.50008", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.5000789881797, "n": 33, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.498, "setup": "triinhex", "side": 2.5000789881797, "solution_path": "data/solutions/generated/triinhex_033_5b836a27d2bb958c.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/5b836a27d2bb958c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@34", "density": 0.9066102013779274, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 2.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "friedman_metric_expression": "5/2 = 2.500", "friedman_metric_symbol": "s", "friedman_metric_value": 2.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "5/2 = 2.500", "metric_symbol": "s", "metric_value": 2.5, "reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "a712744ff3b5bcc9", "improvement": -7.7851001305973e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2753913921730298e-06, "max_pair_overlap_depth": -7.960301433351802e-06, "metric_expression": "2.50008", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.500077851001306, "n": 34, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.5, "setup": "triinhex", "side": 2.500077851001306, "solution_path": "data/solutions/generated/triinhex_034_a712744ff3b5bcc9.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/a712744ff3b5bcc9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@35", "density": 0.93316535041203, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 2.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "friedman_metric_expression": "5/2 = 2.500", "friedman_metric_symbol": "s", "friedman_metric_value": 2.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@35", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "5/2 = 2.500", "metric_symbol": "s", "metric_value": 2.5, "reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "ec49778cf450c37b", "improvement": -0.00022500750012577342, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6207066397040256e-06, "max_pair_overlap_depth": -1.5837731757728513e-06, "metric_expression": "2.50023", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.5002250075001258, "n": 35, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.5, "setup": "triinhex", "side": 2.5002250075001258, "solution_path": "data/solutions/generated/triinhex_35_ec49778cf450c37b.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/ec49778cf450c37b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@36", "density": 0.8942711196026824, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_display_metric_value": 2.59123, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/36.gif", "friedman_metric_expression": "2.59123+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.59123, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@36", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "2.59123+", "metric_symbol": "s", "metric_value": 2.59123, "reference_text": "s = 2.59123+ | Found by Nathan Roll | in April 2026.", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/36.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.59123+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "d30ec5c19b8369f3", "improvement": 0.000983935961939686, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.744185746811731e-07, "max_pair_overlap_depth": -1.519675368655271e-06, "metric_expression": "2.59025", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.5902460640380602, "n": 36, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.59123, "setup": "triinhex", "side": 2.5902460640380602, "solution_path": "data/solutions/record_hunt/triinhex_36_d30ec5c19b8369f3.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/d30ec5c19b8369f3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@37", "density": 0.899950790089805, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_display_metric_value": 2.61943, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/37.gif", "friedman_metric_expression": "2.61943+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.61943, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@37", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "2.61943+", "metric_symbol": "s", "metric_value": 2.61943, "reference_text": "s = 2.61943+ | Found by Nathan Roll | in April 2026.", "source_image": "37.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/37.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.61943+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "c791d76ac960cbca", "improvement": 0.0017542149405089802, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.903248309191345e-07, "max_pair_overlap_depth": -8.609976616114068e-07, "metric_expression": "2.61768", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.617675785059491, "n": 37, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.61943, "setup": "triinhex", "side": 2.617675785059491, "solution_path": "data/solutions/record_hunt/triinhex_37_c791d76ac960cbca.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/c791d76ac960cbca.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@38", "density": 0.8907392561961515, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 2.666, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "friedman_metric_expression": "8/3 = 2.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.6666666666666665, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "8/3 = 2.666+", "metric_symbol": "s", "metric_value": 2.666, "reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "76fd196e8c79a5c9", "improvement": 0.00017103375581761782, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.7850003642140776e-06, "max_pair_overlap_depth": -3.863933217385096e-06, "metric_expression": "2.66650", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.666495632910849, "n": 38, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.6666666666666665, "setup": "triinhex", "side": 2.666495632910849, "solution_path": "data/solutions/generated/triinhex_038_76fd196e8c79a5c9.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/76fd196e8c79a5c9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@39", "density": 0.9136318214810123, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 2.666, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "friedman_metric_expression": "8/3 = 2.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.6666666666666665, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "8/3 = 2.666+", "metric_symbol": "s", "metric_value": 2.666, "reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "a314b4bb8467e5e8", "improvement": -0.0006284483037841682, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.891404577705932e-07, "max_pair_overlap_depth": -6.19203720853001e-07, "metric_expression": "2.66730", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.6672951149704507, "n": 39, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.6666666666666665, "setup": "triinhex", "side": 2.6672951149704507, "solution_path": "data/solutions/generated/triinhex_39_a314b4bb8467e5e8.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/a314b4bb8467e5e8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@40", "density": 0.9051419512423183, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_display_metric_value": 2.71622, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/40.gif", "friedman_metric_expression": "2.71622+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.71622, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@40", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "2.71622+", "metric_symbol": "s", "metric_value": 2.71622, "reference_text": "s = 2.71622+ | Found by Nathan Roll | in April 2026.", "source_image": "40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/40.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.71622+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "8b6d682b66356562", "improvement": 0.0023063615780789526, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2777984478773679e-07, "max_pair_overlap_depth": -4.470141119483628e-07, "metric_expression": "2.71391", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.713913638421921, "n": 40, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.71622, "setup": "triinhex", "side": 2.713913638421921, "solution_path": "data/solutions/record_hunt/triinhex_40_8b6d682b66356562.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/8b6d682b66356562.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@1", "density": 0.4152122478191623, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 0.4647, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/1.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": ".46470+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.4647, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triinoct@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": ".46470+", "metric_symbol": "s", "metric_value": 0.4647, "reference_text": "s = .46470+ | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/1.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = .46470+ | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "92c66f395ff03ab9", "improvement": -4.251046545072912e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3282842257895898e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.46474", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.46474251046545073, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.4647, "setup": "triinoct", "side": 0.46474251046545073, "solution_path": "data/solutions/generated/triinoct_001_92c66f395ff03ab9.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/92c66f395ff03ab9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@2", "density": 0.40823825072318354, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 0.66282, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/2.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "\u221a3/\u221a(4+2\u221a2) = .66282+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.6628271480711836, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinoct@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a3/\u221a(4+2\u221a2) = .66282+", "metric_symbol": "s", "metric_value": 0.66282, "reference_text": "s = \u221a3/\u221a(4+2\u221a2) = .66282+ | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/2.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = \u221a3/\u221a(4+2\u221a2) = .66282+ | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "5706480ca6648c20", "improvement": -8.150353080438322e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.197393779037103e-06, "max_pair_overlap_depth": -5.033792755404498e-07, "metric_expression": "0.66284", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.662835298424264, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.6628271480711836, "setup": "triinoct", "side": 0.662835298424264, "solution_path": "data/solutions/generated/triinoct_002_5706480ca6648c20.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/5706480ca6648c20.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@3", "density": 0.49592364137420614, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 0.73651, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/3.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": ".73651+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.73651, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@3", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": ".73651+", "metric_symbol": "s", "metric_value": 0.73651, "reference_text": "s = .73651+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/3.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = .73651+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "f3eee07e4d3df15b", "improvement": -3.739655668555386e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.662035887956301e-06, "max_pair_overlap_depth": -2.2250265259982083e-06, "metric_expression": "0.73655", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.7365473965566856, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.73651, "setup": "triinoct", "side": 0.7365473965566856, "solution_path": "data/solutions/generated/triinoct_003_f3eee07e4d3df15b.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/f3eee07e4d3df15b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@4", "density": 0.593540115018531, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 0.77733, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/4.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": ".77733+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.77733, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@4", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": ".77733+", "metric_symbol": "s", "metric_value": 0.77733, "reference_text": "s = .77733+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/4.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = .77733+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "daeed392d4fde104", "improvement": -8.413889807601382e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.025085624522854e-06, "max_pair_overlap_depth": -2.0675467336764286e-05, "metric_expression": "0.77741", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.777414138898076, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.77733, "setup": "triinoct", "side": 0.777414138898076, "solution_path": "data/solutions/generated/triinoct_004_daeed392d4fde104.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/daeed392d4fde104.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@5", "density": 0.6941546982548611, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 0.80367, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/5.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": ".80367+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.80367, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@5", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": ".80367+", "metric_symbol": "s", "metric_value": 0.80367, "reference_text": "s = .80367+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/5.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = .80367+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "a0addde9772ff582", "improvement": -4.920494762683525e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.8458025218911135e-06, "max_pair_overlap_depth": -2.636296310584707e-05, "metric_expression": "0.80372", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.8037192049476268, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.80367, "setup": "triinoct", "side": 0.8037192049476268, "solution_path": "data/solutions/generated/triinoct_005_a0addde9772ff582.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/a0addde9772ff582.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@6", "density": 0.8085136476900721, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 0.81574, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/6.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": ".81574+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.81574, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@6", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": ".81574+", "metric_symbol": "s", "metric_value": 0.81574, "reference_text": "s = .81574+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/6.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = .81574+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "e7ac2b490b8118b6", "improvement": -5.196804299267832e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.999019070763348e-06, "max_pair_overlap_depth": -1.523375553563397e-05, "metric_expression": "0.81579", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.8157919680429927, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.81574, "setup": "triinoct", "side": 0.8157919680429927, "solution_path": "data/solutions/generated/triinoct_006_e7ac2b490b8118b6.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/e7ac2b490b8118b6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@7", "density": 0.7344053269175495, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 0.92453, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/7.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": ".92453+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.92453, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@7", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": ".92453+", "metric_symbol": "s", "metric_value": 0.92453, "reference_text": "s = .92453+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/7.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = .92453+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "f1951fc893682894", "improvement": -1.6137063615029312e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.877767128601322e-06, "max_pair_overlap_depth": -4.487804835917597e-06, "metric_expression": "0.92455", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.924546137063615, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.92453, "setup": "triinoct", "side": 0.924546137063615, "solution_path": "data/solutions/generated/triinoct_007_f1951fc893682894.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/f1951fc893682894.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@8", "density": 0.7351940708693757, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 0.98782, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/8.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": ".98782+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.98782, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@8", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": ".98782+", "metric_symbol": "s", "metric_value": 0.98782, "reference_text": "s = .98782+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/8.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = .98782+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "cdfdb28bbd7c958a", "improvement": -3.106647506945226e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6027742606714177e-06, "max_pair_overlap_depth": -8.534452089259403e-06, "metric_expression": "0.98785", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.9878510664750695, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.98782, "setup": "triinoct", "side": 0.9878510664750695, "solution_path": "data/solutions/generated/triinoct_008_cdfdb28bbd7c958a.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/cdfdb28bbd7c958a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@9", "density": 0.7931382286148597, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.00875, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/9.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.00875+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.00875, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@9", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.00875+", "metric_symbol": "s", "metric_value": 1.00875, "reference_text": "s = 1.00875+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/9.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.00875+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "0a4766beda41f84b", "improvement": -2.4953411784212065e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.992353374519455e-07, "max_pair_overlap_depth": -5.523000253249144e-06, "metric_expression": "1.00877", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0087749534117842, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.00875, "setup": "triinoct", "side": 1.0087749534117842, "solution_path": "data/solutions/generated/triinoct_009_0a4766beda41f84b.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/0a4766beda41f84b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@10", "density": 0.7747683390429897, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.07565, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/10.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.07565+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.07565, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@10", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.07565+", "metric_symbol": "s", "metric_value": 1.07565, "reference_text": "s = 1.07565+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/10.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.07565+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "df6976316812d041", "improvement": -0.00022432883231693346, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.3385179497460716e-06, "max_pair_overlap_depth": -1.8668924055276204e-05, "metric_expression": "1.07587", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.075874328832317, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.07565, "setup": "triinoct", "side": 1.075874328832317, "solution_path": "data/solutions/generated/triinoct_010_df6976316812d041.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/df6976316812d041.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@11", "density": 0.7515390994133405, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.14571, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/11.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.14571+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.14571, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@11", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.14571+", "metric_symbol": "s", "metric_value": 1.14571, "reference_text": "s = 1.14571+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/11.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.14571+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "11036479a300844a", "improvement": 1.760556295749005e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.2318282708152993e-06, "max_pair_overlap_depth": -7.937162014970411e-06, "metric_expression": "1.14569", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.1456923944370425, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.14571, "setup": "triinoct", "side": 1.1456923944370425, "solution_path": "data/solutions/generated/triinoct_011_11036479a300844a.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/11036479a300844a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@12", "density": 0.74788706506276, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.19929, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/12.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.19929+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.19929, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@12", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.19929+", "metric_symbol": "s", "metric_value": 1.19929, "reference_text": "s = 1.19929+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/12.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.19929+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "1fa5264e0f579a94", "improvement": -0.0002647906752053508, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2204761718366964e-06, "max_pair_overlap_depth": -1.4073169272155184e-06, "metric_expression": "1.19955", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.1995547906752053, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.19929, "setup": "triinoct", "side": 1.1995547906752053, "solution_path": "data/solutions/generated/triinoct_012_1fa5264e0f579a94.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/1fa5264e0f579a94.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@13", "density": 0.7604201292225432, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.23759, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/13.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.23759+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.23759, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@13", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.23759+", "metric_symbol": "s", "metric_value": 1.23759, "reference_text": "s = 1.23759+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/13.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.23759+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "ebb5825b80b24749", "improvement": -0.0006144239243295324, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.763415979262496e-06, "max_pair_overlap_depth": -3.350137919300167e-06, "metric_expression": "1.23820", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.2382044239243295, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.23759, "setup": "triinoct", "side": 1.2382044239243295, "solution_path": "data/solutions/generated/triinoct_013_ebb5825b80b24749.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/ebb5825b80b24749.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@14", "density": 0.7704458772851622, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.27677, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/14.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.27677+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.27677, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@14", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.27677+", "metric_symbol": "s", "metric_value": 1.27677, "reference_text": "s = 1.27677+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "14.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/14.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.27677+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "e00a18106d2fcfee", "improvement": 0.00021236461691676034, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.593194459024069e-06, "max_pair_overlap_depth": -5.874056281496287e-06, "metric_expression": "1.27656", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.2765576353830832, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.27677, "setup": "triinoct", "side": 1.2765576353830832, "solution_path": "data/solutions/generated/triinoct_014_e00a18106d2fcfee.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/e00a18106d2fcfee.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@15", "density": 0.7924237027261557, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.30275, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/15.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.30275+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.30275, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@15", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.30275+", "metric_symbol": "s", "metric_value": 1.30275, "reference_text": "s = 1.30275+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/15.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.30275+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "e14eda962017d06d", "improvement": -0.0001598827367932376, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3032093708899356e-06, "max_pair_overlap_depth": -6.895788391969582e-06, "metric_expression": "1.30291", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.3029098827367933, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.30275, "setup": "triinoct", "side": 1.3029098827367933, "solution_path": "data/solutions/generated/triinoct_015_e14eda962017d06d.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/e14eda962017d06d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@16", "density": 0.7920450821484247, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.34584, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/16.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.34584+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.34584, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@16", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.34584+", "metric_symbol": "s", "metric_value": 1.34584, "reference_text": "s = 1.34584+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/16.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.34584+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "640352ab60961c58", "improvement": -0.00012112963758759143, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.464975954309231e-06, "max_pair_overlap_depth": -7.38266966116008e-07, "metric_expression": "1.34596", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.3459611296375875, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.34584, "setup": "triinoct", "side": 1.3459611296375875, "solution_path": "data/solutions/generated/triinoct_16_640352ab60961c58.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/640352ab60961c58.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@17", "density": 0.7893502976721624, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.38964, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/17.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.38964+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.38964, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@17", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.38964+", "metric_symbol": "s", "metric_value": 1.38964, "reference_text": "s = 1.38964+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/17.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.38964+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "6f00b933407c7c80", "improvement": -0.0001111742572472707, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.693112749768053e-07, "max_pair_overlap_depth": -2.384134229149737e-06, "metric_expression": "1.38975", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.3897511742572473, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.38964, "setup": "triinoct", "side": 1.3897511742572473, "solution_path": "data/solutions/generated/triinoct_017_6f00b933407c7c80.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/6f00b933407c7c80.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@18", "density": 0.8027011318687396, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.41836, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/18.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.41836+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.41836, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@18", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.41836+", "metric_symbol": "s", "metric_value": 1.41836, "reference_text": "s = 1.41836+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/18.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.41836+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "91a694d1aa76789c", "improvement": 0.0002602110634655208, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.835525154559248e-06, "max_pair_overlap_depth": -9.960192069113916e-06, "metric_expression": "1.41810", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.4180997889365345, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.41836, "setup": "triinoct", "side": 1.4180997889365345, "solution_path": "data/solutions/generated/triinoct_018_91a694d1aa76789c.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/91a694d1aa76789c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@19", "density": 0.7911354610751659, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.46749, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/19.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.46749+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.46749, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.46749+", "metric_symbol": "s", "metric_value": 1.46749, "reference_text": "s = 1.46749+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/19.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.46749+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "f92a5a5a3b54909a", "improvement": -8.00911599283527e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.983793930902579e-06, "max_pair_overlap_depth": -8.286875174401409e-06, "metric_expression": "1.46757", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.4675700911599283, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.46749, "setup": "triinoct", "side": 1.4675700911599283, "solution_path": "data/solutions/generated/triinoct_019_f92a5a5a3b54909a.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/f92a5a5a3b54909a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@20", "density": 0.7990175319982477, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.49832, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/20.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.49832+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.49832, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@20", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.49832+", "metric_symbol": "s", "metric_value": 1.49832, "reference_text": "s = 1.49832+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/20.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.49832+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "ead92a925f9f00a7", "improvement": 6.988050923584233e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.3276003687482804e-06, "max_pair_overlap_depth": -2.2158170135400113e-06, "metric_expression": "1.49825", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.4982501194907643, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.49832, "setup": "triinoct", "side": 1.4982501194907643, "solution_path": "data/solutions/generated/triinoct_020_ead92a925f9f00a7.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/ead92a925f9f00a7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@21", "density": 0.8078137663314585, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.52615, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/21.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.52615+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.52615, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@21", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.52615+", "metric_symbol": "s", "metric_value": 1.52615, "reference_text": "s = 1.52615+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/21.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.52615+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "e350f46688d32a68", "improvement": -0.0007180233722772211, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.407426670083604e-06, "max_pair_overlap_depth": -1.1097264517423433e-05, "metric_expression": "1.52687", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.5268680233722771, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.52615, "setup": "triinoct", "side": 1.5268680233722771, "solution_path": "data/solutions/generated/triinoct_021_e350f46688d32a68.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/e350f46688d32a68.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@22", "density": 0.8155579012833859, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.55545, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/22.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.55545+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.55545, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@22", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.55545+", "metric_symbol": "s", "metric_value": 1.55545, "reference_text": "s = 1.55545+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/22.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.55545+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "c1314ed0099ebdb6", "improvement": 8.823677085589843e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.5323101194107617e-06, "max_pair_overlap_depth": -6.490133103720375e-06, "metric_expression": "1.55536", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.555361763229144, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.55545, "setup": "triinoct", "side": 1.555361763229144, "solution_path": "data/solutions/generated/triinoct_022_c1314ed0099ebdb6.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/c1314ed0099ebdb6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@23", "density": 0.8210902170609379, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.58458, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/23.gif", "friedman_metric_expression": "1.58458+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.58458, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@23", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.58458+", "metric_symbol": "s", "metric_value": 1.58458, "reference_text": "s = 1.58458+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/23.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.58458+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "4ca1a825a22b1f04", "improvement": -0.0003714249913302492, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.321393677649287e-06, "max_pair_overlap_depth": -1.5960535921788477e-06, "metric_expression": "1.58495", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.5849514249913303, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.58458, "setup": "triinoct", "side": 1.5849514249913303, "solution_path": "data/solutions/generated/triinoct_023_4ca1a825a22b1f04.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/4ca1a825a22b1f04.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@24", "density": 0.8373304168984339, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.60261, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/24.gif", "friedman_metric_expression": "1.60261+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.60261, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@24", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.60261+", "metric_symbol": "s", "metric_value": 1.60261, "reference_text": "s = 1.60261+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.60261+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "e197b92ecac28558", "improvement": -0.0006526103809141315, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.085338835265612e-06, "max_pair_overlap_depth": -9.98840296584369e-06, "metric_expression": "1.60326", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.6032626103809142, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.60261, "setup": "triinoct", "side": 1.6032626103809142, "solution_path": "data/solutions/generated/triinoct_024_e197b92ecac28558.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/e197b92ecac28558.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@25", "density": 0.8354970198268096, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.63797, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/25.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.63797+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.63797, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@25", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.63797+", "metric_symbol": "s", "metric_value": 1.63797, "reference_text": "s = 1.63797+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/25.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.63797+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "e322401fc5bafe4d", "improvement": -0.00014742221399233202, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.350806641875647e-06, "max_pair_overlap_depth": -2.3762008580785476e-06, "metric_expression": "1.63812", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.6381174222139923, "n": 25, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.63797, "setup": "triinoct", "side": 1.6381174222139923, "solution_path": "data/solutions/generated/triinoct_025_e322401fc5bafe4d.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/e322401fc5bafe4d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@26", "density": 0.8292613760828756, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.67666, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/26.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.67666+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.67666, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@26", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.67666+", "metric_symbol": "s", "metric_value": 1.67666, "reference_text": "s = 1.67666+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/26.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.67666+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "7cb3797cd10b21d8", "improvement": -0.0001676725391090983, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.6314473196666756e-05, "max_pair_overlap_depth": -5.591511314406716e-06, "metric_expression": "1.67683", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.6768276725391091, "n": 26, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.67666, "setup": "triinoct", "side": 1.6768276725391091, "solution_path": "data/solutions/generated/triinoct_026_7cb3797cd10b21d8.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/7cb3797cd10b21d8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@27", "density": 0.8297818493323376, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.70882, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/27.gif", "friedman_metric_expression": "1.70882+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.70882, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@27", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.70882+", "metric_symbol": "s", "metric_value": 1.70882, "reference_text": "s = 1.70882+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/27.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.70882+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "c7748eb19b34ff2e", "improvement": 0.0005858720037632548, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.055699391789948e-06, "max_pair_overlap_depth": -3.877030372301249e-07, "metric_expression": "1.70823", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.7082341279962368, "n": 27, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.70882, "setup": "triinoct", "side": 1.7082341279962368, "solution_path": "data/solutions/generated/triinoct_27_c7748eb19b34ff2e.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/c7748eb19b34ff2e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@28", "density": 0.8299146316504411, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.73954, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/28.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.73954+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.73954, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@28", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.73954+", "metric_symbol": "s", "metric_value": 1.73954, "reference_text": "s = 1.73954+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/28.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.73954+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "26e8795d82a701d8", "improvement": 9.867973407984287e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2195571711171888e-06, "max_pair_overlap_depth": -8.650951147992636e-06, "metric_expression": "1.73944", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.7394413202659202, "n": 28, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.73954, "setup": "triinoct", "side": 1.7394413202659202, "solution_path": "data/solutions/generated/triinoct_028_26e8795d82a701d8.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/26e8795d82a701d8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@29", "density": 0.8439313801960897, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.75576, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/29.gif", "friedman_metric_expression": "1.75576+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.75576, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@29", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.75576+", "metric_symbol": "s", "metric_value": 1.75576, "reference_text": "s = 1.75576+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/29.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.75576+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "0575780ea85d68dd", "improvement": 0.00029203482208850495, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.530531415212805e-06, "max_pair_overlap_depth": -1.1528245769332202e-05, "metric_expression": "1.75547", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.7554679651779115, "n": 29, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.75576, "setup": "triinoct", "side": 1.7554679651779115, "solution_path": "data/solutions/generated/triinoct_29_0575780ea85d68dd.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/0575780ea85d68dd.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@30", "density": 0.8466211131481989, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.78101, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/30.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.78101+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.78101, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@30", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.78101+", "metric_symbol": "s", "metric_value": 1.78101, "reference_text": "s = 1.78101+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/30.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.78101+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "4c08385c68f67e77", "improvement": -0.0016296314900829945, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.472767326523421e-06, "max_pair_overlap_depth": -3.1822885246945987e-06, "metric_expression": "1.78264", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.782639631490083, "n": 30, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.78101, "setup": "triinoct", "side": 1.782639631490083, "solution_path": "data/solutions/generated/triinoct_030_4c08385c68f67e77.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/4c08385c68f67e77.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@1", "density": 0.4121951299103008, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 0.781, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/1.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": ".781+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.781, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triinpen@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": ".781+", "metric_symbol": "s", "metric_value": 0.781, "reference_text": "s = cos(42\u00b0) / cos(18\u00b0) | s = .781+ | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/1.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = cos(42\u00b0) / cos(18\u00b0) | s = .781+ | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "6d3af7533c544064", "improvement": -0.0004017935524769367, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.010333690326338e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.78140", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.781401793552477, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.781, "setup": "triinpen", "side": 0.781401793552477, "solution_path": "data/solutions/generated/triinpen_001_6d3af7533c544064.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/6d3af7533c544064.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@2", "density": 0.4392461428307515, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.07, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/2.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.070+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.07, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triinpen@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1.070+", "metric_symbol": "s", "metric_value": 1.07, "reference_text": "s = \u221a(6/(3+\u221a5)) | s = 1.070+ | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/2.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = \u221a(6/(3+\u221a5)) | s = 1.070+ | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "eebb278fed1959e5", "improvement": -0.0005004432401414238, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.540244142797655e-06, "max_pair_overlap_depth": -4.677606255020384e-06, "metric_expression": "1.07050", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0705004432401415, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.07, "setup": "triinpen", "side": 1.0705004432401415, "solution_path": "data/solutions/generated/triinpen_002_eebb278fed1959e5.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/eebb278fed1959e5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@3", "density": 0.5773621092377123, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2012", "friedman_display_metric_value": 1.143, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/3.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.143+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.143, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@3", "credit": "Maurizio Morandi", "date": "August 2012", "family_updated": "", "metric_expression": "1.143+", "metric_symbol": "s", "metric_value": 1.143, "reference_text": "s = 1.143+ | Found by Maurizio Morandi | in August 2012. |", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/3.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.143+ | Found by Maurizio Morandi | in August 2012. |", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "6ec3c588fb678646", "improvement": -0.0005688574140261249, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4403665141977852e-06, "max_pair_overlap_depth": -4.738354987265936e-06, "metric_expression": "1.14357", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.1435688574140261, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.143, "setup": "triinpen", "side": 1.1435688574140261, "solution_path": "data/solutions/generated/triinpen_003_6ec3c588fb678646.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/6ec3c588fb678646.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@4", "density": 0.6999227205319379, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2012", "friedman_display_metric_value": 1.199, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/4.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.199+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.199, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@4", "credit": "Maurizio Morandi", "date": "July 2012", "family_updated": "", "metric_expression": "1.199+", "metric_symbol": "s", "metric_value": 1.199, "reference_text": "s = 1.199+ | Found by Maurizio Morandi | in July 2012. |", "source_image": "4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/4.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.199+ | Found by Maurizio Morandi | in July 2012. |", "friedman_source_image": "4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "c45dd63fd5a8806b", "improvement": -0.0003081410566185827, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9487802360351315e-06, "max_pair_overlap_depth": -2.0674441409240796e-05, "metric_expression": "1.19931", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.1993081410566186, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.199, "setup": "triinpen", "side": 1.1993081410566186, "solution_path": "data/solutions/generated/triinpen_004_c45dd63fd5a8806b.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/c45dd63fd5a8806b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@5", "density": 0.818292233169356, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "March 2012", "friedman_display_metric_value": 1.24, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/5.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.240+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.24, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@5", "credit": "Erich Friedman", "date": "March 2012", "family_updated": "", "metric_expression": "1.240+", "metric_symbol": "s", "metric_value": 1.24, "reference_text": "s = 1 + 2sin(12\u00b0)/\u221a3 | s = 1.240+ | Found by Erich Friedman | in March 2012.", "source_image": "5.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/5.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1 + 2sin(12\u00b0)/\u221a3 | s = 1.240+ | Found by Erich Friedman | in March 2012.", "friedman_source_image": "5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "a99f063702c9d4e8", "improvement": -9.974870359874544e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.477405190997757e-06, "max_pair_overlap_depth": -1.386320747689962e-05, "metric_expression": "1.24010", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.2400997487035987, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.24, "setup": "triinpen", "side": 1.2400997487035987, "solution_path": "data/solutions/generated/triinpen_005_a99f063702c9d4e8.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/a99f063702c9d4e8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@6", "density": 0.7771309707429922, "friedman_analytical_or_proved": false, "friedman_credit": "Dominik Kamp", "friedman_date": "April 2026", "friedman_display_metric_value": 1.393, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/6.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.393+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.393, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@6", "credit": "Dominik Kamp", "date": "April 2026", "family_updated": "", "metric_expression": "1.393+", "metric_symbol": "s", "metric_value": 1.393, "reference_text": "s = 1.393+ | Found by Dominik Kamp | in April 2026.", "source_image": "6.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/6.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.393+ | Found by Dominik Kamp | in April 2026.", "friedman_source_image": "6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "8d12939187f41554", "improvement": -0.0009729568537997224, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4992545061493154e-06, "max_pair_overlap_depth": -6.033095825291185e-06, "metric_expression": "1.39397", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.3939729568537997, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.393, "setup": "triinpen", "side": 1.3939729568537997, "solution_path": "data/solutions/generated/triinpen_006_8d12939187f41554.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Dominik Kamp", "svg_path": "data/svg/8d12939187f41554.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@7", "density": 0.7037922543518549, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2012", "friedman_display_metric_value": 1.581, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/7.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.581+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.581, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@7", "credit": "David W. Cantrell", "date": "July 2012", "family_updated": "", "metric_expression": "1.581+", "metric_symbol": "s", "metric_value": 1.581, "reference_text": "s = 1.581+ | Found by David W. Cantrell | in July 2012.", "source_image": "7.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/7.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.581+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "d149692a95cde76c", "improvement": -0.0011680508685436575, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.5825119043122948e-06, "max_pair_overlap_depth": -1.774591125650038e-05, "metric_expression": "1.58217", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.5821680508685436, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.581, "setup": "triinpen", "side": 1.5821680508685436, "solution_path": "data/solutions/generated/triinpen_007_d149692a95cde76c.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/d149692a95cde76c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@8", "density": 0.7311911118691055, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2012", "friedman_display_metric_value": 1.659, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/8.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.659+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.659, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@8", "credit": "Maurizio Morandi", "date": "July 2012", "family_updated": "", "metric_expression": "1.659+", "metric_symbol": "s", "metric_value": 1.659, "reference_text": "s = 1.659+ | Found by Maurizio Morandi | in July 2012.", "source_image": "8.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/8.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.659+ | Found by Maurizio Morandi | in July 2012.", "friedman_source_image": "8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "2ac4629603f9ce00", "improvement": -0.0004163833859911481, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2708160845523109e-06, "max_pair_overlap_depth": -2.147963686768839e-05, "metric_expression": "1.65942", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.6594163833859912, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.659, "setup": "triinpen", "side": 1.6594163833859912, "solution_path": "data/solutions/generated/triinpen_008_2ac4629603f9ce00.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/2ac4629603f9ce00.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@9", "density": 0.7240666005522262, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2012", "friedman_display_metric_value": 1.767, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/9.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.767+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.767, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triinpen@9", "credit": "Maurizio Morandi", "date": "July 2012", "family_updated": "", "metric_expression": "1.767+", "metric_symbol": "s", "metric_value": 1.767, "reference_text": "s = 1.767+ | Found by Maurizio Morandi in July 2012. | Improved slightly by David W. Cantrell in August 2012.", "source_image": "9.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/9.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.767+ | Found by Maurizio Morandi in July 2012. | Improved slightly by David W. Cantrell in August 2012.", "friedman_source_image": "9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "72279a3b92ae69ca", "improvement": -0.0017148783247660226, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.918216101924126e-06, "max_pair_overlap_depth": -2.2857021414468548e-08, "metric_expression": "1.76871", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.768714878324766, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.767, "setup": "triinpen", "side": 1.768714878324766, "solution_path": "data/solutions/generated/triinpen_009_72279a3b92ae69ca.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/72279a3b92ae69ca.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@10", "density": 0.7626299188806616, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_display_metric_value": 1.815, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/10.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.815+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.815, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@10", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "1.815+", "metric_symbol": "s", "metric_value": 1.815, "reference_text": "s = 1.815+ | Found by Timo Berthold et al | in January 2026.", "source_image": "10.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/10.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.815+ | Found by Timo Berthold et al | in January 2026.", "friedman_source_image": "10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "f05f442bda1c650b", "improvement": -0.0016401662315850274, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.176875820916777e-06, "max_pair_overlap_depth": -3.546498963225009e-06, "metric_expression": "1.81664", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.816640166231585, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.815, "setup": "triinpen", "side": 1.816640166231585, "solution_path": "data/solutions/generated/triinpen_010_f05f442bda1c650b.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/f05f442bda1c650b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@11", "density": 0.7898687600512876, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_display_metric_value": 1.871, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/11.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.871+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.871, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@11", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "1.871+", "metric_symbol": "s", "metric_value": 1.871, "reference_text": "s = 1.871+ | Found by Timo Berthold et al | in January 2026.", "source_image": "11.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/11.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.871+ | Found by Timo Berthold et al | in January 2026.", "friedman_source_image": "11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "ca41afc6c9b25b21", "improvement": -0.0011675168118052692, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.191218876790302e-06, "max_pair_overlap_depth": -1.6407344776342425e-05, "metric_expression": "1.87217", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.8721675168118053, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.871, "setup": "triinpen", "side": 1.8721675168118053, "solution_path": "data/solutions/generated/triinpen_011_ca41afc6c9b25b21.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/ca41afc6c9b25b21.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@12", "density": 0.774567014021955, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 1.973, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/12.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.973+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.973, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@12", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "1.973+", "metric_symbol": "s", "metric_value": 1.973, "reference_text": "s = 1.973+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "12.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/12.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.973+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "bf7ddcc735398246", "improvement": -0.0016355699317964767, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.087403974087953e-06, "max_pair_overlap_depth": -1.3435552785878713e-05, "metric_expression": "1.97464", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.9746355699317966, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.973, "setup": "triinpen", "side": 1.9746355699317966, "solution_path": "data/solutions/generated/triinpen_012_bf7ddcc735398246.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/bf7ddcc735398246.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@13", "density": 0.8029051605923488, "friedman_analytical_or_proved": false, "friedman_credit": "Timo Berthold et al", "friedman_date": "January 2026", "friedman_display_metric_value": 2.017, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/13.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.017+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.017, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@13", "credit": "Timo Berthold et al", "date": "January 2026", "family_updated": "", "metric_expression": "2.017+", "metric_symbol": "s", "metric_value": 2.017, "reference_text": "s = 2.017+ | Found by Timo Berthold et al | in January 2026.", "source_image": "13.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/13.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.017+ | Found by Timo Berthold et al | in January 2026.", "friedman_source_image": "13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "ff07ea08219353cb", "improvement": -0.0016702531518792973, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.615779077054135e-07, "max_pair_overlap_depth": -4.3930654851198625e-05, "metric_expression": "2.01867", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.018670253151879, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.017, "setup": "triinpen", "side": 2.018670253151879, "solution_path": "data/solutions/generated/triinpen_013_ff07ea08219353cb.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Timo Berthold et al", "svg_path": "data/svg/ff07ea08219353cb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@14", "density": 0.8070990172681682, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 2.088, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/14.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.088+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.088, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@14", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "2.088+", "metric_symbol": "s", "metric_value": 2.088, "reference_text": "s = 2.088+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "14.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/14.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.088+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "bc900c323229ee0c", "improvement": -0.0014233339778941811, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.2035527022044616e-06, "max_pair_overlap_depth": -3.9869300561434784e-05, "metric_expression": "2.08942", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0894233339778943, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.088, "setup": "triinpen", "side": 2.0894233339778943, "solution_path": "data/solutions/generated/triinpen_014_bc900c323229ee0c.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/bc900c323229ee0c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@15", "density": 0.8370246386712876, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.123, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/15.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.123+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.123, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@15", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.123+", "metric_symbol": "s", "metric_value": 2.123, "reference_text": "s = 2.123+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "15.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/15.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.123+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "39b13eec51bf2ea6", "improvement": -0.000744857935933041, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.959192129393714e-06, "max_pair_overlap_depth": -3.112528873211451e-05, "metric_expression": "2.12374", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.1237448579359333, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.123, "setup": "triinpen", "side": 2.1237448579359333, "solution_path": "data/solutions/generated/triinpen_015_39b13eec51bf2ea6.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/39b13eec51bf2ea6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@16", "density": 0.8497807683719915, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.17598, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/16.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.17598+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.17598, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@16", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.17598+", "metric_symbol": "s", "metric_value": 2.17598, "reference_text": "s = 2.17598+ | Found by Ian Watson | in April 2026.", "source_image": "16.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/16.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.17598+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "852225bc33edeebe", "improvement": -0.0008893975034314217, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.337598971955443e-06, "max_pair_overlap_depth": -3.396060024770525e-05, "metric_expression": "2.17687", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.1768693975034314, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.17598, "setup": "triinpen", "side": 2.1768693975034314, "solution_path": "data/solutions/generated/triinpen_016_852225bc33edeebe.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/852225bc33edeebe.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@17", "density": 0.8546812093159708, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.23658, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/17.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.23658+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.23658, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@17", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.23658+", "metric_symbol": "s", "metric_value": 2.23658, "reference_text": "s = 2.23658+ | Found by Ian Watson | in April 2026.", "source_image": "17.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/17.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.23658+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "a8618eee7fdaba2a", "improvement": -0.0008435999825509022, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.39992551681681e-07, "max_pair_overlap_depth": -1.7412872881594765e-05, "metric_expression": "2.23742", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.237423599982551, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.23658, "setup": "triinpen", "side": 2.237423599982551, "solution_path": "data/solutions/generated/triinpen_017_a8618eee7fdaba2a.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/a8618eee7fdaba2a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@18", "density": 0.8594655455888001, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.29382, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/18.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.29382+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.29382, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@18", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.29382+", "metric_symbol": "s", "metric_value": 2.29382, "reference_text": "s = 2.29382+ | Found by Ian Watson | in April 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/18.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.29382+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "6bf4f9b0915d39ee", "improvement": -0.0020529370652000445, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4774387061990001e-05, "max_pair_overlap_depth": -2.9541451285197695e-08, "metric_expression": "2.29587", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.2958729370652002, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.29382, "setup": "triinpen", "side": 2.2958729370652002, "solution_path": "data/solutions/generated/triinpen_018_6bf4f9b0915d39ee.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/6bf4f9b0915d39ee.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@19", "density": 0.8695364674141102, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.344, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "friedman_metric_expression": "2.344+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.344, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.344+", "metric_symbol": "s", "metric_value": 2.344, "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "16349db1062e3f6e", "improvement": -0.0010857736775151672, "max_boundary_excess": -4.742170658284962e-06, "max_pair_overlap_depth": -3.982018692783029e-06, "metric_expression": "2.34509", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.345085773677515, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 2.344, "setup": "triinpen", "side": 2.345085773677515, "solution_path": "data/solutions/generated/triinpen_19_16349db1062e3f6e.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T17:16:20+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/16349db1062e3f6e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@19", "density": 0.8682311373154191, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.344, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "friedman_metric_expression": "2.344+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.344, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.344+", "metric_symbol": "s", "metric_value": 2.344, "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "7110ea9122a5788e", "improvement": -0.002847954985398804, "max_boundary_excess": -1.7569722225895958e-06, "max_pair_overlap_depth": -1.2055081872186513e-06, "metric_expression": "2.34685", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.3468479549853987, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 2.344, "setup": "triinpen", "side": 2.3468479549853987, "solution_path": "data/solutions/generated/triinpen_19_7110ea9122a5788e.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T16:24:14+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/7110ea9122a5788e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@19", "density": 0.8685173440819363, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.344, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "friedman_metric_expression": "2.344+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.344, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.344+", "metric_symbol": "s", "metric_value": 2.344, "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "875caebde6570989", "improvement": -0.0024612389835776405, "max_boundary_excess": -1.6095450684584371e-06, "max_pair_overlap_depth": -1.2689748558725178e-05, "metric_expression": "2.34646", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.3464612389835775, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 2.344, "setup": "triinpen", "side": 2.3464612389835775, "solution_path": "data/solutions/generated/triinpen_19_875caebde6570989.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T17:13:54+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/875caebde6570989.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@19", "density": 0.8695579661683754, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.344, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "friedman_metric_expression": "2.344+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.344, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.344+", "metric_symbol": "s", "metric_value": 2.344, "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "e25d367759fc397e", "improvement": -0.0010567838134889485, "max_boundary_excess": -1.7918571290641098e-06, "max_pair_overlap_depth": -4.335928559529023e-07, "metric_expression": "2.34506", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.345056783813489, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 2.344, "setup": "triinpen", "side": 2.345056783813489, "solution_path": "data/solutions/generated/triinpen_19_e25d367759fc397e.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T17:17:49+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/e25d367759fc397e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@19", "density": 0.868021512388566, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.344, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.344+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.344, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.344+", "metric_symbol": "s", "metric_value": 2.344, "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "eaa1430599d74148", "improvement": -0.003131316702724707, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9139572150349214e-06, "max_pair_overlap_depth": -1.0705368373109536e-05, "metric_expression": "2.34713", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.3471313167027246, "n": 19, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "record_type": "verified", "reference_side": 2.344, "setup": "triinpen", "side": 2.3471313167027246, "solution_path": "data/solutions/generated/triinpen_19_eaa1430599d74148.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/eaa1430599d74148.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@20", "density": 0.8487102106795418, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.4335, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/20.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.43350+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.4335, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@20", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.43350+", "metric_symbol": "s", "metric_value": 2.4335, "reference_text": "s = 2.43350+ | Found by Ian Watson | in April 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/20.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.43350+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "760faebc4d0b131b", "improvement": -0.001848490502489586, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.176183787084704e-07, "max_pair_overlap_depth": -8.807499014995557e-06, "metric_expression": "2.43535", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.4353484905024896, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.4335, "setup": "triinpen", "side": 2.4353484905024896, "solution_path": "data/solutions/generated/triinpen_020_760faebc4d0b131b.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/760faebc4d0b131b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@21", "density": 0.8589998748063701, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.479, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/21.gif", "friedman_metric_expression": "2.479+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.479, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@21", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.479+", "metric_symbol": "s", "metric_value": 2.479, "reference_text": "s = 2.479+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/21.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.479+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "115c20fad199fe9d", "improvement": -0.0014982727861765355, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.811024693767028e-06, "max_pair_overlap_depth": -2.8209410938284663e-06, "metric_expression": "2.48050", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.4804982727861766, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.479, "setup": "triinpen", "side": 2.4804982727861766, "solution_path": "data/solutions/generated/triinpen_021_115c20fad199fe9d.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/115c20fad199fe9d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@22", "density": 0.8389716031782235, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.5674, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/22.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.56740+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.5674, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@22", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.56740+", "metric_symbol": "s", "metric_value": 2.5674, "reference_text": "s = 2.56740+ | Found by Ian Watson | in April 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/22.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.56740+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "929a1aedb3cfabb6", "improvement": -0.0015966714037367602, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.137059676377362e-07, "max_pair_overlap_depth": -8.172541590134585e-06, "metric_expression": "2.56900", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.568996671403737, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.5674, "setup": "triinpen", "side": 2.568996671403737, "solution_path": "data/solutions/generated/triinpen_022_929a1aedb3cfabb6.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/929a1aedb3cfabb6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@23", "density": 0.8432972889244729, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.61831, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/23.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.61831+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.61831, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@23", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.61831+", "metric_symbol": "s", "metric_value": 2.61831, "reference_text": "s = 2.61831+ | Found by Ian Watson | in April 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/23.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.61831+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "c0d3905a26f7ef33", "improvement": -0.001678576890473682, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.992582537021139e-06, "max_pair_overlap_depth": -4.362218652298466e-06, "metric_expression": "2.61999", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.619988576890474, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.61831, "setup": "triinpen", "side": 2.619988576890474, "solution_path": "data/solutions/generated/triinpen_023_c0d3905a26f7ef33.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/c0d3905a26f7ef33.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@24", "density": 0.8488309418600493, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.66641, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/24.gif", "friedman_metric_expression": "2.66641+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.66641, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@24", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.66641+", "metric_symbol": "s", "metric_value": 2.66641, "reference_text": "s = 2.66641+ | Found by Ian Watson | in April 2026.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.66641+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "7bc3466b163ec849", "improvement": -0.0011908775198370414, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.421732660736982e-06, "max_pair_overlap_depth": -3.3708625798434255e-05, "metric_expression": "2.66760", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.667600877519837, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.66641, "setup": "triinpen", "side": 2.667600877519837, "solution_path": "data/solutions/generated/triinpen_24_7bc3466b163ec849.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/7bc3466b163ec849.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@25", "density": 0.8491607934363294, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.72, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/25.gif", "friedman_metric_expression": "2.720+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.72, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@25", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.720+", "metric_symbol": "s", "metric_value": 2.72, "reference_text": "s = 2.720+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/25.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.720+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "0f20f89eba855e21", "improvement": -0.0020799025832594076, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.997044244500036e-06, "max_pair_overlap_depth": -8.121085018242269e-06, "metric_expression": "2.72208", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.7220799025832596, "n": 25, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.72, "setup": "triinpen", "side": 2.7220799025832596, "solution_path": "data/solutions/generated/triinpen_25_0f20f89eba855e21.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T13:47:12+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/0f20f89eba855e21.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@26", "density": 0.8520841245254238, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.771, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/26.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.771+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.771, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@26", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.771+", "metric_symbol": "s", "metric_value": 2.771, "reference_text": "s = 2.771+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/26.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.771+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "f991467944e6e634", "improvement": -0.00022168609627781777, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2986540650513047e-06, "max_pair_overlap_depth": -8.90414151222263e-06, "metric_expression": "2.77122", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.7712216860962777, "n": 26, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.771, "setup": "triinpen", "side": 2.7712216860962777, "solution_path": "data/solutions/generated/triinpen_026_f991467944e6e634.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/f991467944e6e634.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@27", "density": 0.8551322064876743, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.81761, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/27.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.81761+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.81761, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@27", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.81761+", "metric_symbol": "s", "metric_value": 2.81761, "reference_text": "s = 2.81761+ | Found by Ian Watson | in April 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/27.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.81761+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "d6f1d3073209f163", "improvement": -0.0013640775641627911, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.642891580892597e-06, "max_pair_overlap_depth": -2.2253597504739986e-06, "metric_expression": "2.81897", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.818974077564163, "n": 27, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.81761, "setup": "triinpen", "side": 2.818974077564163, "solution_path": "data/solutions/generated/triinpen_027_d6f1d3073209f163.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/d6f1d3073209f163.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@28", "density": 0.8558072548880046, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_display_metric_value": 2.868, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/28.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.868+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.868, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@28", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "", "metric_expression": "2.868+", "metric_symbol": "s", "metric_value": 2.868, "reference_text": "s = 2.868+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/28.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.868+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "2caa877f5aa08139", "improvement": -0.0015702794780372287, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.305293369328324e-06, "max_pair_overlap_depth": -1.9072024115107666e-05, "metric_expression": "2.86957", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.869570279478037, "n": 28, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.868, "setup": "triinpen", "side": 2.869570279478037, "solution_path": "data/solutions/generated/triinpen_028_2caa877f5aa08139.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T03:19:00+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/2caa877f5aa08139.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@29", "density": 0.8642558401713053, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 2.903, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/29.gif", "friedman_metric_expression": "2.903+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.903, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@29", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "2.903+", "metric_symbol": "s", "metric_value": 2.903, "reference_text": "s = 2.903+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/29.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.903+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "9730db96941e5b52", "improvement": -0.003053928319848076, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.800701997238751e-06, "max_pair_overlap_depth": -5.0014115865471e-06, "metric_expression": "2.90605", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.906053928319848, "n": 29, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "record_type": "verified", "reference_side": 2.903, "setup": "triinpen", "side": 2.906053928319848, "solution_path": "data/solutions/generated/triinpen_29_9730db96941e5b52.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T07:13:53+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/9730db96941e5b52.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@29", "density": 0.8648910353285495, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 2.903, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/29.gif", "friedman_metric_expression": "2.903+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.903, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@29", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "2.903+", "metric_symbol": "s", "metric_value": 2.903, "reference_text": "s = 2.903+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/29.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.903+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "9da834ae740d1c15", "improvement": -0.0019865970893109264, "max_boundary_excess": -1.1757076758929644e-06, "max_pair_overlap_depth": -9.047152447871909e-06, "metric_expression": "2.90499", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.904986597089311, "n": 29, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 2.903, "setup": "triinpen", "side": 2.904986597089311, "solution_path": "data/solutions/generated/triinpen_29_9da834ae740d1c15.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T17:13:54+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/9da834ae740d1c15.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@30", "density": 0.8662355090431414, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 2.952, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/30.gif", "friedman_metric_expression": "2.952+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.952, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@30", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "2.952+", "metric_symbol": "s", "metric_value": 2.952, "reference_text": "s = 2.952+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/30.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.952+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "29e4e0e684891d8a", "improvement": -0.00035425771249730786, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.990812967166742e-06, "max_pair_overlap_depth": -2.800943013125945e-05, "metric_expression": "2.95235", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.9523542577124973, "n": 30, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.952, "setup": "triinpen", "side": 2.9523542577124973, "solution_path": "data/solutions/generated/triinpen_30_29e4e0e684891d8a.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/29e4e0e684891d8a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@31", "density": 0.8713888671331285, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 2.992, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/31.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.992+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.992, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "2.992+", "metric_symbol": "s", "metric_value": 2.992, "reference_text": "s = 2.992+ | Found by Emerson Connelly | in April 2026.", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/31.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.992+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "44a0bb3f581e92e2", "improvement": -0.0002692889761504169, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.7795814276238894e-06, "max_pair_overlap_depth": -1.3596177029562284e-05, "metric_expression": "2.99227", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.9922692889761504, "n": 31, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.992, "setup": "triinpen", "side": 2.9922692889761504, "solution_path": "data/solutions/generated/triinpen_031_44a0bb3f581e92e2.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/44a0bb3f581e92e2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@32", "density": 0.8781198099192385, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 3.029, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/32.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.029+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.029, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.029+", "metric_symbol": "s", "metric_value": 3.029, "reference_text": "s = 3.029+ | Found by Emerson Connelly | in April 2026.", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/32.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.029+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "310badf403ba4fce", "improvement": 0.0005254132016050406, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.877563686504985e-07, "max_pair_overlap_depth": -2.5172545809359903e-05, "metric_expression": "3.02847", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.028474586798395, "n": 32, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.029, "setup": "triinpen", "side": 3.028474586798395, "solution_path": "data/solutions/generated/triinpen_032_310badf403ba4fce.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/310badf403ba4fce.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@33", "density": 0.8767362450469284, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 3.078, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/33.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.078+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.078, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.078+", "metric_symbol": "s", "metric_value": 3.078, "reference_text": "s = 3.078+ | Found by Emerson Connelly | in April 2026.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/33.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.078+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "2cf1b1f38810795d", "improvement": 0.00014382895343612034, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.9579559668821387e-06, "max_pair_overlap_depth": -6.152141676318834e-06, "metric_expression": "3.07786", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0778561710465637, "n": 33, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.078, "setup": "triinpen", "side": 3.0778561710465637, "solution_path": "data/solutions/generated/triinpen_033_2cf1b1f38810795d.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/2cf1b1f38810795d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@34", "density": 0.8808233124500154, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 3.114, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/34.gif", "friedman_metric_expression": "3.114+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.114, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.114+", "metric_symbol": "s", "metric_value": 3.114, "reference_text": "s = 3.114+ | Found by Emerson Connelly | in April 2026.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/34.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.114+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "6034a27a1d11d106", "improvement": -0.0028857983751366945, "max_boundary_excess": -1.228515372563353e-06, "max_pair_overlap_depth": -9.40092923262803e-06, "metric_expression": "3.11689", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.1168857983751366, "n": 34, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 3.114, "setup": "triinpen", "side": 3.1168857983751366, "solution_path": "data/solutions/generated/triinpen_34_6034a27a1d11d106.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T17:13:54+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/6034a27a1d11d106.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@34", "density": 0.8805067280135348, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 3.114, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/34.gif", "friedman_metric_expression": "3.114+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.114, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.114+", "metric_symbol": "s", "metric_value": 3.114, "reference_text": "s = 3.114+ | Found by Emerson Connelly | in April 2026.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/34.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.114+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "faff9872314d8b1a", "improvement": -0.003446083050953952, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4825467113644516e-07, "max_pair_overlap_depth": -8.773672566686486e-06, "metric_expression": "3.11745", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.117446083050954, "n": 34, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "record_type": "verified", "reference_side": 3.114, "setup": "triinpen", "side": 3.117446083050954, "solution_path": "data/solutions/generated/triinpen_34_faff9872314d8b1a.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T14:34:18+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/faff9872314d8b1a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@35", "density": 0.8875886550862264, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 3.15, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/35.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.150+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.15, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@35", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.150+", "metric_symbol": "s", "metric_value": 3.15, "reference_text": "s = 3.150+ | Found by Emerson Connelly | in April 2026.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/35.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.150+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "8fe5da1df972c0b3", "improvement": -0.0003150122852528803, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4152162741179605e-06, "max_pair_overlap_depth": -9.46789992128938e-06, "metric_expression": "3.15032", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.150315012285253, "n": 35, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.15, "setup": "triinpen", "side": 3.150315012285253, "solution_path": "data/solutions/generated/triinpen_035_8fe5da1df972c0b3.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/8fe5da1df972c0b3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@36", "density": 0.8985572699958073, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 3.177, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/36.gif", "friedman_metric_expression": "3.177+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.177, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@36", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.177+", "metric_symbol": "s", "metric_value": 3.177, "reference_text": "s = 3.177+ | Found by Emerson Connelly | in April 2026.", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/36.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.177+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "5183a03ffc16bcf9", "improvement": 0.0015578799748001693, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.498547309348074e-07, "max_pair_overlap_depth": -2.3029919912209706e-06, "metric_expression": "3.17544", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.1754421200252, "n": 36, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.177, "setup": "triinpen", "side": 3.1754421200252, "solution_path": "data/solutions/record_hunt/triinpen_36_5183a03ffc16bcf9.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/5183a03ffc16bcf9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@37", "density": 0.9016389565813171, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_display_metric_value": 3.21529, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/37.gif", "friedman_metric_expression": "3.21529+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.21529, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@37", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "3.21529+", "metric_symbol": "s", "metric_value": 3.21529, "reference_text": "s = 3.21529+ | Found by Nathan Roll | in April 2026.", "source_image": "37.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/37.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.21529+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "08996b45ff04652c", "improvement": 0.0015527990845791706, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.641732962649716e-07, "max_pair_overlap_depth": -1.845774424413804e-07, "metric_expression": "3.21374", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.213737200915421, "n": 37, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.21529, "setup": "triinpen", "side": 3.213737200915421, "solution_path": "data/solutions/record_hunt/triinpen_37_08996b45ff04652c.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/08996b45ff04652c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@38", "density": 0.9010687984988149, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_display_metric_value": 3.25877, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/38.gif", "friedman_metric_expression": "3.25877+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.25877, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@38", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "3.25877+", "metric_symbol": "s", "metric_value": 3.25877, "reference_text": "s = 3.25877+ | Found by Nathan Roll | in April 2026.", "source_image": "38.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/38.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.25877+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "cca381f54ee9b299", "improvement": 0.0008632130758914336, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.177049878621715e-07, "max_pair_overlap_depth": -8.114145322313249e-07, "metric_expression": "3.25791", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.2579067869241087, "n": 38, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.25877, "setup": "triinpen", "side": 3.2579067869241087, "solution_path": "data/solutions/record_hunt/triinpen_38_cca381f54ee9b299.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/cca381f54ee9b299.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@39", "density": 0.9025101556269666, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 3.295, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/39.gif", "friedman_metric_expression": "3.295+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.295, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.295+", "metric_symbol": "s", "metric_value": 3.295, "reference_text": "s = 3.295+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/39.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.295+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "67a6bbf24108966a", "improvement": -0.002859023967915597, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9740347935670834e-06, "max_pair_overlap_depth": -1.0007850107629501e-05, "metric_expression": "3.29786", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.2978590239679155, "n": 39, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.295, "setup": "triinpen", "side": 3.2978590239679155, "solution_path": "data/solutions/generated/triinpen_039_67a6bbf24108966a.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/67a6bbf24108966a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@40", "density": 0.9091859235070038, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_display_metric_value": 3.32786, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/40.gif", "friedman_metric_expression": "3.32786+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.32786, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@40", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "3.32786+", "metric_symbol": "s", "metric_value": 3.32786, "reference_text": "s = 3.32786+ | Found by Nathan Roll | in April 2026.", "source_image": "40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/40.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.32786+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "032ceee4e789eff6", "improvement": 0.0002725631872593226, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4037127820689358e-07, "max_pair_overlap_depth": -1.074379339049969e-06, "metric_expression": "3.32759", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.3275874368127405, "n": 40, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.32786, "setup": "triinpen", "side": 3.3275874368127405, "solution_path": "data/solutions/record_hunt/triinpen_40_032ceee4e789eff6.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/032ceee4e789eff6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@1", "density": 0.4640965865243202, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 0.965, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t1.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(\u221a2+\u221a6)/4 = .965+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.9659258262890683, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "(\u221a2+\u221a6)/4 = .965+", "metric_symbol": "s", "metric_value": 0.965, "reference_text": "s = (\u221a2+\u221a6)/4 = .965+ | Trivial.", "source_image": "t1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t1.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = (\u221a2+\u221a6)/4 = .965+ | Trivial.", "friedman_source_image": "t1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "d0da9c9aae58c37e", "improvement": -5.233021067585497e-06, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.031269735994051e-07, "max_pair_overlap_depth": 0.0, "metric_expression": "0.96593", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 0.9659310593101359, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 0.9659258262890683, "setup": "triinsqu", "side": 0.9659310593101359, "solution_path": "data/solutions/generated/triinsqu_001_d0da9c9aae58c37e.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/d0da9c9aae58c37e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@2", "density": 0.5773345801938596, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.224, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t2.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a6/2 = 1.224+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.224744871391589, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "\u221a6/2 = 1.224+", "metric_symbol": "s", "metric_value": 1.224, "reference_text": "s = \u221a6/2 = 1.224+ | Trivial.", "source_image": "t2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t2.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = \u221a6/2 = 1.224+ | Trivial.", "friedman_source_image": "t2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "536a8bec14614050", "improvement": -1.6641032099640185e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.5296142902332335e-06, "max_pair_overlap_depth": -8.602274652714007e-06, "metric_expression": "1.22476", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.2247615124236886, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.224744871391589, "setup": "triinsqu", "side": 1.2247615124236886, "solution_path": "data/solutions/generated/triinsqu_002_536a8bec14614050.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/536a8bec14614050.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@3", "density": 0.594304450868366, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1996", "friedman_display_metric_value": 1.478, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t3.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a3/2+\u221a6/4 = 1.478+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.478397839480233, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@3", "credit": "Erich Friedman", "date": "1996", "family_updated": "", "metric_expression": "\u221a3/2+\u221a6/4 = 1.478+", "metric_symbol": "s", "metric_value": 1.478, "reference_text": "s = \u221a3/2+\u221a6/4 = 1.478+ | Found by Erich Friedman | in 1996.", "source_image": "t3.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t3.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = \u221a3/2+\u221a6/4 = 1.478+ | Found by Erich Friedman | in 1996.", "friedman_source_image": "t3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "85d51e7a9d3c3790", "improvement": -5.152175446831997e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.5025974997417175e-07, "max_pair_overlap_depth": -2.9708917167997617e-05, "metric_expression": "1.47845", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.4784493612347014, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.478397839480233, "setup": "triinsqu", "side": 1.4784493612347014, "solution_path": "data/solutions/generated/triinsqu_003_85d51e7a9d3c3790.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/85d51e7a9d3c3790.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@4", "density": 0.6961073829345906, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1996", "friedman_display_metric_value": 1.577, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t4.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1+1/\u221a3 = 1.577+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.5773502691896257, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@4", "credit": "Erich Friedman", "date": "1996", "family_updated": "", "metric_expression": "1+1/\u221a3 = 1.577+", "metric_symbol": "s", "metric_value": 1.577, "reference_text": "s = 1+1/\u221a3 = 1.577+ | Found by Erich Friedman | in 1996.", "source_image": "t4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t4.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 1+1/\u221a3 = 1.577+ | Found by Erich Friedman | in 1996.", "friedman_source_image": "t4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "10004832454b0f3c", "improvement": -5.102829618142124e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.301219061208287e-07, "max_pair_overlap_depth": -2.378752457826705e-05, "metric_expression": "1.57740", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.5774012974858072, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.5773502691896257, "setup": "triinsqu", "side": 1.5774012974858072, "solution_path": "data/solutions/generated/triinsqu_004_10004832454b0f3c.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/10004832454b0f3c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@5", "density": 0.6658433228069607, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1996", "friedman_display_metric_value": 1.803, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t5.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.803+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.803, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@5", "credit": "Erich Friedman", "date": "1996", "family_updated": "", "metric_expression": "1.803+", "metric_symbol": "s", "metric_value": 1.803, "reference_text": "s = 1.803+ | Found by Erich Friedman | in 1996.", "source_image": "t5.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t5.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 1.803+ | Found by Erich Friedman | in 1996.", "friedman_source_image": "t5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "f41eeaee150f1c15", "improvement": -0.0002224086857132157, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.6751531743821273e-06, "max_pair_overlap_depth": -2.226142234541817e-05, "metric_expression": "1.80322", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.8032224086857132, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.803, "setup": "triinsqu", "side": 1.8032224086857132, "solution_path": "data/solutions/generated/triinsqu_005_f41eeaee150f1c15.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/f41eeaee150f1c15.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@6", "density": 0.7181966221398873, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1996", "friedman_display_metric_value": 1.901, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t6.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "9/2\u20133\u221a3/2 = 1.901+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.901923788646684, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@6", "credit": "Erich Friedman", "date": "1996", "family_updated": "", "metric_expression": "9/2\u20133\u221a3/2 = 1.901+", "metric_symbol": "s", "metric_value": 1.901, "reference_text": "s = 9/2\u20133\u221a3/2 = 1.901+ | Found by Erich Friedman | in 1996.", "source_image": "t6.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t6.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 9/2\u20133\u221a3/2 = 1.901+ | Found by Erich Friedman | in 1996.", "friedman_source_image": "t6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "47de8ba8f0c9310c", "improvement": -4.884617092226762e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.131503356462894e-07, "max_pair_overlap_depth": -1.0226066655058541e-06, "metric_expression": "1.90197", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.9019726348176063, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.901923788646684, "setup": "triinsqu", "side": 1.9019726348176063, "solution_path": "data/solutions/generated/triinsqu_006_47de8ba8f0c9310c.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/47de8ba8f0c9310c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@7", "density": 0.7576992844833931, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1996", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t7.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@7", "credit": "Erich Friedman", "date": "1996", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Found by Erich Friedman | in 1996.", "source_image": "t7.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t7.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2 | Found by Erich Friedman | in 1996.", "friedman_source_image": "t7.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "d4eecc11473f7bf7", "improvement": -9.626783869354227e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -7.867700488247924e-07, "max_pair_overlap_depth": -1.9950288099523666e-05, "metric_expression": "2.00010", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0000962678386935, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "triinsqu", "side": 2.0000962678386935, "solution_path": "data/solutions/generated/triinsqu_007_d4eecc11473f7bf7.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/d4eecc11473f7bf7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@8", "density": 0.7868902975296777, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1996", "friedman_display_metric_value": 2.098, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t8.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3\u221a3/2\u20131/2 = 2.098+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.098076211353316, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@8", "credit": "Erich Friedman", "date": "1996", "family_updated": "", "metric_expression": "3\u221a3/2\u20131/2 = 2.098+", "metric_symbol": "s", "metric_value": 2.098, "reference_text": "s = 3\u221a3/2\u20131/2 = 2.098+ | Found by Erich Friedman | in 1996.", "source_image": "t8.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t8.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3\u221a3/2\u20131/2 = 2.098+ | Found by Erich Friedman | in 1996.", "friedman_source_image": "t8.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "bd28b88a6ba9b99d", "improvement": -8.191924448874843e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0169734543243664e-06, "max_pair_overlap_depth": -2.636538231393093e-05, "metric_expression": "2.09816", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0981581305978048, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.098076211353316, "setup": "triinsqu", "side": 2.0981581305978048, "solution_path": "data/solutions/generated/triinsqu_008_bd28b88a6ba9b99d.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/bd28b88a6ba9b99d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@9", "density": 0.7446998211864622, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2008", "friedman_display_metric_value": 2.287, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t9.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.287+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.287, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@9", "credit": "Maurizio Morandi", "date": "July 2008", "family_updated": "", "metric_expression": "2.287+", "metric_symbol": "s", "metric_value": 2.287, "reference_text": "s = 2.287+ | Found by Maurizio Morandi | in July 2008.", "source_image": "t9.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t9.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.287+ | Found by Maurizio Morandi | in July 2008.", "friedman_source_image": "t9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "458e49fec5e5573c", "improvement": -0.0006045303821253789, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.745466993473377e-07, "max_pair_overlap_depth": -5.124657140087585e-06, "metric_expression": "2.28760", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.2876045303821253, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.287, "setup": "triinsqu", "side": 2.2876045303821253, "solution_path": "data/solutions/generated/triinsqu_009_458e49fec5e5573c.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/458e49fec5e5573c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@10", "density": 0.7662234065167978, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_display_metric_value": 2.377, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t10.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.377+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.377, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@10", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "2.377+", "metric_symbol": "s", "metric_value": 2.377, "reference_text": "s = 2.377+ | Found by David W. Cantrell | in July 2002.", "source_image": "t10.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t10.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.377+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "t10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "5b0eaf84f54fe48c", "improvement": -0.00023770927049060475, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.324926068512563e-07, "max_pair_overlap_depth": -1.1896205976635876e-05, "metric_expression": "2.37724", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.3772377092704904, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.377, "setup": "triinsqu", "side": 2.3772377092704904, "solution_path": "data/solutions/generated/triinsqu_10_5b0eaf84f54fe48c.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/5b0eaf84f54fe48c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@11", "density": 0.7671858882860172, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2008", "friedman_display_metric_value": 2.49, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t11.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.490+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.49, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@11", "credit": "Maurizio Morandi", "date": "June 2008", "family_updated": "", "metric_expression": "2.490+", "metric_symbol": "s", "metric_value": 2.49, "reference_text": "s = 2.490+ | Found by Maurizio Morandi | in June 2008.", "source_image": "t11.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t11.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.490+ | Found by Maurizio Morandi | in June 2008.", "friedman_source_image": "t11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "b95fbc7e7009bb63", "improvement": -0.0017034740442234408, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.171896607131735e-07, "max_pair_overlap_depth": -3.917476745979309e-05, "metric_expression": "2.49170", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.4917034740442237, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.49, "setup": "triinsqu", "side": 2.4917034740442237, "solution_path": "data/solutions/generated/triinsqu_011_b95fbc7e7009bb63.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/b95fbc7e7009bb63.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@12", "density": 0.792908624011719, "friedman_analytical_or_proved": false, "friedman_credit": "Dominik Kamp", "friedman_date": "April 2026", "friedman_display_metric_value": 2.558, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t12.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.558+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.558, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@12", "credit": "Dominik Kamp", "date": "April 2026", "family_updated": "", "metric_expression": "2.558+", "metric_symbol": "s", "metric_value": 2.558, "reference_text": "s = 2.558+ | Found by Dominik Kamp | in April 2026.", "source_image": "t12.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t12.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.558+ | Found by Dominik Kamp | in April 2026.", "friedman_source_image": "t12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "297283972e34795d", "improvement": -0.0019375473066665094, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.5442542765183254e-06, "max_pair_overlap_depth": -1.2119755173123359e-05, "metric_expression": "2.55994", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.5599375473066663, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.558, "setup": "triinsqu", "side": 2.5599375473066663, "solution_path": "data/solutions/generated/triinsqu_012_297283972e34795d.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Dominik Kamp", "svg_path": "data/svg/297283972e34795d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@13", "density": 0.8355745862678572, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_display_metric_value": 2.595, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t13.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.595+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.595, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@13", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "2.595+", "metric_symbol": "s", "metric_value": 2.595, "reference_text": "s = 2.595+ | Found by David W. Cantrell | in July 2002.", "source_image": "t13.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t13.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.595+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "t13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "7628e283de25ee68", "improvement": -0.0005499010705918295, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8264727928819919e-06, "max_pair_overlap_depth": -1.755464108432747e-05, "metric_expression": "2.59555", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.595549901070592, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.595, "setup": "triinsqu", "side": 2.595549901070592, "solution_path": "data/solutions/generated/triinsqu_13_7628e283de25ee68.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/7628e283de25ee68.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@14", "density": 0.8144966370845219, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2002", "friedman_display_metric_value": 2.726, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t14.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.726+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.726, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@14", "credit": "David W. Cantrell", "date": "July 2002", "family_updated": "", "metric_expression": "2.726+", "metric_symbol": "s", "metric_value": 2.726, "reference_text": "s = 2.726+ | Found by David W. Cantrell | in July 2002.", "source_image": "t14.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t14.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.726+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "t14.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "601dc4458719752d", "improvement": -0.0021590642579867314, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.4175513847981196e-06, "max_pair_overlap_depth": -2.112817484914431e-05, "metric_expression": "2.72816", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.7281590642579867, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.726, "setup": "triinsqu", "side": 2.7281590642579867, "solution_path": "data/solutions/generated/triinsqu_014_601dc4458719752d.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/601dc4458719752d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@15", "density": 0.8108430550585584, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.8299, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t15.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.8299+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.8299, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@15", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.8299+", "metric_symbol": "s", "metric_value": 2.8299, "reference_text": "s = 2.8299+ | Found by Ian Watson | in April 2026.", "source_image": "t15.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t15.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.8299+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t15.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "430e70d954ae3759", "improvement": -0.0003679073759270679, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0258685225063818e-06, "max_pair_overlap_depth": -3.8614458098606974e-05, "metric_expression": "2.83027", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.830267907375927, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.8299, "setup": "triinsqu", "side": 2.830267907375927, "solution_path": "data/solutions/generated/triinsqu_015_430e70d954ae3759.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/430e70d954ae3759.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@16", "density": 0.8226134516626242, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 2.9, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t16.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.9000+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.9, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@16", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "2.9000+", "metric_symbol": "s", "metric_value": 2.9, "reference_text": "s = 2.9000+ | Found by Ian Watson | in April 2026.", "source_image": "t16.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t16.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.9000+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "2350476c07d7060c", "improvement": -0.002100218284964317, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.0129376531587966e-06, "max_pair_overlap_depth": -5.176872598853383e-06, "metric_expression": "2.90210", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.9021002182849642, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.9, "setup": "triinsqu", "side": 2.9021002182849642, "solution_path": "data/solutions/generated/triinsqu_016_2350476c07d7060c.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/2350476c07d7060c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@17", "density": 0.8272516069770434, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2008", "friedman_display_metric_value": 2.982, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t17.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.982+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.982, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@17", "credit": "Maurizio Morandi", "date": "July 2008", "family_updated": "", "metric_expression": "2.982+", "metric_symbol": "s", "metric_value": 2.982, "reference_text": "s = 2.982+ | Found by Maurizio Morandi | in July 2008.", "source_image": "t17.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t17.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 2.982+ | Found by Maurizio Morandi | in July 2008.", "friedman_source_image": "t17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "79a5506fa7f0974c", "improvement": -0.0010186525102788835, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8787966733926961e-06, "max_pair_overlap_depth": -9.562062775358982e-06, "metric_expression": "2.98302", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.983018652510279, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.982, "setup": "triinsqu", "side": 2.983018652510279, "solution_path": "data/solutions/generated/triinsqu_017_79a5506fa7f0974c.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/79a5506fa7f0974c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@18", "density": 0.8369229075763384, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2008", "friedman_display_metric_value": 3.051, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t18.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.051+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.051, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@18", "credit": "Maurizio Morandi", "date": "July 2008", "family_updated": "", "metric_expression": "3.051+", "metric_symbol": "s", "metric_value": 3.051, "reference_text": "s = 3.051+ | Found by Maurizio Morandi | in July 2008.", "source_image": "t18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t18.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3.051+ | Found by Maurizio Morandi | in July 2008.", "friedman_source_image": "t18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "0d24ad1cca3bbb64", "improvement": -0.0007140908076439523, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6577344713731995e-06, "max_pair_overlap_depth": -7.637757528100586e-06, "metric_expression": "3.05171", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.051714090807644, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.051, "setup": "triinsqu", "side": 3.051714090807644, "solution_path": "data/solutions/generated/triinsqu_018_0d24ad1cca3bbb64.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/0d24ad1cca3bbb64.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@19", "density": 0.8400046005998116, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.1293, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t19.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.12930+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.1293, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@19", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.12930+", "metric_symbol": "s", "metric_value": 3.1293, "reference_text": "s = 3.12930+ | Found by Ian Watson | in April 2026.", "source_image": "t19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t19.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3.12930+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "def5af7572515998", "improvement": -0.0002816463880579434, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.93050707669818e-06, "max_pair_overlap_depth": -4.5439275512260124e-06, "metric_expression": "3.12958", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.129581646388058, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.1293, "setup": "triinsqu", "side": 3.129581646388058, "solution_path": "data/solutions/generated/triinsqu_019_def5af7572515998.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/def5af7572515998.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@20", "density": 0.8288697801794981, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.2305, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t20.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.2305+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.2305, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@20", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.2305+", "metric_symbol": "s", "metric_value": 3.2305, "reference_text": "s = 3.2305+ | Found by Ian Watson | in April 2026.", "source_image": "t20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t20.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3.2305+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "43e53f43942a4488", "improvement": -0.0018781535798377824, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.815940991194715e-07, "max_pair_overlap_depth": -1.1219130352735363e-05, "metric_expression": "3.23238", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.232378153579838, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.2305, "setup": "triinsqu", "side": 3.232378153579838, "solution_path": "data/solutions/generated/triinsqu_020_43e53f43942a4488.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/43e53f43942a4488.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@21", "density": 0.8291397947988184, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.3111, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t21.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.3111+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.3111, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@21", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.3111+", "metric_symbol": "s", "metric_value": 3.3111, "reference_text": "s = 3.3111+ | Found by Ian Watson | in April 2026.", "source_image": "t21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t21.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3.3111+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "986572060ddb345a", "improvement": -0.0005626159903786565, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2145623034941338e-06, "max_pair_overlap_depth": -2.9730022631513364e-06, "metric_expression": "3.31166", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.311662615990379, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.3111, "setup": "triinsqu", "side": 3.311662615990379, "solution_path": "data/solutions/generated/triinsqu_021_986572060ddb345a.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/986572060ddb345a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@22", "density": 0.8356286267983878, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.3757, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t22.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.3757+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.3757, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@22", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.3757+", "metric_symbol": "s", "metric_value": 3.3757, "reference_text": "22. | | s = 3.3757+ | Found by Ian Watson | in April 2026.", "source_image": "t22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t22.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "22. | | s = 3.3757+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "4d69d20a7a35e585", "improvement": -0.0007086456724314516, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2855965547198588e-06, "max_pair_overlap_depth": -1.8710922459974633e-05, "metric_expression": "3.37641", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.3764086456724316, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.3757, "setup": "triinsqu", "side": 3.3764086456724316, "solution_path": "data/solutions/generated/triinsqu_022_4d69d20a7a35e585.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/4d69d20a7a35e585.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@23", "density": 0.8452320475065837, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.4311, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t23.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.4311+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.4311, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@23", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.4311+", "metric_symbol": "s", "metric_value": 3.4311, "reference_text": "23. | | s = 3.4311+ | Found by Ian Watson | in April 2026.", "source_image": "t23.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t23.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "23. | | s = 3.4311+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "959574dda9a01133", "improvement": -0.001524187888661821, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.8602101761622194e-08, "max_pair_overlap_depth": -2.5255431334025857e-06, "metric_expression": "3.43262", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.4326241878886616, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.4311, "setup": "triinsqu", "side": 3.4326241878886616, "solution_path": "data/solutions/generated/triinsqu_023_959574dda9a01133.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/959574dda9a01133.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@24", "density": 0.8636751606923448, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2008", "friedman_display_metric_value": 3.468, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t24.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.468+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.468, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@24", "credit": "Maurizio Morandi", "date": "August 2008", "family_updated": "", "metric_expression": "3.468+", "metric_symbol": "s", "metric_value": 3.468, "reference_text": "24. | | s = 3.468+ | Found by Maurizio Morandi | in August 2008.", "source_image": "t24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t24.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "24. | | s = 3.468+ | Found by Maurizio Morandi | in August 2008.", "friedman_source_image": "t24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "d96b5ad8b1001b9a", "improvement": -0.0008116902395634007, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.1658397103314651e-06, "max_pair_overlap_depth": -6.191240536246312e-06, "metric_expression": "3.46881", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.4688116902395634, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.468, "setup": "triinsqu", "side": 3.4688116902395634, "solution_path": "data/solutions/generated/triinsqu_024_d96b5ad8b1001b9a.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/d96b5ad8b1001b9a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@25", "density": 0.8645393394550887, "friedman_analytical_or_proved": false, "friedman_credit": "David W. Cantrell", "friedman_date": "August 2012", "friedman_display_metric_value": 3.537, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t25.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.537+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.537, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@25", "credit": "David W. Cantrell", "date": "August 2012", "family_updated": "", "metric_expression": "3.537+", "metric_symbol": "s", "metric_value": 3.537, "reference_text": "25. | | s = 3.537+ | Found by David W. Cantrell | in August 2012.", "source_image": "t25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t25.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "25. | | s = 3.537+ | Found by David W. Cantrell | in August 2012.", "friedman_source_image": "t25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "8da962f4a2ed3f11", "improvement": -0.0015712315473748184, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -6.272129416634903e-07, "max_pair_overlap_depth": -1.1961418790784606e-05, "metric_expression": "3.53857", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.5385712315473747, "n": 25, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.537, "setup": "triinsqu", "side": 3.5385712315473747, "solution_path": "data/solutions/generated/triinsqu_025_8da962f4a2ed3f11.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/8da962f4a2ed3f11.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@26", "density": 0.8796434821316925, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "September 2008", "friedman_display_metric_value": 3.575, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t26.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.575+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.575, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@26", "credit": "Maurizio Morandi", "date": "September 2008", "family_updated": "", "metric_expression": "3.575+", "metric_symbol": "s", "metric_value": 3.575, "reference_text": "26. | | s = 3.575+ | Found by Maurizio Morandi | in September 2008.", "source_image": "t26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t26.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "26. | | s = 3.575+ | Found by Maurizio Morandi | in September 2008.", "friedman_source_image": "t26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "c36ce120aca7c2e7", "improvement": -0.002532991640289417, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0954385221262358e-06, "max_pair_overlap_depth": -5.476191583808632e-07, "metric_expression": "3.57753", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.5775329916402896, "n": 26, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.575, "setup": "triinsqu", "side": 3.5775329916402896, "solution_path": "data/solutions/generated/triinsqu_026_c36ce120aca7c2e7.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/c36ce120aca7c2e7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@27", "density": 0.8658956992776567, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.6726, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t27.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.6726+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.6726, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@27", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.6726+", "metric_symbol": "s", "metric_value": 3.6726, "reference_text": "27. | | s = 3.6726+ | Found by Ian Watson | in April 2026.", "source_image": "t27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t27.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "27. | | s = 3.6726+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "4c91417b38b8be95", "improvement": -0.0019097898938134072, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.750472262434879e-07, "max_pair_overlap_depth": -1.515528041828862e-05, "metric_expression": "3.67451", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.6745097898938135, "n": 27, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.6726, "setup": "triinsqu", "side": 3.6745097898938135, "solution_path": "data/solutions/generated/triinsqu_027_4c91417b38b8be95.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/4c91417b38b8be95.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@28", "density": 0.8583067572738268, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.7571, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t28.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.7571+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.7571, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@28", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.7571+", "metric_symbol": "s", "metric_value": 3.7571, "reference_text": "28. | | s = 3.7571+ | Found by Ian Watson | in April 2026.", "source_image": "t28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t28.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "28. | | s = 3.7571+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "9b7285926a894eec", "improvement": -0.0013438626171571322, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.7756377540625622e-06, "max_pair_overlap_depth": -5.481622750158621e-06, "metric_expression": "3.75844", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.758443862617157, "n": 28, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.7571, "setup": "triinsqu", "side": 3.758443862617157, "solution_path": "data/solutions/generated/triinsqu_028_9b7285926a894eec.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/9b7285926a894eec.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@29", "density": 0.8613056568479127, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_display_metric_value": 3.818, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t29.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.818+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.818, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@29", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "", "metric_expression": "3.818+", "metric_symbol": "s", "metric_value": 3.818, "reference_text": "29. | | s = 3.818+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "t29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t29.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "29. | | s = 3.818+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "t29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "a02ae61c838755d7", "improvement": -0.0003054483997071422, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.731563201531232e-06, "max_pair_overlap_depth": -2.352291984759891e-06, "metric_expression": "3.81831", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.818305448399707, "n": 29, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.818, "setup": "triinsqu", "side": 3.818305448399707, "solution_path": "data/solutions/generated/triinsqu_029_a02ae61c838755d7.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ignacio Vallejo", "svg_path": "data/svg/a02ae61c838755d7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@30", "density": 0.868927959047152, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 3.8662, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t30.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.8662+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.8662, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@30", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "3.8662+", "metric_symbol": "s", "metric_value": 3.8662, "reference_text": "30. | | s = 3.8662+ | Found by Ian Watson | in April 2026.", "source_image": "t30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t30.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "30. | | s = 3.8662+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "d3cf7ea5ce255135", "improvement": -0.00030930450574828683, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -4.0741990212131443e-07, "max_pair_overlap_depth": -7.811820435188466e-06, "metric_expression": "3.86651", "metric_recovery_tolerance_abs": 0.0001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.8665093045057484, "n": 30, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.8662, "setup": "triinsqu", "side": 3.8665093045057484, "solution_path": "data/solutions/generated/triinsqu_030_d3cf7ea5ce255135.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/d3cf7ea5ce255135.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@31", "density": 0.8672905272682435, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 3.936, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t31.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.936+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.936, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "3.936+", "metric_symbol": "s", "metric_value": 3.936, "reference_text": "31. | | s = 3.936+ | Found by Emerson Connelly | in April 2026.", "source_image": "t31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t31.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "31. | | s = 3.936+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "90f4b9b8010910a7", "improvement": 0.001868580153832955, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.1286553127417914e-06, "max_pair_overlap_depth": -1.3206709677193729e-05, "metric_expression": "3.93413", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.934131419846167, "n": 31, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.936, "setup": "triinsqu", "side": 3.934131419846167, "solution_path": "data/solutions/generated/triinsqu_031_90f4b9b8010910a7.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/90f4b9b8010910a7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@32", "density": 0.8750673712051059, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2026", "friedman_display_metric_value": 3.979, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t32.gif", "friedman_metric_expression": "6\u20137\u221a3/6 = 3.979+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.9792740578363097, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@32", "credit": "Maurizio Morandi", "date": "May 2026", "family_updated": "", "metric_expression": "6\u20137\u221a3/6 = 3.979+", "metric_symbol": "s", "metric_value": 3.9792740578363097, "reference_text": "32. | | s = 6\u20137\u221a3/6 = 3.979+ | Found by Maurizio Morandi | in May 2026.", "source_image": "t32.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t32.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "32. | | s = 6\u20137\u221a3/6 = 3.979+ | Found by Maurizio Morandi | in May 2026.", "friedman_source_image": "t32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "300596cf09652b9a", "improvement": -6.517413177142828e-06, "max_boundary_excess": -1.927630533637451e-06, "max_pair_overlap_depth": -1.4532438436631878e-05, "metric_expression": "3.97928", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.979280575249487, "n": 32, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "original_submitted_by": "polygon-packer-c image seed", "record_type": "verified", "reference_side": 3.9792740578363097, "setup": "triinsqu", "side": 3.979280575249487, "solution_path": "data/solutions/generated/triinsqu_32_300596cf09652b9a.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T16:24:14+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/300596cf09652b9a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@32", "density": 0.8675921732131934, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2026", "friedman_display_metric_value": 3.979, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t32.gif", "friedman_metric_expression": "6\u20137\u221a3/6 = 3.979+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.9792740578363097, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@32", "credit": "Maurizio Morandi", "date": "May 2026", "family_updated": "", "metric_expression": "6\u20137\u221a3/6 = 3.979+", "metric_symbol": "s", "metric_value": 3.979, "reference_text": "32. | | s = 6\u20137\u221a3/6 = 3.979+ | Found by Maurizio Morandi | in May 2026.", "source_image": "t32.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t32.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "32. | | s = 6\u20137\u221a3/6 = 3.979+ | Found by Maurizio Morandi | in May 2026.", "friedman_source_image": "t32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "f42801b713b9238d", "improvement": -0.017112545300743243, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.208596980261035e-06, "max_pair_overlap_depth": -2.3341135757526388e-06, "metric_expression": "3.99639", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.996386603137053, "n": 32, "notes": "Best available verified coordinate reconstruction, but its evaluator metric is outside the benchmark recovery band for the Friedman reference.", "record_type": "verified", "reference_side": 3.9792740578363097, "setup": "triinsqu", "side": 3.996386603137053, "solution_path": "data/solutions/generated/triinsqu_32_f42801b713b9238d.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/f42801b713b9238d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@33", "density": 0.8675949776849048, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.058, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t33.gif", "friedman_metric_expression": "4.058+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.058, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.058+", "metric_symbol": "s", "metric_value": 4.058, "reference_text": "33. | | s = 4.058+ | Found by Emerson Connelly | in April 2026.", "source_image": "t33.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t33.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "33. | | s = 4.058+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "a6f49f2f24228d1b", "improvement": -0.00034322121207797096, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.0747182587902822e-06, "max_pair_overlap_depth": -2.8024820216354662e-05, "metric_expression": "4.05834", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.058343221212078, "n": 33, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.058, "setup": "triinsqu", "side": 4.058343221212078, "solution_path": "data/solutions/generated/triinsqu_33_a6f49f2f24228d1b.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/a6f49f2f24228d1b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@34", "density": 0.8767333914896571, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.098, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t34.gif", "friedman_metric_expression": "4.098+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.098, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.098+", "metric_symbol": "s", "metric_value": 4.098, "reference_text": "34. | | s = 4.098+ | Found by Emerson Connelly | in April 2026.", "source_image": "t34.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t34.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "34. | | s = 4.098+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "61b4d5d6bf22a206", "improvement": 0.00015051348449990343, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.6262786795626285e-06, "max_pair_overlap_depth": -1.499292058504409e-05, "metric_expression": "4.09785", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0978494865155, "n": 34, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.098, "setup": "triinsqu", "side": 4.0978494865155, "solution_path": "data/solutions/generated/triinsqu_34_61b4d5d6bf22a206.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/61b4d5d6bf22a206.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@35", "density": 0.8677502962014568, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_display_metric_value": 4.176, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t35.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "9(2\u221a3\u20133) = 4.176+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.176914536239791, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@35", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "", "metric_expression": "9(2\u221a3\u20133) = 4.176+", "metric_symbol": "s", "metric_value": 4.176, "reference_text": "35. | | s = 9(2\u221a3\u20133) = 4.176+ | Found by Erich Friedman | in April 2026.", "source_image": "t35.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t35.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "35. | | s = 9(2\u221a3\u20133) = 4.176+ | Found by Erich Friedman | in April 2026.", "friedman_source_image": "t35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "ab6aa3f219e08b42", "improvement": -0.0022257983324101005, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.770482464101941e-07, "max_pair_overlap_depth": -3.3297730506198775e-06, "metric_expression": "4.17914", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.179140334572201, "n": 35, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.176914536239791, "setup": "triinsqu", "side": 4.179140334572201, "solution_path": "data/solutions/generated/triinsqu_035_ab6aa3f219e08b42.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/ab6aa3f219e08b42.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@36", "density": 0.8790676097280682, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.214, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t36.gif", "friedman_metric_expression": "4.214+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.214, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@36", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.214+", "metric_symbol": "s", "metric_value": 4.214, "reference_text": "36. | | s = 4.214+ | Found by Emerson Connelly | in April 2026.", "source_image": "t36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t36.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "36. | | s = 4.214+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "aae755b2130a7a83", "improvement": 0.0029496973593481357, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.160284450281608e-07, "max_pair_overlap_depth": -9.933313802612531e-07, "metric_expression": "4.21105", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.211050302640652, "n": 36, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.214, "setup": "triinsqu", "side": 4.211050302640652, "solution_path": "data/solutions/record_hunt/triinsqu_36_aae755b2130a7a83.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/aae755b2130a7a83.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@37", "density": 0.8782570037473258, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_display_metric_value": 4.27233, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t37.gif", "friedman_metric_expression": "4.27233+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.27233, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@37", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "4.27233+", "metric_symbol": "s", "metric_value": 4.27233, "reference_text": "37. | | s = 4.27233+ | Found by Nathan Roll | in April 2026.", "source_image": "t37.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t37.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "37. | | s = 4.27233+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "t37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "46406dc33c9746a7", "improvement": 0.0012238102051549404, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.826527513923834e-07, "max_pair_overlap_depth": -6.105510335085995e-07, "metric_expression": "4.27111", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.271106189794845, "n": 37, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.27233, "setup": "triinsqu", "side": 4.271106189794845, "solution_path": "data/solutions/record_hunt/triinsqu_37_46406dc33c9746a7.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/46406dc33c9746a7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@38", "density": 0.87940001283733, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.327, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t38.gif", "friedman_metric_expression": "4.327+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.327, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.327+", "metric_symbol": "s", "metric_value": 4.327, "reference_text": "38. | | s = 4.327+ | Found by Emerson Connelly | in April 2026.", "source_image": "t38.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t38.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "38. | | s = 4.327+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "f44a4bd75616bc73", "improvement": 0.0013748413573368978, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.0707071410413964e-07, "max_pair_overlap_depth": -1.0916553592199563e-06, "metric_expression": "4.32563", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.325625158642663, "n": 38, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.327, "setup": "triinsqu", "side": 4.325625158642663, "solution_path": "data/solutions/record_hunt/triinsqu_38_f44a4bd75616bc73.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/f44a4bd75616bc73.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@39", "density": 0.880118042721229, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.383, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t39.gif", "friedman_metric_expression": "4.383+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.383, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.383+", "metric_symbol": "s", "metric_value": 4.383, "reference_text": "39. | | s = 4.383+ | Found by Emerson Connelly | in April 2026.", "source_image": "t39.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t39.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "39. | | s = 4.383+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "263f7876a25d297b", "improvement": 0.002616247848735931, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.607883972834501e-07, "max_pair_overlap_depth": -1.86255866918561e-06, "metric_expression": "4.38038", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.380383752151264, "n": 39, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.383, "setup": "triinsqu", "side": 4.380383752151264, "solution_path": "data/solutions/record_hunt/triinsqu_39_263f7876a25d297b.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/263f7876a25d297b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@40", "density": 0.878868813713771, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 4.437, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t40.gif", "friedman_metric_expression": "4.437+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.437, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "4.437+", "metric_symbol": "s", "metric_value": 4.437, "reference_text": "40. | | s = 4.437+ | Found by Emerson Connelly | in April 2026.", "source_image": "t40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t40.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "40. | | s = 4.437+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "ccf2360cc8917adc", "improvement": -0.002338759632142029, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.520888573265893e-06, "max_pair_overlap_depth": -1.6780429565876886e-05, "metric_expression": "4.43934", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.439338759632142, "n": 40, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.437, "setup": "triinsqu", "side": 4.439338759632142, "solution_path": "data/solutions/generated/triinsqu_040_ccf2360cc8917adc.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/ccf2360cc8917adc.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@1", "density": 1.0, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 1.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt1.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@1", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial.", "source_image": "tt1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt1.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 1 | Trivial.", "friedman_source_image": "tt1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "b09a5ce4a2c03ad3", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 5.551115123125788e-17, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 1.0, "n": 1, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 1.0, "setup": "triintri", "side": 1.0, "solution_path": "data/solutions/generated/triintri_001_b09a5ce4a2c03ad3.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T18:08:37+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/b09a5ce4a2c03ad3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@2", "density": 0.5, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@2", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "tt4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "tt4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "2d6f654db11412d8", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 1.6653345369377346e-16, "max_pair_overlap_depth": 0.0, "metric_expression": "2.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "n": 2, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "triintri", "side": 2.0, "solution_path": "data/solutions/generated/triintri_002_2d6f654db11412d8.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T18:08:37+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/2d6f654db11412d8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@3", "density": 0.75, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@3", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "tt4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "tt4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "76381d42f8f17f41", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 1.6653345369377346e-16, "max_pair_overlap_depth": 3.3306690738754696e-16, "metric_expression": "2.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "n": 3, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "triintri", "side": 2.0, "solution_path": "data/solutions/generated/triintri_003_76381d42f8f17f41.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T18:08:37+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/76381d42f8f17f41.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@4", "density": 1.0, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 2.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@4", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "tt4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "tt4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "be1b0b4b1802d8fa", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 1.6653345369377346e-16, "max_pair_overlap_depth": 3.3306690738754696e-16, "metric_expression": "2.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.0, "n": 4, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.0, "setup": "triintri", "side": 2.0, "solution_path": "data/solutions/generated/triintri_004_be1b0b4b1802d8fa.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T18:08:37+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/be1b0b4b1802d8fa.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@5", "density": 0.66984024663198, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 2.732, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt5.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "1 + \u221a3 = 2.732+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.732050807568877, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@5", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "1 + \u221a3 = 2.732+", "metric_symbol": "s", "metric_value": 2.732, "reference_text": "s = 1 + \u221a3 = 2.732+ | Proved by Erich Friedman | in 1997.", "source_image": "tt5.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt5.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 1 + \u221a3 = 2.732+ | Proved by Erich Friedman | in 1997.", "friedman_source_image": "tt5.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "b4ac2c13e986485e", "improvement": -6.675552642354532e-05, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.644640909821311e-06, "max_pair_overlap_depth": -6.265774057961264e-06, "metric_expression": "2.73212", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.7321175630953007, "n": 5, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.732050807568877, "setup": "triintri", "side": 2.7321175630953007, "solution_path": "data/solutions/generated/triintri_005_b4ac2c13e986485e.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/b4ac2c13e986485e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@6", "density": 0.6768918015337515, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2008", "friedman_display_metric_value": 2.977, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt6.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "13/8 + 3\u221a13/8 = 2.977+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.977081728298996, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@6", "credit": "Maurizio Morandi", "date": "August 2008", "family_updated": "", "metric_expression": "13/8 + 3\u221a13/8 = 2.977+", "metric_symbol": "s", "metric_value": 2.977, "reference_text": "s = 13/8 + 3\u221a13/8 = 2.977+ | Found by Maurizio Morandi | in August 2008.", "source_image": "tt6.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt6.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 13/8 + 3\u221a13/8 = 2.977+ | Found by Maurizio Morandi | in August 2008.", "friedman_source_image": "tt6.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "df20f3104adbd6a1", "improvement": -0.0001730311672321072, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.3999156171376625e-07, "max_pair_overlap_depth": -1.9147124426771578e-05, "metric_expression": "2.97725", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 2.977254759466228, "n": 6, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 2.977081728298996, "setup": "triintri", "side": 2.977254759466228, "solution_path": "data/solutions/generated/triintri_006_df20f3104adbd6a1.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/df20f3104adbd6a1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@7", "density": 0.777777777777778, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@7", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "s = 3 | Trivial.", "source_image": "tt9.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 3 | Trivial.", "friedman_source_image": "tt9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "355f218b5ea40614", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 2.9605947323337506e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "3.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0, "n": 7, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.0, "setup": "triintri", "side": 3.0, "solution_path": "data/solutions/generated/triintri_007_355f218b5ea40614.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T18:08:37+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/355f218b5ea40614.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@8", "density": 0.8888888888888892, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@8", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "s = 3 | Trivial.", "source_image": "tt9.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 3 | Trivial.", "friedman_source_image": "tt9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "43e3200cf32d77a9", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 2.9605947323337506e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "3.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0, "n": 8, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.0, "setup": "triintri", "side": 3.0, "solution_path": "data/solutions/generated/triintri_008_43e3200cf32d77a9.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T18:08:37+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/43e3200cf32d77a9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@9", "density": 1.0000000000000004, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 3.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@9", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "s = 3 | Trivial.", "source_image": "tt9.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt9.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 3 | Trivial.", "friedman_source_image": "tt9.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "4242c6a66848e1ea", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 2.9605947323337516e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "3.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.0, "n": 9, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.0, "setup": "triintri", "side": 3.0, "solution_path": "data/solutions/generated/triintri_009_4242c6a66848e1ea.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T18:08:37+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4242c6a66848e1ea.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@10", "density": 0.8162770652591925, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 3.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt10.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "7/2 = 3.500", "friedman_metric_symbol": "s", "friedman_metric_value": 3.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@10", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "7/2 = 3.500", "metric_symbol": "s", "metric_value": 3.5, "reference_text": "s = 7/2 = 3.500 | Found by Erich Friedman | in 1997.", "source_image": "tt10.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt10.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 7/2 = 3.500 | Found by Erich Friedman | in 1997.", "friedman_source_image": "tt10.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "bcf7fa93627e2e22", "improvement": -0.00010604617003595607, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -8.918936789115156e-08, "max_pair_overlap_depth": -1.2701382657187565e-05, "metric_expression": "3.50011", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.500106046170036, "n": 10, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.5, "setup": "triintri", "side": 3.500106046170036, "solution_path": "data/solutions/generated/triintri_010_bcf7fa93627e2e22.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/bcf7fa93627e2e22.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@11", "density": 0.792568600317471, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 3.722, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt11.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "9/4 + 9\u221a21/28 = 3.722+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.7229707590929486, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@11", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "9/4 + 9\u221a21/28 = 3.722+", "metric_symbol": "s", "metric_value": 3.722, "reference_text": "s = 9/4 + 9\u221a21/28 = 3.722+ | Found by Erich Friedman | in 1997.", "source_image": "tt11.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt11.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 9/4 + 9\u221a21/28 = 3.722+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tt11.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "8c37202a929dc807", "improvement": -0.002472140302997694, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.7247990718051686e-06, "max_pair_overlap_depth": -2.4227159337045223e-05, "metric_expression": "3.72544", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.7254428993959463, "n": 11, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.7229707590929486, "setup": "triintri", "side": 3.7254428993959463, "solution_path": "data/solutions/generated/triintri_11_8c37202a929dc807.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/8c37202a929dc807.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@12", "density": 0.7960259433336867, "friedman_analytical_or_proved": true, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2007", "friedman_display_metric_value": 3.879, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt12.gif", "friedman_metric_expression": "2 + 2cos(\u03c0/9) = 3.879+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.879385241571817, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@12", "credit": "David W. Cantrell", "date": "July 2007", "family_updated": "", "metric_expression": "2 + 2cos(\u03c0/9) = 3.879+", "metric_symbol": "s", "metric_value": 3.879, "reference_text": "s = 2 + 2cos(\u03c0/9) = 3.879+ | Found by David W. Cantrell | in July 2007.", "source_image": "tt12.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt12.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 2 + 2cos(\u03c0/9) = 3.879+ | Found by David W. Cantrell | in July 2007.", "friedman_source_image": "tt12.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "7642b05605706588", "improvement": -0.00325375295575947, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -9.358547413541538e-08, "max_pair_overlap_depth": -4.590975868801195e-06, "metric_expression": "3.88264", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.8826389945275763, "n": 12, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.879385241571817, "setup": "triintri", "side": 3.8826389945275763, "solution_path": "data/solutions/generated/triintri_12_7642b05605706588.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T07:13:53+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/7642b05605706588.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@13", "density": 0.8146483132163195, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_display_metric_value": 3.992, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt13.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "3.992+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.992, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triintri@13", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "", "metric_expression": "3.992+", "metric_symbol": "s", "metric_value": 3.992, "reference_text": "s = 3.992+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt13.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt13.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 3.992+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt13.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "afe3e3dc6de1bc36", "improvement": -0.0027223080586638027, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.48838412272174e-06, "max_pair_overlap_depth": -3.9197094850562664e-05, "metric_expression": "3.99472", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 3.994722308058664, "n": 13, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 3.992, "setup": "triintri", "side": 3.994722308058664, "solution_path": "data/solutions/generated/triintri_013_afe3e3dc6de1bc36.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/afe3e3dc6de1bc36.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@14", "density": 0.875, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@14", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "s = 4 | Trivial.", "source_image": "tt16.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 4 | Trivial.", "friedman_source_image": "tt16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "8676384ad0301449", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 2.775557561562891e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "4.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "n": 14, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.0, "setup": "triintri", "side": 4.0, "solution_path": "data/solutions/generated/triintri_014_8676384ad0301449.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T18:08:37+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/8676384ad0301449.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@15", "density": 0.9375, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@15", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "s = 4 | Trivial.", "source_image": "tt16.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 4 | Trivial.", "friedman_source_image": "tt16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "31db3ec76cc0421f", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 2.775557561562891e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "4.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "n": 15, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.0, "setup": "triintri", "side": 4.0, "solution_path": "data/solutions/generated/triintri_015_31db3ec76cc0421f.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T18:08:37+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/31db3ec76cc0421f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@16", "density": 1.0, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 4.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@16", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "s = 4 | Trivial.", "source_image": "tt16.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt16.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 4 | Trivial.", "friedman_source_image": "tt16.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "2ffa329b602032d6", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 2.775557561562891e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "4.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.0, "n": 16, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.0, "setup": "triintri", "side": 4.0, "solution_path": "data/solutions/generated/triintri_016_2ffa329b602032d6.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T18:08:37+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/2ffa329b602032d6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@17", "density": 0.8524249732795084, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_display_metric_value": 4.465, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt17.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "4.465+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.465, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triintri@17", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "", "metric_expression": "4.465+", "metric_symbol": "s", "metric_value": 4.465, "reference_text": "s = 4.465+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt17.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt17.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 4.465+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt17.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "ad8aac0e4c06f7d0", "improvement": -0.0007702721912288268, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8241570152012174e-06, "max_pair_overlap_depth": -7.389272764501964e-06, "metric_expression": "4.46577", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.465770272191229, "n": 17, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.465, "setup": "triintri", "side": 4.465770272191229, "solution_path": "data/solutions/generated/triintri_017_ad8aac0e4c06f7d0.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/ad8aac0e4c06f7d0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@18", "density": 0.8888203671574908, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 4.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt18.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "9/2 = 4.500", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@18", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "9/2 = 4.500", "metric_symbol": "s", "metric_value": 4.5, "reference_text": "s = 9/2 = 4.500 | Found by Erich Friedman | in 1997.", "source_image": "tt18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt18.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 9/2 = 4.500 | Found by Erich Friedman | in 1997.", "friedman_source_image": "tt18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "b4cfb14015aca75a", "improvement": -0.00017345566104154386, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.575746594607548e-06, "max_pair_overlap_depth": -5.0550449839370515e-06, "metric_expression": "4.50017", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.5001734556610415, "n": 18, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.5, "setup": "triintri", "side": 4.5001734556610415, "solution_path": "data/solutions/generated/triintri_018_b4cfb14015aca75a.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/b4cfb14015aca75a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@19", "density": 0.872322152073677, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_display_metric_value": 4.666, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt19.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "14/3 = 4.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.666666666666667, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@19", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "", "metric_expression": "14/3 = 4.666+", "metric_symbol": "s", "metric_value": 4.666, "reference_text": "s = 14/3 = 4.666+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt19.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 14/3 = 4.666+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "bf4e89c9b4dd8ae2", "improvement": -0.0003392326096340881, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.331642222161759e-07, "max_pair_overlap_depth": -9.690072424628493e-06, "metric_expression": "4.66701", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.667005899276301, "n": 19, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.666666666666667, "setup": "triintri", "side": 4.667005899276301, "solution_path": "data/solutions/generated/triintri_019_bf4e89c9b4dd8ae2.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/bf4e89c9b4dd8ae2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@20", "density": 0.845304928058783, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_display_metric_value": 4.861, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt20.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "33/8 + 9\u221a21/56 = 4.861+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.861485379546474, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@20", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "", "metric_expression": "33/8 + 9\u221a21/56 = 4.861+", "metric_symbol": "s", "metric_value": 4.861, "reference_text": "s = 33/8 + 9\u221a21/56 = 4.861+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt20.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 33/8 + 9\u221a21/56 = 4.861+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "4dff2c76e1273753", "improvement": -0.0026796085219045196, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.619234998604407e-06, "max_pair_overlap_depth": -7.278337082583519e-06, "metric_expression": "4.86416", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.864164988068379, "n": 20, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.861485379546474, "setup": "triintri", "side": 4.864164988068379, "solution_path": "data/solutions/generated/triintri_020_4dff2c76e1273753.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/4dff2c76e1273753.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@21", "density": 0.8650098201747314, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_display_metric_value": 4.923, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt21.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "4.923+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.923, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triintri@21", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "", "metric_expression": "4.923+", "metric_symbol": "s", "metric_value": 4.923, "reference_text": "s = 4.923+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt21.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 4.923+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "4dc62e9e9421c0aa", "improvement": -0.004187943781052361, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.4013824985741632e-06, "max_pair_overlap_depth": -4.2136074186321926e-06, "metric_expression": "4.92719", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 4.927187943781052, "n": 21, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.923, "setup": "triintri", "side": 4.927187943781052, "solution_path": "data/solutions/generated/triintri_021_4dc62e9e9421c0aa.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/4dc62e9e9421c0aa.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@22", "density": 0.8799245341930954, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_display_metric_value": 4.996, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt22.gif", "friedman_metric_expression": "4.996+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.996, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triintri@22", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "", "metric_expression": "4.996+", "metric_symbol": "s", "metric_value": 4.996, "reference_text": "s = 4.996+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt22.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 4.996+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "2122d833c6fcab70", "improvement": -0.004214405286988132, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -5.380108740330726e-08, "max_pair_overlap_depth": -8.335028905959163e-07, "metric_expression": "5.00021", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.000214405286989, "n": 22, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 4.996, "setup": "triintri", "side": 5.000214405286989, "solution_path": "data/solutions/generated/triintri_022_2122d833c6fcab70.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/2122d833c6fcab70.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@23", "density": 0.9200000000000002, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@23", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "tt25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "tt25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "4f1bdd5d6c07f589", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 7.105427357601002e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "5.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "n": 23, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.0, "setup": "triintri", "side": 5.0, "solution_path": "data/solutions/generated/triintri_023_4f1bdd5d6c07f589.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T18:08:37+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4f1bdd5d6c07f589.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@24", "density": 0.9600000000000002, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@24", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "tt25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "tt25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "64d77fbf13ae0be7", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 7.105427357601002e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "5.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "n": 24, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.0, "setup": "triintri", "side": 5.0, "solution_path": "data/solutions/generated/triintri_024_64d77fbf13ae0be7.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T18:08:37+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/64d77fbf13ae0be7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@25", "density": 1.0000000000000002, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 5.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@25", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "tt25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "tt25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "9c4806b8b37c5d37", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 7.105427357601002e-16, "max_pair_overlap_depth": 4.440892098500626e-16, "metric_expression": "5.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.0, "n": 25, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.0, "setup": "triintri", "side": 5.0, "solution_path": "data/solutions/generated/triintri_025_9c4806b8b37c5d37.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T18:08:37+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/9c4806b8b37c5d37.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@26", "density": 0.8884053356293824, "friedman_analytical_or_proved": false, "friedman_credit": "Joah Frenzley", "friedman_date": "April 2026", "friedman_display_metric_value": 5.406, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt26.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "5.406+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.406, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triintri@26", "credit": "Joah Frenzley", "date": "April 2026", "family_updated": "", "metric_expression": "5.406+", "metric_symbol": "s", "metric_value": 5.406, "reference_text": "s = 5.406+ | Found by Joah Frenzley | in April 2026.", "source_image": "tt26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt26.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5.406+ | Found by Joah Frenzley | in April 2026.", "friedman_source_image": "tt26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "0af5a3765ecc4828", "improvement": -0.0037985715923722907, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.296466577480461e-06, "max_pair_overlap_depth": -2.0400569136769242e-05, "metric_expression": "5.40980", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.409798571592372, "n": 26, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.406, "setup": "triintri", "side": 5.409798571592372, "solution_path": "data/solutions/generated/triintri_026_0af5a3765ecc4828.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Joah Frenzley", "svg_path": "data/svg/0af5a3765ecc4828.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@27", "density": 0.8924996192164427, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 5.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "friedman_metric_expression": "11/2 = 5.500", "friedman_metric_symbol": "s", "friedman_metric_value": 5.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@27", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "11/2 = 5.500", "metric_symbol": "s", "metric_value": 5.5, "reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "source_image": "tt28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "friedman_source_image": "tt28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "f1c2be61e829f1e2", "improvement": -0.00019215549305418023, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.8365186496628e-06, "max_pair_overlap_depth": -1.8064988390742442e-06, "metric_expression": "5.50019", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.500192155493054, "n": 27, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.5, "setup": "triintri", "side": 5.500192155493054, "solution_path": "data/solutions/generated/triintri_027_f1c2be61e829f1e2.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/f1c2be61e829f1e2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@28", "density": 0.9255631973649003, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_display_metric_value": 5.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "friedman_metric_expression": "11/2 = 5.500", "friedman_metric_symbol": "s", "friedman_metric_value": 5.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@28", "credit": "Erich Friedman", "date": "1997", "family_updated": "", "metric_expression": "11/2 = 5.500", "metric_symbol": "s", "metric_value": 5.5, "reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "source_image": "tt28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "friedman_source_image": "tt28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "9562d7d6e075a347", "improvement": -0.00016827626559567932, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.296352348617567e-06, "max_pair_overlap_depth": -7.147352432124165e-08, "metric_expression": "5.50017", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.500168276265596, "n": 28, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.5, "setup": "triintri", "side": 5.500168276265596, "solution_path": "data/solutions/generated/triintri_028_9562d7d6e075a347.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/9562d7d6e075a347.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@29", "density": 0.9023512759650716, "friedman_analytical_or_proved": true, "friedman_credit": "David W. Cantrell", "friedman_date": "July 2007", "friedman_display_metric_value": 5.666, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt29.gif", "friedman_metric_expression": "17/3 = 5.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.666666666666667, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@29", "credit": "David W. Cantrell", "date": "July 2007", "family_updated": "", "metric_expression": "17/3 = 5.666+", "metric_symbol": "s", "metric_value": 5.666, "reference_text": "s = 17/3 = 5.666+ | Found by David W. Cantrell | in July 2007.", "source_image": "tt29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt29.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 17/3 = 5.666+ | Found by David W. Cantrell | in July 2007.", "friedman_source_image": "tt29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "38c7a009f9059275", "improvement": -0.0023949920687824644, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9275914294015247e-06, "max_pair_overlap_depth": -5.088073942505211e-06, "metric_expression": "5.66906", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.669061658735449, "n": 29, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.666666666666667, "setup": "triintri", "side": 5.669061658735449, "solution_path": "data/solutions/generated/triintri_29_38c7a009f9059275.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T13:47:12+00:00", "submitted_by": "David W. Cantrell", "svg_path": "data/svg/38c7a009f9059275.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@30", "density": 0.9060985977127352, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_display_metric_value": 5.75, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt30.gif", "friedman_metric_expression": "23/4 = 5.75", "friedman_metric_symbol": "s", "friedman_metric_value": 5.75, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@30", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "", "metric_expression": "23/4 = 5.75", "metric_symbol": "s", "metric_value": 5.75, "reference_text": "s = 23/4 = 5.75 | Found by Maurizio Morandi | in May 2008.", "source_image": "tt30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt30.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 23/4 = 5.75 | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "149a91e0248df04e", "improvement": -0.004040286099913359, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.2882428961650933e-06, "max_pair_overlap_depth": -6.414942533283785e-06, "metric_expression": "5.75404", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.754040286099913, "n": 30, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.75, "setup": "triintri", "side": 5.754040286099913, "solution_path": "data/solutions/generated/triintri_30_149a91e0248df04e.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T02:08:58+00:00", "submitted_by": "Maurizio Morandi", "svg_path": "data/svg/149a91e0248df04e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@31", "density": 0.8852772627280384, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_display_metric_value": 5.912, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt31.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "5.912+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.912, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triintri@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "", "metric_expression": "5.912+", "metric_symbol": "s", "metric_value": 5.912, "reference_text": "s = 5.912+ | Found by Emerson Connelly | in April 2026.", "source_image": "tt31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt31.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5.912+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "tt31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "c729ec2b23a32942", "improvement": -0.005539858919105356, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -1.9513696602846134e-06, "max_pair_overlap_depth": -3.7790737070775293e-06, "metric_expression": "5.91754", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.917539858919105, "n": 31, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.912, "setup": "triintri", "side": 5.917539858919105, "solution_path": "data/solutions/generated/triintri_031_c729ec2b23a32942.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T02:51:36+00:00", "submitted_by": "Emerson Connelly", "svg_path": "data/svg/c729ec2b23a32942.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@32", "density": 0.9021138463561595, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 5.951, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt32.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "5.951+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.951, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triintri@32", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "5.951+", "metric_symbol": "s", "metric_value": 5.951, "reference_text": "s = 5.951+ | Found by Ian Watson | in April 2026.", "source_image": "tt32.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt32.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5.951+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "tt32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "fa640909a0850f97", "improvement": -0.004857726462081935, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.7950535548187937e-06, "max_pair_overlap_depth": -4.900081183589755e-06, "metric_expression": "5.95586", "metric_recovery_tolerance_abs": 0.001, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 5.955857726462082, "n": 32, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 5.951, "setup": "triintri", "side": 5.955857726462082, "solution_path": "data/solutions/generated/triintri_032_fa640909a0850f97.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T02:29:44+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/fa640909a0850f97.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@33", "density": 0.9166666666666669, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 6.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@33", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial. |", "source_image": "tt36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6 | Trivial. |", "friedman_source_image": "tt36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "34a5032aebc12aff", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 5.921189464667501e-16, "max_pair_overlap_depth": 6.661338147750939e-16, "metric_expression": "6.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.0, "n": 33, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.0, "setup": "triintri", "side": 6.0, "solution_path": "data/solutions/generated/triintri_033_34a5032aebc12aff.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T18:08:37+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/34a5032aebc12aff.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@34", "density": 0.9444444444444448, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 6.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@34", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial. |", "source_image": "tt36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6 | Trivial. |", "friedman_source_image": "tt36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "a2ccd0a19cfa1b75", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 5.921189464667501e-16, "max_pair_overlap_depth": 6.661338147750939e-16, "metric_expression": "6.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.0, "n": 34, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.0, "setup": "triintri", "side": 6.0, "solution_path": "data/solutions/generated/triintri_034_a2ccd0a19cfa1b75.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T18:08:37+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/a2ccd0a19cfa1b75.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@35", "density": 0.9722222222222225, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 6.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@35", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial. |", "source_image": "tt36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6 | Trivial. |", "friedman_source_image": "tt36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "6325f936448cdf94", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 5.921189464667503e-16, "max_pair_overlap_depth": 6.661338147750939e-16, "metric_expression": "6.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.0, "n": 35, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.0, "setup": "triintri", "side": 6.0, "solution_path": "data/solutions/generated/triintri_035_6325f936448cdf94.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T18:08:37+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/6325f936448cdf94.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@36", "density": 1.0000000000000004, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_display_metric_value": 6.0, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@36", "credit": "Trivial", "date": "", "family_updated": "", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial. |", "source_image": "tt36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6 | Trivial. |", "friedman_source_image": "tt36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "4b90836bf07f8a65", "improvement": 0.0, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": 6.661338147750939e-16, "max_pair_overlap_depth": 6.661338147750939e-16, "metric_expression": "6.00000", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.0, "n": 36, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.0, "setup": "triintri", "side": 6.0, "solution_path": "data/solutions/generated/triintri_036_4b90836bf07f8a65.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T18:08:37+00:00", "submitted_by": "Trivial", "svg_path": "data/svg/4b90836bf07f8a65.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@37", "density": 0.9223731676430976, "friedman_analytical_or_proved": true, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_display_metric_value": 6.333, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt37.gif", "friedman_metric_expression": "19/3 = 6.333+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.333333333333333, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@37", "credit": "Ian Watson", "date": "April 2026", "family_updated": "", "metric_expression": "19/3 = 6.333+", "metric_symbol": "s", "metric_value": 6.333, "reference_text": "s = 19/3 = 6.333+ | Found by Ian Watson | in April 2026.", "source_image": "tt37.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt37.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 19/3 = 6.333+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "tt37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "a824891b660555f5", "improvement": -0.00022145462571288022, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.1058084789851627e-06, "max_pair_overlap_depth": -1.0503324543442716e-06, "metric_expression": "6.33355", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.333554787959046, "n": 37, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.333333333333333, "setup": "triintri", "side": 6.333554787959046, "solution_path": "data/solutions/generated/triintri_037_a824891b660555f5.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Ian Watson", "svg_path": "data/svg/a824891b660555f5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@38", "density": 0.9184187453437659, "friedman_analytical_or_proved": false, "friedman_credit": "Nathan Roll", "friedman_date": "April 2026", "friedman_display_metric_value": 6.43454, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt38.gif", "friedman_metric_expression": "6.43454+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.43454, "friedman_metric_value_source": "reported_decimal", "friedman_reference": {"analytical_or_proved": false, "case": "triintri@38", "credit": "Nathan Roll", "date": "April 2026", "family_updated": "", "metric_expression": "6.43454+", "metric_symbol": "s", "metric_value": 6.43454, "reference_text": "s = 6.43454+ | Found by Nathan Roll | in April 2026.", "source_image": "tt38.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt38.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6.43454+ | Found by Nathan Roll | in April 2026.", "friedman_source_image": "tt38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "b1563d97c893e28d", "improvement": 0.002163914058151306, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.8714774987883973e-07, "max_pair_overlap_depth": -1.6883301962034025e-06, "metric_expression": "6.43238", "metric_recovery_tolerance_abs": 1e-05, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.432376085941849, "n": 38, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.43454, "setup": "triintri", "side": 6.432376085941849, "solution_path": "data/solutions/record_hunt/triintri_38_b1563d97c893e28d.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T13:33:44+00:00", "submitted_by": "Nathan Roll", "svg_path": "data/svg/b1563d97c893e28d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@39", "density": 0.922995893638428, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_display_metric_value": 6.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "friedman_metric_expression": "13/2 = 6.500", "friedman_metric_symbol": "s", "friedman_metric_value": 6.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@39", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "", "metric_expression": "13/2 = 6.500", "metric_symbol": "s", "metric_value": 6.5, "reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "source_image": "tt40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "friedman_source_image": "tt40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "5ff069bd30790b7f", "improvement": -0.0002853099319573005, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -2.7141701112233934e-06, "max_pair_overlap_depth": -2.524988351737534e-07, "metric_expression": "6.50029", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.500285309931957, "n": 39, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.5, "setup": "triintri", "side": 6.500285309931957, "solution_path": "data/solutions/generated/triintri_039_5ff069bd30790b7f.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/5ff069bd30790b7f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@40", "density": 0.9466291268019702, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_display_metric_value": 6.5, "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "friedman_metric_expression": "13/2 = 6.500", "friedman_metric_symbol": "s", "friedman_metric_value": 6.5, "friedman_metric_value_source": "exact_expression", "friedman_reference": {"analytical_or_proved": true, "case": "triintri@40", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "", "metric_expression": "13/2 = 6.500", "metric_symbol": "s", "metric_value": 6.5, "reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "source_image": "tt40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "friedman_source_image": "tt40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "7890a1da940c9143", "improvement": -0.00039973752172350885, "leaderboard_consolidated_at": "2026-05-01T15:41:45+00:00", "leaderboard_current_best": true, "max_boundary_excess": -3.4343626129297504e-07, "max_pair_overlap_depth": -3.1212060811469655e-06, "metric_expression": "6.50040", "metric_recovery_tolerance_abs": 1e-08, "metric_recovery_tolerance_rel": 0.001, "metric_symbol": "s", "metric_value": 6.5003997375217235, "n": 40, "notes": "Verified coordinate reconstruction credited to the Friedman-listed finder; the exact evaluator metric is within the benchmark recovery band.", "record_type": "verified", "reference_side": 6.5, "setup": "triintri", "side": 6.5003997375217235, "solution_path": "data/solutions/generated/triintri_040_7890a1da940c9143.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "Erich Friedman", "svg_path": "data/svg/7890a1da940c9143.svg", "tolerance": 1e-08, "verified": true}
diff --git a/data/solutions/generated/cirincir_001_d8dddd0385fd067c.json b/data/solutions/generated/cirincir_001_d8dddd0385fd067c.json
index 90906cb137721e50df5c3a4f911d8bb1753729d1..68f311c9541b2e0cb93cb4a2ef5d75f9aa4bc378 100644
--- a/data/solutions/generated/cirincir_001_d8dddd0385fd067c.json
+++ b/data/solutions/generated/cirincir_001_d8dddd0385fd067c.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.0,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirincir_002_ab9a33067266df01.json b/data/solutions/generated/cirincir_002_ab9a33067266df01.json
index ef6b3c2f0d325654b6faa29c93340ec8084b763a..3726fb25cec26de1c8dacdc63bfa0a9d198a17f7 100644
--- a/data/solutions/generated/cirincir_002_ab9a33067266df01.json
+++ b/data/solutions/generated/cirincir_002_ab9a33067266df01.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirincir_003_fe973ff9a23dc34c.json b/data/solutions/generated/cirincir_003_fe973ff9a23dc34c.json
index 83b6bfe6254e9daf0c8182b9d9075b38baf73894..09dcb15f31cca69e54886418109758f1fd87793e 100644
--- a/data/solutions/generated/cirincir_003_fe973ff9a23dc34c.json
+++ b/data/solutions/generated/cirincir_003_fe973ff9a23dc34c.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.1547005383792515,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirincir_004_9d3e9e7ea6ba298b.json b/data/solutions/generated/cirincir_004_9d3e9e7ea6ba298b.json
index 5fc5d6fde2bcf131a2da101489585c22f64846cc..47b075b1cc158f2e7101606abd32aa2f5f6e37ed 100644
--- a/data/solutions/generated/cirincir_004_9d3e9e7ea6ba298b.json
+++ b/data/solutions/generated/cirincir_004_9d3e9e7ea6ba298b.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.414213562373095,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirincir_005_9c2ab1f687c06eec.json b/data/solutions/generated/cirincir_005_9c2ab1f687c06eec.json
index 519fdca8bdf7025d84fadef80fc1703a69a45460..6c548133765f830c01cdf5268ec0ce3ba459858c 100644
--- a/data/solutions/generated/cirincir_005_9c2ab1f687c06eec.json
+++ b/data/solutions/generated/cirincir_005_9c2ab1f687c06eec.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.701,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Graham"
diff --git a/data/solutions/generated/cirincir_006_5d3d5beee3c5f33c.json b/data/solutions/generated/cirincir_006_5d3d5beee3c5f33c.json
index 31bc15497a64973979af8652df662c4a51e8fd90..352653a369e5d1b180bb0e0bc1f58fde2c0de132 100644
--- a/data/solutions/generated/cirincir_006_5d3d5beee3c5f33c.json
+++ b/data/solutions/generated/cirincir_006_5d3d5beee3c5f33c.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.0,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Graham"
diff --git a/data/solutions/generated/cirincir_007_2b1985e4094e6893.json b/data/solutions/generated/cirincir_007_2b1985e4094e6893.json
index 057cc75f6d8e9c50d4fb4afd9accce903f5b0cfe..af197178bc8f00d10790ccf8375b0d85c33f1dd6 100644
--- a/data/solutions/generated/cirincir_007_2b1985e4094e6893.json
+++ b/data/solutions/generated/cirincir_007_2b1985e4094e6893.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.0,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Graham"
diff --git a/data/solutions/generated/cirincir_008_0193661647fd3854.json b/data/solutions/generated/cirincir_008_0193661647fd3854.json
index df42eb27cb7d87774744a51dbeff35e4394aa35a..221dcbb07e39588d7f7b0ee6cb638f7d56d698f8 100644
--- a/data/solutions/generated/cirincir_008_0193661647fd3854.json
+++ b/data/solutions/generated/cirincir_008_0193661647fd3854.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.304,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Braaksma"
diff --git a/data/solutions/generated/cirincir_009_b51df67181f6833b.json b/data/solutions/generated/cirincir_009_b51df67181f6833b.json
index 8bd0eb0c897f9628adf77785be930771965a88b4..beac1e8efcc5b4fbd5655f7d46c9074042220ea8 100644
--- a/data/solutions/generated/cirincir_009_b51df67181f6833b.json
+++ b/data/solutions/generated/cirincir_009_b51df67181f6833b.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.613,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Pirl"
diff --git a/data/solutions/generated/cirincir_011_e624f391927921fb.json b/data/solutions/generated/cirincir_011_e624f391927921fb.json
index 19be99b21d1f3ef23da3a8c08ebd11274b28b57c..5abd18e63a1214d3f1165da0fe7dc37431a70861 100644
--- a/data/solutions/generated/cirincir_011_e624f391927921fb.json
+++ b/data/solutions/generated/cirincir_011_e624f391927921fb.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.923,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Melissen"
diff --git a/data/solutions/generated/cirincir_012_0d7fc8a14b1c4e0e.json b/data/solutions/generated/cirincir_012_0d7fc8a14b1c4e0e.json
index e60dfd0845930a3f24778c36318296775481fb6b..d74ee319964ab316fa201cfcd5bb7d3b03a66c8e 100644
--- a/data/solutions/generated/cirincir_012_0d7fc8a14b1c4e0e.json
+++ b/data/solutions/generated/cirincir_012_0d7fc8a14b1c4e0e.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.029,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Kravitz"
diff --git a/data/solutions/generated/cirincir_013_a118f33872e0cb30.json b/data/solutions/generated/cirincir_013_a118f33872e0cb30.json
index 15681b0375990332e2e5f8575ee64fc4a8b59a86..c18e38a36aa55f0a5fdb5d167a29b369fd6d13d1 100644
--- a/data/solutions/generated/cirincir_013_a118f33872e0cb30.json
+++ b/data/solutions/generated/cirincir_013_a118f33872e0cb30.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.23606797749979,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "F. Fodor"
diff --git a/data/solutions/generated/cirincir_014_b2ec44e582e5ab93.json b/data/solutions/generated/cirincir_014_b2ec44e582e5ab93.json
index 97cdc3e1d267020d5f1a878df6dc77791a86fe40..bfe5df455060d857d5e01791c4d735f0a1449934 100644
--- a/data/solutions/generated/cirincir_014_b2ec44e582e5ab93.json
+++ b/data/solutions/generated/cirincir_014_b2ec44e582e5ab93.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.328,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Goldberg"
diff --git a/data/solutions/generated/cirincir_015_eeff7b918e6d6618.json b/data/solutions/generated/cirincir_015_eeff7b918e6d6618.json
index 1b6e0180724d3dd3d14870ff699f65cf5dcbf29c..b3d1e3f91f98ea80600c771025f84fda21ecaef1 100644
--- a/data/solutions/generated/cirincir_015_eeff7b918e6d6618.json
+++ b/data/solutions/generated/cirincir_015_eeff7b918e6d6618.json
@@ -45,7 +45,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.05462456891800099,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.521,
     "source_image_url": "https://erich-friedman.github.io/packing/cirincir/ccc15.gif",
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/cirincir_016_7824261a02b5ed90.json b/data/solutions/generated/cirincir_016_7824261a02b5ed90.json
index 4cb3ecd277cc65c39e9bc5886fb4b028966ced38..b3d5da34dc8e91cde5fbd3d103a1b0e02cc7a4e1 100644
--- a/data/solutions/generated/cirincir_016_7824261a02b5ed90.json
+++ b/data/solutions/generated/cirincir_016_7824261a02b5ed90.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.615,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Goldberg"
diff --git a/data/solutions/generated/cirincir_017_68c41c427924b99a.json b/data/solutions/generated/cirincir_017_68c41c427924b99a.json
index 876dc4f0e4c51625f6f71017106fab45b6c7c40b..85c11e2e816fef63b8ada4ac6e8287e21ed6c945 100644
--- a/data/solutions/generated/cirincir_017_68c41c427924b99a.json
+++ b/data/solutions/generated/cirincir_017_68c41c427924b99a.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.792,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Reis"
diff --git a/data/solutions/generated/cirincir_018_6acc78721c0b4ca1.json b/data/solutions/generated/cirincir_018_6acc78721c0b4ca1.json
index 1b56063e909169f616e02611ba941a94447decbd..d911dfe0e01a454a18c445f5e797e81a93c03a7e 100644
--- a/data/solutions/generated/cirincir_018_6acc78721c0b4ca1.json
+++ b/data/solutions/generated/cirincir_018_6acc78721c0b4ca1.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.863703305156273,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Kravitz"
diff --git a/data/solutions/generated/cirincir_019_8325b5bff319f74f.json b/data/solutions/generated/cirincir_019_8325b5bff319f74f.json
index 0a77fa4180809ab4263aea9f698c438d714d209c..1c5e1a8b7b17b4d5ed323e9fa46b532dbe07017e 100644
--- a/data/solutions/generated/cirincir_019_8325b5bff319f74f.json
+++ b/data/solutions/generated/cirincir_019_8325b5bff319f74f.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.863703305156273,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "F. Fodor"
diff --git a/data/solutions/generated/cirincir_020_f0718319f5a05220.json b/data/solutions/generated/cirincir_020_f0718319f5a05220.json
index 7c95f4a099f380b95d070507ea892133c5da1b93..59e840e738d3c8a0d0a4d6dbf9258045290244b0 100644
--- a/data/solutions/generated/cirincir_020_f0718319f5a05220.json
+++ b/data/solutions/generated/cirincir_020_f0718319f5a05220.json
@@ -47,8 +47,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.122,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Goldberg"
diff --git a/data/solutions/generated/cirincir_10_be14c55679a54b28.json b/data/solutions/generated/cirincir_10_be14c55679a54b28.json
index ad38915aaa7dc0e8cf54f7e377a9a414d210c6d1..6d29da550dbaf12d098fd459cbcd0c6d6b57bd58 100644
--- a/data/solutions/generated/cirincir_10_be14c55679a54b28.json
+++ b/data/solutions/generated/cirincir_10_be14c55679a54b28.json
@@ -44,7 +44,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.06260662900137194,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.813,
     "source_url": "https://erich-friedman.github.io/packing/cirincir/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Pirl"
diff --git a/data/solutions/generated/cirinhex_001_37d86bed2252b572.json b/data/solutions/generated/cirinhex_001_37d86bed2252b572.json
index fd0494e447b9612b38218002a6c0a2f6f58e92ac..28fb7108ec01cf125e291814879f6a37b21c4ef7 100644
--- a/data/solutions/generated/cirinhex_001_37d86bed2252b572.json
+++ b/data/solutions/generated/cirinhex_001_37d86bed2252b572.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.1547005383792515,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirinhex_002_4ba45a45587fd527.json b/data/solutions/generated/cirinhex_002_4ba45a45587fd527.json
index 48f5a3d7cc3c7ce0ec1f48ff311a88c58d1a9e2a..ce780f1471cb04d30e3b26c00fe392cdf3c71c63 100644
--- a/data/solutions/generated/cirinhex_002_4ba45a45587fd527.json
+++ b/data/solutions/generated/cirinhex_002_4ba45a45587fd527.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.1547005383792515,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirinhex_003_fa4a26f729d80904.json b/data/solutions/generated/cirinhex_003_fa4a26f729d80904.json
index d591790dbaf38ad5f3000dd0de8a30800ddd397f..6e6baf24736066df1bdc622c9b8b4d58f38e5805 100644
--- a/data/solutions/generated/cirinhex_003_fa4a26f729d80904.json
+++ b/data/solutions/generated/cirinhex_003_fa4a26f729d80904.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.309401076758503,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirinhex_004_4ea68db180a8d4c4.json b/data/solutions/generated/cirinhex_004_4ea68db180a8d4c4.json
index f281227e06a810b3b5fdad580c6871bb3825b260..e96804597d4ff1f02359f39a2ce423a891d0ee77 100644
--- a/data/solutions/generated/cirinhex_004_4ea68db180a8d4c4.json
+++ b/data/solutions/generated/cirinhex_004_4ea68db180a8d4c4.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.6665584304161603,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Shahriar Manzoor"
diff --git a/data/solutions/generated/cirinhex_005_eb88c54ef20a6355.json b/data/solutions/generated/cirinhex_005_eb88c54ef20a6355.json
index 407ab1f92d774dccb8fbfd2a13cc62bd7530f516..0c41103f5018bb15fee2897aef8ca936c3e44689 100644
--- a/data/solutions/generated/cirinhex_005_eb88c54ef20a6355.json
+++ b/data/solutions/generated/cirinhex_005_eb88c54ef20a6355.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.999,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/cirinhex_006_9b7724fab73c49c1.json b/data/solutions/generated/cirinhex_006_9b7724fab73c49c1.json
index b7e1467fbd8ba971d9b62b617d8929222e68e59a..374f24f97c17f70cdcb0f1a74cc4c69d913f98ed 100644
--- a/data/solutions/generated/cirinhex_006_9b7724fab73c49c1.json
+++ b/data/solutions/generated/cirinhex_006_9b7724fab73c49c1.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.1547005383792515,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirinhex_007_7368090471750227.json b/data/solutions/generated/cirinhex_007_7368090471750227.json
index e595df988672a9729e0b99056d8fd998833ec938..d55ebb3164c1a9102cb9ac37aab06567bad02463 100644
--- a/data/solutions/generated/cirinhex_007_7368090471750227.json
+++ b/data/solutions/generated/cirinhex_007_7368090471750227.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.1547005383792515,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirinhex_008_afebd04e4720460b.json b/data/solutions/generated/cirinhex_008_afebd04e4720460b.json
index 9ba2f2d882b89f3e673a419cd6b92db71be0f9f2..e2ef80fc6205ae07bd7696619255c11c250914ce 100644
--- a/data/solutions/generated/cirinhex_008_afebd04e4720460b.json
+++ b/data/solutions/generated/cirinhex_008_afebd04e4720460b.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.709,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinhex_009_64b59a5605599f8e.json b/data/solutions/generated/cirinhex_009_64b59a5605599f8e.json
index f107cb567b0074046707fe876c5ff74571887f68..d5c930ba789a8dac27416d1d6256f1a74db107fb 100644
--- a/data/solutions/generated/cirinhex_009_64b59a5605599f8e.json
+++ b/data/solutions/generated/cirinhex_009_64b59a5605599f8e.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.011843395522108,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinhex_010_cd79fdfeb9e3f24b.json b/data/solutions/generated/cirinhex_010_cd79fdfeb9e3f24b.json
index 610457a5c82bff502934c371f3f2659788fc6d96..1f6cca8437d6d8587eab2aeb0834b2aec5da1003 100644
--- a/data/solutions/generated/cirinhex_010_cd79fdfeb9e3f24b.json
+++ b/data/solutions/generated/cirinhex_010_cd79fdfeb9e3f24b.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.119,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinhex_011_cda2ccbbf4de67aa.json b/data/solutions/generated/cirinhex_011_cda2ccbbf4de67aa.json
index e8ab30e660f75dbbd5ea479a2d51603a9dff6948..8382384895d34f35873fefebb8652433b61a93a1 100644
--- a/data/solutions/generated/cirinhex_011_cda2ccbbf4de67aa.json
+++ b/data/solutions/generated/cirinhex_011_cda2ccbbf4de67aa.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.309401076758503,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/cirinhex_012_c3d795864cfeb74c.json b/data/solutions/generated/cirinhex_012_c3d795864cfeb74c.json
index 5b8cb5ece454473ac25a911a267a8112203a5f9b..cba703920b50387c1fcb4dc054a5dfb4f47c8a9c 100644
--- a/data/solutions/generated/cirinhex_012_c3d795864cfeb74c.json
+++ b/data/solutions/generated/cirinhex_012_c3d795864cfeb74c.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.309401076758503,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/cirinhex_013_62c003d981fbe524.json b/data/solutions/generated/cirinhex_013_62c003d981fbe524.json
index 05101f1fa1515d68d9b19fada69fe4982f16c885..812f1fb9131fd5a6c941971ac3f68da52de1ee07 100644
--- a/data/solutions/generated/cirinhex_013_62c003d981fbe524.json
+++ b/data/solutions/generated/cirinhex_013_62c003d981fbe524.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.06561931753893137,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.618802153517006,
     "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc13.gif",
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/cirinhex_014_d3d8d6f246feeaad.json b/data/solutions/generated/cirinhex_014_d3d8d6f246feeaad.json
index ed34a6b8fc43c77a52cb812073b46b2d227fa054..c7096b5fcdbfd8df75f2544130ed98c3f2115945 100644
--- a/data/solutions/generated/cirinhex_014_d3d8d6f246feeaad.json
+++ b/data/solutions/generated/cirinhex_014_d3d8d6f246feeaad.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.666558430416161,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinhex_015_d923ba7fbcb56e93.json b/data/solutions/generated/cirinhex_015_d923ba7fbcb56e93.json
index 8573d72d7c3466bd4fbc98f676e86c743e285a56..1a016fe59d5c268325859f3831f9b5c7091ec9d7 100644
--- a/data/solutions/generated/cirinhex_015_d923ba7fbcb56e93.json
+++ b/data/solutions/generated/cirinhex_015_d923ba7fbcb56e93.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.961,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinhex_016_b6a042d1d6eee5a4.json b/data/solutions/generated/cirinhex_016_b6a042d1d6eee5a4.json
index ebd71b6ae264078585835bec3af19db88f75e40c..5389e708638573018fea48bb8a1abf1e409daacb 100644
--- a/data/solutions/generated/cirinhex_016_b6a042d1d6eee5a4.json
+++ b/data/solutions/generated/cirinhex_016_b6a042d1d6eee5a4.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.999,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinhex_017_4927714d5d50ab2b.json b/data/solutions/generated/cirinhex_017_4927714d5d50ab2b.json
index 61785eb1d17851125608bb08648ab6ada3301822..ed20d6fcdcdd500d4255ba4ccc9de384738751d1 100644
--- a/data/solutions/generated/cirinhex_017_4927714d5d50ab2b.json
+++ b/data/solutions/generated/cirinhex_017_4927714d5d50ab2b.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.133,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinhex_018_223b1a3f7b7d0e67.json b/data/solutions/generated/cirinhex_018_223b1a3f7b7d0e67.json
index 544dea051ce43b5e02ecfc05791852aa4cac8f81..209d5e5f573fd758bf236d2345bfc128ee03f713 100644
--- a/data/solutions/generated/cirinhex_018_223b1a3f7b7d0e67.json
+++ b/data/solutions/generated/cirinhex_018_223b1a3f7b7d0e67.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.1547005383792515,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirinhex_019_78f9327e80d8ab20.json b/data/solutions/generated/cirinhex_019_78f9327e80d8ab20.json
index 7f3630d6864f941b36e964bbdef90872273f6666..c7c2bf7fdfd9ec38b9df2e04a3edf712d7908a1f 100644
--- a/data/solutions/generated/cirinhex_019_78f9327e80d8ab20.json
+++ b/data/solutions/generated/cirinhex_019_78f9327e80d8ab20.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.1547005383792515,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirinhex_020_247c6c06779a7d8b.json b/data/solutions/generated/cirinhex_020_247c6c06779a7d8b.json
index d849022e29d64f14555c5ebf6cb6b1e9d7457011..eb9acf837246b3a227aafcbeb095eb6e2948d1c4 100644
--- a/data/solutions/generated/cirinhex_020_247c6c06779a7d8b.json
+++ b/data/solutions/generated/cirinhex_020_247c6c06779a7d8b.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.676,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinhex_021_38040eceeb63c1e3.json b/data/solutions/generated/cirinhex_021_38040eceeb63c1e3.json
index 30dad3643fcb23bd2c18bd7c99b20853e1636100..74809d6b42961f99819d7f725a3dbaf1a3114035 100644
--- a/data/solutions/generated/cirinhex_021_38040eceeb63c1e3.json
+++ b/data/solutions/generated/cirinhex_021_38040eceeb63c1e3.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.709,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinhex_022_cd7262f9f7d0d279.json b/data/solutions/generated/cirinhex_022_cd7262f9f7d0d279.json
index 6a31daef8fe7556c06e512981ee69d8e0e4b7324..789ca19b3db1f0f03d7592a4fa71119cfec41d83 100644
--- a/data/solutions/generated/cirinhex_022_cd7262f9f7d0d279.json
+++ b/data/solutions/generated/cirinhex_022_cd7262f9f7d0d279.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.952,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinhex_023_de2d2aabdc650ad2.json b/data/solutions/generated/cirinhex_023_de2d2aabdc650ad2.json
index 865c4ab6ac6f429cadba17656953752c0e681d27..35ba48c1b58aa28637964ff4c9714c746a4a1917 100644
--- a/data/solutions/generated/cirinhex_023_de2d2aabdc650ad2.json
+++ b/data/solutions/generated/cirinhex_023_de2d2aabdc650ad2.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.011843395522108,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinhex_024_61a86ae12328c1ca.json b/data/solutions/generated/cirinhex_024_61a86ae12328c1ca.json
index 42035ee6fede7a67113507860b312571e1517ae8..50bdd461aa816d90d82888cffb05acee2055450a 100644
--- a/data/solutions/generated/cirinhex_024_61a86ae12328c1ca.json
+++ b/data/solutions/generated/cirinhex_024_61a86ae12328c1ca.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.117,
     "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Rob Pratt"
diff --git a/data/solutions/generated/cirinpen_001_2249439da521383e.json b/data/solutions/generated/cirinpen_001_2249439da521383e.json
index 3999e97ac980ec1c58da37af3dd46257afff0736..bd3d8eed381cb4805f1d6967829ef23af6a19798 100644
--- a/data/solutions/generated/cirinpen_001_2249439da521383e.json
+++ b/data/solutions/generated/cirinpen_001_2249439da521383e.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.453,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirinpen_002_042df6c460b769f5.json b/data/solutions/generated/cirinpen_002_042df6c460b769f5.json
index b64ec667ea92c11f23a8d45a5790539d6a860bc9..5e1a8a4c1f99979cf2186e412ffad9ef04e32f09 100644
--- a/data/solutions/generated/cirinpen_002_042df6c460b769f5.json
+++ b/data/solutions/generated/cirinpen_002_042df6c460b769f5.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.689,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirinpen_003_7afe63c4f78d1c3c.json b/data/solutions/generated/cirinpen_003_7afe63c4f78d1c3c.json
index 4528b4d19a59e469e0282bf12e9490e9038b4c9e..f7ff44dbcd04d94cb5e5b4b2432694e0867fed04 100644
--- a/data/solutions/generated/cirinpen_003_7afe63c4f78d1c3c.json
+++ b/data/solutions/generated/cirinpen_003_7afe63c4f78d1c3c.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.015,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "George Sicherman"
diff --git a/data/solutions/generated/cirinpen_004_3b6f81450d56967c.json b/data/solutions/generated/cirinpen_004_3b6f81450d56967c.json
index 65176a18111e79468b132764f30b5b01f81a7385..75c1f83cbc97f4a2c58e7bea8a06e4c423c2a3eb 100644
--- a/data/solutions/generated/cirinpen_004_3b6f81450d56967c.json
+++ b/data/solutions/generated/cirinpen_004_3b6f81450d56967c.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.314,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "George Sicherman"
diff --git a/data/solutions/generated/cirinpen_005_6a788c9a1ab05f1f.json b/data/solutions/generated/cirinpen_005_6a788c9a1ab05f1f.json
index 2e49d5958e949ef8d7d09454801bcbb6aa222808..97087bf0dcef020d3a02ade89421c51f38fb6116 100644
--- a/data/solutions/generated/cirinpen_005_6a788c9a1ab05f1f.json
+++ b/data/solutions/generated/cirinpen_005_6a788c9a1ab05f1f.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.453,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirinpen_006_a73fe466a153c6dc.json b/data/solutions/generated/cirinpen_006_a73fe466a153c6dc.json
index 42d693eaaf194c76a0761ceac4c32fda3c48d5ef..732175bf2a3a0a9e0baf319739391ebbbc9ebfd3 100644
--- a/data/solutions/generated/cirinpen_006_a73fe466a153c6dc.json
+++ b/data/solutions/generated/cirinpen_006_a73fe466a153c6dc.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.804,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirinpen_007_f2fb4964063d721f.json b/data/solutions/generated/cirinpen_007_f2fb4964063d721f.json
index 870aeb8cd537fe88edf37b87f0a04ca7c9ee136d..9e712559167f67875017ca76691d6b7f8b38895b 100644
--- a/data/solutions/generated/cirinpen_007_f2fb4964063d721f.json
+++ b/data/solutions/generated/cirinpen_007_f2fb4964063d721f.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.236,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "George Sicherman"
diff --git a/data/solutions/generated/cirinpen_008_7550c7a4a15ba971.json b/data/solutions/generated/cirinpen_008_7550c7a4a15ba971.json
index 4a5c4381915aec61e489fd323d75035f61cac4fb..3cc6bc8e03a13e0c0a7d0ef8da067fee214f3daa 100644
--- a/data/solutions/generated/cirinpen_008_7550c7a4a15ba971.json
+++ b/data/solutions/generated/cirinpen_008_7550c7a4a15ba971.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.564,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "George Sicherman"
diff --git a/data/solutions/generated/cirinpen_009_44a9c06211e4a669.json b/data/solutions/generated/cirinpen_009_44a9c06211e4a669.json
index 15f7ff55dfa0c9d197349b78d0d45041518d9140..ac52ec9826074828a6da0d1ac5d29db51b49d338 100644
--- a/data/solutions/generated/cirinpen_009_44a9c06211e4a669.json
+++ b/data/solutions/generated/cirinpen_009_44a9c06211e4a669.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.825,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "George Sicherman"
diff --git a/data/solutions/generated/cirinpen_010_38c046e395ee0204.json b/data/solutions/generated/cirinpen_010_38c046e395ee0204.json
index 1834ec7770b7a0a9b02b67e522d7b45196a77276..556be5eb0d4c24246f9c8443e8190f08c3bb52d3 100644
--- a/data/solutions/generated/cirinpen_010_38c046e395ee0204.json
+++ b/data/solutions/generated/cirinpen_010_38c046e395ee0204.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.095,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "George Sicherman"
diff --git a/data/solutions/generated/cirinpen_011_3c4a20ceb03b166b.json b/data/solutions/generated/cirinpen_011_3c4a20ceb03b166b.json
index 84f790884f4301a79eba68dee634850f1efd42b9..67c4942d683323bd099dcc30374ca13d81a90988 100644
--- a/data/solutions/generated/cirinpen_011_3c4a20ceb03b166b.json
+++ b/data/solutions/generated/cirinpen_011_3c4a20ceb03b166b.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.24,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinpen_012_1156bc3b50d815fe.json b/data/solutions/generated/cirinpen_012_1156bc3b50d815fe.json
index eb2268f0f8a4199e8e83f9d26c8564647a36ffef..ad53a3695e0c4f3a75e175b181bbae6c98ac16b4 100644
--- a/data/solutions/generated/cirinpen_012_1156bc3b50d815fe.json
+++ b/data/solutions/generated/cirinpen_012_1156bc3b50d815fe.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.407,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "George Sicherman"
diff --git a/data/solutions/generated/cirinpen_013_213cdbfbbdb494b1.json b/data/solutions/generated/cirinpen_013_213cdbfbbdb494b1.json
index 0c58ee830dd987082060c7df801c8d16c25e171f..6588edd77bb483f8e46a7a80db67551586545fd4 100644
--- a/data/solutions/generated/cirinpen_013_213cdbfbbdb494b1.json
+++ b/data/solutions/generated/cirinpen_013_213cdbfbbdb494b1.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.651,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "George Sicherman"
diff --git a/data/solutions/generated/cirinpen_014_44805be876ac7787.json b/data/solutions/generated/cirinpen_014_44805be876ac7787.json
index 1512dc61b6c3090e1b9d7eb9e48a86818566744a..c92e0b13acd28f7ac81d19b809193297cc9f3859 100644
--- a/data/solutions/generated/cirinpen_014_44805be876ac7787.json
+++ b/data/solutions/generated/cirinpen_014_44805be876ac7787.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.808,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "George Sicherman"
diff --git a/data/solutions/generated/cirinpen_015_36fcf02cb6fd9f92.json b/data/solutions/generated/cirinpen_015_36fcf02cb6fd9f92.json
index 187d4d5daba3fb6471f233c6d24a9a1f2963a882..2d0067b884a12043ed8bf63bb0a132fdc9d15cda 100644
--- a/data/solutions/generated/cirinpen_015_36fcf02cb6fd9f92.json
+++ b/data/solutions/generated/cirinpen_015_36fcf02cb6fd9f92.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.945,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "George Sicherman"
diff --git a/data/solutions/generated/cirinpen_016_39b6519b6fb7eef4.json b/data/solutions/generated/cirinpen_016_39b6519b6fb7eef4.json
index 8f6ca556526879535f53391f65b27f45c51a4630..ff32c83705288b234e9371ea63b8f815e656735f 100644
--- a/data/solutions/generated/cirinpen_016_39b6519b6fb7eef4.json
+++ b/data/solutions/generated/cirinpen_016_39b6519b6fb7eef4.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.129,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "George Sicherman"
diff --git a/data/solutions/generated/cirinpen_017_5e677c639e143e85.json b/data/solutions/generated/cirinpen_017_5e677c639e143e85.json
index 4cc5774331be3fbbf02f16783f8fda60e8a7817d..62b86a34610bfbe36f3a4b3c2bb8ea67618cb779 100644
--- a/data/solutions/generated/cirinpen_017_5e677c639e143e85.json
+++ b/data/solutions/generated/cirinpen_017_5e677c639e143e85.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.419,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinpen_018_34fda06736bbaaf7.json b/data/solutions/generated/cirinpen_018_34fda06736bbaaf7.json
index 8d33bfaecca898a3908755952ef6d28878ff4990..750824c67b03b94c55c4bf11733f5474be52cb21 100644
--- a/data/solutions/generated/cirinpen_018_34fda06736bbaaf7.json
+++ b/data/solutions/generated/cirinpen_018_34fda06736bbaaf7.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.586,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinpen_019_dfaba7cef14e53f5.json b/data/solutions/generated/cirinpen_019_dfaba7cef14e53f5.json
index 4250b45197d90b3e6c805f856f32fa7cfaba4575..7025ce309766f15c0c1e5d1cb4d759198ed62f2a 100644
--- a/data/solutions/generated/cirinpen_019_dfaba7cef14e53f5.json
+++ b/data/solutions/generated/cirinpen_019_dfaba7cef14e53f5.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.777,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinpen_020_d513055d785b23f7.json b/data/solutions/generated/cirinpen_020_d513055d785b23f7.json
index 4c5c7a3fcf2494fd6d1f83fe75b915ba67647f59..036973bb91840b1de8c92a1cbd7a8c045917d41e 100644
--- a/data/solutions/generated/cirinpen_020_d513055d785b23f7.json
+++ b/data/solutions/generated/cirinpen_020_d513055d785b23f7.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.944,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinpen_021_71add6eacc6c4fb9.json b/data/solutions/generated/cirinpen_021_71add6eacc6c4fb9.json
index 06aa8e383ab4afee537c20f889faf97340e09940..8813af829191cf868c20ef1d48d995ce28aeca12 100644
--- a/data/solutions/generated/cirinpen_021_71add6eacc6c4fb9.json
+++ b/data/solutions/generated/cirinpen_021_71add6eacc6c4fb9.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.06000958593551745,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.107,
     "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.21.gif",
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/cirinpen_022_ebdb05232e56526e.json b/data/solutions/generated/cirinpen_022_ebdb05232e56526e.json
index 1051302e9e58b6c9636f15481d8453607f895b9c..1b36031df61cabdfcd35bd2d95107eab84fb727f 100644
--- a/data/solutions/generated/cirinpen_022_ebdb05232e56526e.json
+++ b/data/solutions/generated/cirinpen_022_ebdb05232e56526e.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.271,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinpen_023_0115bd21477c01e6.json b/data/solutions/generated/cirinpen_023_0115bd21477c01e6.json
index 298baf94ee2feda13c8820527f3cfcac6391d186..b2c92f341c3277db122fda10d141c878133bef0b 100644
--- a/data/solutions/generated/cirinpen_023_0115bd21477c01e6.json
+++ b/data/solutions/generated/cirinpen_023_0115bd21477c01e6.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.397,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinpen_024_9eb26a95274f1d1d.json b/data/solutions/generated/cirinpen_024_9eb26a95274f1d1d.json
index e84f51bffea5cfe3aabd193516855b9a6beb4d0f..32cbf293fec6e4e199037f206d994403243fc7b0 100644
--- a/data/solutions/generated/cirinpen_024_9eb26a95274f1d1d.json
+++ b/data/solutions/generated/cirinpen_024_9eb26a95274f1d1d.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.534,
     "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/cirinsqu_001_329c377d412c468f.json b/data/solutions/generated/cirinsqu_001_329c377d412c468f.json
index d4cc5906ac999535e1a9a3fb333d0de1315be470..cf596aea0b02f1e7252f045a5ac6effd7d03db49 100644
--- a/data/solutions/generated/cirinsqu_001_329c377d412c468f.json
+++ b/data/solutions/generated/cirinsqu_001_329c377d412c468f.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirinsqu_002_e3bab8445b304ebe.json b/data/solutions/generated/cirinsqu_002_e3bab8445b304ebe.json
index e994eba886782f4cc0a9b617688fd8d8dac79639..c122489d4e947bde51d7973670ce483e09473e46 100644
--- a/data/solutions/generated/cirinsqu_002_e3bab8445b304ebe.json
+++ b/data/solutions/generated/cirinsqu_002_e3bab8445b304ebe.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.414213562373095,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirinsqu_003_63c314af1da3741c.json b/data/solutions/generated/cirinsqu_003_63c314af1da3741c.json
index 1dadd74b8cb30275da2e45451eb1f48ad537200d..a9a1a89b577a41f2846e19892b4515cf493b16da 100644
--- a/data/solutions/generated/cirinsqu_003_63c314af1da3741c.json
+++ b/data/solutions/generated/cirinsqu_003_63c314af1da3741c.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.9318516525781364,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirinsqu_004_9917d423eeeb95cb.json b/data/solutions/generated/cirinsqu_004_9917d423eeeb95cb.json
index 07cda58cc1cb1c400a4b8a6450f2b64b9f63a59d..d6e3977855e05138511ce9d797cc133e90d9cad2 100644
--- a/data/solutions/generated/cirinsqu_004_9917d423eeeb95cb.json
+++ b/data/solutions/generated/cirinsqu_004_9917d423eeeb95cb.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.0,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirinsqu_005_f91bd37c36f9320b.json b/data/solutions/generated/cirinsqu_005_f91bd37c36f9320b.json
index 08a2572c2da54a8c4f75d7e7829376ee91b43565..0ca2d7d70889ad6a93d20c507598852bdac69010 100644
--- a/data/solutions/generated/cirinsqu_005_f91bd37c36f9320b.json
+++ b/data/solutions/generated/cirinsqu_005_f91bd37c36f9320b.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.82842712474619,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirinsqu_006_96dda57e28868925.json b/data/solutions/generated/cirinsqu_006_96dda57e28868925.json
index 5e1fe0cd54811a7a9bb8efae0011ff92ae20002e..d1034354a2c27e5e6c82fb9cc4812b5f52d7fd39 100644
--- a/data/solutions/generated/cirinsqu_006_96dda57e28868925.json
+++ b/data/solutions/generated/cirinsqu_006_96dda57e28868925.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.328201177351374,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Graham"
diff --git a/data/solutions/generated/cirinsqu_007_7e4d3361af467e5d.json b/data/solutions/generated/cirinsqu_007_7e4d3361af467e5d.json
index 00eeca684cd263d8c05867205631c590c4d32fe4..faaaf590dbecbebd3406bbf8722acea70e4a02eb 100644
--- a/data/solutions/generated/cirinsqu_007_7e4d3361af467e5d.json
+++ b/data/solutions/generated/cirinsqu_007_7e4d3361af467e5d.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.732050807568878,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Schaer"
diff --git a/data/solutions/generated/cirinsqu_008_67f6750a9af94d2c.json b/data/solutions/generated/cirinsqu_008_67f6750a9af94d2c.json
index 678973457a97f05bd352820829def19721f4cf9e..a4783bd6a80dd605a7e467dd62a1bfe4625dbc13 100644
--- a/data/solutions/generated/cirinsqu_008_67f6750a9af94d2c.json
+++ b/data/solutions/generated/cirinsqu_008_67f6750a9af94d2c.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.863703305156273,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Schaer/Meir"
diff --git a/data/solutions/generated/cirinsqu_009_a35561fa5a518c8b.json b/data/solutions/generated/cirinsqu_009_a35561fa5a518c8b.json
index 52559983391d3572d27e6a21fbf66d579e58ed9b..5505bce0f399016ff49a9614ebc7584318875447 100644
--- a/data/solutions/generated/cirinsqu_009_a35561fa5a518c8b.json
+++ b/data/solutions/generated/cirinsqu_009_a35561fa5a518c8b.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.0,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Schaer"
diff --git a/data/solutions/generated/cirinsqu_011_b0ae38086de8cdf9.json b/data/solutions/generated/cirinsqu_011_b0ae38086de8cdf9.json
index 1a3763d804022e672435566aa5b0f9ee150e9816..484a9361e105100de342ca6a32f294212e9e30be 100644
--- a/data/solutions/generated/cirinsqu_011_b0ae38086de8cdf9.json
+++ b/data/solutions/generated/cirinsqu_011_b0ae38086de8cdf9.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.022,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Peikert"
diff --git a/data/solutions/generated/cirinsqu_012_e58733a8646795ab.json b/data/solutions/generated/cirinsqu_012_e58733a8646795ab.json
index f164e1bd85cc4dc572125fbce3e74591102120b7..ad714e57dea4d71d0ac65e8fe7c1439675ce0819 100644
--- a/data/solutions/generated/cirinsqu_012_e58733a8646795ab.json
+++ b/data/solutions/generated/cirinsqu_012_e58733a8646795ab.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.1449575542752655,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Peikert"
diff --git a/data/solutions/generated/cirinsqu_013_60997371c312edb4.json b/data/solutions/generated/cirinsqu_013_60997371c312edb4.json
index d133e574d734e1ec13d979d937fd64b9524dc1c8..d4ac71b9287453be0671b99773ad925e97af5ee7 100644
--- a/data/solutions/generated/cirinsqu_013_60997371c312edb4.json
+++ b/data/solutions/generated/cirinsqu_013_60997371c312edb4.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.463,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Peikert"
diff --git a/data/solutions/generated/cirinsqu_014_2ccdf5f3d4bee77b.json b/data/solutions/generated/cirinsqu_014_2ccdf5f3d4bee77b.json
index 386d175e6a842c5cfdd08bbc73cd86f18939f769..228f351b2969fe56d6836d627fd319f246bb8e96 100644
--- a/data/solutions/generated/cirinsqu_014_2ccdf5f3d4bee77b.json
+++ b/data/solutions/generated/cirinsqu_014_2ccdf5f3d4bee77b.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.732050807568878,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Wengerodt"
diff --git a/data/solutions/generated/cirinsqu_015_edc16b42d64e4d82.json b/data/solutions/generated/cirinsqu_015_edc16b42d64e4d82.json
index fbad4106b24c2e201f2bfbb26fe1809ad6e34135..5d3fac1845c6d88ae4b002258ce47f7e51aff75f 100644
--- a/data/solutions/generated/cirinsqu_015_edc16b42d64e4d82.json
+++ b/data/solutions/generated/cirinsqu_015_edc16b42d64e4d82.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.863703305156273,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Peikert"
diff --git a/data/solutions/generated/cirinsqu_016_6ef91613d0db44e8.json b/data/solutions/generated/cirinsqu_016_6ef91613d0db44e8.json
index 595cc7e1c758b6ba58e628795c24f37315d25263..c3093834f1ad5050f5b2a74c5021224e373e0eef 100644
--- a/data/solutions/generated/cirinsqu_016_6ef91613d0db44e8.json
+++ b/data/solutions/generated/cirinsqu_016_6ef91613d0db44e8.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.0,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Wengerodt"
diff --git a/data/solutions/generated/cirinsqu_017_9211255584acb7a4.json b/data/solutions/generated/cirinsqu_017_9211255584acb7a4.json
index bad752a96939c767a00e67e489432eba5e59662f..a9f55ceae59374490d91d66ef83b1422c52c4c91 100644
--- a/data/solutions/generated/cirinsqu_017_9211255584acb7a4.json
+++ b/data/solutions/generated/cirinsqu_017_9211255584acb7a4.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.532,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Peikert"
diff --git a/data/solutions/generated/cirinsqu_018_4872462eca76de82.json b/data/solutions/generated/cirinsqu_018_4872462eca76de82.json
index 5dd1e4fa6527df98af25f23c9a256b3e8e756b1f..1f035df0061c60e5c94e13c5ee95489b32d5cf5b 100644
--- a/data/solutions/generated/cirinsqu_018_4872462eca76de82.json
+++ b/data/solutions/generated/cirinsqu_018_4872462eca76de82.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.656402354702749,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Peikert"
diff --git a/data/solutions/generated/cirinsqu_019_72fa8cf8e074fd32.json b/data/solutions/generated/cirinsqu_019_72fa8cf8e074fd32.json
index d80f3d36170bfd3226279b567270a8888c3c7edf..b8118104581b3eaa42d78471073369450d449b18 100644
--- a/data/solutions/generated/cirinsqu_019_72fa8cf8e074fd32.json
+++ b/data/solutions/generated/cirinsqu_019_72fa8cf8e074fd32.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.907,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Peikert"
diff --git a/data/solutions/generated/cirinsqu_020_ed16784370181dab.json b/data/solutions/generated/cirinsqu_020_ed16784370181dab.json
index cb82bd377f6970729bf24914fea4aad100f4d65e..50ebf60086afaf4c93c950b1a740eff852ab9122 100644
--- a/data/solutions/generated/cirinsqu_020_ed16784370181dab.json
+++ b/data/solutions/generated/cirinsqu_020_ed16784370181dab.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.978083352821736,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Peikert"
diff --git a/data/solutions/generated/cirinsqu_021_65afc927a4d3cb10.json b/data/solutions/generated/cirinsqu_021_65afc927a4d3cb10.json
index edf7df56881c4c203aaf9d05fad80f0694b8cd56..081cea064c11efecd6473cac18d7769113ec9122 100644
--- a/data/solutions/generated/cirinsqu_021_65afc927a4d3cb10.json
+++ b/data/solutions/generated/cirinsqu_021_65afc927a4d3cb10.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.358,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Erich Friedman Packing Center"
diff --git a/data/solutions/generated/cirinsqu_022_27d48d864449f174.json b/data/solutions/generated/cirinsqu_022_27d48d864449f174.json
index f7f5c1acbff3505b0cc9fb025d65a72b3b9100fc..8671c4d5b0ffd878c3b85aef484bf5f8785e597b 100644
--- a/data/solutions/generated/cirinsqu_022_27d48d864449f174.json
+++ b/data/solutions/generated/cirinsqu_022_27d48d864449f174.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.463,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Erich Friedman Packing Center"
diff --git a/data/solutions/generated/cirinsqu_023_cfa99060ee2203a1.json b/data/solutions/generated/cirinsqu_023_cfa99060ee2203a1.json
index 0ce6c7ee8ebd38a350cf26739d272f9f44d20cbb..e86a9689a6899967c15be9777e1d387e6450d87f 100644
--- a/data/solutions/generated/cirinsqu_023_cfa99060ee2203a1.json
+++ b/data/solutions/generated/cirinsqu_023_cfa99060ee2203a1.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.727406610312546,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Erich Friedman Packing Center"
diff --git a/data/solutions/generated/cirinsqu_024_e2eca298edbdb88c.json b/data/solutions/generated/cirinsqu_024_e2eca298edbdb88c.json
index 30f7a9093ca0692f657d0c483a8f07778ca4599d..f5ed1b6b81c91c60bf926c654edb582a4a3df404 100644
--- a/data/solutions/generated/cirinsqu_024_e2eca298edbdb88c.json
+++ b/data/solutions/generated/cirinsqu_024_e2eca298edbdb88c.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.863703305156273,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Erich Friedman Packing Center"
diff --git a/data/solutions/generated/cirinsqu_10_522948d614943781.json b/data/solutions/generated/cirinsqu_10_522948d614943781.json
index 3b4f246fb2b4bc3556a7fca976ddeaf9209d7c63..36777ac461dfc511da6c7b6cbbabb4e78e694eee 100644
--- a/data/solutions/generated/cirinsqu_10_522948d614943781.json
+++ b/data/solutions/generated/cirinsqu_10_522948d614943781.json
@@ -47,7 +47,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 1.0052492910490174e-15,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.747,
     "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "De Groot"
diff --git a/data/solutions/generated/cirintri_001_10a7a380c7f5376a.json b/data/solutions/generated/cirintri_001_10a7a380c7f5376a.json
index 323be75206ce82af18adbc166899be6297ac9931..a677584a0e5438cdf49bdd4c097702ec72940502 100644
--- a/data/solutions/generated/cirintri_001_10a7a380c7f5376a.json
+++ b/data/solutions/generated/cirintri_001_10a7a380c7f5376a.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.4641016151377544,
     "source_url": "https://erich-friedman.github.io/packing/cirintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirintri_002_f5cde1b8295da3ad.json b/data/solutions/generated/cirintri_002_f5cde1b8295da3ad.json
index 369e33f087d211dd05bbb9d3535cbb2630101101..f6a7d9e5448392e4dbb2ded9a585e8140edc532e 100644
--- a/data/solutions/generated/cirintri_002_f5cde1b8295da3ad.json
+++ b/data/solutions/generated/cirintri_002_f5cde1b8295da3ad.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.464101615137754,
     "source_url": "https://erich-friedman.github.io/packing/cirintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirintri_003_fcee9d6e8b7c5ce0.json b/data/solutions/generated/cirintri_003_fcee9d6e8b7c5ce0.json
index 9944475cec874d11361442adc07e2ee0e5ea76cf..b6bfad09a3dc7e33aa888468423d33a6e6a23906 100644
--- a/data/solutions/generated/cirintri_003_fcee9d6e8b7c5ce0.json
+++ b/data/solutions/generated/cirintri_003_fcee9d6e8b7c5ce0.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.464101615137754,
     "source_url": "https://erich-friedman.github.io/packing/cirintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/cirintri_004_9e0c39beb3cc8aa7.json b/data/solutions/generated/cirintri_004_9e0c39beb3cc8aa7.json
index 37479ae13722a3feeefb284f45838bc24a846adc..24b69982ad74615ac005fda36fc8508acbeff1d0 100644
--- a/data/solutions/generated/cirintri_004_9e0c39beb3cc8aa7.json
+++ b/data/solutions/generated/cirintri_004_9e0c39beb3cc8aa7.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.928203230275509,
     "source_url": "https://erich-friedman.github.io/packing/cirintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Milano"
diff --git a/data/solutions/generated/cirintri_005_ad32c3b8e4c714b5.json b/data/solutions/generated/cirintri_005_ad32c3b8e4c714b5.json
index 8a03b37ca50fc25548d00f2cf71d426c73080565..2d2e6775e00463c457cb19aea4dfb03ab33b5597 100644
--- a/data/solutions/generated/cirintri_005_ad32c3b8e4c714b5.json
+++ b/data/solutions/generated/cirintri_005_ad32c3b8e4c714b5.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.464101615137754,
     "source_url": "https://erich-friedman.github.io/packing/cirintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Milano"
diff --git a/data/solutions/generated/cirintri_006_09bddcb97a85d368.json b/data/solutions/generated/cirintri_006_09bddcb97a85d368.json
index f94b3186a69579b251d203e3c2dbbd8482146204..c9697d90505fe5f7273368ff436878b2b58ee96d 100644
--- a/data/solutions/generated/cirintri_006_09bddcb97a85d368.json
+++ b/data/solutions/generated/cirintri_006_09bddcb97a85d368.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.464101615137754,
     "source_url": "https://erich-friedman.github.io/packing/cirintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Oler/Groemer"
diff --git a/data/solutions/generated/cirintri_007_1d479488f6f25560.json b/data/solutions/generated/cirintri_007_1d479488f6f25560.json
index cc9883342078bec3164511eb16dc94990519dfae..235b15599de7bc4aedf378728cafec70e5ea6c2d 100644
--- a/data/solutions/generated/cirintri_007_1d479488f6f25560.json
+++ b/data/solutions/generated/cirintri_007_1d479488f6f25560.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.928203230275509,
     "source_url": "https://erich-friedman.github.io/packing/cirintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Melissen"
diff --git a/data/solutions/generated/cirintri_008_ad6e4ca149e6364f.json b/data/solutions/generated/cirintri_008_ad6e4ca149e6364f.json
index 3e9638c93386ae8e3d58b9885adca0fc0960a2d3..18b1e7790e908649296f03567b2b447a50aefd5a 100644
--- a/data/solutions/generated/cirintri_008_ad6e4ca149e6364f.json
+++ b/data/solutions/generated/cirintri_008_ad6e4ca149e6364f.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.08590453848289066,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.293810046163108,
     "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct8.gif",
     "source_url": "https://erich-friedman.github.io/packing/cirintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/cirintri_009_108d2156f1819ef5.json b/data/solutions/generated/cirintri_009_108d2156f1819ef5.json
index bba8d12e636d3d52fc7ff0d7b5650e6b79f83490..2d6dbaf3c6a37eb97cb89c26901a1a6e8ef67c77 100644
--- a/data/solutions/generated/cirintri_009_108d2156f1819ef5.json
+++ b/data/solutions/generated/cirintri_009_108d2156f1819ef5.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.464101615137755,
     "source_url": "https://erich-friedman.github.io/packing/cirintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Melissen"
diff --git a/data/solutions/generated/cirintri_010_abf88e494059d012.json b/data/solutions/generated/cirintri_010_abf88e494059d012.json
index 7db1add0ced31f53bca730c764b16e46429856aa..d1a3fed857cca403d9b41428bf77a1b0566ecc48 100644
--- a/data/solutions/generated/cirintri_010_abf88e494059d012.json
+++ b/data/solutions/generated/cirintri_010_abf88e494059d012.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.464101615137755,
     "source_url": "https://erich-friedman.github.io/packing/cirintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Oler/Groemer"
diff --git a/data/solutions/generated/cirintri_011_64f835afcfaa2245.json b/data/solutions/generated/cirintri_011_64f835afcfaa2245.json
index af91b3333b066c6cd24ca59d53ad842256dc492b..eaecaadb999e50031edc689ab98766548033311a 100644
--- a/data/solutions/generated/cirintri_011_64f835afcfaa2245.json
+++ b/data/solutions/generated/cirintri_011_64f835afcfaa2245.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 10.730087938848659,
     "source_url": "https://erich-friedman.github.io/packing/cirintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Melissen"
diff --git a/data/solutions/generated/cirintri_012_c94cd40d17cad41e.json b/data/solutions/generated/cirintri_012_c94cd40d17cad41e.json
index fb495dcaa3cb1c80fbc840958baaf1a12ec66df0..c34e7bea08c04de4d734eaa05c8439ae6199053a 100644
--- a/data/solutions/generated/cirintri_012_c94cd40d17cad41e.json
+++ b/data/solutions/generated/cirintri_012_c94cd40d17cad41e.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 10.928203230275509,
     "source_url": "https://erich-friedman.github.io/packing/cirintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Melissen"
diff --git a/data/solutions/generated/cirintri_013_4ca74ad9707b79ad.json b/data/solutions/generated/cirintri_013_4ca74ad9707b79ad.json
index 6dfef59117b05b82002b8fb2c030bd7d69a5cb5b..6fa90e2af52786d80323277573da553c82afa92d 100644
--- a/data/solutions/generated/cirintri_013_4ca74ad9707b79ad.json
+++ b/data/solutions/generated/cirintri_013_4ca74ad9707b79ad.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 11.406495853751709,
     "source_url": "https://erich-friedman.github.io/packing/cirintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Melissen"
diff --git a/data/solutions/generated/cirintri_014_67743153538612b8.json b/data/solutions/generated/cirintri_014_67743153538612b8.json
index 0cd80278e12ad904c3e6581e11f40272a8477a53..a0496846b2262fc066295c46b9640dd8f9247142 100644
--- a/data/solutions/generated/cirintri_014_67743153538612b8.json
+++ b/data/solutions/generated/cirintri_014_67743153538612b8.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 11.464101615137755,
     "source_url": "https://erich-friedman.github.io/packing/cirintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erd\u0151s/Oler"
diff --git a/data/solutions/generated/cirintri_015_2a26f9d337f635e0.json b/data/solutions/generated/cirintri_015_2a26f9d337f635e0.json
index e979bb7bb4da3b79b8c97b0b5308300b2cbf06bc..f4af628896be92a95231b00fe7a5e88cac613ca1 100644
--- a/data/solutions/generated/cirintri_015_2a26f9d337f635e0.json
+++ b/data/solutions/generated/cirintri_015_2a26f9d337f635e0.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 11.464101615137755,
     "source_url": "https://erich-friedman.github.io/packing/cirintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erd\u0151s/Groemer"
diff --git a/data/solutions/generated/domindom_001_6b50d5741feee5dc.json b/data/solutions/generated/domindom_001_6b50d5741feee5dc.json
index de25eaa3cefb7181531ff8af762735a08ccbb332..60f8784a7633285774c55aa3753d044d78be1fe5 100644
--- a/data/solutions/generated/domindom_001_6b50d5741feee5dc.json
+++ b/data/solutions/generated/domindom_001_6b50d5741feee5dc.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.0,
     "source_url": "https://erich-friedman.github.io/packing/domindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/domindom_002_e1760976ec64bd64.json b/data/solutions/generated/domindom_002_e1760976ec64bd64.json
index f8254ce89ba064e9e071bd3f11aa6b4a8e6ca381..80ae999c62c02154feb1ef63d00082d697f2ede7 100644
--- a/data/solutions/generated/domindom_002_e1760976ec64bd64.json
+++ b/data/solutions/generated/domindom_002_e1760976ec64bd64.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.9711971193069775,
     "source_url": "https://erich-friedman.github.io/packing/domindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/domindom_003_5194ab3dddc343bb.json b/data/solutions/generated/domindom_003_5194ab3dddc343bb.json
index 84cbf1468da545b302d06dc503c94cb9a503358e..c65f342442459bcc9bcd6bc6cd256a17ce246ddf 100644
--- a/data/solutions/generated/domindom_003_5194ab3dddc343bb.json
+++ b/data/solutions/generated/domindom_003_5194ab3dddc343bb.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/domindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/domindom_004_14a703d2c83d5b43.json b/data/solutions/generated/domindom_004_14a703d2c83d5b43.json
index 43dc3dbc5d9ce943068526ca50851af4920e9706..cf4d137124fdc6d7e19da63ed26ae2c2ac57f32e 100644
--- a/data/solutions/generated/domindom_004_14a703d2c83d5b43.json
+++ b/data/solutions/generated/domindom_004_14a703d2c83d5b43.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/domindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/domindom_005_af0995e19f0dc8ce.json b/data/solutions/generated/domindom_005_af0995e19f0dc8ce.json
index a04bd4c7933aef715c7e0399950a684e82e07a85..8da3133d9346e77ac10e7e86bd823d19428158b5 100644
--- a/data/solutions/generated/domindom_005_af0995e19f0dc8ce.json
+++ b/data/solutions/generated/domindom_005_af0995e19f0dc8ce.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.5,
     "source_url": "https://erich-friedman.github.io/packing/domindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/domindom_006_0f3d5defa1e042a8.json b/data/solutions/generated/domindom_006_0f3d5defa1e042a8.json
index c38210f8dec1663f4119310412cd6f96b9206f9d..4f80a55f0bbee9a62b65fe920ad10768c8aafc96 100644
--- a/data/solutions/generated/domindom_006_0f3d5defa1e042a8.json
+++ b/data/solutions/generated/domindom_006_0f3d5defa1e042a8.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.024148871645601474,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.916,
     "source_image_url": "https://erich-friedman.github.io/packing/domindom/6.gif",
     "source_url": "https://erich-friedman.github.io/packing/domindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/domindom_007_7b5335d8b8c4a5db.json b/data/solutions/generated/domindom_007_7b5335d8b8c4a5db.json
index 29ca40b56e9892150cdb8a3cfc483ed559f52260..771c9cf9bd75685f764fbc6d4e9d3bd8ee287763 100644
--- a/data/solutions/generated/domindom_007_7b5335d8b8c4a5db.json
+++ b/data/solutions/generated/domindom_007_7b5335d8b8c4a5db.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.0,
     "source_url": "https://erich-friedman.github.io/packing/domindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/domindom_008_953d10b3e926402a.json b/data/solutions/generated/domindom_008_953d10b3e926402a.json
index 4290561d5609a1f79355736b01f6c7e4f66572db..3f7c3faa623526272afe6e9970543f7ec46566c4 100644
--- a/data/solutions/generated/domindom_008_953d10b3e926402a.json
+++ b/data/solutions/generated/domindom_008_953d10b3e926402a.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.0,
     "source_url": "https://erich-friedman.github.io/packing/domindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/domindom_009_43b9630822b40990.json b/data/solutions/generated/domindom_009_43b9630822b40990.json
index a2e383eb991565a039020b15512a85a7da7368a5..2eda11724ac4672a88dc155cc680643575c910e3 100644
--- a/data/solutions/generated/domindom_009_43b9630822b40990.json
+++ b/data/solutions/generated/domindom_009_43b9630822b40990.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.0,
     "source_url": "https://erich-friedman.github.io/packing/domindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/domindom_010_d7508c45c3f18a7c.json b/data/solutions/generated/domindom_010_d7508c45c3f18a7c.json
index de8d6279cd63da0fe38263e8cdd81c74eabf2f06..c3ed9dad613c5b791730e7f079182e66d9d323cb 100644
--- a/data/solutions/generated/domindom_010_d7508c45c3f18a7c.json
+++ b/data/solutions/generated/domindom_010_d7508c45c3f18a7c.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.5,
     "source_url": "https://erich-friedman.github.io/packing/domindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/domindom_011_0fa9d3de612fbf03.json b/data/solutions/generated/domindom_011_0fa9d3de612fbf03.json
index 4d52fa73978a608508d0479f371e5481c10278b4..940410f9fe8ea8e2283ffe7928caef46d5a58d8f 100644
--- a/data/solutions/generated/domindom_011_0fa9d3de612fbf03.json
+++ b/data/solutions/generated/domindom_011_0fa9d3de612fbf03.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.018638624198504705,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.801041412477616,
     "source_image_url": "https://erich-friedman.github.io/packing/domindom/11.gif",
     "source_url": "https://erich-friedman.github.io/packing/domindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/domindom_012_3a75d33bd56228b0.json b/data/solutions/generated/domindom_012_3a75d33bd56228b0.json
index 76957ff4373ed531711aead5ba7291c3bef6a000..f360f2487c4f12a3e5d42d7f516332ef7f6d2ce4 100644
--- a/data/solutions/generated/domindom_012_3a75d33bd56228b0.json
+++ b/data/solutions/generated/domindom_012_3a75d33bd56228b0.json
@@ -46,8 +46,11 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/deep_profile_remaining_orange.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa_polish",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.914213562373095,
     "source_image_url": "https://erich-friedman.github.io/packing/domindom/12.gif",
     "source_url": "https://erich-friedman.github.io/packing/domindom/",
     "submitted_at": "2026-05-01T03:07:58+00:00",
diff --git a/data/solutions/generated/domindom_014_8be6cbfdbea40909.json b/data/solutions/generated/domindom_014_8be6cbfdbea40909.json
index 4406bfe66aaae3626960ed0fb2d3d3250b87a7b6..3b00864c6f48eb4227bb7067fb164ada1eda2b46 100644
--- a/data/solutions/generated/domindom_014_8be6cbfdbea40909.json
+++ b/data/solutions/generated/domindom_014_8be6cbfdbea40909.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.0,
     "source_url": "https://erich-friedman.github.io/packing/domindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/domindom_015_d2b8e4757dde349c.json b/data/solutions/generated/domindom_015_d2b8e4757dde349c.json
index bfe8e934daee74ef0f9f9209cb6c1d142222f9db..7abc55cd41b71bb649d2aa161579d636f808bbd3 100644
--- a/data/solutions/generated/domindom_015_d2b8e4757dde349c.json
+++ b/data/solutions/generated/domindom_015_d2b8e4757dde349c.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.0,
     "source_url": "https://erich-friedman.github.io/packing/domindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/domindom_016_5102d8436800a7ff.json b/data/solutions/generated/domindom_016_5102d8436800a7ff.json
index 39a3b8f8187771df86eb32f762ee8e1a73bcd54e..bcf11daa1f6bbfcb53aaebd9c45c73ca6c74acb4 100644
--- a/data/solutions/generated/domindom_016_5102d8436800a7ff.json
+++ b/data/solutions/generated/domindom_016_5102d8436800a7ff.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.0,
     "source_url": "https://erich-friedman.github.io/packing/domindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/domindom_017_3b388ddd068a843f.json b/data/solutions/generated/domindom_017_3b388ddd068a843f.json
index 156d396a84fc161dd7deb702ed7552525adbf769..c8d9ad48aa271f30c54c9623fde18b350e650bb1 100644
--- a/data/solutions/generated/domindom_017_3b388ddd068a843f.json
+++ b/data/solutions/generated/domindom_017_3b388ddd068a843f.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.5,
     "source_url": "https://erich-friedman.github.io/packing/domindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/domindom_018_6a5fcb6ec4e55187.json b/data/solutions/generated/domindom_018_6a5fcb6ec4e55187.json
index c56e7c3c1192841cf98f899a690aea5341dbcb1b..c82b67f8d566b984f39a25771e509ff8137e67f0 100644
--- a/data/solutions/generated/domindom_018_6a5fcb6ec4e55187.json
+++ b/data/solutions/generated/domindom_018_6a5fcb6ec4e55187.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.03699277167923271,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.5,
     "source_image_url": "https://erich-friedman.github.io/packing/domindom/18.gif",
     "source_url": "https://erich-friedman.github.io/packing/domindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/domintri_001_6121ec989c6c813b.json b/data/solutions/generated/domintri_001_6121ec989c6c813b.json
index 7aa1ce926b44ef130309c744e41c012750824e1f..23332c91de2fd12cb50cac38a3bbe7b5d9a4b9ad 100644
--- a/data/solutions/generated/domintri_001_6121ec989c6c813b.json
+++ b/data/solutions/generated/domintri_001_6121ec989c6c813b.json
@@ -51,8 +51,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.1547005383792515,
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/domintri_002_75b0ecc0320e01de.json b/data/solutions/generated/domintri_002_75b0ecc0320e01de.json
index 704474442271da60bcad02f3fdc19c798c787793..7afa316e8a81df53cd945f000ad0fe454bc53eb3 100644
--- a/data/solutions/generated/domintri_002_75b0ecc0320e01de.json
+++ b/data/solutions/generated/domintri_002_75b0ecc0320e01de.json
@@ -51,8 +51,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.309401076758503,
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/domintri_003_ecf54a038a2d7184.json b/data/solutions/generated/domintri_003_ecf54a038a2d7184.json
index e46597bd11e8ebf56e72299cbfc32a2cecbf67a0..d9d69bf38f4c8819efab365bd2f642382d24534e 100644
--- a/data/solutions/generated/domintri_003_ecf54a038a2d7184.json
+++ b/data/solutions/generated/domintri_003_ecf54a038a2d7184.json
@@ -51,8 +51,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.309401076758503,
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/domintri_004_6f3730492b03ce4f.json b/data/solutions/generated/domintri_004_6f3730492b03ce4f.json
index b861e068e9a69beea7c1faa1689fdd0e70b79e76..9c73c4b3b7743a3ec9e9f3f771c53c7706cf62c2 100644
--- a/data/solutions/generated/domintri_004_6f3730492b03ce4f.json
+++ b/data/solutions/generated/domintri_004_6f3730492b03ce4f.json
@@ -51,8 +51,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.38188,
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/domintri_005_272a5ede0aa9a415.json b/data/solutions/generated/domintri_005_272a5ede0aa9a415.json
index 589cffb86062720dfe8e04e39e1217dce03c6a22..de079ec328cfcc335176eb7149fb9fa1d3604cfe 100644
--- a/data/solutions/generated/domintri_005_272a5ede0aa9a415.json
+++ b/data/solutions/generated/domintri_005_272a5ede0aa9a415.json
@@ -51,8 +51,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.464101615137754,
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/domintri_006_5709487003259292.json b/data/solutions/generated/domintri_006_5709487003259292.json
index 25b118460d94c73866e8967e960d1ca2e5e6eac4..4ac4dbde2eb931a39f07f2f6a991f781e830a839 100644
--- a/data/solutions/generated/domintri_006_5709487003259292.json
+++ b/data/solutions/generated/domintri_006_5709487003259292.json
@@ -51,8 +51,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.309401076758503,
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/domintri_007_4f3a41ae14776742.json b/data/solutions/generated/domintri_007_4f3a41ae14776742.json
index a8c718ae896d986dc3eb1c5ca118a4921ce37c14..79a162f6e57b25028782356fa6ac1e99adf33483 100644
--- a/data/solutions/generated/domintri_007_4f3a41ae14776742.json
+++ b/data/solutions/generated/domintri_007_4f3a41ae14776742.json
@@ -51,8 +51,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.61409,
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/domintri_008_6c005b2a9a930ec2.json b/data/solutions/generated/domintri_008_6c005b2a9a930ec2.json
index d81aa230d48842fc861d9173fd483df48404ec95..72efd6705f54b8d3ccecbbdc262946898da4b906 100644
--- a/data/solutions/generated/domintri_008_6c005b2a9a930ec2.json
+++ b/data/solutions/generated/domintri_008_6c005b2a9a930ec2.json
@@ -51,8 +51,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.1547005383792515,
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/domintri_009_efd3c01a911fbe39.json b/data/solutions/generated/domintri_009_efd3c01a911fbe39.json
index e1a71910cc7a1483b0a72c9f4ce3e0ac7ae065fe..74af2b80a7dc098b4b62cb20f849c15f2c926b8b 100644
--- a/data/solutions/generated/domintri_009_efd3c01a911fbe39.json
+++ b/data/solutions/generated/domintri_009_efd3c01a911fbe39.json
@@ -49,7 +49,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.11883552411638428,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.309401076758503,
     "source_image_url": "https://erich-friedman.github.io/packing/domintri/9.png",
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/domintri_010_0ce8e56f538c019b.json b/data/solutions/generated/domintri_010_0ce8e56f538c019b.json
index 2e4c3f44eb67250ffee7b4c506aa9a299ed82f4d..671c5790328060ca0c86bf97e842f5f81051ce34 100644
--- a/data/solutions/generated/domintri_010_0ce8e56f538c019b.json
+++ b/data/solutions/generated/domintri_010_0ce8e56f538c019b.json
@@ -49,7 +49,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.12386653253538112,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.618802153517006,
     "source_image_url": "https://erich-friedman.github.io/packing/domintri/10.png",
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/domintri_011_9dea260c7a23e4ab.json b/data/solutions/generated/domintri_011_9dea260c7a23e4ab.json
index c9e48ee7381f60f800459779d02686f9dfae6d6b..0d022dc63cb77444cefd463a4fd7324e3e6a2e50 100644
--- a/data/solutions/generated/domintri_011_9dea260c7a23e4ab.json
+++ b/data/solutions/generated/domintri_011_9dea260c7a23e4ab.json
@@ -49,7 +49,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.13257833043914402,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.154700538379252,
     "source_image_url": "https://erich-friedman.github.io/packing/domintri/11.png",
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/domintri_012_c7b6e34fcb0ca6b3.json b/data/solutions/generated/domintri_012_c7b6e34fcb0ca6b3.json
index 8bf213092af23a40ee73eb8e4cd01bac24c5b408..4ac3589edfdc317012afd2e46c5609921ff9c47e 100644
--- a/data/solutions/generated/domintri_012_c7b6e34fcb0ca6b3.json
+++ b/data/solutions/generated/domintri_012_c7b6e34fcb0ca6b3.json
@@ -49,7 +49,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.1350934282010407,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.309401076758503,
     "source_image_url": "https://erich-friedman.github.io/packing/domintri/12.png",
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/domintri_013_9f9d19c6f117401b.json b/data/solutions/generated/domintri_013_9f9d19c6f117401b.json
index e3c4068d76ec91124871dfff71b7fbaba7b6d8a5..5839bda4ba23a2ae1d6c1f1489928e800e33c987 100644
--- a/data/solutions/generated/domintri_013_9f9d19c6f117401b.json
+++ b/data/solutions/generated/domintri_013_9f9d19c6f117401b.json
@@ -49,7 +49,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.14012443662003674,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.618802153517006,
     "source_image_url": "https://erich-friedman.github.io/packing/domintri/13.png",
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/domintri_014_333566d5c4b3657c.json b/data/solutions/generated/domintri_014_333566d5c4b3657c.json
index f4527f73982e43fa3b1a3fd2b81c76268acd98b9..41154cb1b326a4def9470154312b1b5eea0b321c 100644
--- a/data/solutions/generated/domintri_014_333566d5c4b3657c.json
+++ b/data/solutions/generated/domintri_014_333566d5c4b3657c.json
@@ -49,7 +49,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.050653350382938486,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.773502691896258,
     "source_image_url": "https://erich-friedman.github.io/packing/domintri/14.png",
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/domintri_015_2da1308626a02461.json b/data/solutions/generated/domintri_015_2da1308626a02461.json
index 2b3b86563fd697b85a9a755f7eea31b3f9890c74..9c91dcb1399665c4355a94f7bf2866ac771ffeb2 100644
--- a/data/solutions/generated/domintri_015_2da1308626a02461.json
+++ b/data/solutions/generated/domintri_015_2da1308626a02461.json
@@ -49,7 +49,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.15135133228569636,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.309401076758503,
     "source_image_url": "https://erich-friedman.github.io/packing/domintri/15.png",
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/domintri_016_cc2a76b6a75c7120.json b/data/solutions/generated/domintri_016_cc2a76b6a75c7120.json
index 11373c0242665179414e46ae693efaa080bfe489..1754ad01430294a9566ae782808f9f0fe691e5e2 100644
--- a/data/solutions/generated/domintri_016_cc2a76b6a75c7120.json
+++ b/data/solutions/generated/domintri_016_cc2a76b6a75c7120.json
@@ -49,7 +49,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.024402578745003903,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.464101615137755,
     "source_image_url": "https://erich-friedman.github.io/packing/domintri/16.png",
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/domintri_017_842ace76b15a5c6d.json b/data/solutions/generated/domintri_017_842ace76b15a5c6d.json
index 13c618c32bcf764c0989564365719bbf9f484ae9..896c31863faa2b7e5d92aad7a7477921e505f6c4 100644
--- a/data/solutions/generated/domintri_017_842ace76b15a5c6d.json
+++ b/data/solutions/generated/domintri_017_842ace76b15a5c6d.json
@@ -49,7 +49,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.13475666883458026,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.773502691896258,
     "source_image_url": "https://erich-friedman.github.io/packing/domintri/17.png",
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/domintri_018_286272298adf99a4.json b/data/solutions/generated/domintri_018_286272298adf99a4.json
index dec593ac7614d0dc28bd2c4185107e09af8efbfb..a4e8d798a663d1224fc861d209dcb1217ef1d35c 100644
--- a/data/solutions/generated/domintri_018_286272298adf99a4.json
+++ b/data/solutions/generated/domintri_018_286272298adf99a4.json
@@ -51,8 +51,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.928203230275509,
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/domintri_019_77c1eb98f0e7fed4.json b/data/solutions/generated/domintri_019_77c1eb98f0e7fed4.json
index 42784f87e34780aebb0933ba095a4dc4ca5d83b0..4af477e07166c68adbab2029c04bb59ccf8e2697 100644
--- a/data/solutions/generated/domintri_019_77c1eb98f0e7fed4.json
+++ b/data/solutions/generated/domintri_019_77c1eb98f0e7fed4.json
@@ -49,7 +49,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.024779176754823707,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 10.309401076758503,
     "source_image_url": "https://erich-friedman.github.io/packing/domintri/19.png",
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/domintri_020_19214c32485a435f.json b/data/solutions/generated/domintri_020_19214c32485a435f.json
index fa0ac3e26ffb0d0722593c1ecd55244f46afc034..272108bb1ab50a1333e1e64be6b3d0453dced144 100644
--- a/data/solutions/generated/domintri_020_19214c32485a435f.json
+++ b/data/solutions/generated/domintri_020_19214c32485a435f.json
@@ -49,7 +49,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.02698101501945161,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 10.464101615137755,
     "source_image_url": "https://erich-friedman.github.io/packing/domintri/20.png",
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/domintri_021_797030ebf0f8c4e4.json b/data/solutions/generated/domintri_021_797030ebf0f8c4e4.json
index be9ba9d1ad33205b37172f9395b0c9d77d39dabf..e3f339c2216eeb45d02f2fe09a771fa834f963df 100644
--- a/data/solutions/generated/domintri_021_797030ebf0f8c4e4.json
+++ b/data/solutions/generated/domintri_021_797030ebf0f8c4e4.json
@@ -49,7 +49,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.026891145419845264,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 10.660254037844387,
     "source_image_url": "https://erich-friedman.github.io/packing/domintri/21.png",
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/domintri_022_90061b49654f08af.json b/data/solutions/generated/domintri_022_90061b49654f08af.json
index ade8f9060abd18b43d1412a078367e02518cdfe1..c6ecaf61c6511d96de93b4cab44c8dc3c5a28a20 100644
--- a/data/solutions/generated/domintri_022_90061b49654f08af.json
+++ b/data/solutions/generated/domintri_022_90061b49654f08af.json
@@ -49,7 +49,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.0630933998580761,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 10.928203230275509,
     "source_image_url": "https://erich-friedman.github.io/packing/domintri/22.png",
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/domintri_023_8ca8e97a5947c876.json b/data/solutions/generated/domintri_023_8ca8e97a5947c876.json
index 78faa0c5ed8b2b2a7168426e4ffe44d83f11e8d5..dc80dee2d1ed7e661898a9c7607c3fba72ecdcec 100644
--- a/data/solutions/generated/domintri_023_8ca8e97a5947c876.json
+++ b/data/solutions/generated/domintri_023_8ca8e97a5947c876.json
@@ -49,7 +49,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.06440108594250483,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 11.154700538379252,
     "source_image_url": "https://erich-friedman.github.io/packing/domintri/23.png",
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/domintri_024_f8436aa831ae57e5.json b/data/solutions/generated/domintri_024_f8436aa831ae57e5.json
index e850a5b7f689c52841602e4a4196f95df3a941f4..985148306ccd588ca5d1570efc4d67a5cb3e1e00 100644
--- a/data/solutions/generated/domintri_024_f8436aa831ae57e5.json
+++ b/data/solutions/generated/domintri_024_f8436aa831ae57e5.json
@@ -49,7 +49,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.0696454921345634,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 11.309401076758503,
     "source_image_url": "https://erich-friedman.github.io/packing/domintri/24.png",
     "source_url": "https://erich-friedman.github.io/packing/domintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/hexincir_001_48f5aa37c90550c8.json b/data/solutions/generated/hexincir_001_48f5aa37c90550c8.json
index ee6279d75161cedbb7cbc74956a76b6bfd92e629..25907291271cecb63c0c2d106cd31765348fa820 100644
--- a/data/solutions/generated/hexincir_001_48f5aa37c90550c8.json
+++ b/data/solutions/generated/hexincir_001_48f5aa37c90550c8.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.0,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexincir_002_3b6bd2554e997adc.json b/data/solutions/generated/hexincir_002_3b6bd2554e997adc.json
index 3e1d372369019503ec00e0e8e2278b6ce9d6a669..c5a5dc19aa447e3bdf5a213cd246dda423c06290 100644
--- a/data/solutions/generated/hexincir_002_3b6bd2554e997adc.json
+++ b/data/solutions/generated/hexincir_002_3b6bd2554e997adc.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.8027756377319946,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexincir_003_194e619a74e29452.json b/data/solutions/generated/hexincir_003_194e619a74e29452.json
index d462801317e8d27c8bd24687d6283b755953619f..876a289af15b816fcff858f4b9fa832c205d74cc 100644
--- a/data/solutions/generated/hexincir_003_194e619a74e29452.json
+++ b/data/solutions/generated/hexincir_003_194e619a74e29452.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexincir_004_355b11dfc363f5ba.json b/data/solutions/generated/hexincir_004_355b11dfc363f5ba.json
index 1ab7e5cacd187b63c2edc3942f296af4f48bbbf7..2bbc2585d034efee7abdfccfd34d6bfdb8593a90 100644
--- a/data/solutions/generated/hexincir_004_355b11dfc363f5ba.json
+++ b/data/solutions/generated/hexincir_004_355b11dfc363f5ba.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.239601355301926,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexincir_005_9427b00c077aafc3.json b/data/solutions/generated/hexincir_005_9427b00c077aafc3.json
index 62723e45f3907d78b731b7e17e08a754f15244c9..cd1af4ae354007d185a2711f27f478bb10ebc0bb 100644
--- a/data/solutions/generated/hexincir_005_9427b00c077aafc3.json
+++ b/data/solutions/generated/hexincir_005_9427b00c077aafc3.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.471,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexincir_006_d7d900dd0bba32a3.json b/data/solutions/generated/hexincir_006_d7d900dd0bba32a3.json
index bb6bd0adc540417942586420576254d422f8f19e..580e992e974052fb40cff69158b6c68ab8617a60 100644
--- a/data/solutions/generated/hexincir_006_d7d900dd0bba32a3.json
+++ b/data/solutions/generated/hexincir_006_d7d900dd0bba32a3.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.6457513110645907,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexincir_007_5cd27a740cc9b2a5.json b/data/solutions/generated/hexincir_007_5cd27a740cc9b2a5.json
index 9618bcd55084d5309357318d504b569f85d1f0fa..98beea815f11087cca3d458ed79866230e51af50 100644
--- a/data/solutions/generated/hexincir_007_5cd27a740cc9b2a5.json
+++ b/data/solutions/generated/hexincir_007_5cd27a740cc9b2a5.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.6457513110645907,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexincir_008_7d27528d78a05a43.json b/data/solutions/generated/hexincir_008_7d27528d78a05a43.json
index 854cf13d9701bb6c564c70c3d31daa50ed263487..6c2370fcd5e1004d758ea9c3dde26ee074ac1201 100644
--- a/data/solutions/generated/hexincir_008_7d27528d78a05a43.json
+++ b/data/solutions/generated/hexincir_008_7d27528d78a05a43.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.984,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexincir_009_5f9496662ac0b661.json b/data/solutions/generated/hexincir_009_5f9496662ac0b661.json
index a1c11f4d2647f15e5c3e3e59a5996c171c005c48..d1ea2a604337bf9c96049edeaefcfa720ac86f8a 100644
--- a/data/solutions/generated/hexincir_009_5f9496662ac0b661.json
+++ b/data/solutions/generated/hexincir_009_5f9496662ac0b661.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.301,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexincir_010_8fccd3008565aabb.json b/data/solutions/generated/hexincir_010_8fccd3008565aabb.json
index bfd13ef06f89820a51d501824be5fe70d355271b..9f78fdec948514ca2abe4874a8ff08080b218a59 100644
--- a/data/solutions/generated/hexincir_010_8fccd3008565aabb.json
+++ b/data/solutions/generated/hexincir_010_8fccd3008565aabb.json
@@ -49,8 +49,10 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.",
     "profile": "cg",
+    "reference_side": 3.5,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Nathan Roll"
diff --git a/data/solutions/generated/hexincir_011_2d2e76ec34c49fb5.json b/data/solutions/generated/hexincir_011_2d2e76ec34c49fb5.json
index a7b19860f30fa66e6dd9781daa28304a56c2c6aa..fca0b4a76b42acefa5a3b831997343e0ffaedcfd 100644
--- a/data/solutions/generated/hexincir_011_2d2e76ec34c49fb5.json
+++ b/data/solutions/generated/hexincir_011_2d2e76ec34c49fb5.json
@@ -49,8 +49,10 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.",
     "profile": "cg",
+    "reference_side": 3.605551275463989,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Nathan Roll"
diff --git a/data/solutions/generated/hexincir_012_5515c10818a71365.json b/data/solutions/generated/hexincir_012_5515c10818a71365.json
index e8e1a8345e88492f069c82dd122847b6e43512ee..c7f4e81f8befb1a162e96ab2282444798f2dd875 100644
--- a/data/solutions/generated/hexincir_012_5515c10818a71365.json
+++ b/data/solutions/generated/hexincir_012_5515c10818a71365.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.605551275463989,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexincir_013_defdebc1228b1d63.json b/data/solutions/generated/hexincir_013_defdebc1228b1d63.json
index eb67052b78308d8373703f363d38e7a77b098333..21644533b768806e705c30e4ffae4519584bbca3 100644
--- a/data/solutions/generated/hexincir_013_defdebc1228b1d63.json
+++ b/data/solutions/generated/hexincir_013_defdebc1228b1d63.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.82298,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexincir_014_cf6592c7009ff83d.json b/data/solutions/generated/hexincir_014_cf6592c7009ff83d.json
index cc57cf87b6db82505cd7671d2c42565a42c24f38..6e93445ff9b087e92306e4325706770ce0386240 100644
--- a/data/solutions/generated/hexincir_014_cf6592c7009ff83d.json
+++ b/data/solutions/generated/hexincir_014_cf6592c7009ff83d.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.877788212345415,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexincir_015_ea523b99f3bf81fb.json b/data/solutions/generated/hexincir_015_ea523b99f3bf81fb.json
index 75b898be6e8efdf00272301dd6061168e2d3b956..19d890902b8ca434d471a1cae1505927e8237ada 100644
--- a/data/solutions/generated/hexincir_015_ea523b99f3bf81fb.json
+++ b/data/solutions/generated/hexincir_015_ea523b99f3bf81fb.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.08174,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexincir_016_928ee7a851bce6e5.json b/data/solutions/generated/hexincir_016_928ee7a851bce6e5.json
index 42f9a4b501a80670e5364a9a738a03c59bb041fc..6949e3779334d260f3ceac79412a4f859df0f87e 100644
--- a/data/solutions/generated/hexincir_016_928ee7a851bce6e5.json
+++ b/data/solutions/generated/hexincir_016_928ee7a851bce6e5.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.13966,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexincir_017_e582b760dc061cd3.json b/data/solutions/generated/hexincir_017_e582b760dc061cd3.json
index 4e4042f8b4ada66c05d98b1f99da7cfe54d68c0c..af7fa30bab3e00207a473f84cfd65d1d411ee567 100644
--- a/data/solutions/generated/hexincir_017_e582b760dc061cd3.json
+++ b/data/solutions/generated/hexincir_017_e582b760dc061cd3.json
@@ -46,8 +46,11 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/deep_profile_remaining_orange.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steep_deep",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.3017,
     "source_image_url": "https://erich-friedman.github.io/packing/hexincir/17.png",
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T03:07:58+00:00",
diff --git a/data/solutions/generated/hexincir_018_12eaac899664a007.json b/data/solutions/generated/hexincir_018_12eaac899664a007.json
index c056a6ec461b6d17c84e0adef88ee9c73ae2a9d5..eb5e9a0a186df98e8e14d368e08eb15a511ad39b 100644
--- a/data/solutions/generated/hexincir_018_12eaac899664a007.json
+++ b/data/solutions/generated/hexincir_018_12eaac899664a007.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.358898943540673,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexincir_019_b4bf200670caf09c.json b/data/solutions/generated/hexincir_019_b4bf200670caf09c.json
index 5b4760814034ee64ec1b871e7a7e93a6304bda10..87bd4f16db7d3eee3abad88c6f55359485048647 100644
--- a/data/solutions/generated/hexincir_019_b4bf200670caf09c.json
+++ b/data/solutions/generated/hexincir_019_b4bf200670caf09c.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.358898943540673,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexincir_020_30108dc5d1ea9a14.json b/data/solutions/generated/hexincir_020_30108dc5d1ea9a14.json
index 54626260c35ad2d54c834e1bda0a5c345a803d50..d74e4d92e064385d5acc3537d5662d7000a94986 100644
--- a/data/solutions/generated/hexincir_020_30108dc5d1ea9a14.json
+++ b/data/solutions/generated/hexincir_020_30108dc5d1ea9a14.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.62598,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexincir_021_49a047c29bb184c3.json b/data/solutions/generated/hexincir_021_49a047c29bb184c3.json
index 069765873709efc84f92c28ae3961b02a9ddb8ca..af78d7346c8f0500701113b2562eae7a6125644b 100644
--- a/data/solutions/generated/hexincir_021_49a047c29bb184c3.json
+++ b/data/solutions/generated/hexincir_021_49a047c29bb184c3.json
@@ -45,8 +45,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.68339,
     "source_url": "https://erich-friedman.github.io/packing/hexincir/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Enea Victor"
diff --git a/data/solutions/generated/hexindom_001_899222ca3c83cd8e.json b/data/solutions/generated/hexindom_001_899222ca3c83cd8e.json
index ba3811b93f38eb92cab7018a2f383742434627c5..dddcd6800bdade1c332a87ecd5d5f9e7b576c588 100644
--- a/data/solutions/generated/hexindom_001_899222ca3c83cd8e.json
+++ b/data/solutions/generated/hexindom_001_899222ca3c83cd8e.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.7320508075688772,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexindom_002_419ae881803808e0.json b/data/solutions/generated/hexindom_002_419ae881803808e0.json
index be43a33694dbc38ec9076ab7f8175076cdf80b37..77052857d652f63c1641c7f1c568cc8ce0999495 100644
--- a/data/solutions/generated/hexindom_002_419ae881803808e0.json
+++ b/data/solutions/generated/hexindom_002_419ae881803808e0.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.8946,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexindom_003_b8984cccc8c8714d.json b/data/solutions/generated/hexindom_003_b8984cccc8c8714d.json
index b663fe9f016ce21351fe36e20d28bcddb9d487c7..b264c5f3d70697bbf976988f8fec050d29c23d0a 100644
--- a/data/solutions/generated/hexindom_003_b8984cccc8c8714d.json
+++ b/data/solutions/generated/hexindom_003_b8984cccc8c8714d.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.5358983848622456,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexindom_004_de86d3aed3d6a439.json b/data/solutions/generated/hexindom_004_de86d3aed3d6a439.json
index dd0b06ec666c205f8c4da9c1ddff11b5bb717087..401f7004529f85251a39ce81ebb642316538c50e 100644
--- a/data/solutions/generated/hexindom_004_de86d3aed3d6a439.json
+++ b/data/solutions/generated/hexindom_004_de86d3aed3d6a439.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.9474411167423495,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexindom_005_6c9e9b8c4daf8e17.json b/data/solutions/generated/hexindom_005_6c9e9b8c4daf8e17.json
index c258ede9c5aef6bfbea56aa358fdcc6d705d2540..5a50eb0d95542a26b64844d522664ec819b60e42 100644
--- a/data/solutions/generated/hexindom_005_6c9e9b8c4daf8e17.json
+++ b/data/solutions/generated/hexindom_005_6c9e9b8c4daf8e17.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.248711305964282,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexindom_006_3331b621360b9c32.json b/data/solutions/generated/hexindom_006_3331b621360b9c32.json
index d7742ae4a79395c4f0837ac5cc063cc66967ebf5..8bd02ea37da32f52a436d0e2820a45dca1d26b0b 100644
--- a/data/solutions/generated/hexindom_006_3331b621360b9c32.json
+++ b/data/solutions/generated/hexindom_006_3331b621360b9c32.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.4120262828465795,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexindom_007_1cf3d5c48cc9bce3.json b/data/solutions/generated/hexindom_007_1cf3d5c48cc9bce3.json
index 99ad18ec130dcf8fdcb4a58ce8062ccf8aca4fa2..7628b42ce2c4cfdb2baede4346f0dad55508e0c0 100644
--- a/data/solutions/generated/hexindom_007_1cf3d5c48cc9bce3.json
+++ b/data/solutions/generated/hexindom_007_1cf3d5c48cc9bce3.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.4873,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexindom_008_645a3046b41a06e7.json b/data/solutions/generated/hexindom_008_645a3046b41a06e7.json
index f3e4d4f6170555ec24cd09a1c08ebf198fd7cafc..14120bef8b2fea76c5453ff598e2954cd1a4baf0 100644
--- a/data/solutions/generated/hexindom_008_645a3046b41a06e7.json
+++ b/data/solutions/generated/hexindom_008_645a3046b41a06e7.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.6906,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexindom_009_412a5c4dab2378db.json b/data/solutions/generated/hexindom_009_412a5c4dab2378db.json
index 1602162d7296a2c2bb3eadd9f3f415e5825b2101..f68a483c8be79b0b275add9327d6d7ca43e54f6c 100644
--- a/data/solutions/generated/hexindom_009_412a5c4dab2378db.json
+++ b/data/solutions/generated/hexindom_009_412a5c4dab2378db.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.060023094349489,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexindom_010_b404bfce93e4b698.json b/data/solutions/generated/hexindom_010_b404bfce93e4b698.json
index d212543100fd951e555324e5a4e4dec5cfcc2c2c..b06d5db36a85877f199234fcf1651b9f4bc131c7 100644
--- a/data/solutions/generated/hexindom_010_b404bfce93e4b698.json
+++ b/data/solutions/generated/hexindom_010_b404bfce93e4b698.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.176914536239791,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexindom_011_de36b527dfa03258.json b/data/solutions/generated/hexindom_011_de36b527dfa03258.json
index 8cef0ce9ce9e42a792ee23acb38427bdbffd8691..0c704b55b06130c151bbca37e4a4460ecbac1bb2 100644
--- a/data/solutions/generated/hexindom_011_de36b527dfa03258.json
+++ b/data/solutions/generated/hexindom_011_de36b527dfa03258.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.5036,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexindom_012_32dafbf1407bbd72.json b/data/solutions/generated/hexindom_012_32dafbf1407bbd72.json
index 711718d1666e82ef17ba9bbe309b8c5190fd76c0..59b790b816aea910781c50aec19f7c29c1f8e85e 100644
--- a/data/solutions/generated/hexindom_012_32dafbf1407bbd72.json
+++ b/data/solutions/generated/hexindom_012_32dafbf1407bbd72.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.02506590488520361,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.613609451185303,
     "source_image_url": "https://erich-friedman.github.io/packing/hexindom/12.png",
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/hexindom_013_4d59f64640558812.json b/data/solutions/generated/hexindom_013_4d59f64640558812.json
index 1f7bb032fa4f7234ee76a809a55a12348c1534e8..dc61b399921e391ad32e604dcc71abba1a222a97 100644
--- a/data/solutions/generated/hexindom_013_4d59f64640558812.json
+++ b/data/solutions/generated/hexindom_013_4d59f64640558812.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.8137,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexindom_014_1f0ed34d05c35380.json b/data/solutions/generated/hexindom_014_1f0ed34d05c35380.json
index 87cffc099598007864101b40f366aeaa0d5fd3a6..a11b521572fa8475d2dc5b08b85fcaac19e1b86c 100644
--- a/data/solutions/generated/hexindom_014_1f0ed34d05c35380.json
+++ b/data/solutions/generated/hexindom_014_1f0ed34d05c35380.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.849942264126276,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexindom_015_1b00a25adb5cc2e4.json b/data/solutions/generated/hexindom_015_1b00a25adb5cc2e4.json
index 82050787f3206452bb2b75219d86a62e4a817429..8a6e395e253a7b2c9e3b9093608ce4773e86d565 100644
--- a/data/solutions/generated/hexindom_015_1b00a25adb5cc2e4.json
+++ b/data/solutions/generated/hexindom_015_1b00a25adb5cc2e4.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.95163268328005,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexindom_016_f690e0f9c2986401.json b/data/solutions/generated/hexindom_016_f690e0f9c2986401.json
index 8d8249747e357b7bb4d8682debe3b5aece3a6d48..944cbb6d704ede44481c86ebd82890533eae1c0b 100644
--- a/data/solutions/generated/hexindom_016_f690e0f9c2986401.json
+++ b/data/solutions/generated/hexindom_016_f690e0f9c2986401.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.196152422706632,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexindom_017_fe395a0426baa674.json b/data/solutions/generated/hexindom_017_fe395a0426baa674.json
index 70ccb7bbe3d1ee564eacce4ce3aa1ab56046afd9..5b881276304d915ec9e8e3d39c68747b91ae9877 100644
--- a/data/solutions/generated/hexindom_017_fe395a0426baa674.json
+++ b/data/solutions/generated/hexindom_017_fe395a0426baa674.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.196152422706632,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexindom_018_24be62ab2c11bd5c.json b/data/solutions/generated/hexindom_018_24be62ab2c11bd5c.json
index c33057fdcef131837d273aba35311ef4965ac863..775a8f24b0d35e0661313092cc1ffac5467f7a41 100644
--- a/data/solutions/generated/hexindom_018_24be62ab2c11bd5c.json
+++ b/data/solutions/generated/hexindom_018_24be62ab2c11bd5c.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.4081865357972925,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexindom_019_ca10088586ed125c.json b/data/solutions/generated/hexindom_019_ca10088586ed125c.json
index 20ddd9f45e6a8d8b15f59e7235114a80e9f4d1b4..0d623748e896f8ec6e3f9696d442c921082af14e 100644
--- a/data/solutions/generated/hexindom_019_ca10088586ed125c.json
+++ b/data/solutions/generated/hexindom_019_ca10088586ed125c.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.653,
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexindom_020_49ce661db444ec25.json b/data/solutions/generated/hexindom_020_49ce661db444ec25.json
index 073f162306fd95fc865367c8c1681394785d301f..bdc33d7d0e93062a90593e0e8d30b921b0d70a16 100644
--- a/data/solutions/generated/hexindom_020_49ce661db444ec25.json
+++ b/data/solutions/generated/hexindom_020_49ce661db444ec25.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.031518191308315374,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.8012,
     "source_image_url": "https://erich-friedman.github.io/packing/hexindom/20.png",
     "source_url": "https://erich-friedman.github.io/packing/hexindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/hexinhex_001_fd6c6df7b6a9fd4f.json b/data/solutions/generated/hexinhex_001_fd6c6df7b6a9fd4f.json
index fbb1c785e1a6339ec24a4d5bdc9679ed3e89330f..fa14c1f11457b2bb163cffd0cb917140a1cfc97c 100644
--- a/data/solutions/generated/hexinhex_001_fd6c6df7b6a9fd4f.json
+++ b/data/solutions/generated/hexinhex_001_fd6c6df7b6a9fd4f.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.0,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexinhex_002_4c0cc36e970c84b1.json b/data/solutions/generated/hexinhex_002_4c0cc36e970c84b1.json
index 21a8ca58a19b529fb3a175ed7b0804023feeb9a4..f6739e10f840afb833d5963e6428cfa967a11f9b 100644
--- a/data/solutions/generated/hexinhex_002_4c0cc36e970c84b1.json
+++ b/data/solutions/generated/hexinhex_002_4c0cc36e970c84b1.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexinhex_003_2e22e12b6d11de4d.json b/data/solutions/generated/hexinhex_003_2e22e12b6d11de4d.json
index bcb5b760fcfeaeee7d37e81d98c5659380ad4dc5..8c474f8d5b453e21e699a82b849793e487761bb6 100644
--- a/data/solutions/generated/hexinhex_003_2e22e12b6d11de4d.json
+++ b/data/solutions/generated/hexinhex_003_2e22e12b6d11de4d.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexinhex_004_73ddab3f27a95ffe.json b/data/solutions/generated/hexinhex_004_73ddab3f27a95ffe.json
index 2844fdd60d983f362b722492f1918df84415481c..acbb83752571951e22ee4a8d93a90b844b5ad85d 100644
--- a/data/solutions/generated/hexinhex_004_73ddab3f27a95ffe.json
+++ b/data/solutions/generated/hexinhex_004_73ddab3f27a95ffe.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.3333333333333335,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexinhex_005_f45300c86d046ee7.json b/data/solutions/generated/hexinhex_005_f45300c86d046ee7.json
index 142515d0a0843df3be492c1fd2ed6bc96b6dacca..0dbd45cfe41361514d2c7d9b1714fb563d9ff1de 100644
--- a/data/solutions/generated/hexinhex_005_f45300c86d046ee7.json
+++ b/data/solutions/generated/hexinhex_005_f45300c86d046ee7.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.6666666666666665,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/hexinhex_006_06b9c79146f8c119.json b/data/solutions/generated/hexinhex_006_06b9c79146f8c119.json
index 36d128c644bc1d8862e76bb48bfdb6147d13b159..a6e9e292d4e2b27ae1bb5a0b47247aa65553cd0f 100644
--- a/data/solutions/generated/hexinhex_006_06b9c79146f8c119.json
+++ b/data/solutions/generated/hexinhex_006_06b9c79146f8c119.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.8867513459481287,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinhex_007_d2a43d4ca2836467.json b/data/solutions/generated/hexinhex_007_d2a43d4ca2836467.json
index aa278e07ea86fbd30ec6ec083c526254302a4547..3512b5ea5dafe644d8c6ae77ddabf34e4dae6c9f 100644
--- a/data/solutions/generated/hexinhex_007_d2a43d4ca2836467.json
+++ b/data/solutions/generated/hexinhex_007_d2a43d4ca2836467.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.8867513459481287,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinhex_008_8d9e02005a596470.json b/data/solutions/generated/hexinhex_008_8d9e02005a596470.json
index 70baf16e8010351aa3e45ee82417a7bb4f5e135f..3428891464c26de8288dbc038b1aa60a0555892f 100644
--- a/data/solutions/generated/hexinhex_008_8d9e02005a596470.json
+++ b/data/solutions/generated/hexinhex_008_8d9e02005a596470.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.3144585576580217,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinhex_009_21c530fbe612f27c.json b/data/solutions/generated/hexinhex_009_21c530fbe612f27c.json
index a02a719a9ef772f76306ab8bb2cb8bbe46da7a0e..e5857f819c0d9b554a2833aabc205196d6847c71 100644
--- a/data/solutions/generated/hexinhex_009_21c530fbe612f27c.json
+++ b/data/solutions/generated/hexinhex_009_21c530fbe612f27c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.628917115316043,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinhex_010_fd5a10d8a6354174.json b/data/solutions/generated/hexinhex_010_fd5a10d8a6354174.json
index efecc7b918118992c36598cb6c6d7ffd36d1bc34..e5d12981e0db4c17bf16fae32acc639a1aa060f0 100644
--- a/data/solutions/generated/hexinhex_010_fd5a10d8a6354174.json
+++ b/data/solutions/generated/hexinhex_010_fd5a10d8a6354174.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.732050807568877,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinhex_011_cf10a9116bb04a72.json b/data/solutions/generated/hexinhex_011_cf10a9116bb04a72.json
index a392bd320c2a5fe566a4bc9d025a682f3b919970..ec91e59d1104b48e34260d87120168de0227ad54 100644
--- a/data/solutions/generated/hexinhex_011_cf10a9116bb04a72.json
+++ b/data/solutions/generated/hexinhex_011_cf10a9116bb04a72.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.9245008972987527,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Johann Schellhorn"
diff --git a/data/solutions/generated/hexinhex_012_bdc671b076ad0ffe.json b/data/solutions/generated/hexinhex_012_bdc671b076ad0ffe.json
index 8aeceee01886351402c3252eefe7d9abe58bfdca..2c7a43b3d35239f1bacfb5326d4006e9c57900ef 100644
--- a/data/solutions/generated/hexinhex_012_bdc671b076ad0ffe.json
+++ b/data/solutions/generated/hexinhex_012_bdc671b076ad0ffe.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.94164,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Alexander Novikov et al"
diff --git a/data/solutions/generated/hexinhex_013_1ac594ff5f07e3d9.json b/data/solutions/generated/hexinhex_013_1ac594ff5f07e3d9.json
index 9a56223d53c4314a6b1e2f2c880b86ada3710f05..be6d9802be0a487a3cb11f296f29718d10e72201 100644
--- a/data/solutions/generated/hexinhex_013_1ac594ff5f07e3d9.json
+++ b/data/solutions/generated/hexinhex_013_1ac594ff5f07e3d9.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.0,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexinhex_014_f86af09d863723a2.json b/data/solutions/generated/hexinhex_014_f86af09d863723a2.json
index 2d4803c2d932c13ef65de89902c8032eccee391c..77579470e346e08d522d201d1f747fc6d505694f 100644
--- a/data/solutions/generated/hexinhex_014_f86af09d863723a2.json
+++ b/data/solutions/generated/hexinhex_014_f86af09d863723a2.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.26899,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Dominik Kamp"
diff --git a/data/solutions/generated/hexinhex_015_536c412ab623afbc.json b/data/solutions/generated/hexinhex_015_536c412ab623afbc.json
index 37d2a497235b0a0d37ea7d86a1370483f7c4ce62..7f7a0cf863d679410673e4999029dfa38975cfcd 100644
--- a/data/solutions/generated/hexinhex_015_536c412ab623afbc.json
+++ b/data/solutions/generated/hexinhex_015_536c412ab623afbc.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.011434198623460913,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.44727,
     "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/15.gif",
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/hexinhex_016_17cb432379a18c18.json b/data/solutions/generated/hexinhex_016_17cb432379a18c18.json
index 89ffbb1d049c9ff5158b754fbc5c35fb9d459841..37bc51a27406112fdfdf9f2f94332ce53def9179 100644
--- a/data/solutions/generated/hexinhex_016_17cb432379a18c18.json
+++ b/data/solutions/generated/hexinhex_016_17cb432379a18c18.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.52746,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Timo Berthold et al"
diff --git a/data/solutions/generated/hexinhex_017_df809b176b000a6d.json b/data/solutions/generated/hexinhex_017_df809b176b000a6d.json
index fb92a39a01c12cb98c930a5abf298d9488681a86..f93c5fc6d48f0c5ae4040deb8bc623c4a8ee6ea5 100644
--- a/data/solutions/generated/hexinhex_017_df809b176b000a6d.json
+++ b/data/solutions/generated/hexinhex_017_df809b176b000a6d.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.6136,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Timo Berthold et al"
diff --git a/data/solutions/generated/hexinhex_018_e320d39029a817c1.json b/data/solutions/generated/hexinhex_018_e320d39029a817c1.json
index 81e012f44b326a67b487d48eabd3e5c4bccc0bf5..43866f570d7c7d391c269b6f3116447359aed353 100644
--- a/data/solutions/generated/hexinhex_018_e320d39029a817c1.json
+++ b/data/solutions/generated/hexinhex_018_e320d39029a817c1.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.618802153517006,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinhex_019_4b11a1a09f2a5b70.json b/data/solutions/generated/hexinhex_019_4b11a1a09f2a5b70.json
index 788d8001ca6e2c7154718e0183167344a388c551..305ef6fe5cdec9d727e62801a738b1ed38739b47 100644
--- a/data/solutions/generated/hexinhex_019_4b11a1a09f2a5b70.json
+++ b/data/solutions/generated/hexinhex_019_4b11a1a09f2a5b70.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.618802153517006,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinhex_020_2830e2dec38749ef.json b/data/solutions/generated/hexinhex_020_2830e2dec38749ef.json
index 0e63641549cfb7eb1e6fd28f045563ebe706b349..454cb99a7e5936078773a190604b2c422a83df5a 100644
--- a/data/solutions/generated/hexinhex_020_2830e2dec38749ef.json
+++ b/data/solutions/generated/hexinhex_020_2830e2dec38749ef.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.0,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexinhex_021_4a431b677be571c9.json b/data/solutions/generated/hexinhex_021_4a431b677be571c9.json
index cdcb91fbd81f1b0e38a5eab022fd36a8ad5a6f0d..fff8991e61e8721a779387e2d2899705a9f5cd32 100644
--- a/data/solutions/generated/hexinhex_021_4a431b677be571c9.json
+++ b/data/solutions/generated/hexinhex_021_4a431b677be571c9.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.0,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexinhex_022_003a713177cb171c.json b/data/solutions/generated/hexinhex_022_003a713177cb171c.json
index cddeb384ffb7e90bbca5d2a11034da275fc0ff43..6e76ed397e30a932058dbb0dcc00c661c2adff16 100644
--- a/data/solutions/generated/hexinhex_022_003a713177cb171c.json
+++ b/data/solutions/generated/hexinhex_022_003a713177cb171c.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.285640646055102,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinhex_023_e0a82406671652d2.json b/data/solutions/generated/hexinhex_023_e0a82406671652d2.json
index a6caddc87cf086fb29e9d33821c40d8b18f88d36..53f3fdd4ca8f5ae8880c367e8864e1d4f3b6a889 100644
--- a/data/solutions/generated/hexinhex_023_e0a82406671652d2.json
+++ b/data/solutions/generated/hexinhex_023_e0a82406671652d2.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.04756980167421457,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.4,
     "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/23.gif",
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/hexinhex_024_c96649ff013a9455.json b/data/solutions/generated/hexinhex_024_c96649ff013a9455.json
index f640ac0dadd361dd1b5084a75f45241aaa1e6581..c57f6981b3e366486dfdbca938fb7b3c27ee6e90 100644
--- a/data/solutions/generated/hexinhex_024_c96649ff013a9455.json
+++ b/data/solutions/generated/hexinhex_024_c96649ff013a9455.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.484827557301445,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinhex_025_4ac680367830872b.json b/data/solutions/generated/hexinhex_025_4ac680367830872b.json
index 53ee4073f52ece06c8bcfa4929f15cc7a754fe59..c4878fc8d6e962dc4067104ea4066812b72dbd70 100644
--- a/data/solutions/generated/hexinhex_025_4ac680367830872b.json
+++ b/data/solutions/generated/hexinhex_025_4ac680367830872b.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.6239,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Alex Kravatsky et al"
diff --git a/data/solutions/generated/hexinhex_026_8ed8c9fb94f18119.json b/data/solutions/generated/hexinhex_026_8ed8c9fb94f18119.json
index 4e39177656cc278cc11987ab23b6b5ea0ae3f4c3..135aa0902c211bd5e4947e53b82411a3c469e2ba 100644
--- a/data/solutions/generated/hexinhex_026_8ed8c9fb94f18119.json
+++ b/data/solutions/generated/hexinhex_026_8ed8c9fb94f18119.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.05029819407690666,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.70972,
     "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/26.gif",
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/hexinhex_027_4e9628a9f49def85.json b/data/solutions/generated/hexinhex_027_4e9628a9f49def85.json
index efbdd53af7b6e994fb42c3f73910b7a6e2df317e..765c06f8cec2aa01d5bcbd94074079e2172c210d 100644
--- a/data/solutions/generated/hexinhex_027_4e9628a9f49def85.json
+++ b/data/solutions/generated/hexinhex_027_4e9628a9f49def85.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.71415,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Alex Kravatsky et al"
diff --git a/data/solutions/generated/hexinhex_028_ba522f97744aed1a.json b/data/solutions/generated/hexinhex_028_ba522f97744aed1a.json
index 6628a19a31acabff8c27ee78ceb4c0994e9029b5..cfba3f4b742448848bb8ad9106a5a8e9d057f30a 100644
--- a/data/solutions/generated/hexinhex_028_ba522f97744aed1a.json
+++ b/data/solutions/generated/hexinhex_028_ba522f97744aed1a.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.028151423541621028,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.90893,
     "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/28.gif",
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T02:51:36+00:00",
diff --git a/data/solutions/generated/hexinhex_029_dba25a591b8992bc.json b/data/solutions/generated/hexinhex_029_dba25a591b8992bc.json
index 509e834318de28f4fc30825e42a6e5cb44abd81e..1f27e8e5a983000790995986c9b695197b8077d3 100644
--- a/data/solutions/generated/hexinhex_029_dba25a591b8992bc.json
+++ b/data/solutions/generated/hexinhex_029_dba25a591b8992bc.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.0,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexinhex_030_100db5f9f28894cc.json b/data/solutions/generated/hexinhex_030_100db5f9f28894cc.json
index f8ae18d6af101acb4b87e7385cb0d91d50e8ee10..cd8576bab55ce893dec80fa083a21a199c1627f3 100644
--- a/data/solutions/generated/hexinhex_030_100db5f9f28894cc.json
+++ b/data/solutions/generated/hexinhex_030_100db5f9f28894cc.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.0,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexinhex_031_d503e2b08764a35e.json b/data/solutions/generated/hexinhex_031_d503e2b08764a35e.json
index 818e0bc6c6c007b661085b624e0214404c894389..97b229f07ac93d629804a47176c7a9bdc85b9a81 100644
--- a/data/solutions/generated/hexinhex_031_d503e2b08764a35e.json
+++ b/data/solutions/generated/hexinhex_031_d503e2b08764a35e.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.0,
     "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexinsqu_001_1cfff36edc20de72.json b/data/solutions/generated/hexinsqu_001_1cfff36edc20de72.json
index c717b026234d60b242e3432f1b62544ee419b79a..3892fd6b76b0dbcbf79c9fdc69a3e6832b325096 100644
--- a/data/solutions/generated/hexinsqu_001_1cfff36edc20de72.json
+++ b/data/solutions/generated/hexinsqu_001_1cfff36edc20de72.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.9318516525781366,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexinsqu_002_ff43d04cda84c856.json b/data/solutions/generated/hexinsqu_002_ff43d04cda84c856.json
index 97afc96928c5d713bfbf40cf9cac4474a0fa3b0a..60b6ea5de4d1cec7ddffa27b4cb2a1035a4adbda 100644
--- a/data/solutions/generated/hexinsqu_002_ff43d04cda84c856.json
+++ b/data/solutions/generated/hexinsqu_002_ff43d04cda84c856.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.156596523969726,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexinsqu_003_9525d376eafe3c9c.json b/data/solutions/generated/hexinsqu_003_9525d376eafe3c9c.json
index c10e970eaec17261e2483f1a78d58ef0a0645c3c..8c6d82b57408216df508fa35a04e30321926dd85 100644
--- a/data/solutions/generated/hexinsqu_003_9525d376eafe3c9c.json
+++ b/data/solutions/generated/hexinsqu_003_9525d376eafe3c9c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.491958430170919,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinsqu_004_33ddf042dd02d191.json b/data/solutions/generated/hexinsqu_004_33ddf042dd02d191.json
index 4c517e136a05bad8a886096f6f9657538d44f3c3..b51b7978bd431aa8bab507e4ac5deeacaf6aff21 100644
--- a/data/solutions/generated/hexinsqu_004_33ddf042dd02d191.json
+++ b/data/solutions/generated/hexinsqu_004_33ddf042dd02d191.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.7250025969142437,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinsqu_005_38f2dc66ba941978.json b/data/solutions/generated/hexinsqu_005_38f2dc66ba941978.json
index 250044cd68b13e14f0d2fb7e96a25d53fc51b30f..ca11866ad538f2ac841b1d3b2ade24d214d11949 100644
--- a/data/solutions/generated/hexinsqu_005_38f2dc66ba941978.json
+++ b/data/solutions/generated/hexinsqu_005_38f2dc66ba941978.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.43782217350893,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinsqu_006_31291850c6887128.json b/data/solutions/generated/hexinsqu_006_31291850c6887128.json
index fceaf8c80dff76baf4f6bdb97ef523c9675680eb..717e7a77207423894bf181a6ab54ff22f385de3c 100644
--- a/data/solutions/generated/hexinsqu_006_31291850c6887128.json
+++ b/data/solutions/generated/hexinsqu_006_31291850c6887128.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.813824682488909,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinsqu_007_a4c696c014daab3c.json b/data/solutions/generated/hexinsqu_007_a4c696c014daab3c.json
index 6db7d27f7ed1fad05b95fa052b670d02bcfe149c..3d699df01b420966534fcc5913b2af76d92daace 100644
--- a/data/solutions/generated/hexinsqu_007_a4c696c014daab3c.json
+++ b/data/solutions/generated/hexinsqu_007_a4c696c014daab3c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.196152422706632,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexinsqu_008_b1252a56565d2ec0.json b/data/solutions/generated/hexinsqu_008_b1252a56565d2ec0.json
index 5abc296d9809e6ae50f3b542523669fd942ca6a1..52d98d4fab3c2314ebba9dbf9e0d2192200a6d9b 100644
--- a/data/solutions/generated/hexinsqu_008_b1252a56565d2ec0.json
+++ b/data/solutions/generated/hexinsqu_008_b1252a56565d2ec0.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.196152422706632,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexinsqu_009_5b4ef4c36dcfba05.json b/data/solutions/generated/hexinsqu_009_5b4ef4c36dcfba05.json
index 4549a2be7b4ab0e04cf75d1bcc3d8e1d157ea721..5c25398d8f0f9c5f41e57af27b9b4f1d39eb2d5f 100644
--- a/data/solutions/generated/hexinsqu_009_5b4ef4c36dcfba05.json
+++ b/data/solutions/generated/hexinsqu_009_5b4ef4c36dcfba05.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.518153541250351,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinsqu_010_031f63d864cce10c.json b/data/solutions/generated/hexinsqu_010_031f63d864cce10c.json
index 8993ede514e66f9e5f9649a97501ed1e0c6cce7b..75f8446ba908207606eb79097e16f184e13bf851 100644
--- a/data/solutions/generated/hexinsqu_010_031f63d864cce10c.json
+++ b/data/solutions/generated/hexinsqu_010_031f63d864cce10c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.10469,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexinsqu_011_f0fe574f6ed3708e.json b/data/solutions/generated/hexinsqu_011_f0fe574f6ed3708e.json
index c6f482ff0f571704e110e49f9b80eedc991a9117..aca6beb5d121af184cc48452a81beb3da2e00f28 100644
--- a/data/solutions/generated/hexinsqu_011_f0fe574f6ed3708e.json
+++ b/data/solutions/generated/hexinsqu_011_f0fe574f6ed3708e.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.33218,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maksymilian Jankowski"
diff --git a/data/solutions/generated/hexinsqu_012_70f372d7c2d3b859.json b/data/solutions/generated/hexinsqu_012_70f372d7c2d3b859.json
index 2cd188573133337bd2f3eed5ee9c7b879b561939..19b49b8926c665aa2e7134c7526004e8040c96a6 100644
--- a/data/solutions/generated/hexinsqu_012_70f372d7c2d3b859.json
+++ b/data/solutions/generated/hexinsqu_012_70f372d7c2d3b859.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.38735523975174,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinsqu_013_96118c364cb8b05d.json b/data/solutions/generated/hexinsqu_013_96118c364cb8b05d.json
index 1b9597e6eb601f157cb149fb6cc0b966fda35eaf..d64c726005ccb44912f8f40f8daac3cced519bc1 100644
--- a/data/solutions/generated/hexinsqu_013_96118c364cb8b05d.json
+++ b/data/solutions/generated/hexinsqu_013_96118c364cb8b05d.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.75558,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexinsqu_014_8b7d0912d343dc8b.json b/data/solutions/generated/hexinsqu_014_8b7d0912d343dc8b.json
index 7a8b3d88c770bea3d3aaeeb17c3c8aa85750b9e7..a810e0492fefca074dd46852d5d5ddaab69656eb 100644
--- a/data/solutions/generated/hexinsqu_014_8b7d0912d343dc8b.json
+++ b/data/solutions/generated/hexinsqu_014_8b7d0912d343dc8b.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.928203230275509,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexinsqu_015_0691341c684bd112.json b/data/solutions/generated/hexinsqu_015_0691341c684bd112.json
index 8e4c4d92991153fbacf024179f9565b3da32a1d8..ad78de6042ff8cd9b3547ebf8fd5224864a0c550 100644
--- a/data/solutions/generated/hexinsqu_015_0691341c684bd112.json
+++ b/data/solutions/generated/hexinsqu_015_0691341c684bd112.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.96367,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maksymilian Jankowski"
diff --git a/data/solutions/generated/hexinsqu_016_03465bdf660197b5.json b/data/solutions/generated/hexinsqu_016_03465bdf660197b5.json
index 63e662ef7e60a519922b361c18980c617d4066f5..afbda5315c33af91c5bda166be4c6b5dfa76b763 100644
--- a/data/solutions/generated/hexinsqu_016_03465bdf660197b5.json
+++ b/data/solutions/generated/hexinsqu_016_03465bdf660197b5.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.311304485586458,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinsqu_017_080714e7afd39346.json b/data/solutions/generated/hexinsqu_017_080714e7afd39346.json
index 9df277ec483d1f3ecf16679ebfb21122113aef17..2e4ba67a8f0f97eeb1b71012883e0bf353e376ca 100644
--- a/data/solutions/generated/hexinsqu_017_080714e7afd39346.json
+++ b/data/solutions/generated/hexinsqu_017_080714e7afd39346.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.607695154586736,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maksymilian Jankowski"
diff --git a/data/solutions/generated/hexinsqu_018_39a9a99a50ac7cba.json b/data/solutions/generated/hexinsqu_018_39a9a99a50ac7cba.json
index 123567fa8bb793330abaa6a6ca6007a7146e360f..b0e8e512dc7f893ebc4bb4a16e4f3fc1627de8ea 100644
--- a/data/solutions/generated/hexinsqu_018_39a9a99a50ac7cba.json
+++ b/data/solutions/generated/hexinsqu_018_39a9a99a50ac7cba.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.014294272099327444,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.702119491982255,
     "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/18.png",
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/hexinsqu_019_10d9f5dde53d25ba.json b/data/solutions/generated/hexinsqu_019_10d9f5dde53d25ba.json
index 3892db30ff1ebba343c7afd64a9cb65068fd183f..dd0e96340110d66d2f10600a021567be5e78f3b9 100644
--- a/data/solutions/generated/hexinsqu_019_10d9f5dde53d25ba.json
+++ b/data/solutions/generated/hexinsqu_019_10d9f5dde53d25ba.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.924682452694517,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinsqu_020_3d530c0ac6e7e3b1.json b/data/solutions/generated/hexinsqu_020_3d530c0ac6e7e3b1.json
index 916df1942b49fa5b336556082b242a22746478fb..a1070776c6ce62185ad6090a9ce3e3483f326d44 100644
--- a/data/solutions/generated/hexinsqu_020_3d530c0ac6e7e3b1.json
+++ b/data/solutions/generated/hexinsqu_020_3d530c0ac6e7e3b1.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.948953900455056,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexinsqu_021_5d369a2740fde606.json b/data/solutions/generated/hexinsqu_021_5d369a2740fde606.json
index 1977005c3e7c0c1fd071de842d02c8bec9e16154..f9b4f502f841a85c5a23370bfc78abd81870fb4c 100644
--- a/data/solutions/generated/hexinsqu_021_5d369a2740fde606.json
+++ b/data/solutions/generated/hexinsqu_021_5d369a2740fde606.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.381,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexinsqu_022_2f0b0033f0c66708.json b/data/solutions/generated/hexinsqu_022_2f0b0033f0c66708.json
index 3d78e824edaa19d3cd797a652102a8454867f3a4..d67dd40cc282177b70446ef7a843f02a7755878b 100644
--- a/data/solutions/generated/hexinsqu_022_2f0b0033f0c66708.json
+++ b/data/solutions/generated/hexinsqu_022_2f0b0033f0c66708.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.568,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexinsqu_023_31cc17034bd25d7b.json b/data/solutions/generated/hexinsqu_023_31cc17034bd25d7b.json
index 7ea550f7a06b2a61bf478d442af02e5441c40ea7..3fd606fd6ab7da5d0df9d9f554f1a8abaacbac37 100644
--- a/data/solutions/generated/hexinsqu_023_31cc17034bd25d7b.json
+++ b/data/solutions/generated/hexinsqu_023_31cc17034bd25d7b.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.660254037844387,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexinsqu_024_941fbce4f50492c6.json b/data/solutions/generated/hexinsqu_024_941fbce4f50492c6.json
index e8f1c0d5404cebbf12ce541492fee7d3e6cc8c81..e357c9045fae55db7fe2426f27583ea27ddba001 100644
--- a/data/solutions/generated/hexinsqu_024_941fbce4f50492c6.json
+++ b/data/solutions/generated/hexinsqu_024_941fbce4f50492c6.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.795,
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexinsqu_025_a62e2508884336f7.json b/data/solutions/generated/hexinsqu_025_a62e2508884336f7.json
index a7614670e9860dda71d37dceedbe69d4edc6f157..b5699cbf5f0209719e02209aa47c3cbde611e96f 100644
--- a/data/solutions/generated/hexinsqu_025_a62e2508884336f7.json
+++ b/data/solutions/generated/hexinsqu_025_a62e2508884336f7.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.023918039292708648,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.065084377558867,
     "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/25.png",
     "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/hexintri_001_c2fff75544b88239.json b/data/solutions/generated/hexintri_001_c2fff75544b88239.json
index ad499bdae7702e12cfeabc2fd403b99883f31d20..246b0e29e133583ae879e07e0ea86356bde7b486 100644
--- a/data/solutions/generated/hexintri_001_c2fff75544b88239.json
+++ b/data/solutions/generated/hexintri_001_c2fff75544b88239.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.0,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexintri_002_b77426ecb97f3ce6.json b/data/solutions/generated/hexintri_002_b77426ecb97f3ce6.json
index 0cf264ef8a967812c7d672e15208dd12636c8a02..edd3ea995e6e771449bd0efdf45f26f3eeebc986 100644
--- a/data/solutions/generated/hexintri_002_b77426ecb97f3ce6.json
+++ b/data/solutions/generated/hexintri_002_b77426ecb97f3ce6.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.0,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexintri_003_748bfe1ef47ea18c.json b/data/solutions/generated/hexintri_003_748bfe1ef47ea18c.json
index 8b70c3da4a27382fd4934bdde933c866ecf37fd4..2d886bf4a58f108cb5207c5d7b8aab2f11f0a8e6 100644
--- a/data/solutions/generated/hexintri_003_748bfe1ef47ea18c.json
+++ b/data/solutions/generated/hexintri_003_748bfe1ef47ea18c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.0,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexintri_004_4bf531bb9fa044b6.json b/data/solutions/generated/hexintri_004_4bf531bb9fa044b6.json
index b8d2a223216541509ecc9dca56fb2b2262fc4408..42579f0068f5083af7dab6464e01188f177114ab 100644
--- a/data/solutions/generated/hexintri_004_4bf531bb9fa044b6.json
+++ b/data/solutions/generated/hexintri_004_4bf531bb9fa044b6.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.0,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexintri_005_92331a16a75cf6c4.json b/data/solutions/generated/hexintri_005_92331a16a75cf6c4.json
index 1b048422f9b9dcd44d28e1985686126ca8de9f50..f3211e2915e9223d03d78a71e44454c0108296f3 100644
--- a/data/solutions/generated/hexintri_005_92331a16a75cf6c4.json
+++ b/data/solutions/generated/hexintri_005_92331a16a75cf6c4.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.830127018922194,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/hexintri_006_f3621ba5529eef9a.json b/data/solutions/generated/hexintri_006_f3621ba5529eef9a.json
index 5aec4793179c7560abc9977fb3083d2fe9e3a227..ed4abb925aea8b8209c6afb09ff5f7e142c9dcad 100644
--- a/data/solutions/generated/hexintri_006_f3621ba5529eef9a.json
+++ b/data/solutions/generated/hexintri_006_f3621ba5529eef9a.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.898979485566356,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexintri_007_635b0cc9d15ec460.json b/data/solutions/generated/hexintri_007_635b0cc9d15ec460.json
index bc3707be375e1125fc8e4f9dea7cbb924a8c0eb9..de529156f74b2aac44a211039dc3ca7c12fa681f 100644
--- a/data/solutions/generated/hexintri_007_635b0cc9d15ec460.json
+++ b/data/solutions/generated/hexintri_007_635b0cc9d15ec460.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.0,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexintri_008_adf439e6f7b2afb5.json b/data/solutions/generated/hexintri_008_adf439e6f7b2afb5.json
index 36012eabab82b1cbb85dc950db7d8aaf6c8e412b..932045588e65a42e649dcec6f4dae5d5e39cce84 100644
--- a/data/solutions/generated/hexintri_008_adf439e6f7b2afb5.json
+++ b/data/solutions/generated/hexintri_008_adf439e6f7b2afb5.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 1.2822736797742482,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.333333333333334,
     "source_image_url": "https://erich-friedman.github.io/packing/hexintri/8.gif",
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/hexintri_009_936a184a58977242.json b/data/solutions/generated/hexintri_009_936a184a58977242.json
index 4d67c92ec5f2d43dd73f778a3f399af03ae0ef16..c7334a1af832eece7f29e144427474d7bd195622 100644
--- a/data/solutions/generated/hexintri_009_936a184a58977242.json
+++ b/data/solutions/generated/hexintri_009_936a184a58977242.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.660254037844387,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexintri_010_5df6cec7a90f52fe.json b/data/solutions/generated/hexintri_010_5df6cec7a90f52fe.json
index 9af21d646076fa7406676d7c39d5555ac06c3c14..a50a0de9217d8af1ca1b104996871274952c3ecb 100644
--- a/data/solutions/generated/hexintri_010_5df6cec7a90f52fe.json
+++ b/data/solutions/generated/hexintri_010_5df6cec7a90f52fe.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.660254037844387,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexintri_011_d582cb032b9c575f.json b/data/solutions/generated/hexintri_011_d582cb032b9c575f.json
index 047a8b5aed608a14dfa3a02bdb7fc0303bae4e4c..f5332d5bd5b992ca853f195768ac5ca6f3484f8a 100644
--- a/data/solutions/generated/hexintri_011_d582cb032b9c575f.json
+++ b/data/solutions/generated/hexintri_011_d582cb032b9c575f.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.54823,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexintri_012_b6e20361c3af5615.json b/data/solutions/generated/hexintri_012_b6e20361c3af5615.json
index 7eeaf9240721997777c054ee55ef7c94314ee1fc..534810b2a44a9fcc2192a440dabd578af878687b 100644
--- a/data/solutions/generated/hexintri_012_b6e20361c3af5615.json
+++ b/data/solutions/generated/hexintri_012_b6e20361c3af5615.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 10.0,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexintri_013_da55bd8ffef5f50e.json b/data/solutions/generated/hexintri_013_da55bd8ffef5f50e.json
index b3e72a3b81510f0f3f65da7928af2703588e735e..cae4df5984286f8fef3829da585bcf16421ec267 100644
--- a/data/solutions/generated/hexintri_013_da55bd8ffef5f50e.json
+++ b/data/solutions/generated/hexintri_013_da55bd8ffef5f50e.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 10.392304845413264,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexintri_014_272118e9284c579f.json b/data/solutions/generated/hexintri_014_272118e9284c579f.json
index 81d8dd3f1c391a36d5ac226288c34c6359edc61e..f361b201bd3e9231823718d11761a7e5c231ec44 100644
--- a/data/solutions/generated/hexintri_014_272118e9284c579f.json
+++ b/data/solutions/generated/hexintri_014_272118e9284c579f.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 10.392304845413264,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexintri_015_83460d360e93ff66.json b/data/solutions/generated/hexintri_015_83460d360e93ff66.json
index 9a38793244192d555b4a1a4ca7a0c2f4732617f5..4cd6870efd5100d6f846de28df07169455b137cd 100644
--- a/data/solutions/generated/hexintri_015_83460d360e93ff66.json
+++ b/data/solutions/generated/hexintri_015_83460d360e93ff66.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 10.392304845413264,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexintri_017_8137d039fd339f48.json b/data/solutions/generated/hexintri_017_8137d039fd339f48.json
index 9496d55ba5eb2e3035651ab19cfa13c4ef4a0ef4..82bf56b44477cf914448e5cf8bacb23d91dec26d 100644
--- a/data/solutions/generated/hexintri_017_8137d039fd339f48.json
+++ b/data/solutions/generated/hexintri_017_8137d039fd339f48.json
@@ -49,8 +49,11 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/deep_profile_remaining_orange.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg_deep",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 11.63457,
     "source_image_url": "https://erich-friedman.github.io/packing/hexintri/17.gif",
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T03:07:58+00:00",
diff --git a/data/solutions/generated/hexintri_018_8f10cd5e01be9029.json b/data/solutions/generated/hexintri_018_8f10cd5e01be9029.json
index acb779e9c60b3f02b127f1b18fb551481500b4de..0fe04fe73c563d0bbc87d998ad463d9e9779efbd 100644
--- a/data/solutions/generated/hexintri_018_8f10cd5e01be9029.json
+++ b/data/solutions/generated/hexintri_018_8f10cd5e01be9029.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 12.0,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexintri_019_18178ad9efaf7172.json b/data/solutions/generated/hexintri_019_18178ad9efaf7172.json
index a4565a82249504ef8bee1e6ca28129495df74186..a4ffaab12873f8acb070bc901812a9a408b00750 100644
--- a/data/solutions/generated/hexintri_019_18178ad9efaf7172.json
+++ b/data/solutions/generated/hexintri_019_18178ad9efaf7172.json
@@ -49,8 +49,11 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/deep_profile_remaining_orange.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa_polish",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 12.0,
     "source_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif",
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T03:07:58+00:00",
diff --git a/data/solutions/generated/hexintri_020_f59179c5b6665dc4.json b/data/solutions/generated/hexintri_020_f59179c5b6665dc4.json
index 1d6611d961292dd1385438c003b8e1d7c5298dc0..e615cf337c473103c4f17d37426661d735ee2986 100644
--- a/data/solutions/generated/hexintri_020_f59179c5b6665dc4.json
+++ b/data/solutions/generated/hexintri_020_f59179c5b6665dc4.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 12.12435565298214,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexintri_021_6cf726ac83ba7d7f.json b/data/solutions/generated/hexintri_021_6cf726ac83ba7d7f.json
index 227ef89250839e52fd6f012b23e7dc28ef85a64f..e885ed759999ccebe8c1f8f8ef30513c144c6203 100644
--- a/data/solutions/generated/hexintri_021_6cf726ac83ba7d7f.json
+++ b/data/solutions/generated/hexintri_021_6cf726ac83ba7d7f.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 12.12435565298214,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/hexintri_16_89d5bef670451c83.json b/data/solutions/generated/hexintri_16_89d5bef670451c83.json
index 37461c075079792fc49eacd564c49aa447102d4f..8ac54f59475b592ac13f883444accad9ceec0d3b 100644
--- a/data/solutions/generated/hexintri_16_89d5bef670451c83.json
+++ b/data/solutions/generated/hexintri_16_89d5bef670451c83.json
@@ -49,7 +49,10 @@
     "generator_profile": "sa_escape",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_20260501T070815Z_broad.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 11.36599,
     "source_url": "https://erich-friedman.github.io/packing/hexintri/",
     "submitted_at": "2026-05-01T07:13:53+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/hexintri_19_f5757609f28a7743.json b/data/solutions/generated/hexintri_19_f5757609f28a7743.json
new file mode 100644
index 0000000000000000000000000000000000000000..20011ba1ecb874d5a68f422bf212498af666ca2d
--- /dev/null
+++ b/data/solutions/generated/hexintri_19_f5757609f28a7743.json
@@ -0,0 +1,181 @@
+{
+  "case": "hexintri@19",
+  "container": {
+    "circumradius": 6.928429777468251,
+    "orientation_radians": 0.0,
+    "side_length": 12.000392391248141,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "hexintri@19",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "",
+    "metric_expression": "12",
+    "metric_symbol": "s",
+    "metric_value": 12.0,
+    "reference_text": "s = 12 | Trivial. |",
+    "source_image": "19.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif",
+    "source_page": "https://erich-friedman.github.io/packing/hexintri/",
+    "title": "Hexagons in Triangles"
+  },
+  "item": {
+    "circumradius": 1.0000000000000002,
+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "hexintri@19",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "",
+      "metric_expression": "12",
+      "metric_symbol": "s",
+      "metric_value": 12.0,
+      "reference_text": "s = 12 | Trivial. |",
+      "source_image": "19.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif",
+      "source_page": "https://erich-friedman.github.io/packing/hexintri/",
+      "title": "Hexagons in Triangles"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "sa_escape",
+    "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_20260501_systematic_broad.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 12.0,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/hexintri_019_20260501_systematic_sa_escape.state",
+    "source_url": "https://erich-friedman.github.io/packing/hexintri/",
+    "submitted_at": "2026-05-01T16:24:14+00:00",
+    "submitted_by": "Trivial"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.5235886583276639,
+      "x": 0.8660241077024715,
+      "y": 1.5000094081036912
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.5236057102110647,
+      "x": -2.5981707068665028,
+      "y": 4.500163671804832
+    },
+    {
+      "id": 3,
+      "rotation_radians": 1.5707981830345474,
+      "x": 2.598281114490688,
+      "y": -1.499993126343184
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.5236055992438322,
+      "x": -0.00016417038283375387,
+      "y": -3.0002146179113156
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.5236117719328421,
+      "x": -1.7320865838224881,
+      "y": 3.000154394431203
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.5235991834570215,
+      "x": 5.196337673159825,
+      "y": 2.5656429297019328e-09
+    },
+    {
+      "id": 7,
+      "rotation_radians": -0.5236001651978002,
+      "x": -1.7321156980700223,
+      "y": 4.87638491497187e-05
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.5235921014610386,
+      "x": -1.7322682541585839,
+      "y": -3.0000520254432512
+    },
+    {
+      "id": 9,
+      "rotation_radians": 0.5235941293267923,
+      "x": 3.0198528138825914e-05,
+      "y": 3.0000923435356968
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.523593757530385,
+      "x": -2.5981785212163917,
+      "y": -4.500177254966031
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.5235958935213669,
+      "x": 1.732125016112933,
+      "y": 2.279789207015865e-06
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.5236013978976652,
+      "x": -0.8660829447455913,
+      "y": -1.5000988226289511
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.5235825084897745,
+      "x": 5.385036214572055e-06,
+      "y": -5.797784334824366e-05
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.52361813620529,
+      "x": 0.8661682682852371,
+      "y": -1.5003420979194821
+    },
+    {
+      "id": 15,
+      "rotation_radians": -0.5236023843064656,
+      "x": -2.5981698169449206,
+      "y": -1.4999567515515848
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.5235912078139561,
+      "x": 2.598105569218768,
+      "y": 1.5000876234701421
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.5236015958010076,
+      "x": -0.8660571235023609,
+      "y": 1.5000863915930651
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.5235954704701841,
+      "x": -2.598176741383893,
+      "y": 1.5001088219490708
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.5236054495323321,
+      "x": 3.464251307468749,
+      "y": 0.0001038015260423479
+    }
+  ],
+  "problem": "19 equal items for Hexagons in Triangles",
+  "setup": "hexintri",
+  "source_image": "https://erich-friedman.github.io/packing/hexintri/19.gif",
+  "source_page": "https://erich-friedman.github.io/packing/hexintri/"
+}
diff --git a/data/solutions/generated/octinoct_001_13c63959e19cfeb5.json b/data/solutions/generated/octinoct_001_13c63959e19cfeb5.json
index 6665bef2809f8506ed89ffeb5c5a997bdc57f9c2..3b8fd274c6b10f73386ab51db45b72209e4359b9 100644
--- a/data/solutions/generated/octinoct_001_13c63959e19cfeb5.json
+++ b/data/solutions/generated/octinoct_001_13c63959e19cfeb5.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.0,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/octinoct_002_937fb450c622d9b9.json b/data/solutions/generated/octinoct_002_937fb450c622d9b9.json
index cfc737d7f1fe8c1c96ac86514f472f615052060d..0b0778c714456fcd253910e92e86a750a0f3abf7 100644
--- a/data/solutions/generated/octinoct_002_937fb450c622d9b9.json
+++ b/data/solutions/generated/octinoct_002_937fb450c622d9b9.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/octinoct_003_4cb37df94277ed6e.json b/data/solutions/generated/octinoct_003_4cb37df94277ed6e.json
index 2032afb8a4e798f4f0188a72d9f77d4aae621866..ec468363e9433ab1940e9eb28139a7ff723455af 100644
--- a/data/solutions/generated/octinoct_003_4cb37df94277ed6e.json
+++ b/data/solutions/generated/octinoct_003_4cb37df94277ed6e.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.1715728752538097,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_004_8759832408431e84.json b/data/solutions/generated/octinoct_004_8759832408431e84.json
index 96eb67cb744ec88900c19296d5b8914cf73a0061..84c4d7de2bf12051382df95908f8630930dc95da 100644
--- a/data/solutions/generated/octinoct_004_8759832408431e84.json
+++ b/data/solutions/generated/octinoct_004_8759832408431e84.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.3889551651687704,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_005_d3468761b0fe9922.json b/data/solutions/generated/octinoct_005_d3468761b0fe9922.json
index 936361a57dbfde165524bd4f63ed2310fc8b5a38..f458ead1badb45a200f3d394f240d0efc51c9573 100644
--- a/data/solutions/generated/octinoct_005_d3468761b0fe9922.json
+++ b/data/solutions/generated/octinoct_005_d3468761b0fe9922.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.7071067811865475,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_006_3c4b2267adcca69f.json b/data/solutions/generated/octinoct_006_3c4b2267adcca69f.json
index a4ffe58805a91cd9fe1439cf3cda0e8a0b030c46..2c3ebb2d5027d7718bfa36763201fd70718ea49f 100644
--- a/data/solutions/generated/octinoct_006_3c4b2267adcca69f.json
+++ b/data/solutions/generated/octinoct_006_3c4b2267adcca69f.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.98915,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_007_a0053fa5c22778e9.json b/data/solutions/generated/octinoct_007_a0053fa5c22778e9.json
index 529c8423f55c5263cb6cd3993d221a7957d2f275..61edcc8bb54be6418835e744fc923b71667b4bea 100644
--- a/data/solutions/generated/octinoct_007_a0053fa5c22778e9.json
+++ b/data/solutions/generated/octinoct_007_a0053fa5c22778e9.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.0,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/octinoct_008_697fa4dfd3dbc6eb.json b/data/solutions/generated/octinoct_008_697fa4dfd3dbc6eb.json
index 98d11365071ff8ca285eab0f18aa493772bcbe78..89748fbe4232a30dfbd741dd531c61e81174b436 100644
--- a/data/solutions/generated/octinoct_008_697fa4dfd3dbc6eb.json
+++ b/data/solutions/generated/octinoct_008_697fa4dfd3dbc6eb.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.27526,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_009_7face58a13302eec.json b/data/solutions/generated/octinoct_009_7face58a13302eec.json
index ec6b8d5b99b8d08f75d5316932d2d55c59882b67..988c4d18adf3500117b5c2c633c7696c45bca4cf 100644
--- a/data/solutions/generated/octinoct_009_7face58a13302eec.json
+++ b/data/solutions/generated/octinoct_009_7face58a13302eec.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.414213562373095,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_010_bcfc9e294bb15f21.json b/data/solutions/generated/octinoct_010_bcfc9e294bb15f21.json
index 6c92857a63040b30b2c295dd1a09644161ff7313..70b32752312d9354813b41fa9ef83efda46a4de4 100644
--- a/data/solutions/generated/octinoct_010_bcfc9e294bb15f21.json
+++ b/data/solutions/generated/octinoct_010_bcfc9e294bb15f21.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.7071067811865475,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_011_5cff1aa2d330c49e.json b/data/solutions/generated/octinoct_011_5cff1aa2d330c49e.json
index 00a70a63eea9372d1c3012a9cfbe8e202b6fc21a..5f6b7ce333b1d819d5b76bfde136fff1005d7dfc 100644
--- a/data/solutions/generated/octinoct_011_5cff1aa2d330c49e.json
+++ b/data/solutions/generated/octinoct_011_5cff1aa2d330c49e.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.9327,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_012_7bdd4832407bd3be.json b/data/solutions/generated/octinoct_012_7bdd4832407bd3be.json
index ae4373d94f4b52a4eee724facf60ef35bf104a69..65555162359ff40f28450a1a07004d706f6d7e9e 100644
--- a/data/solutions/generated/octinoct_012_7bdd4832407bd3be.json
+++ b/data/solutions/generated/octinoct_012_7bdd4832407bd3be.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.0,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/octinoct_013_867ad172957f0ddb.json b/data/solutions/generated/octinoct_013_867ad172957f0ddb.json
index 6efb26a179b62599331e198a854e19d03be607f6..61dfa7a76d5dd768802f823e9a1b80ae45618215 100644
--- a/data/solutions/generated/octinoct_013_867ad172957f0ddb.json
+++ b/data/solutions/generated/octinoct_013_867ad172957f0ddb.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.17157287525381,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_014_190d6c8f3f4e37d6.json b/data/solutions/generated/octinoct_014_190d6c8f3f4e37d6.json
index 59ba6b71ac6ea91d44ad1afc3223a04c9944761f..ad6603714e6e9ca1a16cc33df59b3fda01b238bf 100644
--- a/data/solutions/generated/octinoct_014_190d6c8f3f4e37d6.json
+++ b/data/solutions/generated/octinoct_014_190d6c8f3f4e37d6.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.28155,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_015_60843ec4ea56ad88.json b/data/solutions/generated/octinoct_015_60843ec4ea56ad88.json
index 7d7625a85f184448998e787367026790717d4212..c044b7b5baa8d28d6a68b5329be9e15a0677209b 100644
--- a/data/solutions/generated/octinoct_015_60843ec4ea56ad88.json
+++ b/data/solutions/generated/octinoct_015_60843ec4ea56ad88.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.45594,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_016_1178c6831eb46264.json b/data/solutions/generated/octinoct_016_1178c6831eb46264.json
index 8428de941a6284e1e92c4462d738c081fe624b85..1afab7cbcc5bd9c0f30447639014b8f2dfa32a6e 100644
--- a/data/solutions/generated/octinoct_016_1178c6831eb46264.json
+++ b/data/solutions/generated/octinoct_016_1178c6831eb46264.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.59824,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_017_ebcfc45448cb8c5f.json b/data/solutions/generated/octinoct_017_ebcfc45448cb8c5f.json
index 9301374d3a6c3e2b698f5c66fdef79666eec3473..5bd7706b052b0d438a752dd50c3f45d84dead0ce 100644
--- a/data/solutions/generated/octinoct_017_ebcfc45448cb8c5f.json
+++ b/data/solutions/generated/octinoct_017_ebcfc45448cb8c5f.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.75741,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_018_46f5ac176d150ffa.json b/data/solutions/generated/octinoct_018_46f5ac176d150ffa.json
index e1183ae3c777807f7b83f23f17123cd116a7dde1..2221211223a50085a976c93fd01cfc1013109593 100644
--- a/data/solutions/generated/octinoct_018_46f5ac176d150ffa.json
+++ b/data/solutions/generated/octinoct_018_46f5ac176d150ffa.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.85717,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_019_4a7169be4bda1825.json b/data/solutions/generated/octinoct_019_4a7169be4bda1825.json
index a4ee5ef2cc79a594217757b592850bb12c6ba278..935f2250f8e2682475e4f896f974e4575bbb16a4 100644
--- a/data/solutions/generated/octinoct_019_4a7169be4bda1825.json
+++ b/data/solutions/generated/octinoct_019_4a7169be4bda1825.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.93586,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_020_ef9ffbe57f51321a.json b/data/solutions/generated/octinoct_020_ef9ffbe57f51321a.json
index 3100fe5f932183e6ba795e57afc71857aaf43749..c61cf2eaeef666331c5e6b1c0fdaa6b882a20257 100644
--- a/data/solutions/generated/octinoct_020_ef9ffbe57f51321a.json
+++ b/data/solutions/generated/octinoct_020_ef9ffbe57f51321a.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.06781,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_021_92c4bcf9428983c2.json b/data/solutions/generated/octinoct_021_92c4bcf9428983c2.json
index 60bb21997c6cd78868ef81d4b727629aec6df20a..3d2c17cd98b4e8829e68a47e7056a80f7aaa92c4 100644
--- a/data/solutions/generated/octinoct_021_92c4bcf9428983c2.json
+++ b/data/solutions/generated/octinoct_021_92c4bcf9428983c2.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.19715,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_022_b8f2befaa2d4a75e.json b/data/solutions/generated/octinoct_022_b8f2befaa2d4a75e.json
index c27d8cf9fb2c3f327c7d70bf4bdc5793a6db3b07..235392c2bffe4ad1e7023db9e521254cc887a44a 100644
--- a/data/solutions/generated/octinoct_022_b8f2befaa2d4a75e.json
+++ b/data/solutions/generated/octinoct_022_b8f2befaa2d4a75e.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.3575,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_023_d6528e8801e36ce0.json b/data/solutions/generated/octinoct_023_d6528e8801e36ce0.json
index fef367df3b52afc3b4fda6f7231697c0de5f0c92..e739991cb46ab0bbf8e3816b3abc2d96da396b6b 100644
--- a/data/solutions/generated/octinoct_023_d6528e8801e36ce0.json
+++ b/data/solutions/generated/octinoct_023_d6528e8801e36ce0.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.4144,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_024_a34ac6a3c52f70df.json b/data/solutions/generated/octinoct_024_a34ac6a3c52f70df.json
index 54191b0cdd52957dcc5ebf62597300bc431562e3..634ba815ba7b2f10a895b1860cb2ef3f045a7c67 100644
--- a/data/solutions/generated/octinoct_024_a34ac6a3c52f70df.json
+++ b/data/solutions/generated/octinoct_024_a34ac6a3c52f70df.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.55464,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_025_113492960b7e7dce.json b/data/solutions/generated/octinoct_025_113492960b7e7dce.json
index 4e8143221e3eff264ffad2c6e83a20394462befa..72e1581bdced3382a22d114d0bd2c42bda083bf4 100644
--- a/data/solutions/generated/octinoct_025_113492960b7e7dce.json
+++ b/data/solutions/generated/octinoct_025_113492960b7e7dce.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.65593,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_026_581188c4895e4037.json b/data/solutions/generated/octinoct_026_581188c4895e4037.json
index ecbe7432abf9703003e8de8708b048470a7b2f16..4378929169b9a6ed397ecaa9bfa10358dc76246d 100644
--- a/data/solutions/generated/octinoct_026_581188c4895e4037.json
+++ b/data/solutions/generated/octinoct_026_581188c4895e4037.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.7394,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_027_25c7f85bc0b15209.json b/data/solutions/generated/octinoct_027_25c7f85bc0b15209.json
index fd85742b382e04144a87d7aa22cb07c52f1fa301..af22cca19715c466d3a80b33b3a35c2f68cd252d 100644
--- a/data/solutions/generated/octinoct_027_25c7f85bc0b15209.json
+++ b/data/solutions/generated/octinoct_027_25c7f85bc0b15209.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.81238,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_028_f8d9c8a9f9a38d45.json b/data/solutions/generated/octinoct_028_f8d9c8a9f9a38d45.json
index 0bf53860b004a816b8fff8c6aa09e69b45bf88cc..4f809b32daffe5ef2ff859c2774bd1f4a0b33939 100644
--- a/data/solutions/generated/octinoct_028_f8d9c8a9f9a38d45.json
+++ b/data/solutions/generated/octinoct_028_f8d9c8a9f9a38d45.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.82842712474619,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_029_30789c6bb8fd99b7.json b/data/solutions/generated/octinoct_029_30789c6bb8fd99b7.json
index 422b559f3077820032a53beb3fef8e83d1373a22..d7be82036ae532226523e63905794cbd471dd200 100644
--- a/data/solutions/generated/octinoct_029_30789c6bb8fd99b7.json
+++ b/data/solutions/generated/octinoct_029_30789c6bb8fd99b7.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.05746,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/octinoct_030_1a16dc8a4d741008.json b/data/solutions/generated/octinoct_030_1a16dc8a4d741008.json
index e0987e12b02e0eed5cb342b66436fa287f5806ba..9024bd607b4a5d6f56345b859abc5c5dd0c84033 100644
--- a/data/solutions/generated/octinoct_030_1a16dc8a4d741008.json
+++ b/data/solutions/generated/octinoct_030_1a16dc8a4d741008.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.15432,
     "source_url": "https://erich-friedman.github.io/packing/octinoct/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/penincir_001_ca75a5cd7cad481c.json b/data/solutions/generated/penincir_001_ca75a5cd7cad481c.json
index 385c9823befc78165b86a9316200c1c6c9abbea2..8fee123b4caa0058ec25544a63f704c833c99a1b 100644
--- a/data/solutions/generated/penincir_001_ca75a5cd7cad481c.json
+++ b/data/solutions/generated/penincir_001_ca75a5cd7cad481c.json
@@ -49,11 +49,15 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.",
+    "original_submitted_by": "Nathan Roll",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.8506508083520399,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
-    "submitted_by": "Nathan Roll"
+    "submitted_by": "Trivial"
   },
   "placements": [
     {
diff --git a/data/solutions/generated/penincir_002_44da10d1d5897aae.json b/data/solutions/generated/penincir_002_44da10d1d5897aae.json
index 0fe2bf34fa2af5cf02d5ea9f2168e8aa3a81d8c1..053ccc1c371b17b2f6f2a2dc2e5864b0b84e4b88 100644
--- a/data/solutions/generated/penincir_002_44da10d1d5897aae.json
+++ b/data/solutions/generated/penincir_002_44da10d1d5897aae.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.5388417685876268,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/penincir_003_350d35e2110a508b.json b/data/solutions/generated/penincir_003_350d35e2110a508b.json
index 9460218b9cae5b12938d8a998ca009b0e9c91733..f80d8c4a96c3c129a11ad745b0bc3e18e6373350 100644
--- a/data/solutions/generated/penincir_003_350d35e2110a508b.json
+++ b/data/solutions/generated/penincir_003_350d35e2110a508b.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.618033988749895,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/penincir_004_d03dba2c6efc98dd.json b/data/solutions/generated/penincir_004_d03dba2c6efc98dd.json
index 1edad1b7054867325dc4adb03c61de31d8062715..96c94e9fd1a4fd01c3fa08e331d24094e7379095 100644
--- a/data/solutions/generated/penincir_004_d03dba2c6efc98dd.json
+++ b/data/solutions/generated/penincir_004_d03dba2c6efc98dd.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.82971,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/penincir_005_97027d267cb23b7f.json b/data/solutions/generated/penincir_005_97027d267cb23b7f.json
index 9b9e3c86462eefadef0a902d7a596af87ecfa0e3..235dae7002304c970243bc96d1118af0da617655 100644
--- a/data/solutions/generated/penincir_005_97027d267cb23b7f.json
+++ b/data/solutions/generated/penincir_005_97027d267cb23b7f.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.03271,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/penincir_006_4b5f96ff666b1595.json b/data/solutions/generated/penincir_006_4b5f96ff666b1595.json
index 6f83bc5cb1ce4bbe4ea19f1e193a8619d2951e23..287c3cf735446b9c22128b4be92d4a173e805a1b 100644
--- a/data/solutions/generated/penincir_006_4b5f96ff666b1595.json
+++ b/data/solutions/generated/penincir_006_4b5f96ff666b1595.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.2270327288232137,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/penincir_007_ef28e611d9e22eb0.json b/data/solutions/generated/penincir_007_ef28e611d9e22eb0.json
index 0e95ed3a7283d5295e4b049be77834c2533d86fd..7e6e7e4bdce5150da2b4e6ae52a5bda2b2e9920c 100644
--- a/data/solutions/generated/penincir_007_ef28e611d9e22eb0.json
+++ b/data/solutions/generated/penincir_007_ef28e611d9e22eb0.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.29474,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/penincir_008_1a134d3903b2814e.json b/data/solutions/generated/penincir_008_1a134d3903b2814e.json
index e4759656b4420e9b752e7bd04df384d328c55278..d48f3955d337fbf41cf4a5f154901ce084b56878 100644
--- a/data/solutions/generated/penincir_008_1a134d3903b2814e.json
+++ b/data/solutions/generated/penincir_008_1a134d3903b2814e.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.48128,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/penincir_009_1ca74640a9bafbff.json b/data/solutions/generated/penincir_009_1ca74640a9bafbff.json
index 349466e3cce2b45803c035209df89a79e541b496..91022496084d4675fc9d66843b90c792102e680b 100644
--- a/data/solutions/generated/penincir_009_1ca74640a9bafbff.json
+++ b/data/solutions/generated/penincir_009_1ca74640a9bafbff.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.70171,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/penincir_010_b50c304b68607cc4.json b/data/solutions/generated/penincir_010_b50c304b68607cc4.json
index 043c303a5eaba697e0b629de23886873a63ca2b9..daa4da4b442134ace7f914bf52dd77c9519ba571 100644
--- a/data/solutions/generated/penincir_010_b50c304b68607cc4.json
+++ b/data/solutions/generated/penincir_010_b50c304b68607cc4.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.79768,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/penincir_011_37f9123e1b2153ff.json b/data/solutions/generated/penincir_011_37f9123e1b2153ff.json
index 7874f998c7b4761c67528d1ad53022c342ac1cfe..8ce7f57bb72e8f3e5fba5565cca9a474d1746623 100644
--- a/data/solutions/generated/penincir_011_37f9123e1b2153ff.json
+++ b/data/solutions/generated/penincir_011_37f9123e1b2153ff.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.9018,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/penincir_012_a564353850abf267.json b/data/solutions/generated/penincir_012_a564353850abf267.json
index 5aa2d9eb25873720e6aa4a044af474c295bdcd56..056913ec9e1edead02159414bd7b766a698e7724 100644
--- a/data/solutions/generated/penincir_012_a564353850abf267.json
+++ b/data/solutions/generated/penincir_012_a564353850abf267.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.01826,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/penincir_013_c39e9475d5bde4a6.json b/data/solutions/generated/penincir_013_c39e9475d5bde4a6.json
index c24c7f98e743aac90ee5c79c025bea9f7b22c36d..e722fcbf742e741a6e974413070ab64b5f94d7e6 100644
--- a/data/solutions/generated/penincir_013_c39e9475d5bde4a6.json
+++ b/data/solutions/generated/penincir_013_c39e9475d5bde4a6.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.0010013752834517463,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.07769,
     "source_image_url": "https://erich-friedman.github.io/packing/penincir/13.png",
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/penincir_014_4798ec354812edfb.json b/data/solutions/generated/penincir_014_4798ec354812edfb.json
index f2e59db69de5c9f853a8dd6236a54c23246ba0db..f3eecbfb2ec53dec10500919b00fb86d1190941e 100644
--- a/data/solutions/generated/penincir_014_4798ec354812edfb.json
+++ b/data/solutions/generated/penincir_014_4798ec354812edfb.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.23385,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/penincir_015_5fb8f24380ed14ba.json b/data/solutions/generated/penincir_015_5fb8f24380ed14ba.json
index 75905117b5cb9367ff244e747e8c7d5927cb5b98..f25cead42cd7fa2a3d4a17d13ad325f466a3902d 100644
--- a/data/solutions/generated/penincir_015_5fb8f24380ed14ba.json
+++ b/data/solutions/generated/penincir_015_5fb8f24380ed14ba.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.33911,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/penincir_016_eb41133064f5f2da.json b/data/solutions/generated/penincir_016_eb41133064f5f2da.json
index 5a00f4c74dd7e1ab261ba9866eef9d95e77b94b4..8ee074c0818a40d25f9816733cd12237d49ea10b 100644
--- a/data/solutions/generated/penincir_016_eb41133064f5f2da.json
+++ b/data/solutions/generated/penincir_016_eb41133064f5f2da.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.43657,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/penincir_017_9469ef74fc89a75b.json b/data/solutions/generated/penincir_017_9469ef74fc89a75b.json
index 86f3cc4c1116cdea5a20d7b966428b5c34c54cce..366b2137042d1f2a905e6ea2653758874408ebe8 100644
--- a/data/solutions/generated/penincir_017_9469ef74fc89a75b.json
+++ b/data/solutions/generated/penincir_017_9469ef74fc89a75b.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.50958,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/penincir_018_767a627015948f32.json b/data/solutions/generated/penincir_018_767a627015948f32.json
index 59b15a91beb2df8e7cfe9dc04c7762d777a665bb..2d6beac12787e84dd916eedaa3ef9495dea178b8 100644
--- a/data/solutions/generated/penincir_018_767a627015948f32.json
+++ b/data/solutions/generated/penincir_018_767a627015948f32.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.6208,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/penincir_019_9d482c8012998879.json b/data/solutions/generated/penincir_019_9d482c8012998879.json
index 17248eee10b3cfdab5570c6b88c7aebae84cd6d4..53127b45b3904d9817f740f84349f43df6adfe56 100644
--- a/data/solutions/generated/penincir_019_9d482c8012998879.json
+++ b/data/solutions/generated/penincir_019_9d482c8012998879.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.67287,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/penincir_020_5271226652403829.json b/data/solutions/generated/penincir_020_5271226652403829.json
index 748572eba3fe0a105f16c09dcabe6dab947e47e8..797b2a4c2c8df57b5b8a539fe6ee2f8c84b39af8 100644
--- a/data/solutions/generated/penincir_020_5271226652403829.json
+++ b/data/solutions/generated/penincir_020_5271226652403829.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.80415,
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/penincir_021_4625f732ad11a859.json b/data/solutions/generated/penincir_021_4625f732ad11a859.json
index 30934a7c7fdd4e7d0a4a793d90378e56736ce51c..27801dac73c0a72e8299c811feb60274c27fc4d9 100644
--- a/data/solutions/generated/penincir_021_4625f732ad11a859.json
+++ b/data/solutions/generated/penincir_021_4625f732ad11a859.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.14077037804734455,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.90735,
     "source_image_url": "https://erich-friedman.github.io/packing/penincir/21.png",
     "source_url": "https://erich-friedman.github.io/packing/penincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/peninpen_001_b3173648630fcdeb.json b/data/solutions/generated/peninpen_001_b3173648630fcdeb.json
index 056a423604d4800b2af082a4bd5a77b4f4a7e7a4..df95e12ff02c6436f78e6cb3538d4d54559fdb93 100644
--- a/data/solutions/generated/peninpen_001_b3173648630fcdeb.json
+++ b/data/solutions/generated/peninpen_001_b3173648630fcdeb.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.0,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/peninpen_002_edac094186a54129.json b/data/solutions/generated/peninpen_002_edac094186a54129.json
index dcdc1d724f6c4851a83824781a27ac2005e2a221..aebd10f5e0594d5d63b4f284aa0e7d68262780d2 100644
--- a/data/solutions/generated/peninpen_002_edac094186a54129.json
+++ b/data/solutions/generated/peninpen_002_edac094186a54129.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/peninpen_003_bf261a4dce178a90.json b/data/solutions/generated/peninpen_003_bf261a4dce178a90.json
index 534cc633597444a9c36b2c875c8d33450484186b..9cfbe036678ab01b684fa7afa97a524b6b5bdfa8 100644
--- a/data/solutions/generated/peninpen_003_bf261a4dce178a90.json
+++ b/data/solutions/generated/peninpen_003_bf261a4dce178a90.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.23606797749979,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninpen_004_85435733af14070a.json b/data/solutions/generated/peninpen_004_85435733af14070a.json
index 799881fff8b442d74328053b17371a83bfc5c70b..8e017e0d37f7db5d63cc5dbd8825194e25ca7834 100644
--- a/data/solutions/generated/peninpen_004_85435733af14070a.json
+++ b/data/solutions/generated/peninpen_004_85435733af14070a.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.44719,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninpen_005_28fa9f787595145b.json b/data/solutions/generated/peninpen_005_28fa9f787595145b.json
index c4cd68fa4824700360ff88c722d610af88b4daf1..248d5c73e0137182521a1da6676a94487d741c42 100644
--- a/data/solutions/generated/peninpen_005_28fa9f787595145b.json
+++ b/data/solutions/generated/peninpen_005_28fa9f787595145b.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.618033988749895,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/peninpen_006_198bd12691483df1.json b/data/solutions/generated/peninpen_006_198bd12691483df1.json
index 26c5ecd3c6b0458ab4cbb97d848299297d2914f9..029b65bdd439ad6a5c9c9368b3c16c2df1685a5c 100644
--- a/data/solutions/generated/peninpen_006_198bd12691483df1.json
+++ b/data/solutions/generated/peninpen_006_198bd12691483df1.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.618033988749895,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/peninpen_007_5b6283ab3dc4c3b5.json b/data/solutions/generated/peninpen_007_5b6283ab3dc4c3b5.json
index 6af0e8d8043bdf2b45e9b643b2015586628f09d9..6578ea5d8b4bd34dc4edddb8144fd80a64ad82b2 100644
--- a/data/solutions/generated/peninpen_007_5b6283ab3dc4c3b5.json
+++ b/data/solutions/generated/peninpen_007_5b6283ab3dc4c3b5.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.07866,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninpen_008_de5f4ff90a59b8bf.json b/data/solutions/generated/peninpen_008_de5f4ff90a59b8bf.json
index 400856d096f40fa96dd75faaa0b73859950023b9..6c3bca6936e3fadccea063ca58c594814b34b6e0 100644
--- a/data/solutions/generated/peninpen_008_de5f4ff90a59b8bf.json
+++ b/data/solutions/generated/peninpen_008_de5f4ff90a59b8bf.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.33514,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninpen_009_291eb24a57cfcd61.json b/data/solutions/generated/peninpen_009_291eb24a57cfcd61.json
index b11abd7b14793f9b1f5439065d666cb066660012..4fc15155862a389851be4ab052ebe563272a26c6 100644
--- a/data/solutions/generated/peninpen_009_291eb24a57cfcd61.json
+++ b/data/solutions/generated/peninpen_009_291eb24a57cfcd61.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.44956,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninpen_010_90badee8fc213075.json b/data/solutions/generated/peninpen_010_90badee8fc213075.json
index 360b0fbf80dfdd34f93f0e9910c00d5151c7bb5e..e7997267e1a66a47ba8c57eb03c1a7d948f73a50 100644
--- a/data/solutions/generated/peninpen_010_90badee8fc213075.json
+++ b/data/solutions/generated/peninpen_010_90badee8fc213075.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.68324,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninpen_011_e62e9f2d5556f0f5.json b/data/solutions/generated/peninpen_011_e62e9f2d5556f0f5.json
index 3ee6ec5c4c5a518d9c091e6195f6cee10ec77cf4..6b112e5d01a0e7a8b3ae58d874d524338ea68a5f 100644
--- a/data/solutions/generated/peninpen_011_e62e9f2d5556f0f5.json
+++ b/data/solutions/generated/peninpen_011_e62e9f2d5556f0f5.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.79704,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninpen_012_6f961579a76d6be8.json b/data/solutions/generated/peninpen_012_6f961579a76d6be8.json
index 842a9add7248d9d58df2f4410ebe7f9c83fb1a83..c26442a762be345db6e1650adfdab239dff1b8ea 100644
--- a/data/solutions/generated/peninpen_012_6f961579a76d6be8.json
+++ b/data/solutions/generated/peninpen_012_6f961579a76d6be8.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.96926,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninpen_013_ce66c878ffee73fc.json b/data/solutions/generated/peninpen_013_ce66c878ffee73fc.json
index 57998754869abaf65855abc5835752f7a2a82f8b..8789d80d2f5d345eff681815ea4249cac04c281b 100644
--- a/data/solutions/generated/peninpen_013_ce66c878ffee73fc.json
+++ b/data/solutions/generated/peninpen_013_ce66c878ffee73fc.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.06523,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninpen_014_367de42acefe1aa2.json b/data/solutions/generated/peninpen_014_367de42acefe1aa2.json
index d6fb915003e820460f96106e9793da5b223ac23d..df4abd3cbaf77bac49c924130c0d0d2618791881 100644
--- a/data/solutions/generated/peninpen_014_367de42acefe1aa2.json
+++ b/data/solutions/generated/peninpen_014_367de42acefe1aa2.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.2112,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninpen_015_251c50a18682e896.json b/data/solutions/generated/peninpen_015_251c50a18682e896.json
index 89f954176b7e0db1a6b04e84a946eca565c7314b..d11f3b7b7c03c9f80e7aec9604f03cd7b6a161a3 100644
--- a/data/solutions/generated/peninpen_015_251c50a18682e896.json
+++ b/data/solutions/generated/peninpen_015_251c50a18682e896.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.23606797749979,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/peninpen_016_e2bb776d24739328.json b/data/solutions/generated/peninpen_016_e2bb776d24739328.json
index c3afdb1a09ebe849e6c4f51525f922d8c56c00f2..f171500aced176aefa67e4135a2686baa2cb187d 100644
--- a/data/solutions/generated/peninpen_016_e2bb776d24739328.json
+++ b/data/solutions/generated/peninpen_016_e2bb776d24739328.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.41636,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninpen_017_54856cb865a77d57.json b/data/solutions/generated/peninpen_017_54856cb865a77d57.json
index ea51212bd4210eef808d4d97c307ba2e7c31ea2c..de21484b581d543e3124a8842348b2bf7c7aaab9 100644
--- a/data/solutions/generated/peninpen_017_54856cb865a77d57.json
+++ b/data/solutions/generated/peninpen_017_54856cb865a77d57.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.65561,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninpen_018_9c442356ca78c3de.json b/data/solutions/generated/peninpen_018_9c442356ca78c3de.json
index 8800be7e44a49f25477566f9230c51ce0a3916ce..ba5adc2b670320143587f526bdd7f4447c1853ca 100644
--- a/data/solutions/generated/peninpen_018_9c442356ca78c3de.json
+++ b/data/solutions/generated/peninpen_018_9c442356ca78c3de.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.77541,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninpen_019_b5440311f7b9b10b.json b/data/solutions/generated/peninpen_019_b5440311f7b9b10b.json
index 39ac72e536e8b1da21f6fbf99bb4e71f4dacb3c3..4267bccaa3965d7f737fc5151eedca4251e5885f 100644
--- a/data/solutions/generated/peninpen_019_b5440311f7b9b10b.json
+++ b/data/solutions/generated/peninpen_019_b5440311f7b9b10b.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.95269,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ian Watson"
diff --git a/data/solutions/generated/peninpen_020_74f61b73dca76fef.json b/data/solutions/generated/peninpen_020_74f61b73dca76fef.json
index 6f767043a55a0e95cd9d1a5eed09778014504bf3..a2bbcfa125c4ba45c2d524f9682168742c41b6ac 100644
--- a/data/solutions/generated/peninpen_020_74f61b73dca76fef.json
+++ b/data/solutions/generated/peninpen_020_74f61b73dca76fef.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.04154,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninpen_021_b731ea055eb53ce1.json b/data/solutions/generated/peninpen_021_b731ea055eb53ce1.json
index b70050c337ef6f3f63663788ef2f4dede76cc17b..71ef48baac36902f21010e30e5f9cebf5a7892cd 100644
--- a/data/solutions/generated/peninpen_021_b731ea055eb53ce1.json
+++ b/data/solutions/generated/peninpen_021_b731ea055eb53ce1.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.043457967738247366,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.15948,
     "source_image_url": "https://erich-friedman.github.io/packing/peninpen/21.png",
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/peninpen_022_07e217f200bb677e.json b/data/solutions/generated/peninpen_022_07e217f200bb677e.json
index fcf6bb8b37ec745d19b5a5d859676e8e88bacddd..1e533477c801a0f0477a9abfef96ddedd6f3625d 100644
--- a/data/solutions/generated/peninpen_022_07e217f200bb677e.json
+++ b/data/solutions/generated/peninpen_022_07e217f200bb677e.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.2674,
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/peninpen_023_4286cb7dfd8b00d7.json b/data/solutions/generated/peninpen_023_4286cb7dfd8b00d7.json
index f7fa4dc0b34c12c42cd6f27052a594869774a37f..9599abb6b682ef09b778e62c52fe2a12d945710e 100644
--- a/data/solutions/generated/peninpen_023_4286cb7dfd8b00d7.json
+++ b/data/solutions/generated/peninpen_023_4286cb7dfd8b00d7.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.054981616329197076,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.34794,
     "source_image_url": "https://erich-friedman.github.io/packing/peninpen/23.png",
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/peninpen_024_8859e051020078b2.json b/data/solutions/generated/peninpen_024_8859e051020078b2.json
index f6d9decf81c9c9f5d6d2452c2d60e9840206cf15..fc0bbe8266321511517b724c0eec38fc3195da2d 100644
--- a/data/solutions/generated/peninpen_024_8859e051020078b2.json
+++ b/data/solutions/generated/peninpen_024_8859e051020078b2.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.04511581594063088,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.49241,
     "source_image_url": "https://erich-friedman.github.io/packing/peninpen/24.png",
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/peninpen_025_0f0645180a7be991.json b/data/solutions/generated/peninpen_025_0f0645180a7be991.json
index 2f8fa2574534588f5701b973c14f2b6f41930fc9..18ed73b93d1b6dc3dee1cc2482c791b51aa4e809 100644
--- a/data/solutions/generated/peninpen_025_0f0645180a7be991.json
+++ b/data/solutions/generated/peninpen_025_0f0645180a7be991.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.057405440430770845,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.5837,
     "source_image_url": "https://erich-friedman.github.io/packing/peninpen/25.png",
     "source_url": "https://erich-friedman.github.io/packing/peninpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/peninsqu_001_ec216f3e37e16785.json b/data/solutions/generated/peninsqu_001_ec216f3e37e16785.json
index 73571a1ae87fc2bce92ba26f7211b9939fabe78a..317cbb305e70714bff0f10f0ec99fa10ec0a67fc 100644
--- a/data/solutions/generated/peninsqu_001_ec216f3e37e16785.json
+++ b/data/solutions/generated/peninsqu_001_ec216f3e37e16785.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.5981133053749155,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/peninsqu_002_bb5e10eb4917963f.json b/data/solutions/generated/peninsqu_002_bb5e10eb4917963f.json
index feb776e14a5f2b67b4cecdb6957a473d41c2f951..cecee3e344b2739cd8241e14efcb5670cc8617c1 100644
--- a/data/solutions/generated/peninsqu_002_bb5e10eb4917963f.json
+++ b/data/solutions/generated/peninsqu_002_bb5e10eb4917963f.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.46345,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/peninsqu_003_52b96ec8c7f6b741.json b/data/solutions/generated/peninsqu_003_52b96ec8c7f6b741.json
index 8c8cb8c658395995fedbc1550da468a23a093dc0..4ae4af5f0bb7fa1a0cfac1389fb1958c6c684a96 100644
--- a/data/solutions/generated/peninsqu_003_52b96ec8c7f6b741.json
+++ b/data/solutions/generated/peninsqu_003_52b96ec8c7f6b741.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.90812,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninsqu_004_a2fcd0b0beef7a6f.json b/data/solutions/generated/peninsqu_004_a2fcd0b0beef7a6f.json
index 14fe702c43f86553ef9544a1880c06caaf05a7ca..5aed13fd10711d05c4e5ad9fcbc773b161b5b5ab 100644
--- a/data/solutions/generated/peninsqu_004_a2fcd0b0beef7a6f.json
+++ b/data/solutions/generated/peninsqu_004_a2fcd0b0beef7a6f.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.10252,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninsqu_005_bda3fbac20c8a756.json b/data/solutions/generated/peninsqu_005_bda3fbac20c8a756.json
index 510d381ac5331300ce569c3e0f01dcae74205222..f245bcb1c27c0aeb6a25dedea58823a18cdd0796 100644
--- a/data/solutions/generated/peninsqu_005_bda3fbac20c8a756.json
+++ b/data/solutions/generated/peninsqu_005_bda3fbac20c8a756.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.54903,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninsqu_006_a267ec5809e79964.json b/data/solutions/generated/peninsqu_006_a267ec5809e79964.json
index 3f7ecd574239e5c21336428bdec114b81dc06e9f..531fd1f4ce9bcc415fec04a19f1880d956f8c92f 100644
--- a/data/solutions/generated/peninsqu_006_a267ec5809e79964.json
+++ b/data/solutions/generated/peninsqu_006_a267ec5809e79964.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.883,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninsqu_007_b5565b951637dc85.json b/data/solutions/generated/peninsqu_007_b5565b951637dc85.json
index b931ae9212146ddf14a541454831b3e622f590da..22c6698fbed7d058c6cb60095894f1d71a00739e 100644
--- a/data/solutions/generated/peninsqu_007_b5565b951637dc85.json
+++ b/data/solutions/generated/peninsqu_007_b5565b951637dc85.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.18038,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninsqu_008_eac74e93d82a54dd.json b/data/solutions/generated/peninsqu_008_eac74e93d82a54dd.json
index 71263a431cbd55e97aef01fb044ceccaa2f5210d..d299f868f55d5eaf13a3f0844151cfc44e91861e 100644
--- a/data/solutions/generated/peninsqu_008_eac74e93d82a54dd.json
+++ b/data/solutions/generated/peninsqu_008_eac74e93d82a54dd.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.38191,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninsqu_009_0270d827693b6f8d.json b/data/solutions/generated/peninsqu_009_0270d827693b6f8d.json
index 12db8491336d369ac6a3675f285c6bc150e137f3..8906f3d47c0af1fde2eb8a59f7d10d9586969406 100644
--- a/data/solutions/generated/peninsqu_009_0270d827693b6f8d.json
+++ b/data/solutions/generated/peninsqu_009_0270d827693b6f8d.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.60033,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninsqu_010_fba502b92276222e.json b/data/solutions/generated/peninsqu_010_fba502b92276222e.json
index 4f5b8a1739e237d7524868b3cef050dd5e21cc90..36aed39ab377c51bf6245c3455f5686b377c5692 100644
--- a/data/solutions/generated/peninsqu_010_fba502b92276222e.json
+++ b/data/solutions/generated/peninsqu_010_fba502b92276222e.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.90584,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninsqu_011_3596998e61e47a27.json b/data/solutions/generated/peninsqu_011_3596998e61e47a27.json
index bd5cfdc5dc89c8ed53d02298e476ed200e199857..fb340e5fd62025c68d13094ec35941d68183115f 100644
--- a/data/solutions/generated/peninsqu_011_3596998e61e47a27.json
+++ b/data/solutions/generated/peninsqu_011_3596998e61e47a27.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.11557,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninsqu_012_72fe010d0104fc76.json b/data/solutions/generated/peninsqu_012_72fe010d0104fc76.json
index c0e04e682a02875ac8b19afb193ef3c81079eaeb..c3bc66352df53f18a7b9423f9dbc4795d7886b98 100644
--- a/data/solutions/generated/peninsqu_012_72fe010d0104fc76.json
+++ b/data/solutions/generated/peninsqu_012_72fe010d0104fc76.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.2325,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninsqu_013_b54e12045e01b08b.json b/data/solutions/generated/peninsqu_013_b54e12045e01b08b.json
index ef0d03728e36d8b59dd4aeddfa58041527fd0560..f263212a7136a4ffa5b31f61704cf90613067ca9 100644
--- a/data/solutions/generated/peninsqu_013_b54e12045e01b08b.json
+++ b/data/solutions/generated/peninsqu_013_b54e12045e01b08b.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.52183,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninsqu_014_70191e649c0c34a4.json b/data/solutions/generated/peninsqu_014_70191e649c0c34a4.json
index 95d57530a4fa8c2143ec8ffb69dac324f8f25a98..9faba6575d396ec4bf12a3d2cdaa98cc50c4dd87 100644
--- a/data/solutions/generated/peninsqu_014_70191e649c0c34a4.json
+++ b/data/solutions/generated/peninsqu_014_70191e649c0c34a4.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.69775,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninsqu_015_f5d70026e15060e9.json b/data/solutions/generated/peninsqu_015_f5d70026e15060e9.json
index 63b46b42ea60e04dddaf6d8578393328e2123d22..4572ae48e2548b81c64c0f2add7c06d386a7504e 100644
--- a/data/solutions/generated/peninsqu_015_f5d70026e15060e9.json
+++ b/data/solutions/generated/peninsqu_015_f5d70026e15060e9.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.91106,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninsqu_016_4644b3e97f0bdea2.json b/data/solutions/generated/peninsqu_016_4644b3e97f0bdea2.json
index cfa2fef974387c626312a16b77b6e54245406dbb..e4f17a15be0527f4c3699148c84419c3ac28f2d0 100644
--- a/data/solutions/generated/peninsqu_016_4644b3e97f0bdea2.json
+++ b/data/solutions/generated/peninsqu_016_4644b3e97f0bdea2.json
@@ -52,8 +52,10 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.",
     "profile": "cg",
+    "reference_side": 6.11021,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Nathan Roll"
diff --git a/data/solutions/generated/peninsqu_017_a6cd0104bc26d2a0.json b/data/solutions/generated/peninsqu_017_a6cd0104bc26d2a0.json
index 0de889fd5776a4213855b8425fb28be7da78bf80..9cb3efaa24e27e9c10818b107c8296d8aa9a1722 100644
--- a/data/solutions/generated/peninsqu_017_a6cd0104bc26d2a0.json
+++ b/data/solutions/generated/peninsqu_017_a6cd0104bc26d2a0.json
@@ -52,8 +52,10 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.",
     "profile": "sa",
+    "reference_side": 6.26466,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Nathan Roll"
diff --git a/data/solutions/generated/peninsqu_018_9705d17615c32308.json b/data/solutions/generated/peninsqu_018_9705d17615c32308.json
index f0ab3c5200920045df874fa523a15fe9db1c465b..954b3170f50fedec57ee31365d7b34628b1018b3 100644
--- a/data/solutions/generated/peninsqu_018_9705d17615c32308.json
+++ b/data/solutions/generated/peninsqu_018_9705d17615c32308.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.33632,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninsqu_019_3b1113745987c1d6.json b/data/solutions/generated/peninsqu_019_3b1113745987c1d6.json
index 027c5ebb099183a2e902b192e7281e0304057254..fef6add5bda61022b23d9c0ff9a937593e416747 100644
--- a/data/solutions/generated/peninsqu_019_3b1113745987c1d6.json
+++ b/data/solutions/generated/peninsqu_019_3b1113745987c1d6.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.55939,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/peninsqu_020_eafd28d28fb8e254.json b/data/solutions/generated/peninsqu_020_eafd28d28fb8e254.json
index 11a80b05e03c8e503a0adb3915d2e76a78f8e068..35d588b0f15a9a37dcf74ad07881672237434dbf 100644
--- a/data/solutions/generated/peninsqu_020_eafd28d28fb8e254.json
+++ b/data/solutions/generated/peninsqu_020_eafd28d28fb8e254.json
@@ -52,8 +52,10 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.",
     "profile": "cg",
+    "reference_side": 6.69588,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Nathan Roll"
diff --git a/data/solutions/generated/peninsqu_21_9d320f91f05e2f0e.json b/data/solutions/generated/peninsqu_21_9d320f91f05e2f0e.json
index 95bde149d65755e40b9d720756c7d1a0420bb65b..082ca7ce0e3416191bfadedf51de02c5499da8e9 100644
--- a/data/solutions/generated/peninsqu_21_9d320f91f05e2f0e.json
+++ b/data/solutions/generated/peninsqu_21_9d320f91f05e2f0e.json
@@ -49,7 +49,10 @@
     "generator_profile": "sa_escape",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_current_broad_broad.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.8554,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T13:47:12+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/peninsqu_22_70964f50e662283c.json b/data/solutions/generated/peninsqu_22_70964f50e662283c.json
index 87ee3117e553ceea9468671805507cffd888f02a..3ebff84cc2d4718eb70412b9c42189b7fc7b3a13 100644
--- a/data/solutions/generated/peninsqu_22_70964f50e662283c.json
+++ b/data/solutions/generated/peninsqu_22_70964f50e662283c.json
@@ -49,7 +49,10 @@
     "generator_profile": "sa_escape",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_current_broad_broad.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.04532,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T13:47:12+00:00",
     "submitted_by": "Teodors Smith"
diff --git a/data/solutions/generated/peninsqu_23_5b526f4bb0fda83c.json b/data/solutions/generated/peninsqu_23_5b526f4bb0fda83c.json
index d287001963d2fca9d039d311275e6772f06c7cd6..43f143fddf6e5e1ce419dbfc8dd7ff8d01a1efcc 100644
--- a/data/solutions/generated/peninsqu_23_5b526f4bb0fda83c.json
+++ b/data/solutions/generated/peninsqu_23_5b526f4bb0fda83c.json
@@ -49,7 +49,10 @@
     "generator_profile": "cg_precise",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_current_broad_broad.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.20731,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T13:47:12+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/peninsqu_24_3e42e9e085ed4c16.json b/data/solutions/generated/peninsqu_24_3e42e9e085ed4c16.json
index 4c43d5b81053af7774fb079a2eb024cd327d5545..2645922f07de07d0a6df05b1fef859f111eccbc5 100644
--- a/data/solutions/generated/peninsqu_24_3e42e9e085ed4c16.json
+++ b/data/solutions/generated/peninsqu_24_3e42e9e085ed4c16.json
@@ -49,7 +49,10 @@
     "generator_profile": "cg_precise",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_current_broad_broad.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.33823,
     "source_url": "https://erich-friedman.github.io/packing/peninsqu/",
     "submitted_at": "2026-05-01T13:47:12+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/squincir_001_e1e16b7d18b1243e.json b/data/solutions/generated/squincir_001_e1e16b7d18b1243e.json
index b7b6d43b7e4a15bc9e000b808c88f8f2822dcbc6..4986a8fd62a5e580d79e6d7c3d8b197ba6e6f280 100644
--- a/data/solutions/generated/squincir_001_e1e16b7d18b1243e.json
+++ b/data/solutions/generated/squincir_001_e1e16b7d18b1243e.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.7071067811865476,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squincir_002_e0e32383f27cd27d.json b/data/solutions/generated/squincir_002_e0e32383f27cd27d.json
index 13a83e7f9be0d7a134fc2bcce95abb14a9fd7d10..99a39959ac71856965866dd3efd9ada6182f7fc4 100644
--- a/data/solutions/generated/squincir_002_e0e32383f27cd27d.json
+++ b/data/solutions/generated/squincir_002_e0e32383f27cd27d.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.118033988749895,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squincir_003_226172dcb69c3daf.json b/data/solutions/generated/squincir_003_226172dcb69c3daf.json
index 0d9ad12a09db0f5b70fb5725d3d30c84fed8de53..c2a1ce3c5b11b90541bfadc780cd7f632edabec4 100644
--- a/data/solutions/generated/squincir_003_226172dcb69c3daf.json
+++ b/data/solutions/generated/squincir_003_226172dcb69c3daf.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.288470508005519,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squincir_004_59645297dac888b6.json b/data/solutions/generated/squincir_004_59645297dac888b6.json
index 45d906899ff4acb29a7740a0b25be6a9ce473717..44bd4d17a4b13a970bc9cc0d34b6861c497b54a1 100644
--- a/data/solutions/generated/squincir_004_59645297dac888b6.json
+++ b/data/solutions/generated/squincir_004_59645297dac888b6.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.4142135623730951,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squincir_005_ee29f4bb5ac19bc4.json b/data/solutions/generated/squincir_005_ee29f4bb5ac19bc4.json
index 566afc24eac15adbc38288b775621f8ccf57747a..01b1091f3fce276cd07da62e680cac884bb9d93a 100644
--- a/data/solutions/generated/squincir_005_ee29f4bb5ac19bc4.json
+++ b/data/solutions/generated/squincir_005_ee29f4bb5ac19bc4.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.5811388300841898,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squincir_006_00816b044d90c514.json b/data/solutions/generated/squincir_006_00816b044d90c514.json
index d474655e91f679459a253b8ea2c36581c6cd5298..3e520715318080271405fde4c6a0ffc823f5a0a7 100644
--- a/data/solutions/generated/squincir_006_00816b044d90c514.json
+++ b/data/solutions/generated/squincir_006_00816b044d90c514.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.688,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squincir_007_f533c6ece1865b92.json b/data/solutions/generated/squincir_007_f533c6ece1865b92.json
index 8915ba254cdc4a29fb0304a0088863e61adaf073..6611b58bb93fb13389c70f0c4db5985e1cab7464 100644
--- a/data/solutions/generated/squincir_007_f533c6ece1865b92.json
+++ b/data/solutions/generated/squincir_007_f533c6ece1865b92.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.8027756377319946,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squincir_008_056dfca89502965a.json b/data/solutions/generated/squincir_008_056dfca89502965a.json
index 064a51735ad1238de72f543fd3fd97f34941061f..203cc54ed5af49d752a153e88f306bbc302e8389 100644
--- a/data/solutions/generated/squincir_008_056dfca89502965a.json
+++ b/data/solutions/generated/squincir_008_056dfca89502965a.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.978,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/squincir_009_a0eb38ed275fd3c7.json b/data/solutions/generated/squincir_009_a0eb38ed275fd3c7.json
index 0fb28a4428b4ff0abab00868bc564b0d8f68745a..dc14d52cc19184257e7bcfa8283e3fa3d9b97f9b 100644
--- a/data/solutions/generated/squincir_009_a0eb38ed275fd3c7.json
+++ b/data/solutions/generated/squincir_009_a0eb38ed275fd3c7.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0775962673243327,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squincir_010_eacd7cf43d9f9c99.json b/data/solutions/generated/squincir_010_eacd7cf43d9f9c99.json
index 13ad56eef902a11a537373215b3ff2361201a832..d4b57eb6d2cbaafa468497c99a486b3ed0cad09b 100644
--- a/data/solutions/generated/squincir_010_eacd7cf43d9f9c99.json
+++ b/data/solutions/generated/squincir_010_eacd7cf43d9f9c99.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.1213203435596424,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squincir_011_ed2b520c292f3457.json b/data/solutions/generated/squincir_011_ed2b520c292f3457.json
index f96537985597a518555ef722d23b6b05a7d1f2ee..499181a41402b39bd485eb292aa2d1f08f44bce8 100644
--- a/data/solutions/generated/squincir_011_ed2b520c292f3457.json
+++ b/data/solutions/generated/squincir_011_ed2b520c292f3457.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.214,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/squincir_012_064666a02cb4bcc6.json b/data/solutions/generated/squincir_012_064666a02cb4bcc6.json
index 94b2f5bdab35e05c5b275a4c124b48330119f4d3..8863ce72b074e7357310044ed63c57cfdfac0ced 100644
--- a/data/solutions/generated/squincir_012_064666a02cb4bcc6.json
+++ b/data/solutions/generated/squincir_012_064666a02cb4bcc6.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.23606797749979,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squincir_013_1ff894504e55415a.json b/data/solutions/generated/squincir_013_1ff894504e55415a.json
index a12d4092784917f7647decb3b7d3ebbf74dc33c8..b9a8b9dee8307298d4b296a7606e5b2092ba6cf8 100644
--- a/data/solutions/generated/squincir_013_1ff894504e55415a.json
+++ b/data/solutions/generated/squincir_013_1ff894504e55415a.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.3607,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/squincir_014_16de07d86777c846.json b/data/solutions/generated/squincir_014_16de07d86777c846.json
index e0d8025cd1e65c1ef9af8bc13b17c698410fe67a..3782205d1e0ce8defb47918a78082b9a5d35c87f 100644
--- a/data/solutions/generated/squincir_014_16de07d86777c846.json
+++ b/data/solutions/generated/squincir_014_16de07d86777c846.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.5,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squincir_015_4a2ad28ea2097ba3.json b/data/solutions/generated/squincir_015_4a2ad28ea2097ba3.json
index 7abaa9eceb0c84d3acd1f034c33162812107d340..ec33e7133f2d0fb04c14e335aca077dfb454e623 100644
--- a/data/solutions/generated/squincir_015_4a2ad28ea2097ba3.json
+++ b/data/solutions/generated/squincir_015_4a2ad28ea2097ba3.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.533,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/squincir_016_94d0a09f4c75dcc4.json b/data/solutions/generated/squincir_016_94d0a09f4c75dcc4.json
index 629ebb76903b2283b6bca772efe46dffab9c39d8..3c9b8dcece5c77fd602d4417fe22a47f2f57b9ce 100644
--- a/data/solutions/generated/squincir_016_94d0a09f4c75dcc4.json
+++ b/data/solutions/generated/squincir_016_94d0a09f4c75dcc4.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.623094546523247,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squincir_017_036910f6c0550e2f.json b/data/solutions/generated/squincir_017_036910f6c0550e2f.json
index 406934721d1837c306858cfb6d204663889541e9..98a5e6281e91cc6fb5e03ea248303fb1af1401bf 100644
--- a/data/solutions/generated/squincir_017_036910f6c0550e2f.json
+++ b/data/solutions/generated/squincir_017_036910f6c0550e2f.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.677,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/squincir_018_d726e310dc0e9eaa.json b/data/solutions/generated/squincir_018_d726e310dc0e9eaa.json
index b0f7af7dc2ea72579615ef51e471570db9d1f75b..2fa500c8aed0870836de91cd134132bc397ac371 100644
--- a/data/solutions/generated/squincir_018_d726e310dc0e9eaa.json
+++ b/data/solutions/generated/squincir_018_d726e310dc0e9eaa.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.7414640249326636,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/squincir_019_1966e8e14b94f055.json b/data/solutions/generated/squincir_019_1966e8e14b94f055.json
index 93b9bac3f4f8d1c668fd16ebdf1a17f081b107f4..2cb37c16833043bbdcd293259e491395079a4376 100644
--- a/data/solutions/generated/squincir_019_1966e8e14b94f055.json
+++ b/data/solutions/generated/squincir_019_1966e8e14b94f055.json
@@ -46,7 +46,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.04349162650704844,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.802,
     "source_image_url": "https://erich-friedman.github.io/packing/squincir/19.gif",
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T02:51:36+00:00",
diff --git a/data/solutions/generated/squincir_020_d2a3e673398d1cd8.json b/data/solutions/generated/squincir_020_d2a3e673398d1cd8.json
index eb63a65c242288c431f8c7a801d63c5d722dadf5..2caa06fdfa0a9d683e829ba297660e4d462ad7bd 100644
--- a/data/solutions/generated/squincir_020_d2a3e673398d1cd8.json
+++ b/data/solutions/generated/squincir_020_d2a3e673398d1cd8.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.01126597462280385,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.893,
     "source_image_url": "https://erich-friedman.github.io/packing/squincir/20.gif",
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squincir_021_af376e36d9f212b7.json b/data/solutions/generated/squincir_021_af376e36d9f212b7.json
index 5ab0c65199a639741f2de5515e6b2b10d21127a7..a583c13658de976021fbd5c88d3bfafe45d63c61 100644
--- a/data/solutions/generated/squincir_021_af376e36d9f212b7.json
+++ b/data/solutions/generated/squincir_021_af376e36d9f212b7.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.05374967664896644,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.9154759474226504,
     "source_image_url": "https://erich-friedman.github.io/packing/squincir/21.gif",
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squincir_022_d08f4c9050539106.json b/data/solutions/generated/squincir_022_d08f4c9050539106.json
index 637eacfe0268d9f23c9a8e28c225af774f0f697b..e4ae02efe985b6f82e4a087d6899a9c228bd36e6 100644
--- a/data/solutions/generated/squincir_022_d08f4c9050539106.json
+++ b/data/solutions/generated/squincir_022_d08f4c9050539106.json
@@ -46,7 +46,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.003529491305419296,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.033,
     "source_image_url": "https://erich-friedman.github.io/packing/squincir/22.gif",
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T02:51:36+00:00",
diff --git a/data/solutions/generated/squincir_023_3cacab4fa2a4614f.json b/data/solutions/generated/squincir_023_3cacab4fa2a4614f.json
index fda3d51f4b272b767bc0b6a12a4116107f697888..7de40883348f656357d3ad4c93f5ed3f987286cf 100644
--- a/data/solutions/generated/squincir_023_3cacab4fa2a4614f.json
+++ b/data/solutions/generated/squincir_023_3cacab4fa2a4614f.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.10034643514353313,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.073,
     "source_image_url": "https://erich-friedman.github.io/packing/squincir/23.gif",
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squincir_024_35e22c7b35c718bd.json b/data/solutions/generated/squincir_024_35e22c7b35c718bd.json
index 27c815415e8c70aae9a8b6baf0a588d346a1e236..a19f18db8b2fb65454e1fe7375be38eb937a3b88 100644
--- a/data/solutions/generated/squincir_024_35e22c7b35c718bd.json
+++ b/data/solutions/generated/squincir_024_35e22c7b35c718bd.json
@@ -45,8 +45,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.11,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/squincir_025_0cabb86031dba8fd.json b/data/solutions/generated/squincir_025_0cabb86031dba8fd.json
index 91e58a327b8bde81632398d3e5131e724b339f66..4115a262b49f800b1b6743e03f0784e4dbfb5843 100644
--- a/data/solutions/generated/squincir_025_0cabb86031dba8fd.json
+++ b/data/solutions/generated/squincir_025_0cabb86031dba8fd.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.012364144288766756,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.175699835381871,
     "source_image_url": "https://erich-friedman.github.io/packing/squincir/25.gif",
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squincir_026_d3c528742ca2afa0.json b/data/solutions/generated/squincir_026_d3c528742ca2afa0.json
index db45252d6e8d82415f76458e8af25ecddc4b5c60..c5bbc951e9ba29f04058d7f71acd4e09189e5953 100644
--- a/data/solutions/generated/squincir_026_d3c528742ca2afa0.json
+++ b/data/solutions/generated/squincir_026_d3c528742ca2afa0.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.012465393974281067,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.2015621187164243,
     "source_image_url": "https://erich-friedman.github.io/packing/squincir/26.gif",
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squincir_027_24101c6f5ef6d134.json b/data/solutions/generated/squincir_027_24101c6f5ef6d134.json
index a4a390d4942ab516eb7727e4548bc03ade0aa400..7338cd397572d4c0ca8b020cc73bd5af46ec4031 100644
--- a/data/solutions/generated/squincir_027_24101c6f5ef6d134.json
+++ b/data/solutions/generated/squincir_027_24101c6f5ef6d134.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.15630845991107953,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.2612651984229135,
     "source_image_url": "https://erich-friedman.github.io/packing/squincir/27.gif",
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squincir_028_33c1007b5e868482.json b/data/solutions/generated/squincir_028_33c1007b5e868482.json
index 0fd7e060c046a7fde467c9c87fc14d889df105be..40cf8ad5f16dff0c76ba162e57339b67a7faec25 100644
--- a/data/solutions/generated/squincir_028_33c1007b5e868482.json
+++ b/data/solutions/generated/squincir_028_33c1007b5e868482.json
@@ -46,7 +46,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.053354384411795075,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.333,
     "source_image_url": "https://erich-friedman.github.io/packing/squincir/28.gif",
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T03:19:00+00:00",
diff --git a/data/solutions/generated/squincir_029_ab533ab0ad8e3eeb.json b/data/solutions/generated/squincir_029_ab533ab0ad8e3eeb.json
index 3adb290b3b7add462a1b4a1a3b729f91075095c0..f4a3f4c8d8ec0032cb72a856e0a58d33ac81254b 100644
--- a/data/solutions/generated/squincir_029_ab533ab0ad8e3eeb.json
+++ b/data/solutions/generated/squincir_029_ab533ab0ad8e3eeb.json
@@ -46,7 +46,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.05235734808206704,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.401,
     "source_image_url": "https://erich-friedman.github.io/packing/squincir/29.gif",
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T02:51:36+00:00",
diff --git a/data/solutions/generated/squincir_030_d6d4b17471528bfa.json b/data/solutions/generated/squincir_030_d6d4b17471528bfa.json
index d1899214c0ca361cefce898d414007c9f9390aba..9a6259b6b7676c15a00109282ce56c3381c6e9d7 100644
--- a/data/solutions/generated/squincir_030_d6d4b17471528bfa.json
+++ b/data/solutions/generated/squincir_030_d6d4b17471528bfa.json
@@ -46,7 +46,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.05523080437402067,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.472,
     "source_image_url": "https://erich-friedman.github.io/packing/squincir/30.gif",
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T02:51:36+00:00",
diff --git a/data/solutions/generated/squincir_031_fdf9170d30584f4f.json b/data/solutions/generated/squincir_031_fdf9170d30584f4f.json
index cc3db32f2e0b8997015c7e3b224ae2b3aa90282e..a494bb79a8def76e3303dab0e5d67c625c340713 100644
--- a/data/solutions/generated/squincir_031_fdf9170d30584f4f.json
+++ b/data/solutions/generated/squincir_031_fdf9170d30584f4f.json
@@ -45,8 +45,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.5355339059327378,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squincir_032_b8bda371acb2b492.json b/data/solutions/generated/squincir_032_b8bda371acb2b492.json
index 0cc5cae4afc3dd6c458aed9871dab261d1ebba85..2b8bba27af212ceca42d10a03337663e87ffc642 100644
--- a/data/solutions/generated/squincir_032_b8bda371acb2b492.json
+++ b/data/solutions/generated/squincir_032_b8bda371acb2b492.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.004711668493325384,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.584,
     "source_image_url": "https://erich-friedman.github.io/packing/squincir/32.gif",
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squincir_033_e5a9fc9a4b7235a0.json b/data/solutions/generated/squincir_033_e5a9fc9a4b7235a0.json
index c0a609099dab9815dbf6db8550b0f63f17d2675e..da1bd2776e96ee446e17d586d7a5b14a7f548746 100644
--- a/data/solutions/generated/squincir_033_e5a9fc9a4b7235a0.json
+++ b/data/solutions/generated/squincir_033_e5a9fc9a4b7235a0.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.2151964213837427,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.605551275463989,
     "source_image_url": "https://erich-friedman.github.io/packing/squincir/33.gif",
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squincir_035_f2d91d98b4c2ee39.json b/data/solutions/generated/squincir_035_f2d91d98b4c2ee39.json
index dd805655cc846879f11cc75e72d36ecee3a979ef..d3b0f591571f55d6c82376cc89bf08f5cb624539 100644
--- a/data/solutions/generated/squincir_035_f2d91d98b4c2ee39.json
+++ b/data/solutions/generated/squincir_035_f2d91d98b4c2ee39.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.014174955972003465,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.640054944640259,
     "source_image_url": "https://erich-friedman.github.io/packing/squincir/35.gif",
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squincir_34_8e846defa45411b2.json b/data/solutions/generated/squincir_34_8e846defa45411b2.json
new file mode 100644
index 0000000000000000000000000000000000000000..dff9d316863345a863a0b766ad97b403b39fceef
--- /dev/null
+++ b/data/solutions/generated/squincir_34_8e846defa45411b2.json
@@ -0,0 +1,268 @@
+{
+  "case": "squincir@34",
+  "container": {
+    "radius": 3.6335692625466023,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squincir@34",
+    "credit": "Maurizio Morandi",
+    "date": "December 2010",
+    "family_updated": "",
+    "metric_expression": "3.629+",
+    "metric_symbol": "r",
+    "metric_value": 3.629,
+    "reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.",
+    "source_image": "34.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squincir/",
+    "title": "Squares in Circles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squincir@34",
+      "credit": "Maurizio Morandi",
+      "date": "December 2010",
+      "family_updated": "",
+      "metric_expression": "3.629+",
+      "metric_symbol": "r",
+      "metric_value": 3.629,
+      "reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.",
+      "source_image": "34.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squincir/",
+      "title": "Squares in Circles"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "sa_escape",
+    "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_20260501_systematic_broad.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.629,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/squincir_034_20260501_systematic_sa_escape.state",
+    "source_url": "https://erich-friedman.github.io/packing/squincir/",
+    "submitted_at": "2026-05-01T16:24:14+00:00",
+    "submitted_by": "Maurizio Morandi"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -5.516518693356074,
+      "x": 3.0184120466580993,
+      "y": -0.43411827131448566
+    },
+    {
+      "id": 2,
+      "rotation_radians": -5.496004274133597,
+      "x": 2.5227233494346275,
+      "y": -1.5048212926160542
+    },
+    {
+      "id": 3,
+      "rotation_radians": -5.5001629414978455,
+      "x": 2.471946439631452,
+      "y": 0.5881018076690959
+    },
+    {
+      "id": 4,
+      "rotation_radians": -5.50219333514613,
+      "x": 2.471651196415407,
+      "y": 1.5894752677335446
+    },
+    {
+      "id": 5,
+      "rotation_radians": -5.516513183990115,
+      "x": 2.017112509489319,
+      "y": -0.49235462550331754
+    },
+    {
+      "id": 6,
+      "rotation_radians": -5.514791683854013,
+      "x": 1.5183611365797995,
+      "y": -2.5171903880876996
+    },
+    {
+      "id": 7,
+      "rotation_radians": -5.498034349103209,
+      "x": 1.5207260676109455,
+      "y": -1.4926375014386235
+    },
+    {
+      "id": 8,
+      "rotation_radians": -5.5049838362960335,
+      "x": 1.456704787610716,
+      "y": 0.526414146834726
+    },
+    {
+      "id": 9,
+      "rotation_radians": -5.505144200017743,
+      "x": 1.466877998527677,
+      "y": 1.531891158203936
+    },
+    {
+      "id": 10,
+      "rotation_radians": -5.518973528094334,
+      "x": 1.4833353558789624,
+      "y": 2.5480614322008623
+    },
+    {
+      "id": 11,
+      "rotation_radians": -5.516505534823786,
+      "x": 1.0171865781973373,
+      "y": -0.4773719843951396
+    },
+    {
+      "id": 12,
+      "rotation_radians": -5.510734552905898,
+      "x": 0.5032245826035338,
+      "y": -2.987608394118827
+    },
+    {
+      "id": 13,
+      "rotation_radians": -5.509960008558664,
+      "x": 0.5139426637056431,
+      "y": -1.9872224683289441
+    },
+    {
+      "id": 14,
+      "rotation_radians": -5.523393178316227,
+      "x": 0.44864225588676854,
+      "y": 1.0154686252584282
+    },
+    {
+      "id": 15,
+      "rotation_radians": -5.52313013205462,
+      "x": 0.46954292126110414,
+      "y": 2.0154440268107363
+    },
+    {
+      "id": 16,
+      "rotation_radians": -5.525054127147628,
+      "x": 0.44984567793722874,
+      "y": 3.0172926744392186
+    },
+    {
+      "id": 17,
+      "rotation_radians": -5.509513923350603,
+      "x": 0.007693814437880773,
+      "y": -0.9809269197535814
+    },
+    {
+      "id": 18,
+      "rotation_radians": -5.523063322412159,
+      "x": 0.026203443415666584,
+      "y": 0.025702419847388792
+    },
+    {
+      "id": 19,
+      "rotation_radians": -5.52465593588285,
+      "x": -0.5041739875844358,
+      "y": -3.0001132379080784
+    },
+    {
+      "id": 20,
+      "rotation_radians": -5.513139407779519,
+      "x": -0.48895202619612327,
+      "y": -1.975277184930976
+    },
+    {
+      "id": 21,
+      "rotation_radians": -5.516458533951393,
+      "x": -0.544358048369117,
+      "y": 1.4633923902027826
+    },
+    {
+      "id": 22,
+      "rotation_radians": -5.515671279120035,
+      "x": -0.5653270407383996,
+      "y": 2.4842742305680976
+    },
+    {
+      "id": 23,
+      "rotation_radians": -5.509437924104241,
+      "x": -0.9872971717246929,
+      "y": -0.5425891733917544
+    },
+    {
+      "id": 24,
+      "rotation_radians": -5.5213177207702255,
+      "x": -0.9641146024385008,
+      "y": 0.4632093641310859
+    },
+    {
+      "id": 25,
+      "rotation_radians": -5.513647743071042,
+      "x": -1.4980993078802065,
+      "y": -2.537559664007265
+    },
+    {
+      "id": 26,
+      "rotation_radians": -5.512927208101287,
+      "x": -1.4927970488885305,
+      "y": -1.5370938582465192
+    },
+    {
+      "id": 27,
+      "rotation_radians": -5.516196581519833,
+      "x": -1.5444251861387541,
+      "y": 1.4787939364331648
+    },
+    {
+      "id": 28,
+      "rotation_radians": -5.52080029083357,
+      "x": -1.5687176771548013,
+      "y": 2.4835586021798868
+    },
+    {
+      "id": 29,
+      "rotation_radians": -5.509402189289167,
+      "x": -1.9872462055275675,
+      "y": -0.5289911939578559
+    },
+    {
+      "id": 30,
+      "rotation_radians": -5.497336849965333,
+      "x": -1.981484928515806,
+      "y": 0.47718151149103005
+    },
+    {
+      "id": 31,
+      "rotation_radians": -5.511186033795906,
+      "x": -2.4946220494353817,
+      "y": -1.5436522328571598
+    },
+    {
+      "id": 32,
+      "rotation_radians": -5.516133566390102,
+      "x": -2.544544033195992,
+      "y": 1.4883158769601854
+    },
+    {
+      "id": 33,
+      "rotation_radians": -5.509398893045089,
+      "x": -2.9870845563085373,
+      "y": -0.5072090835787664
+    },
+    {
+      "id": 34,
+      "rotation_radians": -5.509409098443499,
+      "x": -2.993790658628941,
+      "y": 0.4929994164397615
+    }
+  ],
+  "problem": "34 equal items for Squares in Circles",
+  "setup": "squincir",
+  "source_image": "https://erich-friedman.github.io/packing/squincir/34.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squincir/"
+}
diff --git a/data/solutions/generated/squincir_34_9214fdf4034b8f9a.json b/data/solutions/generated/squincir_34_9214fdf4034b8f9a.json
index c47998c9f01068fe49615e4f900e3d7fd7a81b4a..8fac72ffa374fbfa399bb9053f680510fce8a40c 100644
--- a/data/solutions/generated/squincir_34_9214fdf4034b8f9a.json
+++ b/data/solutions/generated/squincir_34_9214fdf4034b8f9a.json
@@ -46,7 +46,10 @@
     "generator_profile": "cg_deep",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_current_heavy_heavy.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.629,
     "source_url": "https://erich-friedman.github.io/packing/squincir/",
     "submitted_at": "2026-05-01T14:34:18+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/squincir_34_aa2ddbda942a0ffd.json b/data/solutions/generated/squincir_34_aa2ddbda942a0ffd.json
new file mode 100644
index 0000000000000000000000000000000000000000..ad48d1e9ceee4d6bf96a6ebc5efc2296fbdf68bb
--- /dev/null
+++ b/data/solutions/generated/squincir_34_aa2ddbda942a0ffd.json
@@ -0,0 +1,268 @@
+{
+  "case": "squincir@34",
+  "container": {
+    "radius": 3.6315230432891554,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squincir@34",
+    "credit": "Maurizio Morandi",
+    "date": "December 2010",
+    "family_updated": "",
+    "metric_expression": "3.629+",
+    "metric_symbol": "r",
+    "metric_value": 3.629,
+    "reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.",
+    "source_image": "34.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squincir/",
+    "title": "Squares in Circles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squincir@34",
+      "credit": "Maurizio Morandi",
+      "date": "December 2010",
+      "family_updated": "",
+      "metric_expression": "3.629+",
+      "metric_symbol": "r",
+      "metric_value": 3.629,
+      "reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.",
+      "source_image": "34.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squincir/",
+      "title": "Squares in Circles"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "cg_deep",
+    "image_seed_recovery_log": "bench_outputs/current_best_recovery/current_best_recovery_20260501_currentbest_deep_deep.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.629,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/squincir_034_20260501_currentbest_deep_cg_deep.state",
+    "source_url": "https://erich-friedman.github.io/packing/squincir/",
+    "submitted_at": "2026-05-01T17:13:54+00:00",
+    "submitted_by": "Maurizio Morandi"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -2.3729930389979863,
+      "x": -3.018320122888661,
+      "y": 0.4238194932096443
+    },
+    {
+      "id": 2,
+      "rotation_radians": -2.3501299030695826,
+      "x": -2.5284123865086103,
+      "y": 1.4999104933343084
+    },
+    {
+      "id": 3,
+      "rotation_radians": -2.3683652761199268,
+      "x": -2.454942296107073,
+      "y": -0.5854563441481296
+    },
+    {
+      "id": 4,
+      "rotation_radians": -2.3683704511273618,
+      "x": -2.470885033118252,
+      "y": -1.5853777783960532
+    },
+    {
+      "id": 5,
+      "rotation_radians": -2.372992685464978,
+      "x": -2.017105122579438,
+      "y": 0.48683284776423685
+    },
+    {
+      "id": 6,
+      "rotation_radians": -2.3684413907854656,
+      "x": -1.52002668509426,
+      "y": 2.498880751204305
+    },
+    {
+      "id": 7,
+      "rotation_radians": -2.3620172041106735,
+      "x": -1.5224731047723452,
+      "y": 1.4952433357899855
+    },
+    {
+      "id": 8,
+      "rotation_radians": -2.367862702131002,
+      "x": -1.447536581237767,
+      "y": -0.5325203121204232
+    },
+    {
+      "id": 9,
+      "rotation_radians": -2.3694980412368865,
+      "x": -1.4664922255992918,
+      "y": -1.5332437911042547
+    },
+    {
+      "id": 10,
+      "rotation_radians": -2.373734638006147,
+      "x": -1.4846830195966059,
+      "y": -2.5355090981564947
+    },
+    {
+      "id": 11,
+      "rotation_radians": -2.372994808721521,
+      "x": -1.0170334699383288,
+      "y": 0.4813445948940591
+    },
+    {
+      "id": 12,
+      "rotation_radians": -2.3617441975844615,
+      "x": -0.5017428042352318,
+      "y": 2.988638733383322
+    },
+    {
+      "id": 13,
+      "rotation_radians": -2.36174397804498,
+      "x": -0.5166156561104043,
+      "y": 1.9886740913112724
+    },
+    {
+      "id": 14,
+      "rotation_radians": -2.3796311890189052,
+      "x": -0.4519383833925164,
+      "y": -1.0133068012627033
+    },
+    {
+      "id": 15,
+      "rotation_radians": -2.3796300987332213,
+      "x": -0.4723855900180876,
+      "y": -2.013130562855173
+    },
+    {
+      "id": 16,
+      "rotation_radians": -2.380560347978786,
+      "x": -0.4486776805588371,
+      "y": -3.014458955658668
+    },
+    {
+      "id": 17,
+      "rotation_radians": -2.369590413253943,
+      "x": -0.008521522882798407,
+      "y": 0.9819002496320116
+    },
+    {
+      "id": 18,
+      "rotation_radians": -2.376235616077812,
+      "x": -0.02525196207878513,
+      "y": -0.021308377007797672
+    },
+    {
+      "id": 19,
+      "rotation_radians": -2.366312649100017,
+      "x": 0.5005079199012652,
+      "y": 2.976979557158397
+    },
+    {
+      "id": 20,
+      "rotation_radians": -2.3667569642009774,
+      "x": 0.48772910776538414,
+      "y": 1.9767957943966716
+    },
+    {
+      "id": 21,
+      "rotation_radians": -2.377222566209746,
+      "x": 0.5407295865348106,
+      "y": -1.4589542289959025
+    },
+    {
+      "id": 22,
+      "rotation_radians": -2.3758312775655397,
+      "x": 0.5647060461671485,
+      "y": -2.464832070224385
+    },
+    {
+      "id": 23,
+      "rotation_radians": -2.3695279003439778,
+      "x": 0.9856905651145921,
+      "y": 0.5392352106509695
+    },
+    {
+      "id": 24,
+      "rotation_radians": -2.3749350954555535,
+      "x": 0.9676068360867028,
+      "y": -0.46370802379287734
+    },
+    {
+      "id": 25,
+      "rotation_radians": -2.3671951226393837,
+      "x": 1.4961923463469688,
+      "y": 2.535562824310472
+    },
+    {
+      "id": 26,
+      "rotation_radians": -2.3676683996251677,
+      "x": 1.4915985128006495,
+      "y": 1.535273426309079
+    },
+    {
+      "id": 27,
+      "rotation_radians": -2.3772211166576698,
+      "x": 1.5405881934279309,
+      "y": -1.478020542933202
+    },
+    {
+      "id": 28,
+      "rotation_radians": -2.3702986629355336,
+      "x": 1.5673643871584741,
+      "y": -2.482216811100366
+    },
+    {
+      "id": 29,
+      "rotation_radians": -2.369525375518405,
+      "x": 1.985584183124257,
+      "y": 0.523466008677701
+    },
+    {
+      "id": 30,
+      "rotation_radians": -2.371112626411204,
+      "x": 1.9704866479387155,
+      "y": -0.4791752590622585
+    },
+    {
+      "id": 31,
+      "rotation_radians": -2.379486207154129,
+      "x": 2.4998977772843154,
+      "y": 1.5403826108065783
+    },
+    {
+      "id": 32,
+      "rotation_radians": -2.3772207407381374,
+      "x": 2.5405656220731396,
+      "y": -1.4914098820437318
+    },
+    {
+      "id": 33,
+      "rotation_radians": -2.3695256297653975,
+      "x": 2.9854286320289094,
+      "y": 0.5034743409096955
+    },
+    {
+      "id": 34,
+      "rotation_radians": -2.3695306841691006,
+      "x": 2.982014568555958,
+      "y": -0.4966061360727607
+    }
+  ],
+  "problem": "34 equal items for Squares in Circles",
+  "setup": "squincir",
+  "source_image": "https://erich-friedman.github.io/packing/squincir/34.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squincir/"
+}
diff --git a/data/solutions/generated/squindom_001_557f8de873a17a8e.json b/data/solutions/generated/squindom_001_557f8de873a17a8e.json
index 0fe60c1d455653be18f4d38733ed3606812859c0..36fe721fe4542730fe10153efcc9ca99966b7638 100644
--- a/data/solutions/generated/squindom_001_557f8de873a17a8e.json
+++ b/data/solutions/generated/squindom_001_557f8de873a17a8e.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_002_7684110dce2e5290.json b/data/solutions/generated/squindom_002_7684110dce2e5290.json
index 247e55a1c0f37bf49fc4caf22160519a633aff4c..33a00892791c26964d7720a6786ad671ebead1c9 100644
--- a/data/solutions/generated/squindom_002_7684110dce2e5290.json
+++ b/data/solutions/generated/squindom_002_7684110dce2e5290.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_003_3047ca63de76a853.json b/data/solutions/generated/squindom_003_3047ca63de76a853.json
index 61fe6946198dc96c3b8b045e0f8714f7d712f37f..f5f20461171a847ca1f2f6d472a2e209fb2985d3 100644
--- a/data/solutions/generated/squindom_003_3047ca63de76a853.json
+++ b/data/solutions/generated/squindom_003_3047ca63de76a853.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.5,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_004_8d067d60c7138964.json b/data/solutions/generated/squindom_004_8d067d60c7138964.json
index be56cdcbd97c48b7d36bad90b5367db25eb865c7..787b1d82d8e3f2c944fc4d08673cb98b6521290f 100644
--- a/data/solutions/generated/squindom_004_8d067d60c7138964.json
+++ b/data/solutions/generated/squindom_004_8d067d60c7138964.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.93,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Evert Stenlund"
diff --git a/data/solutions/generated/squindom_005_05f6000ecc64a077.json b/data/solutions/generated/squindom_005_05f6000ecc64a077.json
index 311b4dfcf79013919647ce8aacc7bd12ab8daecc..23dfbab090223c8ef73b4b5d5681bd3183cac351 100644
--- a/data/solutions/generated/squindom_005_05f6000ecc64a077.json
+++ b/data/solutions/generated/squindom_005_05f6000ecc64a077.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_006_095d951ace7a918a.json b/data/solutions/generated/squindom_006_095d951ace7a918a.json
index 26db50b33d57102bf2cea9fbf8ae1c08c0c45a53..95f08ee7fd9b516b17b994033b23f47cc7cb4fce 100644
--- a/data/solutions/generated/squindom_006_095d951ace7a918a.json
+++ b/data/solutions/generated/squindom_006_095d951ace7a918a.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_007_50aa0817a0117c40.json b/data/solutions/generated/squindom_007_50aa0817a0117c40.json
index 2116de827e7894b66c2ae354f8d1f930363d069f..cdc856a2ba1d46829711c154a98c668da7162b9a 100644
--- a/data/solutions/generated/squindom_007_50aa0817a0117c40.json
+++ b/data/solutions/generated/squindom_007_50aa0817a0117c40.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_008_0b83841ee591689c.json b/data/solutions/generated/squindom_008_0b83841ee591689c.json
index e0cfc52cf61c24211105626410dc4d43dd85797d..e446eef59f67918625c467f71339c6ff40fd59c5 100644
--- a/data/solutions/generated/squindom_008_0b83841ee591689c.json
+++ b/data/solutions/generated/squindom_008_0b83841ee591689c.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_009_2963ae62200cf2c5.json b/data/solutions/generated/squindom_009_2963ae62200cf2c5.json
index 5fd593b05c5912e049d76a901bf4b448b760fc25..a268e05e795b4e0c3452887ab61f022f38f69b60 100644
--- a/data/solutions/generated/squindom_009_2963ae62200cf2c5.json
+++ b/data/solutions/generated/squindom_009_2963ae62200cf2c5.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.471404520791032,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Evert Stenlund"
diff --git a/data/solutions/generated/squindom_010_7d3cb25d7577069f.json b/data/solutions/generated/squindom_010_7d3cb25d7577069f.json
index faf1a7e7a72e056b4091f25758fca6e7bb356671..94255dd5107eef1a347b1f2eb3cc4b8bb58c053e 100644
--- a/data/solutions/generated/squindom_010_7d3cb25d7577069f.json
+++ b/data/solutions/generated/squindom_010_7d3cb25d7577069f.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.5,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_012_4c82fd3f736a139f.json b/data/solutions/generated/squindom_012_4c82fd3f736a139f.json
index 67415a4e81dde7b84e6d40c85b5601cd98a74d7a..5aa103a203e3b50d5794e75d1d4c568db1ed9b6b 100644
--- a/data/solutions/generated/squindom_012_4c82fd3f736a139f.json
+++ b/data/solutions/generated/squindom_012_4c82fd3f736a139f.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.01610028434125399,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.897056274847714,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/12.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squindom_013_d738dfc349a8c940.json b/data/solutions/generated/squindom_013_d738dfc349a8c940.json
index 93c2e5bbfc61fd4a70c891de4e36cd58beee6a52..f2be7a76d231ab5485e6c9ae2db4a7059affde57 100644
--- a/data/solutions/generated/squindom_013_d738dfc349a8c940.json
+++ b/data/solutions/generated/squindom_013_d738dfc349a8c940.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.013144819906326979,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.976,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/13.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squindom_014_167b47d5e39e076d.json b/data/solutions/generated/squindom_014_167b47d5e39e076d.json
index c0787b44bcc43ee0f4cd199b06c197e5d61be3d4..edf1c0a0766739843868afab77e9db2a157091f4 100644
--- a/data/solutions/generated/squindom_014_167b47d5e39e076d.json
+++ b/data/solutions/generated/squindom_014_167b47d5e39e076d.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_015_6d686963e9ef0ece.json b/data/solutions/generated/squindom_015_6d686963e9ef0ece.json
index 1753b1c9ca70e66371e85ced8ee4784f94dce6f9..ae04824ca680640ff1159e448c535431259ffea0 100644
--- a/data/solutions/generated/squindom_015_6d686963e9ef0ece.json
+++ b/data/solutions/generated/squindom_015_6d686963e9ef0ece.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_016_0f551306e71d2ff0.json b/data/solutions/generated/squindom_016_0f551306e71d2ff0.json
index 9f8ad65cce5553ef3470cb8ee8a2b8e84a4092fa..d6053481eb4cb20a62161120b12fcd746c89dfa4 100644
--- a/data/solutions/generated/squindom_016_0f551306e71d2ff0.json
+++ b/data/solutions/generated/squindom_016_0f551306e71d2ff0.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_017_52c5d2070c49c79c.json b/data/solutions/generated/squindom_017_52c5d2070c49c79c.json
index 6a201a049c16b1b6fb08a70b81fe5e58193431c1..0ffa5ab7ec085c400023d236b8a8f39798a127bb 100644
--- a/data/solutions/generated/squindom_017_52c5d2070c49c79c.json
+++ b/data/solutions/generated/squindom_017_52c5d2070c49c79c.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_018_a6900e1fd3f925c6.json b/data/solutions/generated/squindom_018_a6900e1fd3f925c6.json
index e704c2726f30cc36b7eafd72a032ad621dcbe3b8..86d4911e97d8f8a4a267178ecaf60220de621359 100644
--- a/data/solutions/generated/squindom_018_a6900e1fd3f925c6.json
+++ b/data/solutions/generated/squindom_018_a6900e1fd3f925c6.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_019_cddf920bff527727.json b/data/solutions/generated/squindom_019_cddf920bff527727.json
index 1ce966f3bdb891e91be2f1458c16597af8d34830..3ba8ece9ef92136e0d1709c782d9239324cd2746 100644
--- a/data/solutions/generated/squindom_019_cddf920bff527727.json
+++ b/data/solutions/generated/squindom_019_cddf920bff527727.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 1.5415452636883547,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.447213595499958,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/19.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squindom_020_4a48c58d60a1f36b.json b/data/solutions/generated/squindom_020_4a48c58d60a1f36b.json
index 5a3ec269d748f4758f50115bfcb5558b4b78a2b2..9d9d7bde9f96f3518dda03a699bb78a0a036e8f4 100644
--- a/data/solutions/generated/squindom_020_4a48c58d60a1f36b.json
+++ b/data/solutions/generated/squindom_020_4a48c58d60a1f36b.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.5,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_021_f91a28177536f6d3.json b/data/solutions/generated/squindom_021_f91a28177536f6d3.json
index 175f02f7e7de588ad30db84a83553f1d9ce1066c..1a8452708bd7d730782c7172202c138f0a3d5964 100644
--- a/data/solutions/generated/squindom_021_f91a28177536f6d3.json
+++ b/data/solutions/generated/squindom_021_f91a28177536f6d3.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.5,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_022_d2d5380917cfe7ce.json b/data/solutions/generated/squindom_022_d2d5380917cfe7ce.json
index 0e23eda1d681c5facfd97afce39bae8ac1d42fd0..28cb81cda9e5f778bf52c38eada63227f556dc28 100644
--- a/data/solutions/generated/squindom_022_d2d5380917cfe7ce.json
+++ b/data/solutions/generated/squindom_022_d2d5380917cfe7ce.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.010443308129463803,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.745,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/22.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squindom_023_d12d3a9a87ba3b11.json b/data/solutions/generated/squindom_023_d12d3a9a87ba3b11.json
index 497e1c47336895547a80bdc903250b135af34045..41f0d9285e4279d234c324193b1541020a780234 100644
--- a/data/solutions/generated/squindom_023_d12d3a9a87ba3b11.json
+++ b/data/solutions/generated/squindom_023_d12d3a9a87ba3b11.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 9.930136612989092e-16,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.849,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/23.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squindom_024_f954e5304808181f.json b/data/solutions/generated/squindom_024_f954e5304808181f.json
index 17ce77a8d6cb42c1599e1006e8231c2d3edc5453..3bb037ad8612e8be596ead53d3756932147eea89 100644
--- a/data/solutions/generated/squindom_024_f954e5304808181f.json
+++ b/data/solutions/generated/squindom_024_f954e5304808181f.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.02168884317666257,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.882,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/24.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squindom_025_26273cb13b41bf72.json b/data/solutions/generated/squindom_025_26273cb13b41bf72.json
index 40bef7743c2f73be8b917d15b6232cfa5f07850b..4842e8fb9e3c8b196ee7a2614fc6916f836d32b9 100644
--- a/data/solutions/generated/squindom_025_26273cb13b41bf72.json
+++ b/data/solutions/generated/squindom_025_26273cb13b41bf72.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.029190136006954578,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.939,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/25.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squindom_026_a46204eea3d7f9fe.json b/data/solutions/generated/squindom_026_a46204eea3d7f9fe.json
index 7dbe7696371c90a52c3493d7b0421d530aea64ce..4515433903e299d9ffeab730eae164033274030d 100644
--- a/data/solutions/generated/squindom_026_a46204eea3d7f9fe.json
+++ b/data/solutions/generated/squindom_026_a46204eea3d7f9fe.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.011101417800640017,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.981,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/26.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squindom_027_c68e03cc8f5005db.json b/data/solutions/generated/squindom_027_c68e03cc8f5005db.json
index 1b5301a9f731acfab9a868fd56849e4f80f473f4..fb5828e4ddeec1ee99a10ace4003d6d804843d32 100644
--- a/data/solutions/generated/squindom_027_c68e03cc8f5005db.json
+++ b/data/solutions/generated/squindom_027_c68e03cc8f5005db.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_028_2c8c79126d60cdac.json b/data/solutions/generated/squindom_028_2c8c79126d60cdac.json
index 089ebe5eaf7ebf44565a0669b9a144d5f30011e1..c8d4c44b3207feb145f312fdd7d7a2e923179792 100644
--- a/data/solutions/generated/squindom_028_2c8c79126d60cdac.json
+++ b/data/solutions/generated/squindom_028_2c8c79126d60cdac.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_029_d2548471aff7d9f5.json b/data/solutions/generated/squindom_029_d2548471aff7d9f5.json
index 1e752deaa07bdf90a9d8b5ba8da47b53de04db68..8dc076caf16277e86e2a73200b826e31d0d27713 100644
--- a/data/solutions/generated/squindom_029_d2548471aff7d9f5.json
+++ b/data/solutions/generated/squindom_029_d2548471aff7d9f5.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_030_d67a491f7b4498c0.json b/data/solutions/generated/squindom_030_d67a491f7b4498c0.json
index 7b6b7f790ef86b68dddab09bbe5dabafa8de4e57..a298fef522a733b6d481f551975d734d21cc6a29 100644
--- a/data/solutions/generated/squindom_030_d67a491f7b4498c0.json
+++ b/data/solutions/generated/squindom_030_d67a491f7b4498c0.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_031_86ec622f54cecf7c.json b/data/solutions/generated/squindom_031_86ec622f54cecf7c.json
index b7887c7e9c813299d9961574aacea7b1e6aa5ca8..bc6d80ffcbf183009157c1d39447203e3a0bc53b 100644
--- a/data/solutions/generated/squindom_031_86ec622f54cecf7c.json
+++ b/data/solutions/generated/squindom_031_86ec622f54cecf7c.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 1.7888543819998315,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.0,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squindom_032_2873ac78de186b97.json b/data/solutions/generated/squindom_032_2873ac78de186b97.json
index 6b75a1995a25c965950202306531a0709e46b835..351baab6ed5e76378d1e7871c554efa7db23d830 100644
--- a/data/solutions/generated/squindom_032_2873ac78de186b97.json
+++ b/data/solutions/generated/squindom_032_2873ac78de186b97.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 1.7888543819998315,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.0,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squindom_033_167e5e2a52e9b5fe.json b/data/solutions/generated/squindom_033_167e5e2a52e9b5fe.json
index 1560b6a98c166d5023495896872f88b307764f0f..e528a658b995f9afc1546a37a0abbe3fb401f626 100644
--- a/data/solutions/generated/squindom_033_167e5e2a52e9b5fe.json
+++ b/data/solutions/generated/squindom_033_167e5e2a52e9b5fe.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.0,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.414213562373095,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/33.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squindom_034_b631e5a58c1517e1.json b/data/solutions/generated/squindom_034_b631e5a58c1517e1.json
index e7e7c9d0d21da13d2314cfe983f8bd22ea31c03e..9b2ce962ee350d619216ee806e3a8dc343da9399 100644
--- a/data/solutions/generated/squindom_034_b631e5a58c1517e1.json
+++ b/data/solutions/generated/squindom_034_b631e5a58c1517e1.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.012467831948419774,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.471404520791031,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/34.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squindom_035_dcd4cfae3ff101a2.json b/data/solutions/generated/squindom_035_dcd4cfae3ff101a2.json
index 1749650d0e267c1e4e6d64b6d74f07f2d5765616..6c36452238ec236117d979049a070507a631ff98 100644
--- a/data/solutions/generated/squindom_035_dcd4cfae3ff101a2.json
+++ b/data/solutions/generated/squindom_035_dcd4cfae3ff101a2.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 2.0124611797498106,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.5,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squindom_036_e0fc61bd01777ea3.json b/data/solutions/generated/squindom_036_e0fc61bd01777ea3.json
index 3b369974a7dfe638d1e8acc0ed39e9234fa59c71..6f141bdafdf83cb82325e26219b2b01998b9b30b 100644
--- a/data/solutions/generated/squindom_036_e0fc61bd01777ea3.json
+++ b/data/solutions/generated/squindom_036_e0fc61bd01777ea3.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 2.0124611797498106,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.5,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squindom_037_09a846134d0a3602.json b/data/solutions/generated/squindom_037_09a846134d0a3602.json
index 93a0dd01abd60bbbbb4249c6bd2858ad201ed566..0c9d02a7d327866d4eba2d5af0f1f6839dc3adc6 100644
--- a/data/solutions/generated/squindom_037_09a846134d0a3602.json
+++ b/data/solutions/generated/squindom_037_09a846134d0a3602.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.0,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.747546895706428,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/37.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squindom_038_d4d1cf6ab169d8aa.json b/data/solutions/generated/squindom_038_d4d1cf6ab169d8aa.json
index 704781ea91feceae2cbfc965b7c69e46c6ad261d..b3ed6db811b88ac5529faf04876a378cccad3950 100644
--- a/data/solutions/generated/squindom_038_d4d1cf6ab169d8aa.json
+++ b/data/solutions/generated/squindom_038_d4d1cf6ab169d8aa.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.02669857299806122,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.804737854124365,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/38.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squindom_039_a606e4f52500fa01.json b/data/solutions/generated/squindom_039_a606e4f52500fa01.json
index 5aeceb2a7f4097d167bf89acd26978bea0c916b4..6816850b727ec0b195a0f70160a4f26ac19551f5 100644
--- a/data/solutions/generated/squindom_039_a606e4f52500fa01.json
+++ b/data/solutions/generated/squindom_039_a606e4f52500fa01.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.06011641011830338,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.839,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/39.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squindom_040_bb2811be04efb5ee.json b/data/solutions/generated/squindom_040_bb2811be04efb5ee.json
index 4cfd9624d1644cfab613cc5fce9c567eb0caf107..b6ce15f152728e13c52023561505b7b3246ae20a 100644
--- a/data/solutions/generated/squindom_040_bb2811be04efb5ee.json
+++ b/data/solutions/generated/squindom_040_bb2811be04efb5ee.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.02720431199531836,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.895,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/40.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squindom_042_7faea8ae450b67a1.json b/data/solutions/generated/squindom_042_7faea8ae450b67a1.json
index 622eae360fa121004dcc64824a6e439e8e6ef88a..51c8ac947baa0a78c9c0b59e94c6925235888b52 100644
--- a/data/solutions/generated/squindom_042_7faea8ae450b67a1.json
+++ b/data/solutions/generated/squindom_042_7faea8ae450b67a1.json
@@ -48,7 +48,9 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.04181019869074938,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.",
+    "reference_side": 4.989,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/42.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squindom_043_7f9527ccddc9d648.json b/data/solutions/generated/squindom_043_7f9527ccddc9d648.json
index 46183be568042f4ef190e977e145c397f07a6123..454138e09b024f752e24584ab1cb4e66c73a1416 100644
--- a/data/solutions/generated/squindom_043_7f9527ccddc9d648.json
+++ b/data/solutions/generated/squindom_043_7f9527ccddc9d648.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_044_1ffd758f1f058de5.json b/data/solutions/generated/squindom_044_1ffd758f1f058de5.json
index 3ba6a72583eb559a0b73b99104d09d7143fbdfc0..9cd9f833707c5b72f6525a98b0c08943e2ee499e 100644
--- a/data/solutions/generated/squindom_044_1ffd758f1f058de5.json
+++ b/data/solutions/generated/squindom_044_1ffd758f1f058de5.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_045_d085ed9682ca2968.json b/data/solutions/generated/squindom_045_d085ed9682ca2968.json
index d352fc6edc3444fc742c3c0fd4e25b6dfbfd928b..fdf8a20af5f90db6f240d1110bbac46a202c2e0f 100644
--- a/data/solutions/generated/squindom_045_d085ed9682ca2968.json
+++ b/data/solutions/generated/squindom_045_d085ed9682ca2968.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_046_3b408e84cd206068.json b/data/solutions/generated/squindom_046_3b408e84cd206068.json
index 86755fefba05df8fcb76b4c800eebde895a7da49..45d995e6bfbcfcf3f8395138f4cc08b2d24b8a89 100644
--- a/data/solutions/generated/squindom_046_3b408e84cd206068.json
+++ b/data/solutions/generated/squindom_046_3b408e84cd206068.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_047_2525e331a392c6b9.json b/data/solutions/generated/squindom_047_2525e331a392c6b9.json
index 7c84568de86f6ebb9bf1a0b601e85c6a34874057..d02512c2f77015fbfb2f78589f4552f855fdf49a 100644
--- a/data/solutions/generated/squindom_047_2525e331a392c6b9.json
+++ b/data/solutions/generated/squindom_047_2525e331a392c6b9.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 2.2360679774997894,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.0,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squindom_048_0433c6294c4f3fe7.json b/data/solutions/generated/squindom_048_0433c6294c4f3fe7.json
index 3d8b7da66ac889ffdcc20332bdd48acd96527d18..66dfb611c24e6dff0c955571aba21165d72e0976 100644
--- a/data/solutions/generated/squindom_048_0433c6294c4f3fe7.json
+++ b/data/solutions/generated/squindom_048_0433c6294c4f3fe7.json
@@ -46,8 +46,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.0,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squindom_049_c84a987ae840ebe3.json b/data/solutions/generated/squindom_049_c84a987ae840ebe3.json
index 9131681066157fa7601edb9670413f0f78fb87da..bde16a0db86385ff591d9c664bf5bd76fad612ba 100644
--- a/data/solutions/generated/squindom_049_c84a987ae840ebe3.json
+++ b/data/solutions/generated/squindom_049_c84a987ae840ebe3.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.0,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.0,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squindom_050_df0259815cc5320a.json b/data/solutions/generated/squindom_050_df0259815cc5320a.json
index efd3871103921b62fb25db6dcbf6120c936e8c34..7d53daf2a669b5b2b76600c7a242b90eb4711ea8 100644
--- a/data/solutions/generated/squindom_050_df0259815cc5320a.json
+++ b/data/solutions/generated/squindom_050_df0259815cc5320a.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.0,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.0,
     "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif",
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squindom_11_eadb11fb534aa6a1.json b/data/solutions/generated/squindom_11_eadb11fb534aa6a1.json
index b3cf07da6610764814804adaebfa77d80c27c8b8..7b1573ebe7bd4cb7fb42aa708dc7cd2be7df364b 100644
--- a/data/solutions/generated/squindom_11_eadb11fb534aa6a1.json
+++ b/data/solutions/generated/squindom_11_eadb11fb534aa6a1.json
@@ -47,7 +47,10 @@
     "generator_profile": "cg_precise",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_20260501T070815Z_broad.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.779,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T07:13:53+00:00",
     "submitted_by": "Evert Stenlund"
diff --git a/data/solutions/generated/squindom_41_5bbf9f2ba5ab11a2.json b/data/solutions/generated/squindom_41_5bbf9f2ba5ab11a2.json
new file mode 100644
index 0000000000000000000000000000000000000000..70797b5dbec3423e102409f54f00d8860ded101d
--- /dev/null
+++ b/data/solutions/generated/squindom_41_5bbf9f2ba5ab11a2.json
@@ -0,0 +1,311 @@
+{
+  "case": "squindom@41",
+  "container": {
+    "height": 5.000043288573118,
+    "type": "rectangle",
+    "width": 10.000086577146236
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squindom@41",
+    "credit": "Sigvart Brendberg",
+    "date": "June 2023",
+    "family_updated": "",
+    "metric_expression": "4.927+",
+    "metric_symbol": "s",
+    "metric_value": 4.927,
+    "reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.",
+    "source_image": "41.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000200001000001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squindom@41",
+      "credit": "Sigvart Brendberg",
+      "date": "June 2023",
+      "family_updated": "",
+      "metric_expression": "4.927+",
+      "metric_symbol": "s",
+      "metric_value": 4.927,
+      "reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.",
+      "source_image": "41.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "sa_escape",
+    "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_20260501_systematic_broad.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.927,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/squindom_041_20260501_systematic_sa_escape.state",
+    "source_url": "https://erich-friedman.github.io/packing/squindom/",
+    "submitted_at": "2026-05-01T16:24:14+00:00",
+    "submitted_by": "Sigvart Brendberg"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.7853887568544335,
+      "x": 2.3201731032966117,
+      "y": 1.752568459127371
+    },
+    {
+      "id": 2,
+      "rotation_radians": 5.49778941456046,
+      "x": 4.476412143626909,
+      "y": -2.000012887803005
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.7853936313928833,
+      "x": 1.3201312110754118,
+      "y": 2.0000138592324452
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.7853932677946541,
+      "x": 0.19135610284870183,
+      "y": -7.53086934619874e-06
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.7853965502105764,
+      "x": -0.6918494485299804,
+      "y": 2.0000186408214407
+    },
+    {
+      "id": 6,
+      "rotation_radians": 6.107019581707391,
+      "x": 2.1703478543744907,
+      "y": -0.7968838553418736
+    },
+    {
+      "id": 7,
+      "rotation_radians": 2.356195840323835,
+      "x": -4.317602004256344,
+      "y": 2.0000172484903054
+    },
+    {
+      "id": 8,
+      "rotation_radians": 2.96542703836756,
+      "x": 1.3502499677165762,
+      "y": -1.3691301479238152
+    },
+    {
+      "id": 9,
+      "rotation_radians": 5.497788156477231,
+      "x": -1.838544122506822,
+      "y": 2.0000201436094414
+    },
+    {
+      "id": 10,
+      "rotation_radians": 6.107016287099561,
+      "x": 3.2949555514051445,
+      "y": -1.2317201941897686
+    },
+    {
+      "id": 11,
+      "rotation_radians": 3.9269905300491375,
+      "x": -2.846011161030733,
+      "y": 1.0000089269764778
+    },
+    {
+      "id": 12,
+      "rotation_radians": 2.3561929171354175,
+      "x": -0.8394156553508029,
+      "y": 1.0000064254902108
+    },
+    {
+      "id": 13,
+      "rotation_radians": 3.926989377986832,
+      "x": -0.845946908905818,
+      "y": -1.0000055755653023
+    },
+    {
+      "id": 14,
+      "rotation_radians": 6.107016331349032,
+      "x": 2.474783830288696,
+      "y": -1.8038581132438378
+    },
+    {
+      "id": 15,
+      "rotation_radians": 2.3561961317798925,
+      "x": -3.8605024478282615,
+      "y": 1.0000087190977387
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.785398154016971,
+      "x": -1.845966298573843,
+      "y": -1.000005175972627
+    },
+    {
+      "id": 17,
+      "rotation_radians": 6.106874501694203,
+      "x": 2.3568053039614996,
+      "y": 0.552556419630691
+    },
+    {
+      "id": 18,
+      "rotation_radians": 2.356185820858721,
+      "x": 1.1606366130159165,
+      "y": 0.9999975382817282
+    },
+    {
+      "id": 19,
+      "rotation_radians": 5.497787561716193,
+      "x": -1.8459665277139383,
+      "y": 2.1788352149647195e-06
+    },
+    {
+      "id": 20,
+      "rotation_radians": 3.9269908664749322,
+      "x": -1.7337348814469704,
+      "y": -2.000018450747985
+    },
+    {
+      "id": 21,
+      "rotation_radians": 2.3561959337886136,
+      "x": -3.742959686760145,
+      "y": -2.000019889535645
+    },
+    {
+      "id": 22,
+      "rotation_radians": 5.531202001641568,
+      "x": 1.2078035375581155,
+      "y": -0.015442037010612942
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.7853966732981724,
+      "x": -0.8459427525759702,
+      "y": 4.3788333721660065e-07
+    },
+    {
+      "id": 24,
+      "rotation_radians": 3.1260424375456703,
+      "x": 3.4991067840692183,
+      "y": 0.7929850983759787
+    },
+    {
+      "id": 25,
+      "rotation_radians": 5.497785066330738,
+      "x": 0.1606108258332418,
+      "y": 1.000002989325917
+    },
+    {
+      "id": 26,
+      "rotation_radians": 2.3561992627502746,
+      "x": 3.320193300442303,
+      "y": 2.00001774183137
+    },
+    {
+      "id": 27,
+      "rotation_radians": 4.015787663481595,
+      "x": 4.457672888145119,
+      "y": -0.9576253296068925
+    },
+    {
+      "id": 28,
+      "rotation_radians": 2.356193509077223,
+      "x": -2.860200653688731,
+      "y": 2.0000174424407366
+    },
+    {
+      "id": 29,
+      "rotation_radians": 5.497781966353208,
+      "x": 0.15407172217194906,
+      "y": -1.0000084769965518
+    },
+    {
+      "id": 30,
+      "rotation_radians": 2.9654268560698833,
+      "x": 2.9905202179234207,
+      "y": -0.22474558659300983
+    },
+    {
+      "id": 31,
+      "rotation_radians": 2.3561925811117725,
+      "x": -0.7336307940819536,
+      "y": -2.000018700608119
+    },
+    {
+      "id": 32,
+      "rotation_radians": 2.3561955056054296,
+      "x": -1.8459808191251916,
+      "y": 1.0000106839438063
+    },
+    {
+      "id": 33,
+      "rotation_radians": 5.497786622679781,
+      "x": -2.846000164634451,
+      "y": 1.3017564507707767e-06
+    },
+    {
+      "id": 34,
+      "rotation_radians": 3.9269889554564377,
+      "x": 0.3200993703133264,
+      "y": 2.0000172672381438
+    },
+    {
+      "id": 35,
+      "rotation_radians": 2.3561953304217873,
+      "x": -3.8541768246583517,
+      "y": -5.777962772584565e-07
+    },
+    {
+      "id": 36,
+      "rotation_radians": -0.7853992353238888,
+      "x": -2.7419549466163446,
+      "y": -2.0000186767860195
+    },
+    {
+      "id": 37,
+      "rotation_radians": 4.015793470092883,
+      "x": 4.4576626353748425,
+      "y": 0.04634853152343456
+    },
+    {
+      "id": 38,
+      "rotation_radians": 3.926990048448735,
+      "x": -2.8459863545278425,
+      "y": -1.0000058255051212
+    },
+    {
+      "id": 39,
+      "rotation_radians": 5.497782264679849,
+      "x": 0.27059618173110345,
+      "y": -2.0000174655848832
+    },
+    {
+      "id": 40,
+      "rotation_radians": 5.497788491527687,
+      "x": -4.483609611281647,
+      "y": -1.0000109515553977
+    },
+    {
+      "id": 41,
+      "rotation_radians": 5.189055827037192,
+      "x": 4.3717450721991105,
+      "y": 1.5837567224942526
+    }
+  ],
+  "problem": "41 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/41.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_41_9ed000ff11bd8b55.json b/data/solutions/generated/squindom_41_9ed000ff11bd8b55.json
new file mode 100644
index 0000000000000000000000000000000000000000..cc8f4ef1fec2db7ad7cd5859fe537add8f929eb6
--- /dev/null
+++ b/data/solutions/generated/squindom_41_9ed000ff11bd8b55.json
@@ -0,0 +1,310 @@
+{
+  "case": "squindom@41",
+  "container": {
+    "height": 4.928216572329007,
+    "type": "rectangle",
+    "width": 9.856433144658014
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squindom@41",
+    "credit": "Sigvart Brendberg",
+    "date": "June 2023",
+    "family_updated": "",
+    "metric_expression": "4.927+",
+    "metric_symbol": "s",
+    "metric_value": 4.927,
+    "reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.",
+    "source_image": "41.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squindom@41",
+      "credit": "Sigvart Brendberg",
+      "date": "June 2023",
+      "family_updated": "",
+      "metric_expression": "4.927+",
+      "metric_symbol": "s",
+      "metric_value": 4.927,
+      "reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.",
+      "source_image": "41.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Verified coordinate recovery from fresh CG rectangle-container topology search against the Friedman target; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "recovery_source": "fresh CG rectangle-container topology search against the Friedman target",
+    "recovery_state": "bench_outputs/fresh_recovery/states/squindom_041_cg10000.state",
+    "reference_side": 4.927,
+    "source_url": "https://erich-friedman.github.io/packing/squindom/",
+    "submitted_at": "2026-05-01T18:06:20+00:00",
+    "submitted_by": "Sigvart Brendberg"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.3440496283965092,
+      "x": -3.8349793806377526,
+      "y": -1.798425274446287
+    },
+    {
+      "id": 2,
+      "rotation_radians": -0.34425218465892293,
+      "x": -2.7343853484643503,
+      "y": -1.786832185201194
+    },
+    {
+      "id": 3,
+      "rotation_radians": -0.35016709234508264,
+      "x": -1.609561802355556,
+      "y": -1.7998867368460532
+    },
+    {
+      "id": 4,
+      "rotation_radians": -0.3542323629669199,
+      "x": 0.6547861246290335,
+      "y": -1.8008825428377837
+    },
+    {
+      "id": 5,
+      "rotation_radians": -0.3519680015767426,
+      "x": 1.757715977316509,
+      "y": -1.8003427249875008
+    },
+    {
+      "id": 6,
+      "rotation_radians": -0.351967531195872,
+      "x": 2.8596414640024883,
+      "y": -1.8003309818767261
+    },
+    {
+      "id": 7,
+      "rotation_radians": -0.7547210827810334,
+      "x": 4.411029064039916,
+      "y": -1.9475060542285823
+    },
+    {
+      "id": 8,
+      "rotation_radians": -0.34404855198762463,
+      "x": -4.26254665650618,
+      "y": -0.894408100539464
+    },
+    {
+      "id": 9,
+      "rotation_radians": -0.3448228047903345,
+      "x": -3.1632975956402745,
+      "y": -0.8769992752369787
+    },
+    {
+      "id": 10,
+      "rotation_radians": -0.34522473866414305,
+      "x": -2.0475833063250914,
+      "y": -0.8974266907014814
+    },
+    {
+      "id": 11,
+      "rotation_radians": -0.33502063464069753,
+      "x": -0.46455918088651454,
+      "y": -1.7962894942019594
+    },
+    {
+      "id": 12,
+      "rotation_radians": -0.3519667458706618,
+      "x": 1.3377196166502165,
+      "y": -0.8927915235627976
+    },
+    {
+      "id": 13,
+      "rotation_radians": -0.3519676025737369,
+      "x": 2.43964171350741,
+      "y": -0.8927702038702728
+    },
+    {
+      "id": 14,
+      "rotation_radians": -0.35196742427986644,
+      "x": 3.6110551596379863,
+      "y": -1.0429188019435738
+    },
+    {
+      "id": 15,
+      "rotation_radians": -0.33642110740645786,
+      "x": -3.59858980617969,
+      "y": 0.04020588774900157
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.3364212321288755,
+      "x": -2.474800266805134,
+      "y": 0.011674718747798771
+    },
+    {
+      "id": 17,
+      "rotation_radians": -0.3357513315477024,
+      "x": -0.9223922313723868,
+      "y": -0.9064514836281024
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.33742246578535035,
+      "x": 0.21178913287940276,
+      "y": -0.8950063779084324
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.35127622386323115,
+      "x": 2.0492634620087538,
+      "y": 0.028879461039864194
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.3536559184032356,
+      "x": 3.253021191361683,
+      "y": -0.09958318024565481
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.7853876899153985,
+      "x": 4.428202487571094,
+      "y": -0.03764042143611893
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.769325283860585,
+      "x": -4.405750079748165,
+      "y": 0.9462723169761492
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.3364209745694716,
+      "x": -2.909372586850157,
+      "y": 0.9136634193097595
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.33642122084657805,
+      "x": -1.3566076776021878,
+      "y": -0.005229688825904239
+    },
+    {
+      "id": 25,
+      "rotation_radians": -0.33642127497219015,
+      "x": -0.24655634082678227,
+      "y": -0.0052278295267054985
+    },
+    {
+      "id": 26,
+      "rotation_radians": -0.34125428703889593,
+      "x": 0.8897600316712437,
+      "y": 0.007417609295544672
+    },
+    {
+      "id": 27,
+      "rotation_radians": -0.35991110752788796,
+      "x": 2.80052342227227,
+      "y": 0.7965675407314224
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.7840372272053423,
+      "x": 4.069928159155317,
+      "y": 0.9625848308290715
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.7859717793968601,
+      "x": -4.4257565600399795,
+      "y": 1.9595340639396743
+    },
+    {
+      "id": 30,
+      "rotation_radians": -0.3364212929556072,
+      "x": -1.7906651828423774,
+      "y": 0.8956957242162649
+    },
+    {
+      "id": 31,
+      "rotation_radians": -0.3364213106105973,
+      "x": -0.6806162390273854,
+      "y": 0.8956953378816133
+    },
+    {
+      "id": 32,
+      "rotation_radians": -0.3412535291122922,
+      "x": 0.4315534602485265,
+      "y": 0.896849699755421
+    },
+    {
+      "id": 33,
+      "rotation_radians": -0.3512759804535254,
+      "x": 1.573085487079135,
+      "y": 0.9103944530640137
+    },
+    {
+      "id": 34,
+      "rotation_radians": 0.7873823427128596,
+      "x": 3.416566763884709,
+      "y": 1.9627839756340208
+    },
+    {
+      "id": 35,
+      "rotation_radians": 0.7867591047976716,
+      "x": 4.417273833637376,
+      "y": 1.963096612933755
+    },
+    {
+      "id": 36,
+      "rotation_radians": -0.7836933561145542,
+      "x": -3.4239333353660832,
+      "y": 1.9618385379991372
+    },
+    {
+      "id": 37,
+      "rotation_radians": -0.3364210739033131,
+      "x": -2.2247253040590556,
+      "y": 1.7966191696179172
+    },
+    {
+      "id": 38,
+      "rotation_radians": -0.3364212973068148,
+      "x": -1.1146716058479773,
+      "y": 1.796620084624705
+    },
+    {
+      "id": 39,
+      "rotation_radians": -0.3412536020107051,
+      "x": -0.002509840781485886,
+      "y": 1.7977697741100118
+    },
+    {
+      "id": 40,
+      "rotation_radians": -0.3512760618388533,
+      "x": 1.1147145569078345,
+      "y": 1.8001644042675558
+    },
+    {
+      "id": 41,
+      "rotation_radians": 0.9216132822694576,
+      "x": 2.3536874428092425,
+      "y": 1.9008207318381245
+    }
+  ],
+  "problem": "41 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/41.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_41_cb1462995bd3b2c0.json b/data/solutions/generated/squindom_41_cb1462995bd3b2c0.json
index 8c36fa53b06f6914ec9356e36d8ffb9d2264bce6..f754eb8c9ff338f6a98ff369702aceab76d7a951 100644
--- a/data/solutions/generated/squindom_41_cb1462995bd3b2c0.json
+++ b/data/solutions/generated/squindom_41_cb1462995bd3b2c0.json
@@ -47,7 +47,10 @@
     "generator_profile": "sa_escape",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_current_broad_broad.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.927,
     "source_url": "https://erich-friedman.github.io/packing/squindom/",
     "submitted_at": "2026-05-01T13:47:12+00:00",
     "submitted_by": "Sigvart Brendberg"
diff --git a/data/solutions/generated/squinhex_001_7a4ae27d520be7d9.json b/data/solutions/generated/squinhex_001_7a4ae27d520be7d9.json
index d20bf4602dca0ce2e6813618537a7b0279a78af8..33bbc6d0b68b09bb913ea2cb3159be7890e6bac7 100644
--- a/data/solutions/generated/squinhex_001_7a4ae27d520be7d9.json
+++ b/data/solutions/generated/squinhex_001_7a4ae27d520be7d9.json
@@ -49,8 +49,11 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/deep_profile_remaining_orange.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg_deep",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.7886751345948129,
     "source_image_url": "https://erich-friedman.github.io/packing/squinhex/1.png",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T03:07:58+00:00",
diff --git a/data/solutions/generated/squinhex_002_21fb35b9b51e59c5.json b/data/solutions/generated/squinhex_002_21fb35b9b51e59c5.json
index c73ab9ee85d992035464f9f1125eb445d73251a7..2ada63e502c2b9a9cb4946390e4e8022f051ba49 100644
--- a/data/solutions/generated/squinhex_002_21fb35b9b51e59c5.json
+++ b/data/solutions/generated/squinhex_002_21fb35b9b51e59c5.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.1547005383792515,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squinhex_003_a5c3dc7083e49634.json b/data/solutions/generated/squinhex_003_a5c3dc7083e49634.json
index 6e484c0761ae5f57d27038bb6e0a995a8cb79e3b..d88a15b8d9dbfd01a67962f992e187c3261b7765 100644
--- a/data/solutions/generated/squinhex_003_a5c3dc7083e49634.json
+++ b/data/solutions/generated/squinhex_003_a5c3dc7083e49634.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.3660254037844386,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/squinhex_004_49c10fcc6144044b.json b/data/solutions/generated/squinhex_004_49c10fcc6144044b.json
index 6fcfe20a7b90b341636c898d9e282f34d1d03db5..5be33a219a5bc7ef648ec2442402ada61f718060 100644
--- a/data/solutions/generated/squinhex_004_49c10fcc6144044b.json
+++ b/data/solutions/generated/squinhex_004_49c10fcc6144044b.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.519,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/squinhex_005_1d1f44767245ecd6.json b/data/solutions/generated/squinhex_005_1d1f44767245ecd6.json
index 611be952dd29b67e1c08c2784110b7383d56f049..5658c1c2fdc57b5f9c49b3dc79cc40b401dc15d3 100644
--- a/data/solutions/generated/squinhex_005_1d1f44767245ecd6.json
+++ b/data/solutions/generated/squinhex_005_1d1f44767245ecd6.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.7320508075688772,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squinhex_006_974baf9dad527270.json b/data/solutions/generated/squinhex_006_974baf9dad527270.json
index 3cc484930557bc8fb4b02e112f51167c2a921236..bc613f614b5ac199c3e27f879a84622da16adc9b 100644
--- a/data/solutions/generated/squinhex_006_974baf9dad527270.json
+++ b/data/solutions/generated/squinhex_006_974baf9dad527270.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.821,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/squinhex_007_3877067eb2c9921c.json b/data/solutions/generated/squinhex_007_3877067eb2c9921c.json
index e821c4906c9960fe91e5e8551382abede7bbbe0e..7a07c3a3a618b336e13a00ab430a618da9457e17 100644
--- a/data/solutions/generated/squinhex_007_3877067eb2c9921c.json
+++ b/data/solutions/generated/squinhex_007_3877067eb2c9921c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.861,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/squinhex_008_15b61ced9a55fd6e.json b/data/solutions/generated/squinhex_008_15b61ced9a55fd6e.json
index f4330d05ec448de60afccaa02b07a7c86f75c3a4..a66a10d86cbb009f03ce62e54d1ee2137a2f555d 100644
--- a/data/solutions/generated/squinhex_008_15b61ced9a55fd6e.json
+++ b/data/solutions/generated/squinhex_008_15b61ced9a55fd6e.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.15378,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ian Watson"
diff --git a/data/solutions/generated/squinhex_009_55005bb44a4d74d4.json b/data/solutions/generated/squinhex_009_55005bb44a4d74d4.json
index b3cb831e2f5fc567eb4969b8ea63743b332592c3..6c3fb81647ed0bff50ea395f5331a486837160ad 100644
--- a/data/solutions/generated/squinhex_009_55005bb44a4d74d4.json
+++ b/data/solutions/generated/squinhex_009_55005bb44a4d74d4.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.033464710125207936,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.232050807568877,
     "source_image_url": "https://erich-friedman.github.io/packing/squinhex/9.png",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinhex_010_1dc9bb5dff8e4212.json b/data/solutions/generated/squinhex_010_1dc9bb5dff8e4212.json
index cd0bf774a4eb9f02a043eb86a1afaa3319165933..0bd503ad9d1f62f1a89a75c4f5fde625d2b1808c 100644
--- a/data/solutions/generated/squinhex_010_1dc9bb5dff8e4212.json
+++ b/data/solutions/generated/squinhex_010_1dc9bb5dff8e4212.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.309401076758503,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squinhex_011_705689a83f76dc66.json b/data/solutions/generated/squinhex_011_705689a83f76dc66.json
index 07d4ec6876fb0f87b8d0b9a9636d5fb6a6401baa..7c54517ad5267d696b7cad9e3314d99010300de3 100644
--- a/data/solutions/generated/squinhex_011_705689a83f76dc66.json
+++ b/data/solutions/generated/squinhex_011_705689a83f76dc66.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.40944,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/squinhex_012_2605d29267e364f4.json b/data/solutions/generated/squinhex_012_2605d29267e364f4.json
index 6b293373d99ef819d28646453960034ca42c39c7..cfa5bdfe81acc056ceccabe5f7fc1fa7f1deae7d 100644
--- a/data/solutions/generated/squinhex_012_2605d29267e364f4.json
+++ b/data/solutions/generated/squinhex_012_2605d29267e364f4.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.4433756729740645,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/squinhex_013_051502d315bb277c.json b/data/solutions/generated/squinhex_013_051502d315bb277c.json
index 6bed4d93eb269f58fd1b2da808e96f2b9ed7d41e..5ddbc3423f49efa1c2d9531ede24a6508c17ee17 100644
--- a/data/solutions/generated/squinhex_013_051502d315bb277c.json
+++ b/data/solutions/generated/squinhex_013_051502d315bb277c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.572,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/squinhex_014_525e7cc585bd027c.json b/data/solutions/generated/squinhex_014_525e7cc585bd027c.json
index 00d32ba874e7b2bebed55d8b049d576f1d79a9f1..5bb27a18a6beb41876701fc85d30bfaa6c9fd4d5 100644
--- a/data/solutions/generated/squinhex_014_525e7cc585bd027c.json
+++ b/data/solutions/generated/squinhex_014_525e7cc585bd027c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.62126,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/squinhex_015_b68c71af3475ffed.json b/data/solutions/generated/squinhex_015_b68c71af3475ffed.json
index 4a53a6143b40877d6eaac8efe7dd7b42edc4634a..33f955d9231e55ee5f1eedf70c85de54f0a41d45 100644
--- a/data/solutions/generated/squinhex_015_b68c71af3475ffed.json
+++ b/data/solutions/generated/squinhex_015_b68c71af3475ffed.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.049708492578483456,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.75365,
     "source_image_url": "https://erich-friedman.github.io/packing/squinhex/15.png",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinhex_016_89a68dd125601a79.json b/data/solutions/generated/squinhex_016_89a68dd125601a79.json
index 5f4c226479612d87b1e7b48d8dbb12456d7a3b41..cf7efe76eea544cb135f2c3c8a39c7d04f00f2ad 100644
--- a/data/solutions/generated/squinhex_016_89a68dd125601a79.json
+++ b/data/solutions/generated/squinhex_016_89a68dd125601a79.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.82004,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ian Watson"
diff --git a/data/solutions/generated/squinhex_017_68ba30b81c3844a7.json b/data/solutions/generated/squinhex_017_68ba30b81c3844a7.json
index 53e97acf251b5e4d35cfc4f54f8bc6e58d66971d..89897e05cadff07fc0b92a173947bb08a9e56e2c 100644
--- a/data/solutions/generated/squinhex_017_68ba30b81c3844a7.json
+++ b/data/solutions/generated/squinhex_017_68ba30b81c3844a7.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.043280505344389264,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.8867513459481287,
     "source_image_url": "https://erich-friedman.github.io/packing/squinhex/17.png",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinhex_018_e136eeec3de765c3.json b/data/solutions/generated/squinhex_018_e136eeec3de765c3.json
index 9c07e7af1fc52f69dba7e4f4d43257bf7330667c..a7ffef9df3d920c2c8e970e02ee2222fadb0dda1 100644
--- a/data/solutions/generated/squinhex_018_e136eeec3de765c3.json
+++ b/data/solutions/generated/squinhex_018_e136eeec3de765c3.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.92111,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ian Watson"
diff --git a/data/solutions/generated/squinhex_019_ae3850bdb0ac1880.json b/data/solutions/generated/squinhex_019_ae3850bdb0ac1880.json
index 3f6996c4e1abf85300b8d724398bd33867d36700..3b4b1ae3e1c04f7c4540fd7fdf3612769d52f729 100644
--- a/data/solutions/generated/squinhex_019_ae3850bdb0ac1880.json
+++ b/data/solutions/generated/squinhex_019_ae3850bdb0ac1880.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.93511,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ian Watson"
diff --git a/data/solutions/generated/squinhex_020_79028917ac70723d.json b/data/solutions/generated/squinhex_020_79028917ac70723d.json
index 14dbfb8df80b5b49e464219c779b7fccbaed7b3f..ad86627746d7b1eea39d3fb7d28d1b2986adbfde 100644
--- a/data/solutions/generated/squinhex_020_79028917ac70723d.json
+++ b/data/solutions/generated/squinhex_020_79028917ac70723d.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.08671209546255527,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.16123,
     "source_image_url": "https://erich-friedman.github.io/packing/squinhex/20.png",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinhex_022_a1e7eaf12003fa2e.json b/data/solutions/generated/squinhex_022_a1e7eaf12003fa2e.json
index a7706a6a193b122290e6727042c132ab8cda6081..dc2847042c08b155a53e92bc9714e368a185185f 100644
--- a/data/solutions/generated/squinhex_022_a1e7eaf12003fa2e.json
+++ b/data/solutions/generated/squinhex_022_a1e7eaf12003fa2e.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.31573,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ian Watson"
diff --git a/data/solutions/generated/squinhex_023_de78b89055181fd4.json b/data/solutions/generated/squinhex_023_de78b89055181fd4.json
index fcb0d72ea298f3c46920ccbbd5c18a64a385d28c..670fc807a7602a6284ea2fba66100034116eff74 100644
--- a/data/solutions/generated/squinhex_023_de78b89055181fd4.json
+++ b/data/solutions/generated/squinhex_023_de78b89055181fd4.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.12220329749264153,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.36437,
     "source_image_url": "https://erich-friedman.github.io/packing/squinhex/23.png",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinhex_025_803edc96e272ee7a.json b/data/solutions/generated/squinhex_025_803edc96e272ee7a.json
index 7b847575754dca08feb10184daced5b0c9e5fa0f..c56703cc74df7728f260ca87bd4ffcd400e76971 100644
--- a/data/solutions/generated/squinhex_025_803edc96e272ee7a.json
+++ b/data/solutions/generated/squinhex_025_803edc96e272ee7a.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.06624203518047836,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.4641016151377544,
     "source_image_url": "https://erich-friedman.github.io/packing/squinhex/25.png",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinhex_026_5fb7804364b5caaf.json b/data/solutions/generated/squinhex_026_5fb7804364b5caaf.json
index 2ac91edeaa9fa6519d8aa7cf1ae7a6848083dfa1..790d8f5f7030f92f14f8ff64ffa3593e49b9894b 100644
--- a/data/solutions/generated/squinhex_026_5fb7804364b5caaf.json
+++ b/data/solutions/generated/squinhex_026_5fb7804364b5caaf.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.06307305220243128,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.4939927,
     "source_image_url": "https://erich-friedman.github.io/packing/squinhex/26.png",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinhex_027_9cebbb5918ba8e81.json b/data/solutions/generated/squinhex_027_9cebbb5918ba8e81.json
index ded7d104a88734ed347787ea85fc239ff9b0a5e5..8320e2a13b4724a4db27acfae130d6cf7a20221b 100644
--- a/data/solutions/generated/squinhex_027_9cebbb5918ba8e81.json
+++ b/data/solutions/generated/squinhex_027_9cebbb5918ba8e81.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.06608414128585424,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.5207259421636903,
     "source_image_url": "https://erich-friedman.github.io/packing/squinhex/27.png",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinhex_029_3b329ff6f7babb15.json b/data/solutions/generated/squinhex_029_3b329ff6f7babb15.json
index a17cf1d06a03cd890fa2d14d53066a7df81f2ac3..06fa031d01563024d4b5fe467cec0a9addf04447 100644
--- a/data/solutions/generated/squinhex_029_3b329ff6f7babb15.json
+++ b/data/solutions/generated/squinhex_029_3b329ff6f7babb15.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.10051315508524275,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.66437,
     "source_image_url": "https://erich-friedman.github.io/packing/squinhex/29.png",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinhex_030_0b645f27b41cbed7.json b/data/solutions/generated/squinhex_030_0b645f27b41cbed7.json
index c2cc690e083e7cd385929fedd7c3baf5273ef147..0ececf93e6c28c873936982bd4afc7ddc0519a77 100644
--- a/data/solutions/generated/squinhex_030_0b645f27b41cbed7.json
+++ b/data/solutions/generated/squinhex_030_0b645f27b41cbed7.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.10136814381291175,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.69554,
     "source_image_url": "https://erich-friedman.github.io/packing/squinhex/30.png",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinhex_031_83b47696242e2320.json b/data/solutions/generated/squinhex_031_83b47696242e2320.json
index 0e9dc32ecc1aba032686d5f4b0fcf2be48502b2a..50eacde06ded86f79b4a2d875814157f1a74e355 100644
--- a/data/solutions/generated/squinhex_031_83b47696242e2320.json
+++ b/data/solutions/generated/squinhex_031_83b47696242e2320.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.07102780085885908,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.7841,
     "source_image_url": "https://erich-friedman.github.io/packing/squinhex/31.png",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinhex_032_b233eac9bd8cc0d8.json b/data/solutions/generated/squinhex_032_b233eac9bd8cc0d8.json
index 8ae54edce6aa3b9dc0e888ffe8cf9ced038b1810..30ed619e16c693fb09a03982418b0c294909ab2d 100644
--- a/data/solutions/generated/squinhex_032_b233eac9bd8cc0d8.json
+++ b/data/solutions/generated/squinhex_032_b233eac9bd8cc0d8.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.07358218275243848,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.84795,
     "source_image_url": "https://erich-friedman.github.io/packing/squinhex/32.png",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinhex_033_b14228e93eb45276.json b/data/solutions/generated/squinhex_033_b14228e93eb45276.json
index 01923b5ee8d00a44bc876ae09880e2707edd71c6..ae160a91fcb99892b8bf37a9328b0d05c0e6ee5c 100644
--- a/data/solutions/generated/squinhex_033_b14228e93eb45276.json
+++ b/data/solutions/generated/squinhex_033_b14228e93eb45276.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.05412608720447137,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.88897,
     "source_image_url": "https://erich-friedman.github.io/packing/squinhex/33.png",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squinhex_034_fc2f6f3b6cabd5ed.json b/data/solutions/generated/squinhex_034_fc2f6f3b6cabd5ed.json
index 792953f42c945142ed7e3668f9676c600a77c227..d252cf141aaa91f7e3493e73e53dc08a74f182e6 100644
--- a/data/solutions/generated/squinhex_034_fc2f6f3b6cabd5ed.json
+++ b/data/solutions/generated/squinhex_034_fc2f6f3b6cabd5ed.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.06404576875260815,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.92704,
     "source_image_url": "https://erich-friedman.github.io/packing/squinhex/34.png",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinhex_035_1ea058e93fb408a4.json b/data/solutions/generated/squinhex_035_1ea058e93fb408a4.json
index 97ccf7fd821cc5c1be15c71a78579d1352924212..85ef62be799e9903431291f92ac573fcedada2a6 100644
--- a/data/solutions/generated/squinhex_035_1ea058e93fb408a4.json
+++ b/data/solutions/generated/squinhex_035_1ea058e93fb408a4.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.065553447705068,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.99833,
     "source_image_url": "https://erich-friedman.github.io/packing/squinhex/35.png",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinhex_037_a455ecb05be301ad.json b/data/solutions/generated/squinhex_037_a455ecb05be301ad.json
index aa85de33115529477b5ec14a5a4aea06655053c3..8bc66e828b482f3838b1cf39bb1b775ae1d6c7f5 100644
--- a/data/solutions/generated/squinhex_037_a455ecb05be301ad.json
+++ b/data/solutions/generated/squinhex_037_a455ecb05be301ad.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.041451884327381,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squinhex_039_85e7e9eb3b3b7f5f.json b/data/solutions/generated/squinhex_039_85e7e9eb3b3b7f5f.json
index d8c3b5c3cca6fb9694c51caf0b0e47373c7dfbe3..892fdd978158b14105f46c1a9f98c9cb8f779e33 100644
--- a/data/solutions/generated/squinhex_039_85e7e9eb3b3b7f5f.json
+++ b/data/solutions/generated/squinhex_039_85e7e9eb3b3b7f5f.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.25744,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/squinhex_21_1d2ec517035658cd.json b/data/solutions/generated/squinhex_21_1d2ec517035658cd.json
index fd9a47935912758c729479bf88cf3c4c9706ed06..89d7dd5a74ef0108e103e2175c8dd42e2d9366a9 100644
--- a/data/solutions/generated/squinhex_21_1d2ec517035658cd.json
+++ b/data/solutions/generated/squinhex_21_1d2ec517035658cd.json
@@ -49,7 +49,10 @@
     "generator_profile": "sa_escape",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_current_broad_broad.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.23496,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T13:47:12+00:00",
     "submitted_by": "Ian Watson"
diff --git a/data/solutions/generated/squinhex_21_3fb669c73e695ac9.json b/data/solutions/generated/squinhex_21_3fb669c73e695ac9.json
new file mode 100644
index 0000000000000000000000000000000000000000..11ad88da0f399b537801c030d94b25cd7da426dc
--- /dev/null
+++ b/data/solutions/generated/squinhex_21_3fb669c73e695ac9.json
@@ -0,0 +1,193 @@
+{
+  "case": "squinhex@21",
+  "container": {
+    "circumradius": 3.2382660883592127,
+    "orientation_radians": 0.0,
+    "side_length": 3.2382660883592123,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@21",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "",
+    "metric_expression": "3.23496+",
+    "metric_symbol": "s",
+    "metric_value": 3.23496,
+    "reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.",
+    "source_image": "21.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@21",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "",
+      "metric_expression": "3.23496+",
+      "metric_symbol": "s",
+      "metric_value": 3.23496,
+      "reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.",
+      "source_image": "21.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "sa_escape",
+    "image_seed_recovery_log": "bench_outputs/current_best_recovery/current_best_recovery_20260501_currentbest_deep_deep.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.23496,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/squinhex_021_20260501_currentbest_deep_sa_escape.state",
+    "source_url": "https://erich-friedman.github.io/packing/squinhex/",
+    "submitted_at": "2026-05-01T17:13:54+00:00",
+    "submitted_by": "Ian Watson"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.308698796188492,
+      "x": -2.0602641569895153,
+      "y": -0.7597849758978907
+    },
+    {
+      "id": 2,
+      "rotation_radians": 1.3089671386542157,
+      "x": -1.6816727488895606,
+      "y": -1.69604306966298
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.785389841400165,
+      "x": -0.49864984453848876,
+      "y": -2.1985735971216327
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.785403983776754,
+      "x": 0.5013771785278506,
+      "y": -2.304357217232154
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.9478311350519463,
+      "x": 1.4806425113451749,
+      "y": -1.6370451766920668
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.2617833751396847,
+      "x": -2.4361507068399346,
+      "y": 0.38924725461833887
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.945691107142416,
+      "x": -0.8633236119761295,
+      "y": -0.8233112469257581
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.9477949042737442,
+      "x": 0.199175859042356,
+      "y": -1.1227332091783517
+    },
+    {
+      "id": 9,
+      "rotation_radians": 0.9478215085891848,
+      "x": 1.139935455505825,
+      "y": -0.6795132328763661
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.9478286512722673,
+      "x": 2.126816293352899,
+      "y": -0.5177922027674137
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.26178805259898474,
+      "x": -1.9318068152363466,
+      "y": 1.2528231553793796
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.8891500952080321,
+      "x": -1.1748778186631816,
+      "y": 0.1671590960648079
+    },
+    {
+      "id": 13,
+      "rotation_radians": 1.3509309548416113,
+      "x": 0.01886887503525065,
+      "y": 0.04642593646062316
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.9478276079719444,
+      "x": 1.1459638434391202,
+      "y": 0.3348569218017392
+    },
+    {
+      "id": 15,
+      "rotation_radians": 1.3089842549196695,
+      "x": 2.276099538507194,
+      "y": 0.6663984685270165
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.2617998814376206,
+      "x": -1.4361033674304282,
+      "y": 2.1213911970535904
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.8029509856545524,
+      "x": -0.587500411925873,
+      "y": 1.2188627120549822
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.8029902701748354,
+      "x": 0.4113706969789206,
+      "y": 1.2956714932486662
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.7854066242322177,
+      "x": 0.7469988517430606,
+      "y": 2.3044055814351974
+    },
+    {
+      "id": 20,
+      "rotation_radians": 1.3090230090747577,
+      "x": 1.7760612525699748,
+      "y": 1.5324802334433874
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.7854161169302822,
+      "x": -0.2530475865079794,
+      "y": 2.3029556746927895
+    }
+  ],
+  "problem": "21 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/21.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_21_c6682411cb8007fa.json b/data/solutions/generated/squinhex_21_c6682411cb8007fa.json
new file mode 100644
index 0000000000000000000000000000000000000000..3d3c119e285e142d6cdcc68d03ca6f0d2b457402
--- /dev/null
+++ b/data/solutions/generated/squinhex_21_c6682411cb8007fa.json
@@ -0,0 +1,192 @@
+{
+  "case": "squinhex@21",
+  "container": {
+    "circumradius": 3.236592068068801,
+    "orientation_radians": 0.0,
+    "side_length": 3.2365920680688007,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@21",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "",
+    "metric_expression": "3.23496+",
+    "metric_symbol": "s",
+    "metric_value": 3.23496,
+    "reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.",
+    "source_image": "21.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@21",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "",
+      "metric_expression": "3.23496+",
+      "metric_symbol": "s",
+      "metric_value": 3.23496,
+      "reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.",
+      "source_image": "21.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Verified coordinate recovery from fresh SA+CG topology search against the Friedman target; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "recovery_source": "fresh SA+CG topology search against the Friedman target",
+    "recovery_state": "bench_outputs/fresh_recovery/states/squinhex_021_sa6000.state",
+    "reference_side": 3.23496,
+    "source_url": "https://erich-friedman.github.io/packing/squinhex/",
+    "submitted_at": "2026-05-01T17:21:04+00:00",
+    "submitted_by": "Ian Watson"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.20400958974362862,
+      "x": -0.2367455462249402,
+      "y": 0.06914926330901247
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.21388178792082105,
+      "x": 0.3353481326920234,
+      "y": 1.1346044915794986
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.2740766586820707,
+      "x": -0.9299327932143283,
+      "y": 0.9829104772133705
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.2740571221458176,
+      "x": -0.4326762396124561,
+      "y": 1.8506288807581193
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.21618537501964075,
+      "x": -0.790230273506817,
+      "y": -0.7711397086135581
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.21388189563131133,
+      "x": 1.063150142684831,
+      "y": 0.4174695553906912
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.21618530943636324,
+      "x": 0.9607613718383053,
+      "y": -0.7056189437856609
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.21668476306905243,
+      "x": -1.4300405067455326,
+      "y": 0.08485826226416417
+    },
+    {
+      "id": 9,
+      "rotation_radians": 1.309126115366776,
+      "x": 1.7400876576617932,
+      "y": 1.5096307745569486
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.21618539961275457,
+      "x": 0.05152187896546804,
+      "y": -1.3110709932872704
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.2617935687914985,
+      "x": -2.4353292778601583,
+      "y": 0.3877987244206006
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.2617990684215589,
+      "x": -1.932965641799805,
+      "y": 1.2525160595647842
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.7854664237506569,
+      "x": 0.7480768682531151,
+      "y": 2.302918436319728
+    },
+    {
+      "id": 14,
+      "rotation_radians": 1.3090463616468069,
+      "x": -2.1787648841124048,
+      "y": -0.8301698470460083
+    },
+    {
+      "id": 15,
+      "rotation_radians": 1.30901028914327,
+      "x": 2.275802388656191,
+      "y": 0.6641174694889946
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.3090466768441509,
+      "x": -1.6795864102808817,
+      "y": -1.6967194317271224
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.21618536401110805,
+      "x": -0.5517432051724971,
+      "y": -2.112302717884939
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.2594030691431437,
+      "x": 2.2561980306129548,
+      "y": -0.6919543001046589
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.2618002489868131,
+      "x": -1.4352748372301825,
+      "y": 2.119928659283637
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.2535347080166928,
+      "x": 1.736193657522673,
+      "y": -1.5496757756007273
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.21618554757703154,
+      "x": 0.7260709574526315,
+      "y": -2.1123153776009436
+    }
+  ],
+  "problem": "21 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/21.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_24_73f1ceeaee97d32f.json b/data/solutions/generated/squinhex_24_73f1ceeaee97d32f.json
index 02bd59258a61f2aec622823c28bb86c54577b066..94915dab8c6b6fe2be3850aeec107b7c559ceea0 100644
--- a/data/solutions/generated/squinhex_24_73f1ceeaee97d32f.json
+++ b/data/solutions/generated/squinhex_24_73f1ceeaee97d32f.json
@@ -49,7 +49,10 @@
     "generator_profile": "sa_tight",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_current_heavy_heavy.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.41524,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T14:34:18+00:00",
     "submitted_by": "Ian Watson"
diff --git a/data/solutions/generated/squinhex_28_184baa4d16ce7f9e.json b/data/solutions/generated/squinhex_28_184baa4d16ce7f9e.json
index 648ceeb5bc9d47c4eca1983076dbfa9002c2a303..43eecdbf2f73140b1dead54948061e7398235f21 100644
--- a/data/solutions/generated/squinhex_28_184baa4d16ce7f9e.json
+++ b/data/solutions/generated/squinhex_28_184baa4d16ce7f9e.json
@@ -49,7 +49,10 @@
     "generator_profile": "cg_deep",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_current_heavy_heavy.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.62565,
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "submitted_at": "2026-05-01T14:34:18+00:00",
     "submitted_by": "Ian Watson"
diff --git a/data/solutions/generated/squinhex_36_8da86e16a42a7ee1.json b/data/solutions/generated/squinhex_36_8da86e16a42a7ee1.json
new file mode 100644
index 0000000000000000000000000000000000000000..23b9a260422656b64bdb8a450239c19a0b067562
--- /dev/null
+++ b/data/solutions/generated/squinhex_36_8da86e16a42a7ee1.json
@@ -0,0 +1,283 @@
+{
+  "case": "squinhex@36",
+  "container": {
+    "circumradius": 4.0298356750246205,
+    "orientation_radians": 0.0,
+    "side_length": 4.02983567502462,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squinhex@36",
+    "credit": "Maurizio Morandi",
+    "date": "May 2026",
+    "family_updated": "",
+    "metric_expression": "2+7\u221a3/6 = 4.02072+",
+    "metric_symbol": "s",
+    "metric_value": 4.02072594216369,
+    "reference_text": "s = 2+7\u221a3/6 = 4.02072+ | Found by Maurizio Morandi | in May 2026.",
+    "source_image": "36.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squinhex@36",
+      "credit": "Maurizio Morandi",
+      "date": "May 2026",
+      "family_updated": "",
+      "metric_expression": "2+7\u221a3/6 = 4.02072+",
+      "metric_symbol": "s",
+      "metric_value": 4.02072594216369,
+      "reference_text": "s = 2+7\u221a3/6 = 4.02072+ | Found by Maurizio Morandi | in May 2026.",
+      "source_image": "36.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "cg_deep",
+    "image_seed_recovery_log": "bench_outputs/current_best_recovery/current_best_recovery_20260501_currentbest_deep_deep.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.02072594216369,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/squinhex_036_20260501_currentbest_deep_cg_deep.state",
+    "source_url": "https://erich-friedman.github.io/packing/squinhex/",
+    "submitted_at": "2026-05-01T17:13:54+00:00",
+    "submitted_by": "Maurizio Morandi"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.7853998135500232,
+      "x": 0.5127985917031553,
+      "y": -2.9899278819566737
+    },
+    {
+      "id": 2,
+      "rotation_radians": -0.783174809313103,
+      "x": 1.515075545513556,
+      "y": -2.988815856737878
+    },
+    {
+      "id": 3,
+      "rotation_radians": -0.26179988467087767,
+      "x": -0.6771732501991349,
+      "y": -2.806908261209049
+    },
+    {
+      "id": 4,
+      "rotation_radians": -0.2617992109329729,
+      "x": -1.832399860650803,
+      "y": -2.8060523256928867
+    },
+    {
+      "id": 5,
+      "rotation_radians": -0.783949919844051,
+      "x": 1.16330662698295,
+      "y": -1.989179734753639
+    },
+    {
+      "id": 6,
+      "rotation_radians": -0.26180012264033536,
+      "x": -1.1771933604738083,
+      "y": -1.940861379308233
+    },
+    {
+      "id": 7,
+      "rotation_radians": -0.26177181267998756,
+      "x": -0.026201047832966784,
+      "y": -1.9343629100732036
+    },
+    {
+      "id": 8,
+      "rotation_radians": -0.2618011555498771,
+      "x": -2.3329121710413103,
+      "y": -1.9391421679000826
+    },
+    {
+      "id": 9,
+      "rotation_radians": -1.3089964428744418,
+      "x": 2.346509965635149,
+      "y": -1.9155791359533727
+    },
+    {
+      "id": 10,
+      "rotation_radians": -0.26180286516424106,
+      "x": -1.6772054291708625,
+      "y": -1.0748090653754243
+    },
+    {
+      "id": 11,
+      "rotation_radians": -0.26180170567104755,
+      "x": -0.5266058439538908,
+      "y": -1.0676704334195535
+    },
+    {
+      "id": 12,
+      "rotation_radians": -0.2618020801153004,
+      "x": -2.833631765835425,
+      "y": -1.0718637536498798
+    },
+    {
+      "id": 13,
+      "rotation_radians": -1.3089971055666556,
+      "x": 2.846524437626637,
+      "y": -1.0495282942688389
+    },
+    {
+      "id": 14,
+      "rotation_radians": -0.2617703265566654,
+      "x": 0.5695511886257939,
+      "y": -0.9662293478971516
+    },
+    {
+      "id": 15,
+      "rotation_radians": -1.3101464387836517,
+      "x": 1.836561033010603,
+      "y": -0.7947905902824492
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.2618041296897454,
+      "x": -2.17721148345228,
+      "y": -0.20875277246424048
+    },
+    {
+      "id": 17,
+      "rotation_radians": -0.26159347423474466,
+      "x": -1.0218467215862905,
+      "y": -0.1987405857107715
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.2617996634630807,
+      "x": -3.3337457986829713,
+      "y": -0.2056340407366529
+    },
+    {
+      "id": 19,
+      "rotation_radians": -1.3089975927620316,
+      "x": 3.3466439035828714,
+      "y": -0.1832972347374517
+    },
+    {
+      "id": 20,
+      "rotation_radians": -1.3089977160844892,
+      "x": 2.3386029797437153,
+      "y": 0.07078172941108413
+    },
+    {
+      "id": 21,
+      "rotation_radians": -1.547590352892932,
+      "x": 1.0787212117076603,
+      "y": 0.09666474764143233
+    },
+    {
+      "id": 22,
+      "rotation_radians": -1.308995641630556,
+      "x": -2.9203074244679095,
+      "y": 0.9217319376731398
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.7853991054194351,
+      "x": -0.7372356288620157,
+      "y": 0.984347619539639
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.785399000412849,
+      "x": -1.7372628731836515,
+      "y": 0.9742909537290708
+    },
+    {
+      "id": 25,
+      "rotation_radians": -0.7853965868889737,
+      "x": 0.2627921839200524,
+      "y": 0.9898708095031103
+    },
+    {
+      "id": 26,
+      "rotation_radians": -0.2617635292160005,
+      "x": 1.6778835523884468,
+      "y": 1.0736450577768788
+    },
+    {
+      "id": 27,
+      "rotation_radians": -0.26179668972902287,
+      "x": 2.7650604856870595,
+      "y": 1.1906478745741
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.7853962534642962,
+      "x": 0.8988100202870486,
+      "y": 1.9899019383972538
+    },
+    {
+      "id": 29,
+      "rotation_radians": -0.7853969859907167,
+      "x": -0.10121678394381049,
+      "y": 1.9898982172346795
+    },
+    {
+      "id": 30,
+      "rotation_radians": -0.7853964501641473,
+      "x": -1.1012426997218916,
+      "y": 1.9849910699028912
+    },
+    {
+      "id": 31,
+      "rotation_radians": -0.7854003070967526,
+      "x": -2.1012688269487536,
+      "y": 1.9743197050652834
+    },
+    {
+      "id": 32,
+      "rotation_radians": -0.2617828095045173,
+      "x": 2.2638403910893707,
+      "y": 2.058761693726387
+    },
+    {
+      "id": 33,
+      "rotation_radians": -0.7855099383176111,
+      "x": -1.5169675437587966,
+      "y": 2.986175824582955
+    },
+    {
+      "id": 34,
+      "rotation_radians": -0.7853990323232679,
+      "x": 1.5031679726354825,
+      "y": 2.989926953682956
+    },
+    {
+      "id": 35,
+      "rotation_radians": -0.7853992038040882,
+      "x": 0.4884209261918813,
+      "y": 2.98992738696828
+    },
+    {
+      "id": 36,
+      "rotation_radians": -0.7853974839040493,
+      "x": -0.5157241752518743,
+      "y": 2.989925837156463
+    }
+  ],
+  "problem": "36 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/36.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_36_cbc24f56627bdbaa.json b/data/solutions/generated/squinhex_36_cbc24f56627bdbaa.json
new file mode 100644
index 0000000000000000000000000000000000000000..c45a136786be99a7f9dcb73e6526aef2458017b4
--- /dev/null
+++ b/data/solutions/generated/squinhex_36_cbc24f56627bdbaa.json
@@ -0,0 +1,282 @@
+{
+  "case": "squinhex@36",
+  "container": {
+    "circumradius": 4.020625349363003,
+    "orientation_radians": 0.0,
+    "side_length": 4.020625349363002,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squinhex@36",
+    "credit": "Maurizio Morandi",
+    "date": "May 2026",
+    "family_updated": "",
+    "metric_expression": "2+7\u221a3/6 = 4.02072+",
+    "metric_symbol": "s",
+    "metric_value": 4.02072594216369,
+    "reference_text": "s = 2+7\u221a3/6 = 4.02072+ | Found by Maurizio Morandi | in May 2026.",
+    "source_image": "36.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squinhex@36",
+      "credit": "Maurizio Morandi",
+      "date": "May 2026",
+      "family_updated": "",
+      "metric_expression": "2+7\u221a3/6 = 4.02072+",
+      "metric_symbol": "s",
+      "metric_value": 4.02072594216369,
+      "reference_text": "s = 2+7\u221a3/6 = 4.02072+ | Found by Maurizio Morandi | in May 2026.",
+      "source_image": "36.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Verified coordinate recovery from line-cell seed recovered from the Friedman PNG and refined with CG; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "recovery_source": "line-cell seed recovered from the Friedman PNG and refined with CG",
+    "recovery_state": "bench_outputs/fresh_recovery/states/squinhex_036_linecell_refined.state",
+    "reference_side": 4.02072594216369,
+    "source_url": "https://erich-friedman.github.io/packing/squinhex/",
+    "submitted_at": "2026-05-01T18:08:26+00:00",
+    "submitted_by": "Maurizio Morandi"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 3.9376618567112,
+      "x": -0.6200776620459941,
+      "y": -2.97620602831244
+    },
+    {
+      "id": 2,
+      "rotation_radians": 3.4088308696691905,
+      "x": 1.8235998282815284,
+      "y": -2.7998778613691906
+    },
+    {
+      "id": 3,
+      "rotation_radians": 3.4179042212911948,
+      "x": 0.6719712644272166,
+      "y": -2.801677321858831
+    },
+    {
+      "id": 4,
+      "rotation_radians": 4.475602548910271,
+      "x": -1.8077632732080609,
+      "y": -2.7940678936127203
+    },
+    {
+      "id": 5,
+      "rotation_radians": 3.4179042229306535,
+      "x": -0.005988949251731722,
+      "y": -1.9644828995114938
+    },
+    {
+      "id": 6,
+      "rotation_radians": 3.4043898736916787,
+      "x": 2.327386643602619,
+      "y": -1.9304754003286995
+    },
+    {
+      "id": 7,
+      "rotation_radians": 3.4179042173372003,
+      "x": 1.1602517565716053,
+      "y": -1.9289734297811987
+    },
+    {
+      "id": 8,
+      "rotation_radians": 4.450590721004595,
+      "x": -2.331043181796169,
+      "y": -1.9264190686738334
+    },
+    {
+      "id": 9,
+      "rotation_radians": 4.467896744916656,
+      "x": -1.2541630035464073,
+      "y": -1.7744267168113177
+    },
+    {
+      "id": 10,
+      "rotation_radians": 3.4290188463750937,
+      "x": 0.4809696450497933,
+      "y": -1.0818528854829912
+    },
+    {
+      "id": 11,
+      "rotation_radians": 3.4034050764830086,
+      "x": 2.8288450535883656,
+      "y": -1.0641644028948096
+    },
+    {
+      "id": 12,
+      "rotation_radians": 3.4179042149498438,
+      "x": 1.6586895928542542,
+      "y": -1.0619376739702842
+    },
+    {
+      "id": 13,
+      "rotation_radians": 4.450598199797597,
+      "x": -2.8360633429629414,
+      "y": -1.051624983073269
+    },
+    {
+      "id": 14,
+      "rotation_radians": 4.467896739598229,
+      "x": -1.7542102068444876,
+      "y": -0.9082319688693555
+    },
+    {
+      "id": 15,
+      "rotation_radians": 4.472198376205978,
+      "x": -0.6769664848422579,
+      "y": -0.7323792723466579
+    },
+    {
+      "id": 16,
+      "rotation_radians": 3.4313719367268267,
+      "x": 0.9793181959023617,
+      "y": -0.2122167449640521
+    },
+    {
+      "id": 17,
+      "rotation_radians": 4.458963404415161,
+      "x": -3.3347020751226664,
+      "y": -0.17971061515792836
+    },
+    {
+      "id": 18,
+      "rotation_radians": 3.4353566912389653,
+      "x": 3.3243648153131753,
+      "y": -0.17149347129425502
+    },
+    {
+      "id": 19,
+      "rotation_radians": 3.4179042140792566,
+      "x": 2.165097317582897,
+      "y": -0.1993495976032451
+    },
+    {
+      "id": 20,
+      "rotation_radians": 4.46789674490403,
+      "x": -2.2492974503325573,
+      "y": -0.039059017729590494
+    },
+    {
+      "id": 21,
+      "rotation_radians": 4.472100644089166,
+      "x": -1.1813348338053071,
+      "y": 0.13179205995973706
+    },
+    {
+      "id": 22,
+      "rotation_radians": 4.4678967527735045,
+      "x": -2.7628602773996724,
+      "y": 0.8190153387421137
+    },
+    {
+      "id": 23,
+      "rotation_radians": 4.467896750990393,
+      "x": -1.6989846094951855,
+      "y": 0.9899381655044392
+    },
+    {
+      "id": 24,
+      "rotation_radians": 4.451670367689752,
+      "x": 2.891666986288313,
+      "y": 0.9537698077172666
+    },
+    {
+      "id": 25,
+      "rotation_radians": 3.9554538659409575,
+      "x": -0.2963121597214426,
+      "y": 0.9550575054056063
+    },
+    {
+      "id": 26,
+      "rotation_radians": 3.9435366976069615,
+      "x": 1.7102844734004798,
+      "y": 0.9766911664081254
+    },
+    {
+      "id": 27,
+      "rotation_radians": 3.944429156074008,
+      "x": 0.7095488269840157,
+      "y": 0.964931944471956
+    },
+    {
+      "id": 28,
+      "rotation_radians": 3.9434990808252732,
+      "x": 2.0905785275128848,
+      "y": 1.9831402135264018
+    },
+    {
+      "id": 29,
+      "rotation_radians": 3.94349907986529,
+      "x": 1.0906090439813831,
+      "y": 1.9722142298995564
+    },
+    {
+      "id": 30,
+      "rotation_radians": 3.943499073175113,
+      "x": 0.09052412702018535,
+      "y": 1.9683133313646828
+    },
+    {
+      "id": 31,
+      "rotation_radians": 3.9434990651599064,
+      "x": -0.9097144700461613,
+      "y": 1.9737505332830403
+    },
+    {
+      "id": 32,
+      "rotation_radians": 3.4184044700848983,
+      "x": -2.256986114159385,
+      "y": 2.0344266879507273
+    },
+    {
+      "id": 33,
+      "rotation_radians": 3.9266082849254103,
+      "x": -1.5158314522418792,
+      "y": 2.9724591121001924
+    },
+    {
+      "id": 34,
+      "rotation_radians": 3.926992798794427,
+      "x": -0.5155615086228648,
+      "y": 2.981954562886111
+    },
+    {
+      "id": 35,
+      "rotation_radians": 3.930156015129148,
+      "x": 1.510927514175076,
+      "y": 2.9803731159761337
+    },
+    {
+      "id": 36,
+      "rotation_radians": 3.933893519614131,
+      "x": 0.5086679697713811,
+      "y": 2.977231673559918
+    }
+  ],
+  "problem": "36 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/36.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinoct_001_b63c90f60717ba08.json b/data/solutions/generated/squinoct_001_b63c90f60717ba08.json
index 96d5095be710bd31c4b5161ce9ca212bfaadfa6a..eb2bcf70d01cc70c0816302b1f953ac0dd8ef649 100644
--- a/data/solutions/generated/squinoct_001_b63c90f60717ba08.json
+++ b/data/solutions/generated/squinoct_001_b63c90f60717ba08.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.541196100146197,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squinoct_002_7194ac58cba12fa7.json b/data/solutions/generated/squinoct_002_7194ac58cba12fa7.json
index e1085fcc1c89b6b7c66fadc31326827ea48ee944..4f4f40645f4c43bafa4d3ee2a96a02b80cec0559 100644
--- a/data/solutions/generated/squinoct_002_7194ac58cba12fa7.json
+++ b/data/solutions/generated/squinoct_002_7194ac58cba12fa7.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.87667,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/squinoct_003_3d85991afac60053.json b/data/solutions/generated/squinoct_003_3d85991afac60053.json
index aa4a0b40bd02a95ccb5e1e680c6dc8d92c97c4b8..52a922a4dbec3b913c53f4e160a13c7d0f6384fb 100644
--- a/data/solutions/generated/squinoct_003_3d85991afac60053.json
+++ b/data/solutions/generated/squinoct_003_3d85991afac60053.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.0294372515228594,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squinoct_004_30bfa7c46cf6dd87.json b/data/solutions/generated/squinoct_004_30bfa7c46cf6dd87.json
index e53d794b8ce3e60d4f4d67a48a6b54ab3dacb97e..df8a4b4d63cbdc0f6078846977f224ae1d0d29e2 100644
--- a/data/solutions/generated/squinoct_004_30bfa7c46cf6dd87.json
+++ b/data/solutions/generated/squinoct_004_30bfa7c46cf6dd87.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.082392200292394,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squinoct_005_3bf97518bf42702c.json b/data/solutions/generated/squinoct_005_3bf97518bf42702c.json
index c5abb6f29771652d1aaff98fc0c394b3ca8002b1..f0c2b3ca281e00e57312c47e306c78aada33784b 100644
--- a/data/solutions/generated/squinoct_005_3bf97518bf42702c.json
+++ b/data/solutions/generated/squinoct_005_3bf97518bf42702c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.2426406871192852,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squinoct_006_6368fdc8880da7e0.json b/data/solutions/generated/squinoct_006_6368fdc8880da7e0.json
index fc8c2fa754def31ada5e8eb2d58d1e522e5dff2b..36f858a722e86720d475eead4c2040edf9550eba 100644
--- a/data/solutions/generated/squinoct_006_6368fdc8880da7e0.json
+++ b/data/solutions/generated/squinoct_006_6368fdc8880da7e0.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.3431457505076199,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/squinoct_007_35d0c06f5c122826.json b/data/solutions/generated/squinoct_007_35d0c06f5c122826.json
index 4e93cef7f1a8e14a44f04fce2acc08431163e791..c64b7f83ebfe8420f3ed7eab8902e37a5f3d6ee7 100644
--- a/data/solutions/generated/squinoct_007_35d0c06f5c122826.json
+++ b/data/solutions/generated/squinoct_007_35d0c06f5c122826.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.43691,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/squinoct_008_ecaef16600354c9f.json b/data/solutions/generated/squinoct_008_ecaef16600354c9f.json
index 88b26e49188ee60aa9e41db6a83c750675ce84bc..e99cb874ebcf7bf9b5b4f731b4684b46af07a5b1 100644
--- a/data/solutions/generated/squinoct_008_ecaef16600354c9f.json
+++ b/data/solutions/generated/squinoct_008_ecaef16600354c9f.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.56967,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinoct_009_703059104a2b70f8.json b/data/solutions/generated/squinoct_009_703059104a2b70f8.json
index 72783afa22b3c5089c456866e3e0e57d3fbaa5c9..54ec3d89b7bbc3bec613c9712a594f3e5e1c859c 100644
--- a/data/solutions/generated/squinoct_009_703059104a2b70f8.json
+++ b/data/solutions/generated/squinoct_009_703059104a2b70f8.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.623588300438591,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squinoct_010_03facc71923f1148.json b/data/solutions/generated/squinoct_010_03facc71923f1148.json
index bac60573a5e325e7199a8b337ed499e000a2e94d..78b36532254765e76e42e28fdf318a3bf0d79fb6 100644
--- a/data/solutions/generated/squinoct_010_03facc71923f1148.json
+++ b/data/solutions/generated/squinoct_010_03facc71923f1148.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.681792830507429,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/squinoct_011_78c32afdb2263b2d.json b/data/solutions/generated/squinoct_011_78c32afdb2263b2d.json
index b603584365e0f578fba68be62ca23cbd31157c1b..f6ac3730262603c2dd6c2d3bed212e8eef7851ae 100644
--- a/data/solutions/generated/squinoct_011_78c32afdb2263b2d.json
+++ b/data/solutions/generated/squinoct_011_78c32afdb2263b2d.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.7318,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinoct_012_7a9451cae59dbb40.json b/data/solutions/generated/squinoct_012_7a9451cae59dbb40.json
index 3e160e3a2f4fad3b23633057586f0cde92093df1..b380960d7a740cfc2a46ff1fe9b1a672b24eee07 100644
--- a/data/solutions/generated/squinoct_012_7a9451cae59dbb40.json
+++ b/data/solutions/generated/squinoct_012_7a9451cae59dbb40.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.7533,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/squinoct_013_c5bdcacf094e428e.json b/data/solutions/generated/squinoct_013_c5bdcacf094e428e.json
index 8a4f284b1a80434c1c951a5109fee01b96d436b9..d43c5e5d5972a8a624fb74a6f014f2f765690c83 100644
--- a/data/solutions/generated/squinoct_013_c5bdcacf094e428e.json
+++ b/data/solutions/generated/squinoct_013_c5bdcacf094e428e.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.8976,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinoct_014_994e0dd57a80d4a3.json b/data/solutions/generated/squinoct_014_994e0dd57a80d4a3.json
index 68944f7036b6a66a8299e5533d966b660803fa77..a08af87f75c55cbc19d37d78485bffce2f24cd4d 100644
--- a/data/solutions/generated/squinoct_014_994e0dd57a80d4a3.json
+++ b/data/solutions/generated/squinoct_014_994e0dd57a80d4a3.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.9835,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinoct_015_c898d8b3cd2b55db.json b/data/solutions/generated/squinoct_015_c898d8b3cd2b55db.json
index d64cd3a22d62b17460665b0fe23e5f4c33a93555..4e9520dfa983852c0b2ae033148df1c2ac6b5589 100644
--- a/data/solutions/generated/squinoct_015_c898d8b3cd2b55db.json
+++ b/data/solutions/generated/squinoct_015_c898d8b3cd2b55db.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.03259,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinoct_016_3a2e6d99239355fd.json b/data/solutions/generated/squinoct_016_3a2e6d99239355fd.json
index fad960824e60014d9fc94604b8773c699391a288..b4c27dd2884a3977c2d2876c54ebab07cbe3b697 100644
--- a/data/solutions/generated/squinoct_016_3a2e6d99239355fd.json
+++ b/data/solutions/generated/squinoct_016_3a2e6d99239355fd.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.071067811865475,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squinoct_017_ab660f0510a3dd1c.json b/data/solutions/generated/squinoct_017_ab660f0510a3dd1c.json
index 9f32da64d08896da4b13184e224ba71690bf2015..5318c2f9458a9c05f07e752e91946c9fa4b5d9b3 100644
--- a/data/solutions/generated/squinoct_017_ab660f0510a3dd1c.json
+++ b/data/solutions/generated/squinoct_017_ab660f0510a3dd1c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.071067811865475,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squinoct_018_a7275e2ab7024187.json b/data/solutions/generated/squinoct_018_a7275e2ab7024187.json
index c428a046b7a5fe0fda7f3986d469dabf88f030e4..ecc0768f84a3e4b3e30b0154331812ca67585639 100644
--- a/data/solutions/generated/squinoct_018_a7275e2ab7024187.json
+++ b/data/solutions/generated/squinoct_018_a7275e2ab7024187.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.16778,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinoct_019_330906f1db929cdb.json b/data/solutions/generated/squinoct_019_330906f1db929cdb.json
index 22fcd51cd6321f669c8484bd90a27ae617cf1d6b..8e72b7b38cac42211e5961b02d008812365c7d50 100644
--- a/data/solutions/generated/squinoct_019_330906f1db929cdb.json
+++ b/data/solutions/generated/squinoct_019_330906f1db929cdb.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.22823,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinoct_020_d1597d2fdf3beee1.json b/data/solutions/generated/squinoct_020_d1597d2fdf3beee1.json
index c65e8467b11746fadb1012e0ac10206889d3c196..a1745872d92a2b7a7126430bd182ac931ffe2c1e 100644
--- a/data/solutions/generated/squinoct_020_d1597d2fdf3beee1.json
+++ b/data/solutions/generated/squinoct_020_d1597d2fdf3beee1.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.07064884576243485,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.2873,
     "source_image_url": "https://erich-friedman.github.io/packing/squinoct/20.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinoct_021_a3759fa0325bb184.json b/data/solutions/generated/squinoct_021_a3759fa0325bb184.json
index 67b2c5a06850a783c2348ce2adf271eae9d222bd..85fbcf1d10823637c66b6726e37dd29b4a130004 100644
--- a/data/solutions/generated/squinoct_021_a3759fa0325bb184.json
+++ b/data/solutions/generated/squinoct_021_a3759fa0325bb184.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.32167,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinoct_022_c01cc63fb6a654c8.json b/data/solutions/generated/squinoct_022_c01cc63fb6a654c8.json
index 1b002197d2c857d831406ef3fb35d4ecb9df033f..2904e2cc3b253e9f87003ed06bbcea84e079a34b 100644
--- a/data/solutions/generated/squinoct_022_c01cc63fb6a654c8.json
+++ b/data/solutions/generated/squinoct_022_c01cc63fb6a654c8.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.058898998658080556,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.41811,
     "source_image_url": "https://erich-friedman.github.io/packing/squinoct/22.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinoct_023_004d1c5d4d7bca47.json b/data/solutions/generated/squinoct_023_004d1c5d4d7bca47.json
index 35d806430a5d290bff59c9aeaecabae0ace766ca..8f6541073b40cd8e5df38c7f9a5b2cfd1bdb8a72 100644
--- a/data/solutions/generated/squinoct_023_004d1c5d4d7bca47.json
+++ b/data/solutions/generated/squinoct_023_004d1c5d4d7bca47.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.47329,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinoct_024_4f255616aca5e547.json b/data/solutions/generated/squinoct_024_4f255616aca5e547.json
index 401b954f6036c91240289bd88990b5295bbd4b4e..282ccc37b6a3c9b8c9cab3b591802c4e54b784de 100644
--- a/data/solutions/generated/squinoct_024_4f255616aca5e547.json
+++ b/data/solutions/generated/squinoct_024_4f255616aca5e547.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.4852813742385704,
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squinoct_025_0d3ca23da8f19da7.json b/data/solutions/generated/squinoct_025_0d3ca23da8f19da7.json
index 0b4bb467095c1aefebcaad2cc0c47fd7d3cbcdd8..059001d36b987fcc02bb03826ada1b609f40f7ab 100644
--- a/data/solutions/generated/squinoct_025_0d3ca23da8f19da7.json
+++ b/data/solutions/generated/squinoct_025_0d3ca23da8f19da7.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.07064159717750954,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.491950116270851,
     "source_image_url": "https://erich-friedman.github.io/packing/squinoct/25.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinoct_026_6c0cffa2ebc39455.json b/data/solutions/generated/squinoct_026_6c0cffa2ebc39455.json
index 499fe7595fdc4c5902e03b2a0a3b6753abc8376d..1eb85d20be292f197d6488e1598132b0ba09f142 100644
--- a/data/solutions/generated/squinoct_026_6c0cffa2ebc39455.json
+++ b/data/solutions/generated/squinoct_026_6c0cffa2ebc39455.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.07491756383103289,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.52841,
     "source_image_url": "https://erich-friedman.github.io/packing/squinoct/26.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinoct_027_9243c0031663b10e.json b/data/solutions/generated/squinoct_027_9243c0031663b10e.json
index 14df369923036eb32480aa11f9e3d97d0151f52f..0e25fcaa456f4f1c70be6d0f195669df39dffcec 100644
--- a/data/solutions/generated/squinoct_027_9243c0031663b10e.json
+++ b/data/solutions/generated/squinoct_027_9243c0031663b10e.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.08579496978758638,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.58695,
     "source_image_url": "https://erich-friedman.github.io/packing/squinoct/27.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinoct_028_f74e0430c683aaa0.json b/data/solutions/generated/squinoct_028_f74e0430c683aaa0.json
index 5509fe9b173958335957f9436c9ffd1e52237648..04bf49ebe1cb4236d0861d7496998578aa8ae574 100644
--- a/data/solutions/generated/squinoct_028_f74e0430c683aaa0.json
+++ b/data/solutions/generated/squinoct_028_f74e0430c683aaa0.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.0909828494853955,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.63116,
     "source_image_url": "https://erich-friedman.github.io/packing/squinoct/28.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinoct_029_7d4fefbdad04f318.json b/data/solutions/generated/squinoct_029_7d4fefbdad04f318.json
index 733e325ce46e5f5cf4a508f300c981208a3bc015..840a12ca525f40db8935b2f10a1936ff59a5e0d9 100644
--- a/data/solutions/generated/squinoct_029_7d4fefbdad04f318.json
+++ b/data/solutions/generated/squinoct_029_7d4fefbdad04f318.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.07321366807588527,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.70811,
     "source_image_url": "https://erich-friedman.github.io/packing/squinoct/29.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinoct_030_e6809975fe4af696.json b/data/solutions/generated/squinoct_030_e6809975fe4af696.json
index 3fc3f15d9683eaecfe11e790c2975d989e4c7697..3b0d443d8c7994453a495608e0a82b5c0a2415fe 100644
--- a/data/solutions/generated/squinoct_030_e6809975fe4af696.json
+++ b/data/solutions/generated/squinoct_030_e6809975fe4af696.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.07548785961629396,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.7422,
     "source_image_url": "https://erich-friedman.github.io/packing/squinoct/30.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinpen_001_7c4deaf46828e45f.json b/data/solutions/generated/squinpen_001_7c4deaf46828e45f.json
index 75b5e66116194b4bc579b4719eb3668969a1d286..33fbf7a40ad6c6b13906c5f78f046f1ccf1d4008 100644
--- a/data/solutions/generated/squinpen_001_7c4deaf46828e45f.json
+++ b/data/solutions/generated/squinpen_001_7c4deaf46828e45f.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.936,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squinpen_002_e0d70422bfa035f2.json b/data/solutions/generated/squinpen_002_e0d70422bfa035f2.json
index 969e2d26f8d20a183eb596e04d0645a9ec6d2436..9c4a3257545c584d2421deb96757cd2e9250a509 100644
--- a/data/solutions/generated/squinpen_002_e0d70422bfa035f2.json
+++ b/data/solutions/generated/squinpen_002_e0d70422bfa035f2.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.535,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squinpen_003_20345bd1acea07ee.json b/data/solutions/generated/squinpen_003_20345bd1acea07ee.json
index bd3d81cd26f298e01cc27472197f2c6dde2c3885..3a5a57140ca5ffa73148d5a08e646c4ca15ba71c 100644
--- a/data/solutions/generated/squinpen_003_20345bd1acea07ee.json
+++ b/data/solutions/generated/squinpen_003_20345bd1acea07ee.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.695,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/squinpen_004_3b3728a72d1e463a.json b/data/solutions/generated/squinpen_004_3b3728a72d1e463a.json
index 884b506b66f40447c7d4cdb41822624ff53fda3c..99aa37f168f06bc85a19ae6a529dc7b207a5d498 100644
--- a/data/solutions/generated/squinpen_004_3b3728a72d1e463a.json
+++ b/data/solutions/generated/squinpen_004_3b3728a72d1e463a.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.861,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/squinpen_005_dfdcf10f7cfe5f16.json b/data/solutions/generated/squinpen_005_dfdcf10f7cfe5f16.json
index 7df250d210678155673bbff2bd169df3cb05d90c..c2b9bd1edb766952708bed896ae0d753ebc8f54c 100644
--- a/data/solutions/generated/squinpen_005_dfdcf10f7cfe5f16.json
+++ b/data/solutions/generated/squinpen_005_dfdcf10f7cfe5f16.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.951,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squinpen_006_fbc8fa063fa8154f.json b/data/solutions/generated/squinpen_006_fbc8fa063fa8154f.json
index 6f08fd140edffdf264ff02b4a87f930fa9b1c786..1e04ae217ff34669c0c77c013bc4a5501a698036 100644
--- a/data/solutions/generated/squinpen_006_fbc8fa063fa8154f.json
+++ b/data/solutions/generated/squinpen_006_fbc8fa063fa8154f.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.185,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squinpen_007_a9079c85f43f1608.json b/data/solutions/generated/squinpen_007_a9079c85f43f1608.json
index ee2588e6747b565bd0f49d036e1f75b936d82e59..3b228b5b602438bc69c5aaeb55ab2dbf487ebe6f 100644
--- a/data/solutions/generated/squinpen_007_a9079c85f43f1608.json
+++ b/data/solutions/generated/squinpen_007_a9079c85f43f1608.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.421,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squinpen_008_eedfd38786ce3d06.json b/data/solutions/generated/squinpen_008_eedfd38786ce3d06.json
index 816b92e78ea01e9fc12a4192f62581c2467b0b90..46b8439cd3560c089f63a3fcd4f2af9c3f0ab883 100644
--- a/data/solutions/generated/squinpen_008_eedfd38786ce3d06.json
+++ b/data/solutions/generated/squinpen_008_eedfd38786ce3d06.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.565,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/squinpen_009_b050939c544c8091.json b/data/solutions/generated/squinpen_009_b050939c544c8091.json
index 929da389f58a7237131daf90ab1c169ec7fe3852..f6dcb44a2b3e5f0ef176f8d0b1cab642b19fa3b1 100644
--- a/data/solutions/generated/squinpen_009_b050939c544c8091.json
+++ b/data/solutions/generated/squinpen_009_b050939c544c8091.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.693,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Timo Berthold et al"
diff --git a/data/solutions/generated/squinpen_010_5e3ff0fc92953694.json b/data/solutions/generated/squinpen_010_5e3ff0fc92953694.json
index a408fc987f1db0b0b932f48ec3bda9b9071906d5..2b36f810c879a61d5018b2e5fbc6f4b1c0f3772c 100644
--- a/data/solutions/generated/squinpen_010_5e3ff0fc92953694.json
+++ b/data/solutions/generated/squinpen_010_5e3ff0fc92953694.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.793,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Timo Berthold et al"
diff --git a/data/solutions/generated/squinpen_011_eed6c273a2c34445.json b/data/solutions/generated/squinpen_011_eed6c273a2c34445.json
index bd2079cb157796d3b4a5f9d561f00a1ca7971797..b44e2515c8f11a9c0032af3cb9a6c0e83d90349d 100644
--- a/data/solutions/generated/squinpen_011_eed6c273a2c34445.json
+++ b/data/solutions/generated/squinpen_011_eed6c273a2c34445.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.89,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Timo Berthold et al"
diff --git a/data/solutions/generated/squinpen_012_0dc0d2750d6b1986.json b/data/solutions/generated/squinpen_012_0dc0d2750d6b1986.json
index cc190ba16cb420d979aae20ce6e9c3f9e88e8e25..2c9142074da22a4412e464b6e3eb93aa0c995468 100644
--- a/data/solutions/generated/squinpen_012_0dc0d2750d6b1986.json
+++ b/data/solutions/generated/squinpen_012_0dc0d2750d6b1986.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.969,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Timo Berthold et al"
diff --git a/data/solutions/generated/squinpen_014_c910e2e69c5e952c.json b/data/solutions/generated/squinpen_014_c910e2e69c5e952c.json
index 7f822c2f3ac396d934dbb2d519c2badc45253862..2af8c636b1a1e1c4e790951a3fc26581b5815de5 100644
--- a/data/solutions/generated/squinpen_014_c910e2e69c5e952c.json
+++ b/data/solutions/generated/squinpen_014_c910e2e69c5e952c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.187,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/squinpen_015_d5cf3c3cc0980b70.json b/data/solutions/generated/squinpen_015_d5cf3c3cc0980b70.json
index 10ed5108a7e8b28c2df7093f8598180b3785c8c3..af2bdc9140117e913321807b188183034d2ecd36 100644
--- a/data/solutions/generated/squinpen_015_d5cf3c3cc0980b70.json
+++ b/data/solutions/generated/squinpen_015_d5cf3c3cc0980b70.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.284,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/squinpen_016_9ca0c9eddf5257a6.json b/data/solutions/generated/squinpen_016_9ca0c9eddf5257a6.json
index b35857210079e0fc352919f425717ae1aa7014e5..c47d39737dc74d8f5e8f948747164ae34e7ede26 100644
--- a/data/solutions/generated/squinpen_016_9ca0c9eddf5257a6.json
+++ b/data/solutions/generated/squinpen_016_9ca0c9eddf5257a6.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.48,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinpen_017_c1324401d6fef4ff.json b/data/solutions/generated/squinpen_017_c1324401d6fef4ff.json
index 33e0ee208e9f78bd4700092b0e2dad0ead606b4e..37c58535d5cc1bc7bb17b9bbc7c4e3160e0d61c8 100644
--- a/data/solutions/generated/squinpen_017_c1324401d6fef4ff.json
+++ b/data/solutions/generated/squinpen_017_c1324401d6fef4ff.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.541,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinpen_018_521e6ed1020d53e6.json b/data/solutions/generated/squinpen_018_521e6ed1020d53e6.json
index f96c9fac6f94868772e33159331e1438f07d388b..4f71177f564ddee8a699ccd2c27ee97b9f29ba02 100644
--- a/data/solutions/generated/squinpen_018_521e6ed1020d53e6.json
+++ b/data/solutions/generated/squinpen_018_521e6ed1020d53e6.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.626,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinpen_019_66aeca1af6b9bf65.json b/data/solutions/generated/squinpen_019_66aeca1af6b9bf65.json
index ad7f438c699943f6551827902e4bee20b531d2db..a5c080a50c36b23e0c7ef3d940fcea97cc2e9725 100644
--- a/data/solutions/generated/squinpen_019_66aeca1af6b9bf65.json
+++ b/data/solutions/generated/squinpen_019_66aeca1af6b9bf65.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.71,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinpen_020_8424f972564f51a8.json b/data/solutions/generated/squinpen_020_8424f972564f51a8.json
index bb45d9c0a70ddabf62a5efb5a345708827fd79a8..1b8bebc21055069202d4355618a1a7f803141839 100644
--- a/data/solutions/generated/squinpen_020_8424f972564f51a8.json
+++ b/data/solutions/generated/squinpen_020_8424f972564f51a8.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.802,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinpen_021_7f1bf6bbe100ca6c.json b/data/solutions/generated/squinpen_021_7f1bf6bbe100ca6c.json
index 8adecb2608043178370bf08c0ac388e09660c574..2de47cb067b72907c01a6ce45dea059bf196885f 100644
--- a/data/solutions/generated/squinpen_021_7f1bf6bbe100ca6c.json
+++ b/data/solutions/generated/squinpen_021_7f1bf6bbe100ca6c.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.014043288294021605,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.864,
     "source_image_url": "https://erich-friedman.github.io/packing/squinpen/21.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinpen_022_33b95c59890c6cd7.json b/data/solutions/generated/squinpen_022_33b95c59890c6cd7.json
index 248c4b94f4c1b3adb94c4340767b420d8f3ac7f5..10e4afaad451420573a5ffe9168296eba36244ac 100644
--- a/data/solutions/generated/squinpen_022_33b95c59890c6cd7.json
+++ b/data/solutions/generated/squinpen_022_33b95c59890c6cd7.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.937,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinpen_023_125d15e1f42d4cc7.json b/data/solutions/generated/squinpen_023_125d15e1f42d4cc7.json
index c78fce031955ca9ffe86a3cf27ce2ae6e2505443..13e81d2d95e1137436a77e13847e2c70e52f33fa 100644
--- a/data/solutions/generated/squinpen_023_125d15e1f42d4cc7.json
+++ b/data/solutions/generated/squinpen_023_125d15e1f42d4cc7.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.002,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinpen_024_7b6bed1452ec8f75.json b/data/solutions/generated/squinpen_024_7b6bed1452ec8f75.json
index b3f92b970784543fee391a2b1881f2a6c76fbdfc..95d17bb21b30a6f4e3dd8a06d5035cce340d68fe 100644
--- a/data/solutions/generated/squinpen_024_7b6bed1452ec8f75.json
+++ b/data/solutions/generated/squinpen_024_7b6bed1452ec8f75.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.06736533563452667,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.107,
     "source_image_url": "https://erich-friedman.github.io/packing/squinpen/24.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinpen_025_965f543dd3a1a5b2.json b/data/solutions/generated/squinpen_025_965f543dd3a1a5b2.json
index 8cf7ac47674a4c88dac919a4aea9cf42951097a2..53c7282d3e49da8cb929c859b7842024814a9310 100644
--- a/data/solutions/generated/squinpen_025_965f543dd3a1a5b2.json
+++ b/data/solutions/generated/squinpen_025_965f543dd3a1a5b2.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.169,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinpen_026_12ea954c92ca25d9.json b/data/solutions/generated/squinpen_026_12ea954c92ca25d9.json
index 10ecc141ae44d923626db47599b23adb9f78ca07..649d05092e69997651e66db8a5b9078e0cffc4a1 100644
--- a/data/solutions/generated/squinpen_026_12ea954c92ca25d9.json
+++ b/data/solutions/generated/squinpen_026_12ea954c92ca25d9.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.223,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinpen_027_fc7fa66fe1928440.json b/data/solutions/generated/squinpen_027_fc7fa66fe1928440.json
index 59630f0ab84aa028bbf24492dc6f5169802e4ab6..3429fd94f7a154bb6b26d9c46c446c52f7691718 100644
--- a/data/solutions/generated/squinpen_027_fc7fa66fe1928440.json
+++ b/data/solutions/generated/squinpen_027_fc7fa66fe1928440.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.32010696968586827,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.35,
     "source_image_url": "https://erich-friedman.github.io/packing/squinpen/27.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinpen_028_81b95a9d0915b9b0.json b/data/solutions/generated/squinpen_028_81b95a9d0915b9b0.json
index 89722eeb06b1a3a14a9d829972b86f75f3af62c6..1d7244a4616aea6c1a3db8436f21999af6efd194 100644
--- a/data/solutions/generated/squinpen_028_81b95a9d0915b9b0.json
+++ b/data/solutions/generated/squinpen_028_81b95a9d0915b9b0.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.2837720923309283,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.421,
     "source_image_url": "https://erich-friedman.github.io/packing/squinpen/28.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinpen_029_7cc5c6e51420a8c4.json b/data/solutions/generated/squinpen_029_7cc5c6e51420a8c4.json
index 4ea7d168d441acffacdfb5d02037b3bcdf5af348..795cba575fe75b6fb328b42723c8a70990960ec3 100644
--- a/data/solutions/generated/squinpen_029_7cc5c6e51420a8c4.json
+++ b/data/solutions/generated/squinpen_029_7cc5c6e51420a8c4.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.25298006841215986,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.499,
     "source_image_url": "https://erich-friedman.github.io/packing/squinpen/29.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinpen_031_8b17df7ad9586809.json b/data/solutions/generated/squinpen_031_8b17df7ad9586809.json
index 79977dd04f949e72f7538db55f7d06e9b1d29f86..2b2922e74760da496f7620adff1fd11ce2151d45 100644
--- a/data/solutions/generated/squinpen_031_8b17df7ad9586809.json
+++ b/data/solutions/generated/squinpen_031_8b17df7ad9586809.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.20498547914067852,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.63041,
     "source_image_url": "https://erich-friedman.github.io/packing/squinpen/31.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinpen_032_ded24abc59c82646.json b/data/solutions/generated/squinpen_032_ded24abc59c82646.json
index 43e7d1727f287027435d0f742892406c2990c728..4cfc41a68ee1b9daab47719190802d0fbc0f01dd 100644
--- a/data/solutions/generated/squinpen_032_ded24abc59c82646.json
+++ b/data/solutions/generated/squinpen_032_ded24abc59c82646.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.34596618017915726,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.70774,
     "source_image_url": "https://erich-friedman.github.io/packing/squinpen/32.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinpen_033_a9622b0aeea26f74.json b/data/solutions/generated/squinpen_033_a9622b0aeea26f74.json
index 84b10979110d7efd0a108a477953900f3b526333..d909e5ed857bd46e680ad2bd8d9098afc1d04130 100644
--- a/data/solutions/generated/squinpen_033_a9622b0aeea26f74.json
+++ b/data/solutions/generated/squinpen_033_a9622b0aeea26f74.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.1530095722595505,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.75774,
     "source_image_url": "https://erich-friedman.github.io/packing/squinpen/33.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T03:19:00+00:00",
diff --git a/data/solutions/generated/squinpen_034_d7af1c3ed90603fd.json b/data/solutions/generated/squinpen_034_d7af1c3ed90603fd.json
index 67943188948421fcda5639dd71440c71f465669f..dddf66d398a439345b6ba8bde2fd97e49667d7ce 100644
--- a/data/solutions/generated/squinpen_034_d7af1c3ed90603fd.json
+++ b/data/solutions/generated/squinpen_034_d7af1c3ed90603fd.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.21329750195581923,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.81817,
     "source_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/squinpen_035_d0212c88c498f951.json b/data/solutions/generated/squinpen_035_d0212c88c498f951.json
index 1547d8cb0a4efbf145c795a840d8ab90384802ff..bb093e521c5fe754b13bbf66c5dada223e1cb0f7 100644
--- a/data/solutions/generated/squinpen_035_d0212c88c498f951.json
+++ b/data/solutions/generated/squinpen_035_d0212c88c498f951.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.015690763592442425,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.86994,
     "source_image_url": "https://erich-friedman.github.io/packing/squinpen/35.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinpen_037_dba281681536eecb.json b/data/solutions/generated/squinpen_037_dba281681536eecb.json
index 3cb86a05151bdc898ba7c9589ad41253800fd304..4c300593df5ca1e2cdccf686c4910e962df3e0e2 100644
--- a/data/solutions/generated/squinpen_037_dba281681536eecb.json
+++ b/data/solutions/generated/squinpen_037_dba281681536eecb.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.021526669227806546,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.98234,
     "source_image_url": "https://erich-friedman.github.io/packing/squinpen/37.gif",
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squinpen_13_13449338c659bacc.json b/data/solutions/generated/squinpen_13_13449338c659bacc.json
index 05963aabb2800a74b8ceea4d38f1dcb1a4f5543e..45292e7caca32b89f54f22df0ac0dfbd41606c82 100644
--- a/data/solutions/generated/squinpen_13_13449338c659bacc.json
+++ b/data/solutions/generated/squinpen_13_13449338c659bacc.json
@@ -49,7 +49,10 @@
     "generator_profile": "cg_precise",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_20260501T070815Z_broad.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.121,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T07:13:53+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/squinpen_27_0b33929541015a68.json b/data/solutions/generated/squinpen_27_0b33929541015a68.json
new file mode 100644
index 0000000000000000000000000000000000000000..54085339ed7ffc84b892e686867b7531c33f24e0
--- /dev/null
+++ b/data/solutions/generated/squinpen_27_0b33929541015a68.json
@@ -0,0 +1,229 @@
+{
+  "case": "squinpen@27",
+  "container": {
+    "circumradius": 3.7023988728522115,
+    "orientation_radians": 0.0,
+    "side_length": 4.35243091113361,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@27",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "",
+    "metric_expression": "4.350+",
+    "metric_symbol": "s",
+    "metric_value": 4.35,
+    "reference_text": "s = 4.350+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "27.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/27.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@27",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "",
+      "metric_expression": "4.350+",
+      "metric_symbol": "s",
+      "metric_value": 4.35,
+      "reference_text": "s = 4.350+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "27.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/27.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "sa_escape",
+    "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_20260501_systematic_broad.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.35,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/squinpen_027_20260501_systematic_sa_escape.state",
+    "source_url": "https://erich-friedman.github.io/packing/squinpen/",
+    "submitted_at": "2026-05-01T16:24:14+00:00",
+    "submitted_by": "Ignacio Vallejo"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.4137156167868086,
+      "x": 1.8004796150033153,
+      "y": 1.5384252467177595
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.4714854797315912,
+      "x": -0.06491275379575202,
+      "y": -2.6024895890756636
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.800454200693806,
+      "x": 0.5648340032632496,
+      "y": 0.49846206916422336
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.7811329894533212,
+      "x": -0.4918797227150575,
+      "y": -1.4720411855367033
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.7811325025696242,
+      "x": -0.47854276465926576,
+      "y": 0.527975765395931
+    },
+    {
+      "id": 6,
+      "rotation_radians": 1.413715637872441,
+      "x": 2.4968493891325827,
+      "y": 0.8082438560424149
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.157082475675564,
+      "x": 1.6573881389201361,
+      "y": -1.9640255374369988
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.7811326124090597,
+      "x": -0.43631453307035245,
+      "y": -0.4722408898151663
+    },
+    {
+      "id": 9,
+      "rotation_radians": 0.7855693025371602,
+      "x": -2.494988670045321,
+      "y": 0.6758566546682048
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.15574478290000607,
+      "x": 2.1571968854211527,
+      "y": -1.0878875541854987
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.7862278703450674,
+      "x": -1.4948167122564102,
+      "y": 1.0012720271098194
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.16173865597564807,
+      "x": 1.0662062678847335,
+      "y": -2.7735593435164003
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.788576822326429,
+      "x": -1.4944052897607165,
+      "y": 2.002484097472856
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.7854589571395885,
+      "x": -2.495149823822045,
+      "y": -1.3249368352177533
+    },
+    {
+      "id": 15,
+      "rotation_radians": 0.7853974264762147,
+      "x": -2.4952796311554852,
+      "y": 1.6761778435931596
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.8004551034889462,
+      "x": 0.5168327770629147,
+      "y": 1.4979015398850815
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.4137156348488626,
+      "x": 1.321401234695021,
+      "y": 2.426477770754137
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.8004195290437944,
+      "x": 0.7311559298434266,
+      "y": -0.49921239088693903
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.414047635980977,
+      "x": 1.7676839870818313,
+      "y": 0.11024860540920307
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.7858109274721466,
+      "x": -2.4896250741321593,
+      "y": -0.3244578481383334
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.7761163260867994,
+      "x": -1.4833935118765473,
+      "y": -0.0037870973429687863
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.7811322137078422,
+      "x": -0.49266323852659505,
+      "y": 1.5280713863268853
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.15707563897882135,
+      "x": 2.8353740366010496,
+      "y": -0.34266789514052387
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.7761157335207547,
+      "x": -1.4901493661031413,
+      "y": -1.0038048878103287
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.7761146447934365,
+      "x": -1.4967066007597662,
+      "y": -2.003824347799755
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.7811344289249222,
+      "x": 0.508023933313596,
+      "y": -1.5078674736214819
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.7811321803740617,
+      "x": 0.12289478837206289,
+      "y": 2.5254799249869597
+    }
+  ],
+  "problem": "27 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/27.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_30_45dff6d0a270c6c5.json b/data/solutions/generated/squinpen_30_45dff6d0a270c6c5.json
index a94401c778f5ff8c857098b018c8eca89213070c..e94740fe3c27644d86ddd53a3cdefdd852d58e85 100644
--- a/data/solutions/generated/squinpen_30_45dff6d0a270c6c5.json
+++ b/data/solutions/generated/squinpen_30_45dff6d0a270c6c5.json
@@ -49,7 +49,10 @@
     "generator_profile": "sa_tight",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_current_heavy_heavy.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.55,
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "submitted_at": "2026-05-01T14:34:18+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/squinpen_30_6d45a6352a0ed4b0.json b/data/solutions/generated/squinpen_30_6d45a6352a0ed4b0.json
new file mode 100644
index 0000000000000000000000000000000000000000..362d705f10f9a477d13282f6668b36b61564a000
--- /dev/null
+++ b/data/solutions/generated/squinpen_30_6d45a6352a0ed4b0.json
@@ -0,0 +1,247 @@
+{
+  "case": "squinpen@30",
+  "container": {
+    "circumradius": 3.8756674770107145,
+    "orientation_radians": 0.0,
+    "side_length": 4.556120371552951,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@30",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "",
+    "metric_expression": "4.550+",
+    "metric_symbol": "s",
+    "metric_value": 4.55,
+    "reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "30.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@30",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "",
+      "metric_expression": "4.550+",
+      "metric_symbol": "s",
+      "metric_value": 4.55,
+      "reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "30.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "cg_deep",
+    "image_seed_recovery_log": "bench_outputs/current_best_recovery/current_best_recovery_20260501_currentbest_deep_deep.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.55,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/squinpen_030_20260501_currentbest_deep_cg_deep.state",
+    "source_url": "https://erich-friedman.github.io/packing/squinpen/",
+    "submitted_at": "2026-05-01T17:13:54+00:00",
+    "submitted_by": "Ignacio Vallejo"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -1.4196272968523456,
+      "x": 1.3891161317735556,
+      "y": -0.8653744347689891
+    },
+    {
+      "id": 2,
+      "rotation_radians": -1.4137188641321072,
+      "x": 1.0657274230873424,
+      "y": -2.980628563850092
+    },
+    {
+      "id": 3,
+      "rotation_radians": -0.15603216125315353,
+      "x": 2.7198189384725784,
+      "y": 0.7393211115555295
+    },
+    {
+      "id": 4,
+      "rotation_radians": -0.4712254292116629,
+      "x": -2.5054160296941936,
+      "y": 1.9529124087930831
+    },
+    {
+      "id": 5,
+      "rotation_radians": -0.7851260896698284,
+      "x": -1.6352762106707694,
+      "y": -1.0994532682978464
+    },
+    {
+      "id": 6,
+      "rotation_radians": -0.4666262088170478,
+      "x": -1.518515458098305,
+      "y": 1.2230988567876402
+    },
+    {
+      "id": 7,
+      "rotation_radians": -0.4712227150518488,
+      "x": 0.3466651719387602,
+      "y": 2.883734540580183
+    },
+    {
+      "id": 8,
+      "rotation_radians": -1.4137290374068614,
+      "x": 2.8464000495617574,
+      "y": -0.56599387181195
+    },
+    {
+      "id": 9,
+      "rotation_radians": -1.442170430035277,
+      "x": 1.818164450019128,
+      "y": 0.07431891143942698
+    },
+    {
+      "id": 10,
+      "rotation_radians": -0.4699574013880853,
+      "x": 0.17061831772348224,
+      "y": 0.7228321434800904
+    },
+    {
+      "id": 11,
+      "rotation_radians": -0.46995614927073653,
+      "x": -0.6135135623536778,
+      "y": -0.5867270875832273
+    },
+    {
+      "id": 12,
+      "rotation_radians": -0.7853964215114851,
+      "x": -2.63545850429978,
+      "y": -0.7754267871999654
+    },
+    {
+      "id": 13,
+      "rotation_radians": -0.463154018377343,
+      "x": -1.732769088452943,
+      "y": 0.09746255925031051
+    },
+    {
+      "id": 14,
+      "rotation_radians": -0.5897263585306093,
+      "x": -0.5475102045158929,
+      "y": -1.650401971955481
+    },
+    {
+      "id": 15,
+      "rotation_radians": -0.4712231356874657,
+      "x": -0.6044291763822826,
+      "y": 2.5746870310185637
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.47023763341868924,
+      "x": -0.5559659574332249,
+      "y": 1.5382759303280538
+    },
+    {
+      "id": 17,
+      "rotation_radians": -0.7845696369810142,
+      "x": -2.6350428550826672,
+      "y": -1.7758920113666097
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.47122351901737763,
+      "x": 0.44750482401050495,
+      "y": 1.8649813038976881
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.15603054610263004,
+      "x": 2.130202809670536,
+      "y": 1.5470346184995662
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.176969268352565,
+      "x": 1.245527561319007,
+      "y": 1.0492922441034105
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.6739529738435694,
+      "x": 0.5064371568574066,
+      "y": -1.713963900431699
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.4579946765336417,
+      "x": -2.4858364487885294,
+      "y": 0.9005697791048761
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.4677932512188771,
+      "x": -0.7809462276917094,
+      "y": 0.4117315010266043
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.9129150960893037,
+      "x": -1.601736453120211,
+      "y": -2.1594853625521147
+    },
+    {
+      "id": 25,
+      "rotation_radians": -1.413724145906224,
+      "x": 2.2585805952995384,
+      "y": -1.3750417798705015
+    },
+    {
+      "id": 26,
+      "rotation_radians": -0.46995754473389806,
+      "x": 0.33668290191283773,
+      "y": -0.2749224655163578
+    },
+    {
+      "id": 27,
+      "rotation_radians": -0.4712251115657112,
+      "x": -1.555334368597705,
+      "y": 2.2650673211598455
+    },
+    {
+      "id": 28,
+      "rotation_radians": -1.4137221632773658,
+      "x": 1.6664839475337394,
+      "y": -2.180981247405899
+    },
+    {
+      "id": 29,
+      "rotation_radians": -1.099556394035251,
+      "x": -0.04923874923074568,
+      "y": -2.755088788260188
+    },
+    {
+      "id": 30,
+      "rotation_radians": -0.15591929990403544,
+      "x": 1.54330417282358,
+      "y": 2.356796477029511
+    }
+  ],
+  "problem": "30 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/30.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_30_abcbdd03f9f27f35.json b/data/solutions/generated/squinpen_30_abcbdd03f9f27f35.json
new file mode 100644
index 0000000000000000000000000000000000000000..0bef4417c61c634f3d34c9093f807c2cbc036c5f
--- /dev/null
+++ b/data/solutions/generated/squinpen_30_abcbdd03f9f27f35.json
@@ -0,0 +1,247 @@
+{
+  "case": "squinpen@30",
+  "container": {
+    "circumradius": 3.8758519509947877,
+    "orientation_radians": 0.0,
+    "side_length": 4.556337233727491,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@30",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "",
+    "metric_expression": "4.550+",
+    "metric_symbol": "s",
+    "metric_value": 4.55,
+    "reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "30.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@30",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "",
+      "metric_expression": "4.550+",
+      "metric_symbol": "s",
+      "metric_value": 4.55,
+      "reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "30.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "sa_escape",
+    "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_20260501_systematic_broad.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.55,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/squinpen_030_20260501_systematic_sa_escape.state",
+    "source_url": "https://erich-friedman.github.io/packing/squinpen/",
+    "submitted_at": "2026-05-01T16:24:14+00:00",
+    "submitted_by": "Ignacio Vallejo"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.422421534317079,
+      "x": 1.387396853716426,
+      "y": 0.8656711105957853
+    },
+    {
+      "id": 2,
+      "rotation_radians": 1.4104996655703397,
+      "x": 1.0636491908164865,
+      "y": 2.9812076965542786
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.15627835305334528,
+      "x": 2.720197202418388,
+      "y": -0.7392775558990285
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.47123292160635594,
+      "x": -2.5055743401571613,
+      "y": -1.9554493299765519
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.7853937236795638,
+      "x": -1.635578768807278,
+      "y": 1.1021424355460414
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.46897385690182114,
+      "x": -1.525139923057248,
+      "y": -1.2230034558600387
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.47122963955861696,
+      "x": 0.3471903134368397,
+      "y": -2.8840667922790724
+    },
+    {
+      "id": 8,
+      "rotation_radians": 1.4137246425416516,
+      "x": 2.8464798062176997,
+      "y": 0.5661419266258659
+    },
+    {
+      "id": 9,
+      "rotation_radians": 1.4476752116986755,
+      "x": 1.8224944895555155,
+      "y": -0.07191400381396483
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.47096972350667665,
+      "x": 0.17189301803603158,
+      "y": -0.7239703005470782
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.4709700336810833,
+      "x": -0.6148077491451545,
+      "y": 0.5866289020948942
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.7853940891817885,
+      "x": -2.635615936693134,
+      "y": 0.7781119185637281
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.4553903151108922,
+      "x": -1.7348491300615099,
+      "y": -0.09496403438482101
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.5912861848778658,
+      "x": -0.5484803229497943,
+      "y": 1.650244578728436
+    },
+    {
+      "id": 15,
+      "rotation_radians": 0.4712306143680284,
+      "x": -0.6038945771954517,
+      "y": -2.5750291250678004
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.47122668447131383,
+      "x": -0.5570531192246032,
+      "y": -1.5387312177105283
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.7853945547764178,
+      "x": -2.635611832447507,
+      "y": 1.7781495931048839
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.47122904854166214,
+      "x": 0.45411521121846965,
+      "y": -1.8673062751729883
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.15527280149834385,
+      "x": 2.1310255526164723,
+      "y": -1.547931127165996
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.18255215718110893,
+      "x": 1.24709944042877,
+      "y": -1.044434132121897
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.6741612590783393,
+      "x": 0.5047771516265397,
+      "y": 1.7136556844793704
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.45568164835582753,
+      "x": -2.496530969244054,
+      "y": -0.8937039884671323
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.4695281167959889,
+      "x": -0.7796465620986406,
+      "y": -0.4140017818393702
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.919483366359628,
+      "x": -1.6036165308852248,
+      "y": 2.164538542459703
+    },
+    {
+      "id": 25,
+      "rotation_radians": 1.4137245691774587,
+      "x": 2.2586711365838696,
+      "y": 1.375183203675122
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.47097054984634285,
+      "x": 0.335266764587385,
+      "y": 0.27448415403938486
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.4712313379444187,
+      "x": -1.5549812245164687,
+      "y": -2.265998241873975
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.4118887284433612,
+      "x": 1.6691987843988132,
+      "y": 2.184148460279246
+    },
+    {
+      "id": 29,
+      "rotation_radians": 1.099555270918452,
+      "x": -0.05000002431722605,
+      "y": 2.7550058728859317
+    },
+    {
+      "id": 30,
+      "rotation_radians": 0.155271309919705,
+      "x": 1.5438943509381966,
+      "y": -2.357450462152722
+    }
+  ],
+  "problem": "30 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/30.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_30_c7e14ee67108e002.json b/data/solutions/generated/squinpen_30_c7e14ee67108e002.json
new file mode 100644
index 0000000000000000000000000000000000000000..f709d6defa9d3dca9aee4bbff0a663a986edce6c
--- /dev/null
+++ b/data/solutions/generated/squinpen_30_c7e14ee67108e002.json
@@ -0,0 +1,246 @@
+{
+  "case": "squinpen@30",
+  "container": {
+    "circumradius": 3.8715936028609312,
+    "orientation_radians": 0.0,
+    "side_length": 4.551331245263075,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@30",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "",
+    "metric_expression": "4.550+",
+    "metric_symbol": "s",
+    "metric_value": 4.55,
+    "reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "30.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@30",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "",
+      "metric_expression": "4.550+",
+      "metric_symbol": "s",
+      "metric_value": 4.55,
+      "reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "30.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Verified coordinate recovery from fresh SA+CG topology search against the Friedman target; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "recovery_source": "fresh SA+CG topology search against the Friedman target",
+    "recovery_state": "bench_outputs/fresh_recovery/states/squinpen_030_sa8000.state",
+    "reference_side": 4.55,
+    "source_url": "https://erich-friedman.github.io/packing/squinpen/",
+    "submitted_at": "2026-05-01T17:22:49+00:00",
+    "submitted_by": "Ignacio Vallejo"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.7370780577764973,
+      "x": -2.607342648996298,
+      "y": -1.8007991547395263
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.4712312602460551,
+      "x": -1.5831800025400737,
+      "y": -2.2532093546810255
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.4712312621077298,
+      "x": -0.632091664371387,
+      "y": -2.5622494168969325
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.4712316840596063,
+      "x": 0.31900218588712514,
+      "y": -2.8712740222940183
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.15709019355514722,
+      "x": 1.538555548252313,
+      "y": -2.3604785626238267
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.15709019290103748,
+      "x": 2.1263559957905462,
+      "y": -1.551430033418159
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.7853925215423551,
+      "x": -2.63218126906803,
+      "y": -0.7772041852711007
+    },
+    {
+      "id": 8,
+      "rotation_radians": 1.3447685747109202,
+      "x": -1.443028776792672,
+      "y": -1.0146023260913213
+    },
+    {
+      "id": 9,
+      "rotation_radians": 0.4711917196008681,
+      "x": -0.3659709907401308,
+      "y": -1.5972045084621653
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.15709499916055672,
+      "x": 0.7941143579789712,
+      "y": -1.6837620505761604
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.1570950661580462,
+      "x": 1.3819040431190326,
+      "y": -0.874705935207296
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.15709032429602476,
+      "x": 2.7141543328061886,
+      "y": -0.7423798227092817
+    },
+    {
+      "id": 13,
+      "rotation_radians": 1.3447686536318149,
+      "x": -1.7133087170893968,
+      "y": -0.003961970939338678
+    },
+    {
+      "id": 14,
+      "rotation_radians": 1.4137224968990187,
+      "x": -0.7502543708323439,
+      "y": 0.4049873449037493
+    },
+    {
+      "id": 15,
+      "rotation_radians": 1.4137225867060366,
+      "x": -0.16165339296154585,
+      "y": -0.4034777238474156
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.4137224095793535,
+      "x": 0.740513023458454,
+      "y": 0.056157449734002246
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.4137210044893929,
+      "x": 1.9244683037741894,
+      "y": 0.12795122757008093
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.4137209398155526,
+      "x": 2.8494760512944906,
+      "y": 0.5561485943501107
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.0621449039786028,
+      "x": -2.514573909728259,
+      "y": 0.8153644119876862
+    },
+    {
+      "id": 20,
+      "rotation_radians": 1.0995591785390233,
+      "x": -1.5706331590200484,
+      "y": 1.2057984014562098
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.0995591929460315,
+      "x": -1.5482236314379356,
+      "y": 2.2645776232827646
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.4137223987737322,
+      "x": 0.15270185766194128,
+      "y": 0.8652046568022354
+    },
+    {
+      "id": 23,
+      "rotation_radians": 1.413720382504924,
+      "x": 1.301919751633007,
+      "y": 0.9848111186530715
+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.4137201691770163,
+      "x": 2.2616665525659148,
+      "y": 1.3651964463551765
+    },
+    {
+      "id": 25,
+      "rotation_radians": 1.0995592744112272,
+      "x": -2.499317939398378,
+      "y": 1.9555474640994541
+    },
+    {
+      "id": 26,
+      "rotation_radians": 1.4141998539967018,
+      "x": 0.09810593880186934,
+      "y": 2.6380691025706886
+    },
+    {
+      "id": 27,
+      "rotation_radians": 1.4137200315948621,
+      "x": 1.0858947932478529,
+      "y": 2.983507128249707
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.4202802082208816,
+      "x": -0.43965706456560083,
+      "y": 1.6749885563930573
+    },
+    {
+      "id": 29,
+      "rotation_radians": 1.4137186932910042,
+      "x": 0.6991563803370645,
+      "y": 1.8144532137510168
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.413718757680312,
+      "x": 1.6738583994145293,
+      "y": 2.174246537910892
+    }
+  ],
+  "problem": "30 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/30.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_33_d93824a50e5c0a99.json b/data/solutions/generated/squinpen_33_d93824a50e5c0a99.json
new file mode 100644
index 0000000000000000000000000000000000000000..f4194d7b363b6d2e38774b55ddd309cf25e23967
--- /dev/null
+++ b/data/solutions/generated/squinpen_33_d93824a50e5c0a99.json
@@ -0,0 +1,265 @@
+{
+  "case": "squinpen@33",
+  "container": {
+    "circumradius": 4.050370641067087,
+    "orientation_radians": 0.0,
+    "side_length": 4.761496258275288,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@33",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "",
+    "metric_expression": "4.75774+",
+    "metric_symbol": "s",
+    "metric_value": 4.75774,
+    "reference_text": "s = 4.75774+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "33.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/33.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@33",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "",
+      "metric_expression": "4.75774+",
+      "metric_symbol": "s",
+      "metric_value": 4.75774,
+      "reference_text": "s = 4.75774+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "33.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/33.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "sa_tight",
+    "image_seed_recovery_log": "bench_outputs/current_best_recovery/current_best_recovery_20260501_currentbest_deep_deep.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.75774,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/squinpen_033_20260501_currentbest_deep_sa_tight.state",
+    "source_url": "https://erich-friedman.github.io/packing/squinpen/",
+    "submitted_at": "2026-05-01T17:13:54+00:00",
+    "submitted_by": "Emerson Connelly"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.4712348477314436,
+      "x": 0.40808433082196416,
+      "y": -3.0522940548508477
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.4712353242451186,
+      "x": -0.5429418835148425,
+      "y": -2.743039240494139
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.13108857430672083,
+      "x": 1.5795403154097027,
+      "y": -2.516357049439658
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.47123703902154657,
+      "x": -1.4935123543879705,
+      "y": -2.4323801926464905
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.47125128259850135,
+      "x": -2.4452213213340097,
+      "y": -2.125205975085977
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.1376533150651779,
+      "x": 0.7370814436224803,
+      "y": -1.9596591050298429
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.13302152716018967,
+      "x": 2.1744187081501356,
+      "y": -1.7111292462093866
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.46790760704571005,
+      "x": -0.7024732121439886,
+      "y": -1.6379126449308132
+    },
+    {
+      "id": 9,
+      "rotation_radians": 0.46139587260793663,
+      "x": -1.6538752288253884,
+      "y": -1.3152545872652028
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.13308809918787673,
+      "x": 1.3599123583431485,
+      "y": -1.1299307824825189
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.7664581470063894,
+      "x": -2.73630248439956,
+      "y": -0.9956224090036462
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.1492936035512161,
+      "x": 0.25647544318290083,
+      "y": -0.927158971213778
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.12588131459143403,
+      "x": 2.6812316733193096,
+      "y": -0.8353612153196631
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.45519114428068397,
+      "x": -0.8043799963267305,
+      "y": -0.5451148031412172
+    },
+    {
+      "id": 15,
+      "rotation_radians": 0.1230019367713349,
+      "x": 3.346957967712006,
+      "y": -0.08452378222886624
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.7664541965310301,
+      "x": -2.767402202999125,
+      "y": 0.005168193652371389
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.397437973215746,
+      "x": 0.9561696640651294,
+      "y": -0.035665225291524744
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.7664016222007527,
+      "x": -1.7646773509530278,
+      "y": 0.1356344071957958
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.3971537740452935,
+      "x": 2.0731361982737275,
+      "y": 0.11373312444331801
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.7660762383569266,
+      "x": -0.7556906289241194,
+      "y": 0.5831932654471305
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.0772431212586941,
+      "x": 0.3264982204618358,
+      "y": 0.9054097149492882
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.4192355186762704,
+      "x": 2.773246930139381,
+      "y": 0.8799233709833458
+    },
+    {
+      "id": 23,
+      "rotation_radians": 1.3930870684365764,
+      "x": 1.4975005518119329,
+      "y": 0.9375616379250085
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.7664545079690501,
+      "x": -2.7513747200542933,
+      "y": 1.005067789249875
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.7592459888668752,
+      "x": -1.744726262608417,
+      "y": 1.1482396610624972
+    },
+    {
+      "id": 26,
+      "rotation_radians": 1.4187094296757765,
+      "x": 2.1961414255235345,
+      "y": 1.697184194957081
+    },
+    {
+      "id": 27,
+      "rotation_radians": 1.097737967634821,
+      "x": -0.46669095977685454,
+      "y": 1.7134391826869553
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.0876884757175995,
+      "x": 0.498391041571785,
+      "y": 2.00668565168525
+    },
+    {
+      "id": 29,
+      "rotation_radians": 1.0995340306776549,
+      "x": -2.415286188777416,
+      "y": 2.1349326438760605
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.0995042565441315,
+      "x": -1.4639974603673191,
+      "y": 2.443431012352376
+    },
+    {
+      "id": 31,
+      "rotation_radians": 1.44419669549124,
+      "x": 1.5530182621085866,
+      "y": 2.4799694449993477
+    },
+    {
+      "id": 32,
+      "rotation_radians": 1.0982091523246138,
+      "x": -0.5116323721861339,
+      "y": 2.7506599956821325
+    },
+    {
+      "id": 33,
+      "rotation_radians": 1.1005860929873519,
+      "x": 0.44660698980284497,
+      "y": 3.0642214277105064
+    }
+  ],
+  "problem": "33 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/33.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_34_7dafd61dbd636b00.json b/data/solutions/generated/squinpen_34_7dafd61dbd636b00.json
new file mode 100644
index 0000000000000000000000000000000000000000..85ddf895df2fd0a2efb4632668b3f7566aa342f1
--- /dev/null
+++ b/data/solutions/generated/squinpen_34_7dafd61dbd636b00.json
@@ -0,0 +1,271 @@
+{
+  "case": "squinpen@34",
+  "container": {
+    "circumradius": 4.107850546124187,
+    "orientation_radians": 0.0,
+    "side_length": 4.829067939266757,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@34",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "",
+    "metric_expression": "4.81817+",
+    "metric_symbol": "s",
+    "metric_value": 4.81817,
+    "reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "34.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@34",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "",
+      "metric_expression": "4.81817+",
+      "metric_symbol": "s",
+      "metric_value": 4.81817,
+      "reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "34.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "cg_deep",
+    "image_seed_recovery_log": "bench_outputs/current_best_recovery/current_best_recovery_20260501_currentbest_deep_deep.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.81817,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/squinpen_034_20260501_currentbest_deep_cg_deep.state",
+    "source_url": "https://erich-friedman.github.io/packing/squinpen/",
+    "submitted_at": "2026-05-01T17:13:54+00:00",
+    "submitted_by": "Emerson Connelly"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -1.1476016793671533,
+      "x": -1.8599745341674176,
+      "y": -2.298340545164105
+    },
+    {
+      "id": 2,
+      "rotation_radians": -1.1476020020085849,
+      "x": -0.9209386180737721,
+      "y": -2.6424094088574246
+    },
+    {
+      "id": 3,
+      "rotation_radians": -1.1476004301712044,
+      "x": 0.03046036723943432,
+      "y": -2.953848450068012
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.4231942843268483,
+      "x": 0.9875231119568484,
+      "y": -3.250340179882456
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.15086390960136392,
+      "x": 2.2398386101000476,
+      "y": -1.7151445010940967
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.1506425333157842,
+      "x": 2.827633719007985,
+      "y": -0.9059187149393014
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.42319259518366087,
+      "x": -2.678586878752727,
+      "y": -1.6364632404933779
+    },
+    {
+      "id": 8,
+      "rotation_radians": -1.112893798562474,
+      "x": -0.9315352373559148,
+      "y": -1.5623892175549536
+    },
+    {
+      "id": 9,
+      "rotation_radians": -1.1129673797102289,
+      "x": 0.018311392703280135,
+      "y": -1.8755435153344302
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.4263878470082127,
+      "x": 0.9872686306853697,
+      "y": -2.1803977687491973
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.1577773210984915,
+      "x": 1.4691705138451114,
+      "y": -1.069342920845061
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.0031669097045616324,
+      "x": 3.39954166982476,
+      "y": -0.0006206849287167191
+    },
+    {
+      "id": 13,
+      "rotation_radians": -0.7854049701582329,
+      "x": -2.8233010652854817,
+      "y": -0.48383194271483815
+    },
+    {
+      "id": 14,
+      "rotation_radians": -1.096199011928501,
+      "x": -1.7666145617070343,
+      "y": -0.8858287867251143
+    },
+    {
+      "id": 15,
+      "rotation_radians": -1.1055222101672864,
+      "x": -0.6218608260683494,
+      "y": -0.6071465818914705
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.4595343658633683,
+      "x": 0.32959630176650856,
+      "y": -0.9242348246421659
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.14832761647970655,
+      "x": 0.998354677489953,
+      "y": -0.014441245481746834
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.14971200476752736,
+      "x": 2.0720910966031303,
+      "y": -0.24475162047587545
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.7853993500739894,
+      "x": -2.8232969303396915,
+      "y": 0.5162196757656617
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.7853925663206531,
+      "x": -1.8232459580995042,
+      "y": 0.24318840548496864
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.48548033904921284,
+      "x": -0.7569706726644164,
+      "y": 0.6046010466646565
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.4818419821268095,
+      "x": 0.19546035854236682,
+      "y": 0.9156568310345855
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.05999684867854981,
+      "x": 1.4351138454221306,
+      "y": 0.9588849754779297
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.003227610987140163,
+      "x": 2.7554473826361057,
+      "y": 0.7700193307953072
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.7928340304458312,
+      "x": -2.8195447937627134,
+      "y": 1.5213448015007818
+    },
+    {
+      "id": 26,
+      "rotation_radians": -0.47554164228532864,
+      "x": -1.6630991982554428,
+      "y": 1.371922260023426
+    },
+    {
+      "id": 27,
+      "rotation_radians": -0.4708150968296923,
+      "x": -0.7079131941678949,
+      "y": 1.6791408402371761
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.4751105614418889,
+      "x": 0.24873058393055797,
+      "y": 1.9838300439167462
+    },
+    {
+      "id": 29,
+      "rotation_radians": -0.4579199909919777,
+      "x": 1.2080426610155814,
+      "y": 2.295272600734139
+    },
+    {
+      "id": 30,
+      "rotation_radians": 0.007936908877810638,
+      "x": 2.2058130353245833,
+      "y": 1.6390630612737547
+    },
+    {
+      "id": 31,
+      "rotation_radians": -0.47065791893473957,
+      "x": -1.9025688471354008,
+      "y": 2.3481612072145626
+    },
+    {
+      "id": 32,
+      "rotation_radians": -0.47089495139772714,
+      "x": -0.9495743491138232,
+      "y": 2.6522157772850545
+    },
+    {
+      "id": 33,
+      "rotation_radians": 1.0998435132937443,
+      "x": 0.002822979015475038,
+      "y": 2.957369166642956
+    },
+    {
+      "id": 34,
+      "rotation_radians": 1.1041560085467137,
+      "x": 0.9552845326464182,
+      "y": 3.269700516676237
+    }
+  ],
+  "problem": "34 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/34.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_34_a3f4dd7d0b94e803.json b/data/solutions/generated/squinpen_34_a3f4dd7d0b94e803.json
new file mode 100644
index 0000000000000000000000000000000000000000..5fe3f30b3b6cce220b529d91a6c29678d0154130
--- /dev/null
+++ b/data/solutions/generated/squinpen_34_a3f4dd7d0b94e803.json
@@ -0,0 +1,270 @@
+{
+  "case": "squinpen@34",
+  "container": {
+    "circumradius": 4.0983176143448405,
+    "orientation_radians": 0.0,
+    "side_length": 4.817861305844738,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@34",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "",
+    "metric_expression": "4.81817+",
+    "metric_symbol": "s",
+    "metric_value": 4.81817,
+    "reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "34.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@34",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "",
+      "metric_expression": "4.81817+",
+      "metric_symbol": "s",
+      "metric_value": 4.81817,
+      "reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "34.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Verified coordinate recovery from fresh CG topology search against the Friedman target; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "recovery_source": "fresh CG topology search against the Friedman target",
+    "recovery_state": "bench_outputs/fresh_recovery/states/squinpen_034_cg20000.state",
+    "reference_side": 4.81817,
+    "source_url": "https://erich-friedman.github.io/packing/squinpen/",
+    "submitted_at": "2026-05-01T17:42:33+00:00",
+    "submitted_by": "Emerson Connelly"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.5559789075997348,
+      "x": -2.7149939578021915,
+      "y": -2.034407618023977
+    },
+    {
+      "id": 2,
+      "rotation_radians": -1.0589262089556728,
+      "x": -1.7485083821689216,
+      "y": -2.371400878311401
+    },
+    {
+      "id": 3,
+      "rotation_radians": -1.0589546516450983,
+      "x": -0.7966437057902244,
+      "y": -2.680744071642247
+    },
+    {
+      "id": 4,
+      "rotation_radians": -1.3990740528260506,
+      "x": 0.4490749734784352,
+      "y": -2.4541814778799216
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.16930492314640924,
+      "x": 1.1472951733296142,
+      "y": -3.200722386134981
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.16930256338481103,
+      "x": 1.7258497356169777,
+      "y": -2.3850450731472175
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.5644110905985247,
+      "x": -2.4638634381521327,
+      "y": -1.0617229002572408
+    },
+    {
+      "id": 8,
+      "rotation_radians": -1.0618612661832618,
+      "x": -1.4930580833504659,
+      "y": -1.4028953328407383
+    },
+    {
+      "id": 9,
+      "rotation_radians": -1.0589546075099001,
+      "x": -0.526495611559981,
+      "y": -1.7178952606382432
+    },
+    {
+      "id": 10,
+      "rotation_radians": -1.4015208445152967,
+      "x": 0.2949213423255773,
+      "y": -0.903978035914632
+    },
+    {
+      "id": 11,
+      "rotation_radians": -1.3990740118804577,
+      "x": 1.017125445771816,
+      "y": -1.6310871408370151
+    },
+    {
+      "id": 12,
+      "rotation_radians": -1.4015208595926487,
+      "x": 2.3230094549416975,
+      "y": -1.5825263556246385
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.7286997105185516,
+      "x": -2.7772723620148896,
+      "y": 0.03291669694434806
+    },
+    {
+      "id": 14,
+      "rotation_radians": -0.7949100384463472,
+      "x": -1.7495584418538985,
+      "y": 0.1409052707627611
+    },
+    {
+      "id": 15,
+      "rotation_radians": -1.0647770844675566,
+      "x": -0.7902340038089753,
+      "y": -0.5626260480427765
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.1692753452922066,
+      "x": 0.9113638184174829,
+      "y": -0.11512539806940957
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.16927542676200857,
+      "x": 1.626475939171279,
+      "y": -0.8357054330603377
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.1692763500339911,
+      "x": 2.900908886939905,
+      "y": -0.7663858550417371
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.08975113489802,
+      "x": -2.3073918879900615,
+      "y": 1.1525473337300276
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.4740402600293414,
+      "x": -0.6437964024617605,
+      "y": 0.6373952252919761
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.45402589832068385,
+      "x": 0.3176910464730315,
+      "y": 0.9474013619143582
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.4150724225235685,
+      "x": 1.4748031428908839,
+      "y": 1.054074471840145
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.15546889087482832,
+      "x": 2.068914819176079,
+      "y": 0.23982571155178353
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.1570714381753117,
+      "x": 3.1618543442683458,
+      "y": 0.4382585725216895
+    },
+    {
+      "id": 25,
+      "rotation_radians": 1.0898376024430725,
+      "x": -2.688710148755561,
+      "y": 2.081020442096691
+    },
+    {
+      "id": 26,
+      "rotation_radians": -0.4809422995594009,
+      "x": -1.3563815454453212,
+      "y": 1.462347667468197
+    },
+    {
+      "id": 27,
+      "rotation_radians": -0.48101606063605507,
+      "x": -0.4049055628108169,
+      "y": 1.7704731566358436
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.47951112061501777,
+      "x": 0.5503156433714717,
+      "y": 2.0827600826154815
+    },
+    {
+      "id": 29,
+      "rotation_radians": -0.15708764415934984,
+      "x": 1.9856271042131508,
+      "y": 2.055958539692882
+    },
+    {
+      "id": 30,
+      "rotation_radians": -0.1570714213718594,
+      "x": 2.573388368435226,
+      "y": 1.2468278003835078
+    },
+    {
+      "id": 31,
+      "rotation_radians": -0.48076146071856307,
+      "x": -1.7376868040067022,
+      "y": 2.390887960146608
+    },
+    {
+      "id": 32,
+      "rotation_radians": -0.4804870100654539,
+      "x": -0.7861800931263077,
+      "y": 2.699165431910125
+    },
+    {
+      "id": 33,
+      "rotation_radians": -0.47951151468400216,
+      "x": 0.16495214137386172,
+      "y": 3.009767293436325
+    },
+    {
+      "id": 34,
+      "rotation_radians": -0.15708763163153736,
+      "x": 1.3983470865893017,
+      "y": 2.865515738777695
+    }
+  ],
+  "problem": "34 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/34.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squintri_001_bc8215883b0d29fa.json b/data/solutions/generated/squintri_001_bc8215883b0d29fa.json
index 9bbe83681e70ab6ee5d074a49c44f3f9c350f893..eb2123ef5e71077fe601fa8f82b4737911607a7d 100644
--- a/data/solutions/generated/squintri_001_bc8215883b0d29fa.json
+++ b/data/solutions/generated/squintri_001_bc8215883b0d29fa.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.1547005383792515,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squintri_002_9fcb7fc91bdb6f8d.json b/data/solutions/generated/squintri_002_9fcb7fc91bdb6f8d.json
index 4b84fdcca6f6fd895341972ae4a98185f84241a8..3f5d4c7db4285679677349ea01846b5dc3f4df5b 100644
--- a/data/solutions/generated/squintri_002_9fcb7fc91bdb6f8d.json
+++ b/data/solutions/generated/squintri_002_9fcb7fc91bdb6f8d.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.1547005383792515,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/squintri_003_6a0fd09e2fb037d5.json b/data/solutions/generated/squintri_003_6a0fd09e2fb037d5.json
index 34371ecc1b79ec9638f2bb0c582ddc4f099b47ad..556afd911838292a2b6098ea25b18f22e7f160b1 100644
--- a/data/solutions/generated/squintri_003_6a0fd09e2fb037d5.json
+++ b/data/solutions/generated/squintri_003_6a0fd09e2fb037d5.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.232050807568877,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_004_a14dd3a45e182f53.json b/data/solutions/generated/squintri_004_a14dd3a45e182f53.json
index 49b381bc3e527986ae4bef25d91333ffdc0365be..1ba56a405f64a485cce2695363b54fb095f03aac 100644
--- a/data/solutions/generated/squintri_004_a14dd3a45e182f53.json
+++ b/data/solutions/generated/squintri_004_a14dd3a45e182f53.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.1547005383792515,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_005_b7ec125fb5317da3.json b/data/solutions/generated/squintri_005_b7ec125fb5317da3.json
index e8aa4b7ab56440e1b85e8bc6a82d0631b95f8b44..b7b1c34ce3241263cc1a884f6479b8db1a7eae9e 100644
--- a/data/solutions/generated/squintri_005_b7ec125fb5317da3.json
+++ b/data/solutions/generated/squintri_005_b7ec125fb5317da3.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.309401076758503,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_006_cafd65072dcc4c6f.json b/data/solutions/generated/squintri_006_cafd65072dcc4c6f.json
index 8615c19a34653973ab1aa518bfe8ffff23392d75..3ae5a8ada46b6502527c2d4c3603a27cf361856c 100644
--- a/data/solutions/generated/squintri_006_cafd65072dcc4c6f.json
+++ b/data/solutions/generated/squintri_006_cafd65072dcc4c6f.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.309401076758503,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_007_b90420d34e1bd6e3.json b/data/solutions/generated/squintri_007_b90420d34e1bd6e3.json
index 00d5eed6667b579b03c4af1ab88192c8fc86738b..9edabe48bb07286a3c6d1643c53a481ecc23c4ea 100644
--- a/data/solutions/generated/squintri_007_b90420d34e1bd6e3.json
+++ b/data/solutions/generated/squintri_007_b90420d34e1bd6e3.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.1547005383792515,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_008_9523798d0eb30de3.json b/data/solutions/generated/squintri_008_9523798d0eb30de3.json
index 742d60440f87b7f465a7edd3aa7420fa021362cd..ea212585dd7c304a4913c67ef5863d25df2187a0 100644
--- a/data/solutions/generated/squintri_008_9523798d0eb30de3.json
+++ b/data/solutions/generated/squintri_008_9523798d0eb30de3.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.0040485863791155105,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.301,
     "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts8.gif",
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squintri_009_221ec438e9e78bec.json b/data/solutions/generated/squintri_009_221ec438e9e78bec.json
index 82f0fe1c722b1e8aff14dc8b15d10383663e2e38..02ab1b4cfe823168bc76883924e95c5ebde9b001 100644
--- a/data/solutions/generated/squintri_009_221ec438e9e78bec.json
+++ b/data/solutions/generated/squintri_009_221ec438e9e78bec.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.09021798101202062,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.309401076758503,
     "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts9.gif",
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squintri_010_4b92d4f5e6704540.json b/data/solutions/generated/squintri_010_4b92d4f5e6704540.json
index 111f003ffa5e552c1165647cc2979c0c40e9bb92..b08adff263aa12b0c8556718cd2dff6d40c27899 100644
--- a/data/solutions/generated/squintri_010_4b92d4f5e6704540.json
+++ b/data/solutions/generated/squintri_010_4b92d4f5e6704540.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.464101615137754,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_011_c18f0f7b3b1e0227.json b/data/solutions/generated/squintri_011_c18f0f7b3b1e0227.json
index 4fadd8776186c0639bba67e341d5ddc74ba3b30c..610c70728bf744381de984e667a55c2cab7a0e4f 100644
--- a/data/solutions/generated/squintri_011_c18f0f7b3b1e0227.json
+++ b/data/solutions/generated/squintri_011_c18f0f7b3b1e0227.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.1547005383792515,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_012_d248ead86c97d2e6.json b/data/solutions/generated/squintri_012_d248ead86c97d2e6.json
index 5641995ca1f82ce5d06122cc890ef07fa37ff949..1af3cd62be065de937640fd3a94a4b1f32d6edca 100644
--- a/data/solutions/generated/squintri_012_d248ead86c97d2e6.json
+++ b/data/solutions/generated/squintri_012_d248ead86c97d2e6.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.013269157627681646,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.301,
     "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts12.gif",
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squintri_013_3b7ab78f832490ed.json b/data/solutions/generated/squintri_013_3b7ab78f832490ed.json
index f4569e248b2a53da73f3741718f83224e03e82e4..5ba30eb365260e20f72d069b8d903e9f324eabb1 100644
--- a/data/solutions/generated/squintri_013_3b7ab78f832490ed.json
+++ b/data/solutions/generated/squintri_013_3b7ab78f832490ed.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.309401076758503,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_014_ffc152ae79167d33.json b/data/solutions/generated/squintri_014_ffc152ae79167d33.json
index f91458f10379f465ce6580121db97cf93ed62421..6170217b9c000f11c663033155859d400d177946 100644
--- a/data/solutions/generated/squintri_014_ffc152ae79167d33.json
+++ b/data/solutions/generated/squintri_014_ffc152ae79167d33.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.464101615137754,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_015_37ace9570dd5c15b.json b/data/solutions/generated/squintri_015_37ace9570dd5c15b.json
index 7e9b9d9437fc6914d8fee3e2946861512ad16f5d..8719f97d89d801ea79323d1b1c172cc938c8651a 100644
--- a/data/solutions/generated/squintri_015_37ace9570dd5c15b.json
+++ b/data/solutions/generated/squintri_015_37ace9570dd5c15b.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.464101615137754,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_016_36afe756f11f62d6.json b/data/solutions/generated/squintri_016_36afe756f11f62d6.json
index 9ca046acfba74fbad05f318479de7eaabdad2210..d84b46e32c562936d4bfea92edd41cf21f29ad6d 100644
--- a/data/solutions/generated/squintri_016_36afe756f11f62d6.json
+++ b/data/solutions/generated/squintri_016_36afe756f11f62d6.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.1547005383792515,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_017_3a2c987432da5f1d.json b/data/solutions/generated/squintri_017_3a2c987432da5f1d.json
index 966aaba74d239332a5b30019a4f8c786ee41490b..2ec2a3159193f6ac306e22f952340bdfee05b784 100644
--- a/data/solutions/generated/squintri_017_3a2c987432da5f1d.json
+++ b/data/solutions/generated/squintri_017_3a2c987432da5f1d.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.015375038857276884,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.301,
     "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts17.gif",
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squintri_018_e729e13f2fcc5856.json b/data/solutions/generated/squintri_018_e729e13f2fcc5856.json
index 70feaa067eb1995acfb059251a61f1a694a257a8..59665f1e84cb0de7265c54d30b338d2f46fdf0e5 100644
--- a/data/solutions/generated/squintri_018_e729e13f2fcc5856.json
+++ b/data/solutions/generated/squintri_018_e729e13f2fcc5856.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.012946104191568435,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.309401076758503,
     "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts18.gif",
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squintri_019_805d1e50c1db2842.json b/data/solutions/generated/squintri_019_805d1e50c1db2842.json
index e86150b6f355bbea980329281174c3165ae65b17..47a0d9cc7d9117337cf10ae19f425d987652ec73 100644
--- a/data/solutions/generated/squintri_019_805d1e50c1db2842.json
+++ b/data/solutions/generated/squintri_019_805d1e50c1db2842.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.464101615137754,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_020_f4d21a73470ce742.json b/data/solutions/generated/squintri_020_f4d21a73470ce742.json
index 914811c249b81f6dfb21432832070fdd0981a14b..168973dc899e2efa977e7e0ff7f1aa4f26e4aab3 100644
--- a/data/solutions/generated/squintri_020_f4d21a73470ce742.json
+++ b/data/solutions/generated/squintri_020_f4d21a73470ce742.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.618802153517006,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_021_a2e24601c2557198.json b/data/solutions/generated/squintri_021_a2e24601c2557198.json
index deb1fc58c85660e537cdfe7b2055b2233057f33e..681bdf8891a2f72769a8693fdfbd2d9bf0b0afc7 100644
--- a/data/solutions/generated/squintri_021_a2e24601c2557198.json
+++ b/data/solutions/generated/squintri_021_a2e24601c2557198.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 7.618802153517006,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_022_bbb028380d997350.json b/data/solutions/generated/squintri_022_bbb028380d997350.json
index f530693469fd53ef0b4f067bffc85c6c2595f1c4..9840226ca99def68e3a6c0061ce1faf75799d769 100644
--- a/data/solutions/generated/squintri_022_bbb028380d997350.json
+++ b/data/solutions/generated/squintri_022_bbb028380d997350.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.154700538379252,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_023_b1534ea73e00f283.json b/data/solutions/generated/squintri_023_b1534ea73e00f283.json
index d74c012800a3d7b7ea9b6d67380137f7c5d6c045..068f01bc547ebaa5327102fcad1fc1c9181a0aa8 100644
--- a/data/solutions/generated/squintri_023_b1534ea73e00f283.json
+++ b/data/solutions/generated/squintri_023_b1534ea73e00f283.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.01748092008687252,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.301,
     "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts23.gif",
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squintri_024_648f7ef8ee4a197f.json b/data/solutions/generated/squintri_024_648f7ef8ee4a197f.json
index 079ae9b0d5ba3020824539f99d35d4ee5f870e87..cb6c5e63f3caebce4a2ec8ff896a403db47bc223 100644
--- a/data/solutions/generated/squintri_024_648f7ef8ee4a197f.json
+++ b/data/solutions/generated/squintri_024_648f7ef8ee4a197f.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.006345916661775052,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.309401076758503,
     "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts24.gif",
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squintri_025_a868d8af97a256ad.json b/data/solutions/generated/squintri_025_a868d8af97a256ad.json
index 7d913152f7cf5b36ffb659ed85d93d8fa0334ef0..0f1efc36449a01481e4ca9502e3737df7287dbed 100644
--- a/data/solutions/generated/squintri_025_a868d8af97a256ad.json
+++ b/data/solutions/generated/squintri_025_a868d8af97a256ad.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.006464296380462638,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.464101615137755,
     "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts25.gif",
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squintri_026_249af47eefa3a74b.json b/data/solutions/generated/squintri_026_249af47eefa3a74b.json
index ba64d0dafce05085569513834c619f824bb23259..0856355571bfc6b7ce6df9e3e456c18b0547bd85 100644
--- a/data/solutions/generated/squintri_026_249af47eefa3a74b.json
+++ b/data/solutions/generated/squintri_026_249af47eefa3a74b.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.1464491543344501,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.618802153517006,
     "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif",
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squintri_027_3c62cd2126467cec.json b/data/solutions/generated/squintri_027_3c62cd2126467cec.json
index 3b9400b09874321c056d560a3de3370092ce0d23..d57ee74ced191dda73708c6530e79d9cfa65792d 100644
--- a/data/solutions/generated/squintri_027_3c62cd2126467cec.json
+++ b/data/solutions/generated/squintri_027_3c62cd2126467cec.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.1464491543344501,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.618802153517006,
     "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif",
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squintri_028_0d20b359435ed501.json b/data/solutions/generated/squintri_028_0d20b359435ed501.json
index 95af59d99c32508db69e009e4e7d35189895b88a..f20ed40d2c333e5934b1551c853ac1186c37ec30 100644
--- a/data/solutions/generated/squintri_028_0d20b359435ed501.json
+++ b/data/solutions/generated/squintri_028_0d20b359435ed501.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 8.773502691896258,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_029_3947aab39c0a1a92.json b/data/solutions/generated/squintri_029_3947aab39c0a1a92.json
index bfc5b45374324f21cbb06d3894401793a87672a9..975657b9fa7eac26cbb067ef0d76d4bcc6e91a1d 100644
--- a/data/solutions/generated/squintri_029_3947aab39c0a1a92.json
+++ b/data/solutions/generated/squintri_029_3947aab39c0a1a92.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.154700538379252,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_030_e0b7505d8b6b1d46.json b/data/solutions/generated/squintri_030_e0b7505d8b6b1d46.json
index 196544a40cc75f4366a87ecb3fe537d61ce3d3c8..51fe270965610b30bfc64ac88f2f855acb3d49ba 100644
--- a/data/solutions/generated/squintri_030_e0b7505d8b6b1d46.json
+++ b/data/solutions/generated/squintri_030_e0b7505d8b6b1d46.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.301,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/squintri_031_22b5f5f5707858bb.json b/data/solutions/generated/squintri_031_22b5f5f5707858bb.json
index ce49eac8ee08e25b04c25143c953353c578ef7b3..fc2ce00e721f93e91d2172f088ef4745dd947192 100644
--- a/data/solutions/generated/squintri_031_22b5f5f5707858bb.json
+++ b/data/solutions/generated/squintri_031_22b5f5f5707858bb.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.007109656782339661,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.309401076758503,
     "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts31.gif",
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squintri_032_a44fbd99145b1ab3.json b/data/solutions/generated/squintri_032_a44fbd99145b1ab3.json
index 461327c9698ed4b842b21507ade58754adc844e0..9382dbbe7f01cdba5350108c46636da053663a7a 100644
--- a/data/solutions/generated/squintri_032_a44fbd99145b1ab3.json
+++ b/data/solutions/generated/squintri_032_a44fbd99145b1ab3.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.025559830961602657,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.464101615137755,
     "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts32.gif",
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squintri_033_67de1e08be2d150c.json b/data/solutions/generated/squintri_033_67de1e08be2d150c.json
index e55883012f444b8c13cf5beb93fce3cce3916c38..6b547082e274ff5259a6765c4f01d433fa5207c1 100644
--- a/data/solutions/generated/squintri_033_67de1e08be2d150c.json
+++ b/data/solutions/generated/squintri_033_67de1e08be2d150c.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.16344255817924594,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.618802153517006,
     "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif",
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squintri_034_3661302cdd9d0eb0.json b/data/solutions/generated/squintri_034_3661302cdd9d0eb0.json
index 0de89a753762a8af699e06319e4341bda5ce0062..ec9ea58cd8f86e04a0e0901faae1fd87321f1cb6 100644
--- a/data/solutions/generated/squintri_034_3661302cdd9d0eb0.json
+++ b/data/solutions/generated/squintri_034_3661302cdd9d0eb0.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.618802153517006,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/squintri_035_39d52a823b632afe.json b/data/solutions/generated/squintri_035_39d52a823b632afe.json
index 3bcb9659ad2f09db4bdb547b68854046fd46ad4e..1c21e27c6f13252bd8f70d2a6f4711453dca4464 100644
--- a/data/solutions/generated/squintri_035_39d52a823b632afe.json
+++ b/data/solutions/generated/squintri_035_39d52a823b632afe.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.007464032198281587,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.773502691896258,
     "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif",
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squintri_036_f0473aaa767ebe98.json b/data/solutions/generated/squintri_036_f0473aaa767ebe98.json
index 301f4b6c49514621cf548caa33738fbd3f2fbeca..f1433fb19aaa31d383959cd7513f00f4467c9624 100644
--- a/data/solutions/generated/squintri_036_f0473aaa767ebe98.json
+++ b/data/solutions/generated/squintri_036_f0473aaa767ebe98.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.007464032198281587,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 9.773502691896258,
     "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif",
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/squintri_037_8530be000ac2e9ed.json b/data/solutions/generated/squintri_037_8530be000ac2e9ed.json
index 8753adaf2f67c206704e242382c3bab8fc912d97..4c00611b191df4547ea98169f987590783b43496 100644
--- a/data/solutions/generated/squintri_037_8530be000ac2e9ed.json
+++ b/data/solutions/generated/squintri_037_8530be000ac2e9ed.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 10.154,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/squintri_038_896b636f9d899bf5.json b/data/solutions/generated/squintri_038_896b636f9d899bf5.json
index 6d2201eb21d68e5f3422508627c66b4bbd3257fe..751e8593fa89c4e82f528e3f605db3e9f185ab22 100644
--- a/data/solutions/generated/squintri_038_896b636f9d899bf5.json
+++ b/data/solutions/generated/squintri_038_896b636f9d899bf5.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 10.309,
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/triincir_001_49954bfbb560620d.json b/data/solutions/generated/triincir_001_49954bfbb560620d.json
index 54fae8569ea0d2c774a3141504bccfa689fb0e6c..8a894ac651cb96f2375208043da80cbc1875f599 100644
--- a/data/solutions/generated/triincir_001_49954bfbb560620d.json
+++ b/data/solutions/generated/triincir_001_49954bfbb560620d.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.5773502691896257,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triincir_002_92f5511b689fe041.json b/data/solutions/generated/triincir_002_92f5511b689fe041.json
index 8920dc58a9d90696b727f355ffd4aec771acee53..90d97e9ef5e813f47624dae140b5059b18edf07c 100644
--- a/data/solutions/generated/triincir_002_92f5511b689fe041.json
+++ b/data/solutions/generated/triincir_002_92f5511b689fe041.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.8660254037844386,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triincir_003_6ede8225b5939550.json b/data/solutions/generated/triincir_003_6ede8225b5939550.json
index 20c56e7d52c5bcc3f73c4cc1ef0f81d61354a4df..6340f2b972b88fd212076edb2768a8467e6a893c 100644
--- a/data/solutions/generated/triincir_003_6ede8225b5939550.json
+++ b/data/solutions/generated/triincir_003_6ede8225b5939550.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.9535117355873467,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triincir_004_7f9481f33de5ecda.json b/data/solutions/generated/triincir_004_7f9481f33de5ecda.json
index 6ddb0d166190d5b551c776d116cc75c0e7699259..ce8c0b183b06003ba3ef5f280071ca01d83ad9b3 100644
--- a/data/solutions/generated/triincir_004_7f9481f33de5ecda.json
+++ b/data/solutions/generated/triincir_004_7f9481f33de5ecda.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.98,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triincir_005_cf17d061ebfe392b.json b/data/solutions/generated/triincir_005_cf17d061ebfe392b.json
index e12153a7a0bbe7d3ba8473930d293b1e49a6817f..92635943f291b465ece8c7525d6fb596708a35f3 100644
--- a/data/solutions/generated/triincir_005_cf17d061ebfe392b.json
+++ b/data/solutions/generated/triincir_005_cf17d061ebfe392b.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.0,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triincir_006_fe93ba87f23c6c01.json b/data/solutions/generated/triincir_006_fe93ba87f23c6c01.json
index 5c5acad3cb5bd0613283c831e4d67dceaa21fb50..ae50899d730fd602ea64e28468646698860e94a4 100644
--- a/data/solutions/generated/triincir_006_fe93ba87f23c6c01.json
+++ b/data/solutions/generated/triincir_006_fe93ba87f23c6c01.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.0,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triincir_007_4d32cb6092e127b9.json b/data/solutions/generated/triincir_007_4d32cb6092e127b9.json
index 2258a16a50ac5cf5f941f0b707032b9aea762fd2..fdfb158dcffc5f1143a63087a905dd18e3701a89 100644
--- a/data/solutions/generated/triincir_007_4d32cb6092e127b9.json
+++ b/data/solutions/generated/triincir_007_4d32cb6092e127b9.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.152,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triincir_008_33389e3c966a2171.json b/data/solutions/generated/triincir_008_33389e3c966a2171.json
index c8d417059a314d9175c2dd75bd6f12a00df77d44..5e904f18d7edb5c488bb498acf5f99026e5d8396 100644
--- a/data/solutions/generated/triincir_008_33389e3c966a2171.json
+++ b/data/solutions/generated/triincir_008_33389e3c966a2171.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.263,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/triincir_009_68692b6dc093b182.json b/data/solutions/generated/triincir_009_68692b6dc093b182.json
index 7271574ce398108ff5a1593787fa6e4b316d7853..0e33d45b0275e71bfce58c9a878c0eb5cc8b5ff7 100644
--- a/data/solutions/generated/triincir_009_68692b6dc093b182.json
+++ b/data/solutions/generated/triincir_009_68692b6dc093b182.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.314,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/triincir_010_676585e5c31a1d2f.json b/data/solutions/generated/triincir_010_676585e5c31a1d2f.json
index 68819935e4a6bc7a307732461cd4d2c545825b6f..8b28c2848ef905cc42e290823bf7b971e1a50651 100644
--- a/data/solutions/generated/triincir_010_676585e5c31a1d2f.json
+++ b/data/solutions/generated/triincir_010_676585e5c31a1d2f.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.385,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/triincir_011_27341d9b331a210b.json b/data/solutions/generated/triincir_011_27341d9b331a210b.json
index 571f683ed8c882b1cc72631e0121504192dbfae0..3e5e462b4325184212152cfbcfb27b7ff855fe4b 100644
--- a/data/solutions/generated/triincir_011_27341d9b331a210b.json
+++ b/data/solutions/generated/triincir_011_27341d9b331a210b.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.466,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell after Maurizio Morandi"
diff --git a/data/solutions/generated/triincir_012_0430950ce5a6ad65.json b/data/solutions/generated/triincir_012_0430950ce5a6ad65.json
index 392e606b3165e62323fde9e015c7be42e1c45273..17720572acad524593216d8b0f1f84417a3c8e73 100644
--- a/data/solutions/generated/triincir_012_0430950ce5a6ad65.json
+++ b/data/solutions/generated/triincir_012_0430950ce5a6ad65.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.507,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/triincir_013_2b014eeead965100.json b/data/solutions/generated/triincir_013_2b014eeead965100.json
index 1b0ed4b98c8bed27131e149d309f0e522c2bc2c6..e271dac94129b4d4611770c20a9e12cf3f2d3138 100644
--- a/data/solutions/generated/triincir_013_2b014eeead965100.json
+++ b/data/solutions/generated/triincir_013_2b014eeead965100.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.5275252316519468,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triincir_014_da4114b8f6b7e383.json b/data/solutions/generated/triincir_014_da4114b8f6b7e383.json
index 038f2c6e9adca0e39e757617c1032c3ab97dd3fe..690d440104903a63a150244b5f26e12fe9718953 100644
--- a/data/solutions/generated/triincir_014_da4114b8f6b7e383.json
+++ b/data/solutions/generated/triincir_014_da4114b8f6b7e383.json
@@ -49,8 +49,10 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.",
     "profile": "sa",
+    "reference_side": 1.609,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Nathan Roll"
diff --git a/data/solutions/generated/triincir_015_e8f573cc9f431ed8.json b/data/solutions/generated/triincir_015_e8f573cc9f431ed8.json
index 8e803b67501310d3e9c1e80b1ad232c6f651d099..8b35d1f734e3e3cbdd1a4fa2db984481a633c648 100644
--- a/data/solutions/generated/triincir_015_e8f573cc9f431ed8.json
+++ b/data/solutions/generated/triincir_015_e8f573cc9f431ed8.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.023921585643494763,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.636,
     "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc15.gif",
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triincir_017_47c836632f7377eb.json b/data/solutions/generated/triincir_017_47c836632f7377eb.json
index c6b7fac61979f19744618a3604b4e7a614bb634e..25b13f8c7a05bb97ee446ee879a9587761290e9d 100644
--- a/data/solutions/generated/triincir_017_47c836632f7377eb.json
+++ b/data/solutions/generated/triincir_017_47c836632f7377eb.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.73,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/triincir_018_8d495d33c78cce38.json b/data/solutions/generated/triincir_018_8d495d33c78cce38.json
index 5976542d63355fd0bd30c9997e7ff92cd5a8b77d..401c1237146caa5627be495b323c4a8c47f36d02 100644
--- a/data/solutions/generated/triincir_018_8d495d33c78cce38.json
+++ b/data/solutions/generated/triincir_018_8d495d33c78cce38.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.8027756377319946,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triincir_020_1217493f9010e655.json b/data/solutions/generated/triincir_020_1217493f9010e655.json
index 5d15f7577a491674e1c9dd8c04661629a4afd278..55a4ac75f74832ddc038ce66b644e73342125fee 100644
--- a/data/solutions/generated/triincir_020_1217493f9010e655.json
+++ b/data/solutions/generated/triincir_020_1217493f9010e655.json
@@ -49,8 +49,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.874,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triincir_021_46b1371ff82573dd.json b/data/solutions/generated/triincir_021_46b1371ff82573dd.json
index 03703243920ced111e0360436759a27a241f1f9c..03d128da3bd28d8c33ae998cc12a3cee512a0a9d 100644
--- a/data/solutions/generated/triincir_021_46b1371ff82573dd.json
+++ b/data/solutions/generated/triincir_021_46b1371ff82573dd.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.0009822204900495244,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.91,
     "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc21.gif",
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triincir_022_69faaab68dcae114.json b/data/solutions/generated/triincir_022_69faaab68dcae114.json
index 0a99178d4f06936921fe6caef3127aac1ccbf5a6..365517b548307eac070bd9990f4ea36debc246a7 100644
--- a/data/solutions/generated/triincir_022_69faaab68dcae114.json
+++ b/data/solutions/generated/triincir_022_69faaab68dcae114.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.005763166021060859,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.943,
     "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc22.gif",
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triincir_023_bc03a535bc1be813.json b/data/solutions/generated/triincir_023_bc03a535bc1be813.json
index b3e24b612ed5a0a018159c4ca4e38389a0c727ee..7d1e01601ee1f59bde497a5e19304804e77e13f3 100644
--- a/data/solutions/generated/triincir_023_bc03a535bc1be813.json
+++ b/data/solutions/generated/triincir_023_bc03a535bc1be813.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.0010349629186576983,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.988,
     "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc23.gif",
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triincir_025_460bfc63493e0a99.json b/data/solutions/generated/triincir_025_460bfc63493e0a99.json
index cd1cea95f04ea42c84e76e73a1be0e6c1cfe618a..90938b0e060bd5a345857b18178319c0a6ca03c6 100644
--- a/data/solutions/generated/triincir_025_460bfc63493e0a99.json
+++ b/data/solutions/generated/triincir_025_460bfc63493e0a99.json
@@ -45,8 +45,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.055,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/triincir_027_6af16151fd4089a6.json b/data/solutions/generated/triincir_027_6af16151fd4089a6.json
index 3c2292bdcf293e631c5a3818df1b05a20023e440..da0fed46bbe7b6a5c52d1279e70f26c1338ef3d5 100644
--- a/data/solutions/generated/triincir_027_6af16151fd4089a6.json
+++ b/data/solutions/generated/triincir_027_6af16151fd4089a6.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.007514911716145326,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.138,
     "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc27.gif",
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triincir_028_b8a030f48c690095.json b/data/solutions/generated/triincir_028_b8a030f48c690095.json
index 15fd575b91d8d355f90cc45488f568a0af668b41..3428a99e94a718e432efc31687480ad181b6baf2 100644
--- a/data/solutions/generated/triincir_028_b8a030f48c690095.json
+++ b/data/solutions/generated/triincir_028_b8a030f48c690095.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.011042085883756738,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.191,
     "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc28.gif",
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triincir_029_73bcaf90b9fd2226.json b/data/solutions/generated/triincir_029_73bcaf90b9fd2226.json
index 5bc408171aebe25b12069c577dc63e583030676d..5a09ae3a7cd81134bf792ac6ebf824fccec6f595 100644
--- a/data/solutions/generated/triincir_029_73bcaf90b9fd2226.json
+++ b/data/solutions/generated/triincir_029_73bcaf90b9fd2226.json
@@ -45,8 +45,10 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate improvement; exceeds the displayed Friedman value by more than 0.15%.",
     "profile": "sa",
+    "reference_side": 2.215,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Nathan Roll"
diff --git a/data/solutions/generated/triincir_030_f720ec98817b9983.json b/data/solutions/generated/triincir_030_f720ec98817b9983.json
index 5f42aa1806b282a116228eb740735e45e9b6d386..09bbbf17bcbf7ea7d0b0482c1f7bc9b96154bfbd 100644
--- a/data/solutions/generated/triincir_030_f720ec98817b9983.json
+++ b/data/solutions/generated/triincir_030_f720ec98817b9983.json
@@ -47,7 +47,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.050854277934965525,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.258,
     "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc30.gif",
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triincir_16_8bb5531a7df45934.json b/data/solutions/generated/triincir_16_8bb5531a7df45934.json
index c37720bc1256311bdff8cb5d1ec34c4b3d71e8bd..93a62c56ae422f9880fda48bf3f5d4ba67fe1d63 100644
--- a/data/solutions/generated/triincir_16_8bb5531a7df45934.json
+++ b/data/solutions/generated/triincir_16_8bb5531a7df45934.json
@@ -46,7 +46,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.027220545981561973,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.687,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/triincir_19_975121af758119a3.json b/data/solutions/generated/triincir_19_975121af758119a3.json
index bde325cf8dcd269dfbb7f803bef77ca2afc4f1b0..0c193dbd001dbb5b0acc1492ca28f89432277860 100644
--- a/data/solutions/generated/triincir_19_975121af758119a3.json
+++ b/data/solutions/generated/triincir_19_975121af758119a3.json
@@ -46,7 +46,10 @@
     "generator_profile": "cg_deep",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_current_heavy_heavy.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.8257418583505538,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T14:34:18+00:00",
     "submitted_by": "Haym Hirsh"
diff --git a/data/solutions/generated/triincir_24_e1de703df3a339d6.json b/data/solutions/generated/triincir_24_e1de703df3a339d6.json
index 6a5a630cae409c627b9aa1fd20f4aaad9196242e..ee7b82814250d7ef3d8114115ee45638653622a5 100644
--- a/data/solutions/generated/triincir_24_e1de703df3a339d6.json
+++ b/data/solutions/generated/triincir_24_e1de703df3a339d6.json
@@ -46,7 +46,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.007191923516456017,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triincir_26_8245fa6b2a472124.json b/data/solutions/generated/triincir_26_8245fa6b2a472124.json
index 642816512489efa0a8e1c3e5ecc45480f2310429..af37735c4751fbe8051a394fb3f6814ca7950ecf 100644
--- a/data/solutions/generated/triincir_26_8245fa6b2a472124.json
+++ b/data/solutions/generated/triincir_26_8245fa6b2a472124.json
@@ -46,7 +46,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.06729175389758921,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.109,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/triincir_31_ed4a5072cc8d0adf.json b/data/solutions/generated/triincir_31_ed4a5072cc8d0adf.json
index 2b15fdd1a9e1f30b6ebc5ef75c91da39c359d8a1..854aef42cb3c9da76741a01fa5aa52402e11f53a 100644
--- a/data/solutions/generated/triincir_31_ed4a5072cc8d0adf.json
+++ b/data/solutions/generated/triincir_31_ed4a5072cc8d0adf.json
@@ -46,7 +46,10 @@
     "generator_profile": "cg_precise",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_20260501T070815Z_broad.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.272,
     "source_url": "https://erich-friedman.github.io/packing/triincir/",
     "submitted_at": "2026-05-01T07:13:53+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/triindom_001_37b1dca676a779e3.json b/data/solutions/generated/triindom_001_37b1dca676a779e3.json
index 571fbf88d941759f631337201f24ea3f4d46d803..4deb6dee05ebed1ccc10318d419f7c754ba54b91 100644
--- a/data/solutions/generated/triindom_001_37b1dca676a779e3.json
+++ b/data/solutions/generated/triindom_001_37b1dca676a779e3.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.8660254037844386,
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triindom_002_31518429031d2b51.json b/data/solutions/generated/triindom_002_31518429031d2b51.json
index 789a380d7d3be353c06c611b5f95953f5e8a66f7..8fcf6cab68046dcdc7ea5cb0bac69c98f6caed97 100644
--- a/data/solutions/generated/triindom_002_31518429031d2b51.json
+++ b/data/solutions/generated/triindom_002_31518429031d2b51.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.8660254037844386,
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triindom_003_b10402bd10926cd1.json b/data/solutions/generated/triindom_003_b10402bd10926cd1.json
index d146f21a5d52bf96beb43e25b9fca1befd49df9c..f7a75ee77f6d40d5ceb5b90af8cfadcb6948f802 100644
--- a/data/solutions/generated/triindom_003_b10402bd10926cd1.json
+++ b/data/solutions/generated/triindom_003_b10402bd10926cd1.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.96796,
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/triindom_004_daed4fc0474960d9.json b/data/solutions/generated/triindom_004_daed4fc0474960d9.json
index 0f9d821cd78c26a5a915a972d6caae826e12b032..889fbab0404b82bf003942b507ea1033f6bd097d 100644
--- a/data/solutions/generated/triindom_004_daed4fc0474960d9.json
+++ b/data/solutions/generated/triindom_004_daed4fc0474960d9.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.12036,
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/triindom_005_5f00d1fbe39c88e1.json b/data/solutions/generated/triindom_005_5f00d1fbe39c88e1.json
index 48589b8f3d62afa65b210ea1caad14e62042ad86..7769668675f3189460cfce826bf6f5bc4921e86d 100644
--- a/data/solutions/generated/triindom_005_5f00d1fbe39c88e1.json
+++ b/data/solutions/generated/triindom_005_5f00d1fbe39c88e1.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.26315,
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/triindom_006_cd22df1373fe40ae.json b/data/solutions/generated/triindom_006_cd22df1373fe40ae.json
index 1d86625dd6fa29ea73fa73054a0481b7d05db9fd..3936ebefec0db8f603bde02aad1f34371e892bdb 100644
--- a/data/solutions/generated/triindom_006_cd22df1373fe40ae.json
+++ b/data/solutions/generated/triindom_006_cd22df1373fe40ae.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.37629,
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/triindom_007_070c4bf393378882.json b/data/solutions/generated/triindom_007_070c4bf393378882.json
index 2da3c25b5f27648b7072464d86bd97951ee94cc8..b40833c99290607b9517a92958e3104a7dd49cf9 100644
--- a/data/solutions/generated/triindom_007_070c4bf393378882.json
+++ b/data/solutions/generated/triindom_007_070c4bf393378882.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.49076,
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/triindom_008_dc89b8abdea24aaa.json b/data/solutions/generated/triindom_008_dc89b8abdea24aaa.json
index 56e7f8c649b2906709cb0775ad9eea704ad68b6a..62877cf2205107a30be7c4ad4dea4f9366a90144 100644
--- a/data/solutions/generated/triindom_008_dc89b8abdea24aaa.json
+++ b/data/solutions/generated/triindom_008_dc89b8abdea24aaa.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.56293,
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/triindom_009_9817bdf32d5c0df3.json b/data/solutions/generated/triindom_009_9817bdf32d5c0df3.json
index 72a574f4a6aed7b06f24875aacdfefd07c4a6837..4ddd88f2e2f0e74b3766d0fb65f71eb5bf7de8a2 100644
--- a/data/solutions/generated/triindom_009_9817bdf32d5c0df3.json
+++ b/data/solutions/generated/triindom_009_9817bdf32d5c0df3.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.9098384529005086,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.64908,
     "source_image_url": "https://erich-friedman.github.io/packing/triindom/9.png",
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triindom_010_d60b37ee7b5fe8bb.json b/data/solutions/generated/triindom_010_d60b37ee7b5fe8bb.json
index 99a56a638960a2d118c2e841e0331535da2ff8d2..5e2b262551c90d0baea42aa5fea4e1a46906e400 100644
--- a/data/solutions/generated/triindom_010_d60b37ee7b5fe8bb.json
+++ b/data/solutions/generated/triindom_010_d60b37ee7b5fe8bb.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.013896666541497604,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.68303,
     "source_image_url": "https://erich-friedman.github.io/packing/triindom/10.png",
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/triindom_011_92f51b49b50f6469.json b/data/solutions/generated/triindom_011_92f51b49b50f6469.json
index bbbd09f63c4571ee63d098121dbb7b1d6a8b8e64..3b07cb4a2eb5a8ed36586e3ac4cbe31d7882628e 100644
--- a/data/solutions/generated/triindom_011_92f51b49b50f6469.json
+++ b/data/solutions/generated/triindom_011_92f51b49b50f6469.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.73127,
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/triindom_012_d4d97a50d19ba7f9.json b/data/solutions/generated/triindom_012_d4d97a50d19ba7f9.json
index d8538d62b357d760e19539559377c097cbfac950..81a402c956ae6dc2e518075677bf43a37506ddde 100644
--- a/data/solutions/generated/triindom_012_d4d97a50d19ba7f9.json
+++ b/data/solutions/generated/triindom_012_d4d97a50d19ba7f9.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.7404,
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/triindom_013_734b8b487f97f149.json b/data/solutions/generated/triindom_013_734b8b487f97f149.json
index cf7e7102335ef35b1a5e7e8c76bdf38453ee3530..cab77b12c58c08b46a6bd6c54bac0c5749a9a248 100644
--- a/data/solutions/generated/triindom_013_734b8b487f97f149.json
+++ b/data/solutions/generated/triindom_013_734b8b487f97f149.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.85319,
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/triindom_014_050249738efebc30.json b/data/solutions/generated/triindom_014_050249738efebc30.json
index 882f3647ec843dcdf14d755ebeca9fa69ccec1b6..1133fb8741fcdd0ec9318ddde68f9ce139815d59 100644
--- a/data/solutions/generated/triindom_014_050249738efebc30.json
+++ b/data/solutions/generated/triindom_014_050249738efebc30.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.901923788646684,
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/triindom_015_a012f18849dc81a9.json b/data/solutions/generated/triindom_015_a012f18849dc81a9.json
index e9dfabf144b43dc0008fc7241554c55777d4ee41..feed852eb3409bfb85110847e90abd32e3f51fdf 100644
--- a/data/solutions/generated/triindom_015_a012f18849dc81a9.json
+++ b/data/solutions/generated/triindom_015_a012f18849dc81a9.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.9795,
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/triindom_016_97ac1b8d90281e30.json b/data/solutions/generated/triindom_016_97ac1b8d90281e30.json
index cc3f348db38b845a366d30c75c4da8e99bd1349b..a01d4c299e6d0fd3d94c8f9fa4ced1eb50d38b52 100644
--- a/data/solutions/generated/triindom_016_97ac1b8d90281e30.json
+++ b/data/solutions/generated/triindom_016_97ac1b8d90281e30.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.012513612699216926,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_image_url": "https://erich-friedman.github.io/packing/triindom/16.png",
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/triindom_017_3b35e95b5dec0d61.json b/data/solutions/generated/triindom_017_3b35e95b5dec0d61.json
index dcb4dcad23f7af2c71109779132a52550e2bad04..10aa94fbbf15bb5a5938f1e6a6fb20333beff58f 100644
--- a/data/solutions/generated/triindom_017_3b35e95b5dec0d61.json
+++ b/data/solutions/generated/triindom_017_3b35e95b5dec0d61.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.017364826257857655,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.10306,
     "source_image_url": "https://erich-friedman.github.io/packing/triindom/17.png",
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/triindom_018_c7d745720c03d379.json b/data/solutions/generated/triindom_018_c7d745720c03d379.json
index 197fef0eeb79dbbc8685d895ed4d5362826f49f3..ec806bda58fdc41a57cacd3cfab8f23b0090b5d5 100644
--- a/data/solutions/generated/triindom_018_c7d745720c03d379.json
+++ b/data/solutions/generated/triindom_018_c7d745720c03d379.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.14913,
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/triindom_019_ccdcfac9f05e2d80.json b/data/solutions/generated/triindom_019_ccdcfac9f05e2d80.json
index 59e7c8622d94dc443c7836055f2bed55c70e1f3d..b605e63771aeb47c513c850588fec27a1e5ace02 100644
--- a/data/solutions/generated/triindom_019_ccdcfac9f05e2d80.json
+++ b/data/solutions/generated/triindom_019_ccdcfac9f05e2d80.json
@@ -50,8 +50,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.24848,
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Jonathan Viquerat"
diff --git a/data/solutions/generated/triindom_020_b651b20201d5daf5.json b/data/solutions/generated/triindom_020_b651b20201d5daf5.json
index 2a16cce2162a63c1d115e14141610af8e12c0a7a..b8e221149be623fc8a7675bcafffe605f8a9cf03 100644
--- a/data/solutions/generated/triindom_020_b651b20201d5daf5.json
+++ b/data/solutions/generated/triindom_020_b651b20201d5daf5.json
@@ -48,7 +48,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_remaining_after_rect_fix.jsonl",
     "image_seed_transform_error": 0.018968652992390228,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.2973,
     "source_image_url": "https://erich-friedman.github.io/packing/triindom/20.png",
     "source_url": "https://erich-friedman.github.io/packing/triindom/",
     "submitted_at": "2026-05-01T02:49:16+00:00",
diff --git a/data/solutions/generated/triinhex_001_e9bcdcd079c1c3b7.json b/data/solutions/generated/triinhex_001_e9bcdcd079c1c3b7.json
index 98afd53cca48bb6d05af4097b5847ac6001ee44e..9e15bc02c290b39972c76b5f567e87222585d919 100644
--- a/data/solutions/generated/triinhex_001_e9bcdcd079c1c3b7.json
+++ b/data/solutions/generated/triinhex_001_e9bcdcd079c1c3b7.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.5773502691896257,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triinhex_002_132c3ed1fad59f87.json b/data/solutions/generated/triinhex_002_132c3ed1fad59f87.json
index 78f6bef3669039ae1d63724a3dcc2cac32cb8638..4276b08398418a729dd5f3280e102a20eed4edcd 100644
--- a/data/solutions/generated/triinhex_002_132c3ed1fad59f87.json
+++ b/data/solutions/generated/triinhex_002_132c3ed1fad59f87.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.8660254037844386,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triinhex_003_3f19c46d9d07a54d.json b/data/solutions/generated/triinhex_003_3f19c46d9d07a54d.json
index 1afe58b3594676b5da5e741003a4cebb29b52a69..80ae252659f40ac41b1c5af897147712f1aa7d45 100644
--- a/data/solutions/generated/triinhex_003_3f19c46d9d07a54d.json
+++ b/data/solutions/generated/triinhex_003_3f19c46d9d07a54d.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.9892995268765516,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triinhex_004_9a8f72cbad0da23e.json b/data/solutions/generated/triinhex_004_9a8f72cbad0da23e.json
index e8ed74993882902cc2ca620a2ba45713866a1a4d..ee2d17e726bc8f6d313ec6604917bcaf9e1b8467 100644
--- a/data/solutions/generated/triinhex_004_9a8f72cbad0da23e.json
+++ b/data/solutions/generated/triinhex_004_9a8f72cbad0da23e.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.0,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triinhex_005_0d61e48787b7d5d1.json b/data/solutions/generated/triinhex_005_0d61e48787b7d5d1.json
index 937213e8109c3b458feadf163d16cf414a4085be..40606f099407b5c6fd8cb2d747a131d91305241d 100644
--- a/data/solutions/generated/triinhex_005_0d61e48787b7d5d1.json
+++ b/data/solutions/generated/triinhex_005_0d61e48787b7d5d1.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.0,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triinhex_006_163de15143701be8.json b/data/solutions/generated/triinhex_006_163de15143701be8.json
index 05067e36fd876acbea556d69cb832baba7f877c3..e103e8d4be8601a1658dc7161cd2868f057b9d37 100644
--- a/data/solutions/generated/triinhex_006_163de15143701be8.json
+++ b/data/solutions/generated/triinhex_006_163de15143701be8.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.0,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triinhex_007_af96c8dfd69688ff.json b/data/solutions/generated/triinhex_007_af96c8dfd69688ff.json
index f1135a7c1ff3c9d05d15d3b00c25e80c7b85f45a..78f28925927964b4b306c78b86566576fb5185ce 100644
--- a/data/solutions/generated/triinhex_007_af96c8dfd69688ff.json
+++ b/data/solutions/generated/triinhex_007_af96c8dfd69688ff.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.277,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/triinhex_008_d557994d1935d6fb.json b/data/solutions/generated/triinhex_008_d557994d1935d6fb.json
index e20a9b4eb9a5ced55f36a71825a95073b12fbf5f..a1e6db1bca394b763d953b8725e5d41ade0b374c 100644
--- a/data/solutions/generated/triinhex_008_d557994d1935d6fb.json
+++ b/data/solutions/generated/triinhex_008_d557994d1935d6fb.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.356,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/triinhex_009_e1592cc41ab92d4d.json b/data/solutions/generated/triinhex_009_e1592cc41ab92d4d.json
index c3abad32ba8f988c5ad121fcac4eda3ec0f6c57b..82d2c219fd91199c22b0be132202c7da0a6a4dd9 100644
--- a/data/solutions/generated/triinhex_009_e1592cc41ab92d4d.json
+++ b/data/solutions/generated/triinhex_009_e1592cc41ab92d4d.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.434,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triinhex_010_27f77a1826f41a7d.json b/data/solutions/generated/triinhex_010_27f77a1826f41a7d.json
index 742bfe02e115f6b4271051747b56da200475a098..47ec7dfc2a5b38bf50e2d9544afadca170c4040e 100644
--- a/data/solutions/generated/triinhex_010_27f77a1826f41a7d.json
+++ b/data/solutions/generated/triinhex_010_27f77a1826f41a7d.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.019979165040120542,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.497,
     "source_image_url": "https://erich-friedman.github.io/packing/triinhex/10.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinhex_011_a4d7af61e2935a14.json b/data/solutions/generated/triinhex_011_a4d7af61e2935a14.json
index 4925e73b547eea0a9480d1a6054f981e9b7e6f94..dc0a7070d99c666dd51e6dce2b524db0f805c630 100644
--- a/data/solutions/generated/triinhex_011_a4d7af61e2935a14.json
+++ b/data/solutions/generated/triinhex_011_a4d7af61e2935a14.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.5,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triinhex_012_9de540041e59931a.json b/data/solutions/generated/triinhex_012_9de540041e59931a.json
index e3145374c03b8e9bd7265fbad0d5200b3d03de60..fa03079a554facb572f70bbeda1a92d6ca8a4f14 100644
--- a/data/solutions/generated/triinhex_012_9de540041e59931a.json
+++ b/data/solutions/generated/triinhex_012_9de540041e59931a.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.623,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Timo Berthold et al"
diff --git a/data/solutions/generated/triinhex_013_efc43a6cbf81ae24.json b/data/solutions/generated/triinhex_013_efc43a6cbf81ae24.json
index 39294d206e0b75d3abeb5caaff3c5b5bd6e5b340..189598f1fa4d05e0e15989cb6dd3ebf681094bf3 100644
--- a/data/solutions/generated/triinhex_013_efc43a6cbf81ae24.json
+++ b/data/solutions/generated/triinhex_013_efc43a6cbf81ae24.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.014824520961612252,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.663829237726708,
     "source_image_url": "https://erich-friedman.github.io/packing/triinhex/13.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinhex_015_20b1a0e905211ce9.json b/data/solutions/generated/triinhex_015_20b1a0e905211ce9.json
index a25c3f9a5cf7c48b90d4c3365de4cf461d07b1d0..533bdb06fb3e8ee7f5f3ea4fb23be073b2aba80a 100644
--- a/data/solutions/generated/triinhex_015_20b1a0e905211ce9.json
+++ b/data/solutions/generated/triinhex_015_20b1a0e905211ce9.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.75,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triinhex_016_a0b20d24de5f00ac.json b/data/solutions/generated/triinhex_016_a0b20d24de5f00ac.json
index b48cfe862d71fb8f77e18587b206af02698856f6..0b08b0083acd8544eee9d083dcde386edeb42eb6 100644
--- a/data/solutions/generated/triinhex_016_a0b20d24de5f00ac.json
+++ b/data/solutions/generated/triinhex_016_a0b20d24de5f00ac.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.8,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/triinhex_017_b8b9e4b4d61ec96c.json b/data/solutions/generated/triinhex_017_b8b9e4b4d61ec96c.json
index 3fb2fc080e65796942f4f4b2d2e14a238ba7752f..c172d9309422868e0bed10ecba9428a58b0b9613 100644
--- a/data/solutions/generated/triinhex_017_b8b9e4b4d61ec96c.json
+++ b/data/solutions/generated/triinhex_017_b8b9e4b4d61ec96c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.8333333333333333,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/triinhex_018_7671cfd644a7af24.json b/data/solutions/generated/triinhex_018_7671cfd644a7af24.json
index e047734f9f7f3d5a2bffefad55dc380d40d414c6..b2664617a09477ca08d6cf7e26d892cb722d2734 100644
--- a/data/solutions/generated/triinhex_018_7671cfd644a7af24.json
+++ b/data/solutions/generated/triinhex_018_7671cfd644a7af24.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.0747364477878956,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.8888888888888888,
     "source_image_url": "https://erich-friedman.github.io/packing/triinhex/18.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinhex_020_388fc73ef451e99b.json b/data/solutions/generated/triinhex_020_388fc73ef451e99b.json
index 175e33a52a0f1ad8ccc88dfbc7b88eeaf4ac5e98..c2014c801d6f0fc8146fee179a43f6ae0251dfab 100644
--- a/data/solutions/generated/triinhex_020_388fc73ef451e99b.json
+++ b/data/solutions/generated/triinhex_020_388fc73ef451e99b.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.036343051574550145,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.97591,
     "source_image_url": "https://erich-friedman.github.io/packing/triinhex/20.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T02:51:36+00:00",
diff --git a/data/solutions/generated/triinhex_021_96f74df50573bb81.json b/data/solutions/generated/triinhex_021_96f74df50573bb81.json
index 591839bc74c0a12c86b6493f5a60f35f6207d08a..bff1e55a148a34155d9faffa0058a059f57d4659 100644
--- a/data/solutions/generated/triinhex_021_96f74df50573bb81.json
+++ b/data/solutions/generated/triinhex_021_96f74df50573bb81.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.99878,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ian Watson"
diff --git a/data/solutions/generated/triinhex_022_38182a59461da74e.json b/data/solutions/generated/triinhex_022_38182a59461da74e.json
index 754cf1bd1bdde8cbeca85b6eaedf0bb8e6e485ef..4312f1d7872dc6b6ff715b9ea947010dcae4e4ab 100644
--- a/data/solutions/generated/triinhex_022_38182a59461da74e.json
+++ b/data/solutions/generated/triinhex_022_38182a59461da74e.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triinhex_023_dcd331994270a997.json b/data/solutions/generated/triinhex_023_dcd331994270a997.json
index 0ee2290492ab03f21900b06c312bec55f5a14ad7..7cbd5a2eeb30dc238fd9dce9d65a54ea78d8f914 100644
--- a/data/solutions/generated/triinhex_023_dcd331994270a997.json
+++ b/data/solutions/generated/triinhex_023_dcd331994270a997.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triinhex_024_13936a08bfd4d152.json b/data/solutions/generated/triinhex_024_13936a08bfd4d152.json
index be25c9c60d6fb9ef99e5242d33b5be4e3de1275d..99d076f3e6cdfd6942387b71e6db05eba97637e9 100644
--- a/data/solutions/generated/triinhex_024_13936a08bfd4d152.json
+++ b/data/solutions/generated/triinhex_024_13936a08bfd4d152.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triinhex_025_71a7801cfb4a8d31.json b/data/solutions/generated/triinhex_025_71a7801cfb4a8d31.json
index 7900702327845fea9190f377ebc0525cb446be05..7c983270813b6013da445e0ccc771c1ae66e54d6 100644
--- a/data/solutions/generated/triinhex_025_71a7801cfb4a8d31.json
+++ b/data/solutions/generated/triinhex_025_71a7801cfb4a8d31.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.1666666666666665,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinhex_026_658d7f93b604b663.json b/data/solutions/generated/triinhex_026_658d7f93b604b663.json
index 41950d9546b44448c9ae2cca1da76d34f7ce219e..02c017631425252ba49eef2f579c5084c15bfb5c 100644
--- a/data/solutions/generated/triinhex_026_658d7f93b604b663.json
+++ b/data/solutions/generated/triinhex_026_658d7f93b604b663.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.21991,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ian Watson"
diff --git a/data/solutions/generated/triinhex_027_ace1d8ac458c5bc4.json b/data/solutions/generated/triinhex_027_ace1d8ac458c5bc4.json
index 3c8325a4d5abe97e70a7e7f3032b2e81ab931fca..1833dc4e54e0d69be4eda28134b8298876c2447e 100644
--- a/data/solutions/generated/triinhex_027_ace1d8ac458c5bc4.json
+++ b/data/solutions/generated/triinhex_027_ace1d8ac458c5bc4.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.02629142958836626,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.29541,
     "source_image_url": "https://erich-friedman.github.io/packing/triinhex/27.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinhex_032_8674581436e5e74d.json b/data/solutions/generated/triinhex_032_8674581436e5e74d.json
index c67d7692e665effd9d54047ad1896c5bb1ccd21b..c6b6467292358196228037565c29518cd5d9a6dc 100644
--- a/data/solutions/generated/triinhex_032_8674581436e5e74d.json
+++ b/data/solutions/generated/triinhex_032_8674581436e5e74d.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.465,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/triinhex_033_5b836a27d2bb958c.json b/data/solutions/generated/triinhex_033_5b836a27d2bb958c.json
index b8e4fa3736f16f4fc92c096008a2cefc8e76a85b..e04144a70805284413797efc663c4d2a5603ce14 100644
--- a/data/solutions/generated/triinhex_033_5b836a27d2bb958c.json
+++ b/data/solutions/generated/triinhex_033_5b836a27d2bb958c.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.498,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/triinhex_034_a712744ff3b5bcc9.json b/data/solutions/generated/triinhex_034_a712744ff3b5bcc9.json
index 9d8fce4667624a891d460c45a182e46533b5a5d1..bb103a004a0cabb3f862f77051f09a52a3dd721a 100644
--- a/data/solutions/generated/triinhex_034_a712744ff3b5bcc9.json
+++ b/data/solutions/generated/triinhex_034_a712744ff3b5bcc9.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.5,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/triinhex_038_76fd196e8c79a5c9.json b/data/solutions/generated/triinhex_038_76fd196e8c79a5c9.json
index c0b31b22aa76ebd51d239eafd20bf419a5d920b2..5d7bab5253502d1aa0dabc7b6098034fc41f6a73 100644
--- a/data/solutions/generated/triinhex_038_76fd196e8c79a5c9.json
+++ b/data/solutions/generated/triinhex_038_76fd196e8c79a5c9.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.6666666666666665,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/triinhex_14_dbfe389f1c3777d5.json b/data/solutions/generated/triinhex_14_dbfe389f1c3777d5.json
index c7ae2b9a03597bb025c0bade21e72009963869b7..627817c6d1a711ed9f8281e2070356b44b7164ca 100644
--- a/data/solutions/generated/triinhex_14_dbfe389f1c3777d5.json
+++ b/data/solutions/generated/triinhex_14_dbfe389f1c3777d5.json
@@ -49,7 +49,10 @@
     "generator_profile": "cg_precise",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_20260501T070815Z_broad.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.725,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T07:13:53+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/triinhex_19_451018f1291a5791.json b/data/solutions/generated/triinhex_19_451018f1291a5791.json
index b8a25db11ac36290a402c9246d39ab0494bfea87..3e1bbe97036d21a31f71901a797af240944348eb 100644
--- a/data/solutions/generated/triinhex_19_451018f1291a5791.json
+++ b/data/solutions/generated/triinhex_19_451018f1291a5791.json
@@ -49,7 +49,10 @@
     "generator_profile": "cg_precise",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_20260501T070815Z_broad.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.953,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T07:13:53+00:00",
     "submitted_by": "Alex Adri\u00e1n Nieto"
diff --git a/data/solutions/generated/triinhex_19_545ef4899aee40a3.json b/data/solutions/generated/triinhex_19_545ef4899aee40a3.json
new file mode 100644
index 0000000000000000000000000000000000000000..5c2b25d5d06db0f2b0ef58c08de78bd590cd27cc
--- /dev/null
+++ b/data/solutions/generated/triinhex_19_545ef4899aee40a3.json
@@ -0,0 +1,181 @@
+{
+  "case": "triinhex@19",
+  "container": {
+    "circumradius": 1.954596799569544,
+    "orientation_radians": 0.0,
+    "side_length": 1.9545967995695437,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinhex@19",
+    "credit": "Alex Adri\u00e1n Nieto",
+    "date": "April 2026",
+    "family_updated": "",
+    "metric_expression": "1.953+",
+    "metric_symbol": "s",
+    "metric_value": 1.953,
+    "reference_text": "s = 1.953+ | Found by Alex Adri\u00e1n Nieto | in April 2026.",
+    "source_image": "19.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/19.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinhex@19",
+      "credit": "Alex Adri\u00e1n Nieto",
+      "date": "April 2026",
+      "family_updated": "",
+      "metric_expression": "1.953+",
+      "metric_symbol": "s",
+      "metric_value": 1.953,
+      "reference_text": "s = 1.953+ | Found by Alex Adri\u00e1n Nieto | in April 2026.",
+      "source_image": "19.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/19.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles in Hexagons"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "sa_tight",
+    "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_20260501_systematic_deep_deep.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.953,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/triinhex_019_20260501_systematic_deep_sa_tight.state",
+    "source_url": "https://erich-friedman.github.io/packing/triinhex/",
+    "submitted_at": "2026-05-01T16:53:45+00:00",
+    "submitted_by": "Alex Adri\u00e1n Nieto"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.5291923669798881,
+      "x": 0.922758002983556,
+      "y": 0.5318030069988752
+    },
+    {
+      "id": 2,
+      "rotation_radians": 1.5707837918626064,
+      "x": 1.4318201406459083,
+      "y": 0.24929370794778083
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.5235773772852302,
+      "x": -1.4090873106370172,
+      "y": -0.3674619578182861
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.5148875249862606,
+      "x": -0.836461366469633,
+      "y": -1.1077257424491322
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.5235849564535762,
+      "x": -0.5000109889462562,
+      "y": 1.364661185521821
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.5235864980431506,
+      "x": 1.431839800422515,
+      "y": -0.3280740801843647
+    },
+    {
+      "id": 7,
+      "rotation_radians": 1.5640312588343734,
+      "x": -0.3376286974726305,
+      "y": -1.4006663349695712
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.6153812552500361,
+      "x": -0.12764913432393876,
+      "y": -0.6146487313257687
+    },
+    {
+      "id": 9,
+      "rotation_radians": 1.5708002128971232,
+      "x": 0.9773022553692444,
+      "y": 1.1153514065767844
+    },
+    {
+      "id": 10,
+      "rotation_radians": 1.0533520619949361,
+      "x": 0.7316485788561503,
+      "y": -0.6891550672383707
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.5235894264709977,
+      "x": 0.4772789403557856,
+      "y": 1.404044070921621
+    },
+    {
+      "id": 12,
+      "rotation_radians": 1.681299804285026,
+      "x": -0.5039845448432161,
+      "y": -0.06207226854593359
+    },
+    {
+      "id": 13,
+      "rotation_radians": 1.6944366683041319,
+      "x": 0.48544454840047174,
+      "y": 0.03745971584108592
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.6477396117169718,
+      "x": -0.035855550391996484,
+      "y": 0.28778612565101613
+    },
+    {
+      "id": 15,
+      "rotation_radians": 1.706592301865917,
+      "x": -0.03019400280582519,
+      "y": 0.8878945202931267
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.57077489090034,
+      "x": -1.4090975370875232,
+      "y": 0.20991965788359782
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.006154206045375786,
+      "x": 0.44604259257031764,
+      "y": -1.1909424639247714
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.5707824638924548,
+      "x": -1.0000322009291815,
+      "y": 1.0759840411284434
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.5235775453652464,
+      "x": -0.9090683124014294,
+      "y": 0.498599836642046
+    }
+  ],
+  "problem": "19 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/19.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinhex_28_3435500023858121.json b/data/solutions/generated/triinhex_28_3435500023858121.json
index 431ff7f8b14a89730c501c07d657e7a2ed0a305b..4dcdeb729ca90cf47b0ae182415fb001de280825 100644
--- a/data/solutions/generated/triinhex_28_3435500023858121.json
+++ b/data/solutions/generated/triinhex_28_3435500023858121.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.05683594732720138,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.32289,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Ian Watson"
diff --git a/data/solutions/generated/triinhex_29_4339d1ebd3160f94.json b/data/solutions/generated/triinhex_29_4339d1ebd3160f94.json
index 3b9dc32d92e4eaf76bd90e3ffee32f2a99ec1473..3ebc5fc99165337857c59fcd49f60b5f71452cb4 100644
--- a/data/solutions/generated/triinhex_29_4339d1ebd3160f94.json
+++ b/data/solutions/generated/triinhex_29_4339d1ebd3160f94.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.07906520028491007,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.3333333333333335,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinhex_30_7274d354e73d8050.json b/data/solutions/generated/triinhex_30_7274d354e73d8050.json
index 656e2fc07435f9f0cb4ed9e0d418b8a44c5e30e6..98c38e9eb28da78c343be05ffad196550bbd3e26 100644
--- a/data/solutions/generated/triinhex_30_7274d354e73d8050.json
+++ b/data/solutions/generated/triinhex_30_7274d354e73d8050.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.08866036628188438,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.375,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinhex_31_cae7087451040120.json b/data/solutions/generated/triinhex_31_cae7087451040120.json
index f49567374e318ebc6ea9cb8ff9358683db412cc2..5c9b002f794303df229750d7eca550508773831c 100644
--- a/data/solutions/generated/triinhex_31_cae7087451040120.json
+++ b/data/solutions/generated/triinhex_31_cae7087451040120.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.11402163884943653,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.4,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/triinhex_35_ec49778cf450c37b.json b/data/solutions/generated/triinhex_35_ec49778cf450c37b.json
index 0c7a2727f173f98a0be53f1cd6c5467bbad84c74..615546cdd13714f0adca7468906828d7ca365f4d 100644
--- a/data/solutions/generated/triinhex_35_ec49778cf450c37b.json
+++ b/data/solutions/generated/triinhex_35_ec49778cf450c37b.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.1187725404681634,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.5,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/triinhex_39_a314b4bb8467e5e8.json b/data/solutions/generated/triinhex_39_a314b4bb8467e5e8.json
index 92f2019a350b0da87275304323dcdaaf8af222d7..34a0eb8c55e4f82affea0b4bf3bc1da9877e5f27 100644
--- a/data/solutions/generated/triinhex_39_a314b4bb8467e5e8.json
+++ b/data/solutions/generated/triinhex_39_a314b4bb8467e5e8.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.1266590371552492,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.6666666666666665,
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/triinoct_001_92c66f395ff03ab9.json b/data/solutions/generated/triinoct_001_92c66f395ff03ab9.json
index 3d7db36d7a7a0c7e47403274f10668e7894ab7cf..e4371e478b1dc0b1c35c758ee20d8211d4f22fdb 100644
--- a/data/solutions/generated/triinoct_001_92c66f395ff03ab9.json
+++ b/data/solutions/generated/triinoct_001_92c66f395ff03ab9.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.4647,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triinoct_002_5706480ca6648c20.json b/data/solutions/generated/triinoct_002_5706480ca6648c20.json
index 22acc3a8077dce566f9756b4ddf4f325eacdae0c..3153b109583a4edb638c53b36b8cd6367c5f782c 100644
--- a/data/solutions/generated/triinoct_002_5706480ca6648c20.json
+++ b/data/solutions/generated/triinoct_002_5706480ca6648c20.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.6628271480711836,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triinoct_003_f3eee07e4d3df15b.json b/data/solutions/generated/triinoct_003_f3eee07e4d3df15b.json
index bba2143e01443cc15e535cfa4cd93d8c7b482f6f..84fdd64f4a75a8068f18e795214704083a0960ae 100644
--- a/data/solutions/generated/triinoct_003_f3eee07e4d3df15b.json
+++ b/data/solutions/generated/triinoct_003_f3eee07e4d3df15b.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.73651,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinoct_004_daeed392d4fde104.json b/data/solutions/generated/triinoct_004_daeed392d4fde104.json
index add910a587668f2132fc6682241ca36040925755..07cedcb8e760606f1a0a5086ed9728e8fadda605 100644
--- a/data/solutions/generated/triinoct_004_daeed392d4fde104.json
+++ b/data/solutions/generated/triinoct_004_daeed392d4fde104.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.77733,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinoct_005_a0addde9772ff582.json b/data/solutions/generated/triinoct_005_a0addde9772ff582.json
index 1f90ef82d176174239a63a31b9d21bb52f48b25a..be7d53eb835f976bf4e661c7a9389d99e3d18ae8 100644
--- a/data/solutions/generated/triinoct_005_a0addde9772ff582.json
+++ b/data/solutions/generated/triinoct_005_a0addde9772ff582.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.80367,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinoct_006_e7ac2b490b8118b6.json b/data/solutions/generated/triinoct_006_e7ac2b490b8118b6.json
index 47a5639963e8c12cddf5f5aa1ba85c38735cfdf5..5a1a63c5f4bdfc15a4902a5fa4329ada2670f45b 100644
--- a/data/solutions/generated/triinoct_006_e7ac2b490b8118b6.json
+++ b/data/solutions/generated/triinoct_006_e7ac2b490b8118b6.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.81574,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinoct_007_f1951fc893682894.json b/data/solutions/generated/triinoct_007_f1951fc893682894.json
index 976c225199cbf7ba001e87c10cc3309cb164a747..d0974709f0c1098352712abca0fc82c860dfa332 100644
--- a/data/solutions/generated/triinoct_007_f1951fc893682894.json
+++ b/data/solutions/generated/triinoct_007_f1951fc893682894.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.92453,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinoct_008_cdfdb28bbd7c958a.json b/data/solutions/generated/triinoct_008_cdfdb28bbd7c958a.json
index fd44b4936aa2b876950197fb4cda58af78bad450..b21b4a95be067947c05af2c69777e0d554199448 100644
--- a/data/solutions/generated/triinoct_008_cdfdb28bbd7c958a.json
+++ b/data/solutions/generated/triinoct_008_cdfdb28bbd7c958a.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.98782,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinoct_009_0a4766beda41f84b.json b/data/solutions/generated/triinoct_009_0a4766beda41f84b.json
index 9e9c7204e5154630ad4469e307302db56d95429b..2aefa779d27bc6e5953fc9785baa32bd751d9d0a 100644
--- a/data/solutions/generated/triinoct_009_0a4766beda41f84b.json
+++ b/data/solutions/generated/triinoct_009_0a4766beda41f84b.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.00875,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinoct_010_df6976316812d041.json b/data/solutions/generated/triinoct_010_df6976316812d041.json
index 5db4d096bded14966dbd9e1768e525cba517421a..d5bcc6c54cfc5298be72e2e8735b502ffec4746b 100644
--- a/data/solutions/generated/triinoct_010_df6976316812d041.json
+++ b/data/solutions/generated/triinoct_010_df6976316812d041.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.07565,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinoct_011_11036479a300844a.json b/data/solutions/generated/triinoct_011_11036479a300844a.json
index 997de64deab1e452e5b8d49546efef0b87f42f6b..7e5a1013e453f9b0769d8a3709b09033a148688e 100644
--- a/data/solutions/generated/triinoct_011_11036479a300844a.json
+++ b/data/solutions/generated/triinoct_011_11036479a300844a.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.14571,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinoct_012_1fa5264e0f579a94.json b/data/solutions/generated/triinoct_012_1fa5264e0f579a94.json
index cc107b411c8f7f3e70515350f209fdf633e7b134..5fedfd0bcaf007aff126a268e152c62b48ec80d8 100644
--- a/data/solutions/generated/triinoct_012_1fa5264e0f579a94.json
+++ b/data/solutions/generated/triinoct_012_1fa5264e0f579a94.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.19929,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinoct_013_ebb5825b80b24749.json b/data/solutions/generated/triinoct_013_ebb5825b80b24749.json
index 43b3c4b0ddf6a6756c06e3e38a086617b9b441f8..907f4acee42b03473ecdf35fcea6c0e16d7a259f 100644
--- a/data/solutions/generated/triinoct_013_ebb5825b80b24749.json
+++ b/data/solutions/generated/triinoct_013_ebb5825b80b24749.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.23759,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinoct_014_e00a18106d2fcfee.json b/data/solutions/generated/triinoct_014_e00a18106d2fcfee.json
index 9e351e0e0e8fe9f13773d57b74bdec83df50a3d8..660e165e4cd633682badf410adee9b151d95fd81 100644
--- a/data/solutions/generated/triinoct_014_e00a18106d2fcfee.json
+++ b/data/solutions/generated/triinoct_014_e00a18106d2fcfee.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.048299233655801375,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.27677,
     "source_image_url": "https://erich-friedman.github.io/packing/triinoct/14.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinoct_015_e14eda962017d06d.json b/data/solutions/generated/triinoct_015_e14eda962017d06d.json
index 3d7085225440edab6cff6b0c223fdffab3cdb43d..64d70f596b30b341297b46e60afe8737095ef8e5 100644
--- a/data/solutions/generated/triinoct_015_e14eda962017d06d.json
+++ b/data/solutions/generated/triinoct_015_e14eda962017d06d.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.30275,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinoct_017_6f00b933407c7c80.json b/data/solutions/generated/triinoct_017_6f00b933407c7c80.json
index 02be0d7a7a955a8d5d710c0bbf2b83cc0f2eb3e0..3d0ab5f4013ea23baf2425210ce45938d368663f 100644
--- a/data/solutions/generated/triinoct_017_6f00b933407c7c80.json
+++ b/data/solutions/generated/triinoct_017_6f00b933407c7c80.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.06354508480755121,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.38964,
     "source_image_url": "https://erich-friedman.github.io/packing/triinoct/17.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinoct_018_91a694d1aa76789c.json b/data/solutions/generated/triinoct_018_91a694d1aa76789c.json
index d2258f70b712693dba3f1201b62eeeaadbe2af66..4bd7778c992177f76850436f33dbd2e69151c3af 100644
--- a/data/solutions/generated/triinoct_018_91a694d1aa76789c.json
+++ b/data/solutions/generated/triinoct_018_91a694d1aa76789c.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.05221543036937463,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.41836,
     "source_image_url": "https://erich-friedman.github.io/packing/triinoct/18.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinoct_019_f92a5a5a3b54909a.json b/data/solutions/generated/triinoct_019_f92a5a5a3b54909a.json
index b9656a4000a427400ed69f1171aaef0ed976cd56..646fdc4863de6f40aa0f83d2f6e9a8f4faf5b06f 100644
--- a/data/solutions/generated/triinoct_019_f92a5a5a3b54909a.json
+++ b/data/solutions/generated/triinoct_019_f92a5a5a3b54909a.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.055514025546928615,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.46749,
     "source_image_url": "https://erich-friedman.github.io/packing/triinoct/19.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinoct_020_ead92a925f9f00a7.json b/data/solutions/generated/triinoct_020_ead92a925f9f00a7.json
index 73775cc31ecb4cf71703397ac15a8fb030f51b0c..b9f781fbddb5bf89b83fa13f892c683fde9f91b2 100644
--- a/data/solutions/generated/triinoct_020_ead92a925f9f00a7.json
+++ b/data/solutions/generated/triinoct_020_ead92a925f9f00a7.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.04759130191122192,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.49832,
     "source_image_url": "https://erich-friedman.github.io/packing/triinoct/20.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinoct_021_e350f46688d32a68.json b/data/solutions/generated/triinoct_021_e350f46688d32a68.json
index a5f3a6695561e04e5ad3f601dfd57181553a390a..8350695d4aff8f1338ba2c567108b7ed8a3da5a6 100644
--- a/data/solutions/generated/triinoct_021_e350f46688d32a68.json
+++ b/data/solutions/generated/triinoct_021_e350f46688d32a68.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.05773308853105992,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.52615,
     "source_image_url": "https://erich-friedman.github.io/packing/triinoct/21.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinoct_022_c1314ed0099ebdb6.json b/data/solutions/generated/triinoct_022_c1314ed0099ebdb6.json
index 5a0f1c9b2f95317fe053582c110dcd5e3cb7a9ad..c030be5be9c36941dc8f3f493c95062a4a5e665e 100644
--- a/data/solutions/generated/triinoct_022_c1314ed0099ebdb6.json
+++ b/data/solutions/generated/triinoct_022_c1314ed0099ebdb6.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.059386500034706115,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.55545,
     "source_image_url": "https://erich-friedman.github.io/packing/triinoct/22.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinoct_023_4ca1a825a22b1f04.json b/data/solutions/generated/triinoct_023_4ca1a825a22b1f04.json
index 62c72bed41349623d3aa730907364cb4012eda2b..8e9dea6c7481910411b8c35a391af6642351012b 100644
--- a/data/solutions/generated/triinoct_023_4ca1a825a22b1f04.json
+++ b/data/solutions/generated/triinoct_023_4ca1a825a22b1f04.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.58458,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinoct_024_e197b92ecac28558.json b/data/solutions/generated/triinoct_024_e197b92ecac28558.json
index d03f8334b69503556548d20a37a9076c9f1f6b69..8f9b0af47e563fa2e14441062751a02ce8eda8ec 100644
--- a/data/solutions/generated/triinoct_024_e197b92ecac28558.json
+++ b/data/solutions/generated/triinoct_024_e197b92ecac28558.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.60261,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinoct_025_e322401fc5bafe4d.json b/data/solutions/generated/triinoct_025_e322401fc5bafe4d.json
index a5d1408ba59fe985d8c84347c32c8240085d0544..ad420263d4853f432639f5393fd5100f4ed4c472 100644
--- a/data/solutions/generated/triinoct_025_e322401fc5bafe4d.json
+++ b/data/solutions/generated/triinoct_025_e322401fc5bafe4d.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.04886337169919019,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.63797,
     "source_image_url": "https://erich-friedman.github.io/packing/triinoct/25.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinoct_026_7cb3797cd10b21d8.json b/data/solutions/generated/triinoct_026_7cb3797cd10b21d8.json
index d253f2228da24eb373434cd705cdd570f01d433c..279ad05f2bb508b6406cc91205b4fb8ce666e47e 100644
--- a/data/solutions/generated/triinoct_026_7cb3797cd10b21d8.json
+++ b/data/solutions/generated/triinoct_026_7cb3797cd10b21d8.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.05274189496394424,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.67666,
     "source_image_url": "https://erich-friedman.github.io/packing/triinoct/26.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinoct_028_26e8795d82a701d8.json b/data/solutions/generated/triinoct_028_26e8795d82a701d8.json
index cd0b91cf7496640ba6e54870b3c41c0583883103..dc92a8be7e2bece6b59881972b0c042337118b69 100644
--- a/data/solutions/generated/triinoct_028_26e8795d82a701d8.json
+++ b/data/solutions/generated/triinoct_028_26e8795d82a701d8.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.048915539137173426,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.73954,
     "source_image_url": "https://erich-friedman.github.io/packing/triinoct/28.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinoct_030_4c08385c68f67e77.json b/data/solutions/generated/triinoct_030_4c08385c68f67e77.json
index 592b4193c895872b6f05d467dfab5629daaeedfa..5e3135dc785e69fbda9e126ce50c532a1c444331 100644
--- a/data/solutions/generated/triinoct_030_4c08385c68f67e77.json
+++ b/data/solutions/generated/triinoct_030_4c08385c68f67e77.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.05008166777349011,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.78101,
     "source_image_url": "https://erich-friedman.github.io/packing/triinoct/30.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinoct_16_640352ab60961c58.json b/data/solutions/generated/triinoct_16_640352ab60961c58.json
index b1dfd6fe411479f463ea8d2762412d6907101883..5a1429c53e3140842f34c3744a9f56e4b66d1a9b 100644
--- a/data/solutions/generated/triinoct_16_640352ab60961c58.json
+++ b/data/solutions/generated/triinoct_16_640352ab60961c58.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.03902795442976851,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.34584,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinoct_27_c7748eb19b34ff2e.json b/data/solutions/generated/triinoct_27_c7748eb19b34ff2e.json
index 551230313618ad9d23587c8d4264e11f123cb763..4274a6f48cbd0cc44659caaa9ce2c91f45b48dbf 100644
--- a/data/solutions/generated/triinoct_27_c7748eb19b34ff2e.json
+++ b/data/solutions/generated/triinoct_27_c7748eb19b34ff2e.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.06039550865866634,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.70882,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinoct_29_0575780ea85d68dd.json b/data/solutions/generated/triinoct_29_0575780ea85d68dd.json
index 860b45c586aa7bdeaef6b315460068886d82ff13..1aa621e5e33051e9ac27cf9d1b12c6205b234a3c 100644
--- a/data/solutions/generated/triinoct_29_0575780ea85d68dd.json
+++ b/data/solutions/generated/triinoct_29_0575780ea85d68dd.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.0764865704215557,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.75576,
     "source_url": "https://erich-friedman.github.io/packing/triinoct/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinpen_001_6d3af7533c544064.json b/data/solutions/generated/triinpen_001_6d3af7533c544064.json
index 80de1805d1a6114e67480c1e0cece1f169a13626..aad5a282bb617dbc28acf7e7cd1a0d7228a8e8ac 100644
--- a/data/solutions/generated/triinpen_001_6d3af7533c544064.json
+++ b/data/solutions/generated/triinpen_001_6d3af7533c544064.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.781,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triinpen_002_eebb278fed1959e5.json b/data/solutions/generated/triinpen_002_eebb278fed1959e5.json
index e31fcca4ec57337bfe9504e3531ed34d4f573477..234bceac72297512802554b9fa478ead1c884df1 100644
--- a/data/solutions/generated/triinpen_002_eebb278fed1959e5.json
+++ b/data/solutions/generated/triinpen_002_eebb278fed1959e5.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.07,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triinpen_003_6ec3c588fb678646.json b/data/solutions/generated/triinpen_003_6ec3c588fb678646.json
index 5fc3ec3a6a69f2815b229c025580b4c59b0e1f23..63bbd6bf1b6ee80ec27646b7ee05b42a09c04e1b 100644
--- a/data/solutions/generated/triinpen_003_6ec3c588fb678646.json
+++ b/data/solutions/generated/triinpen_003_6ec3c588fb678646.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.143,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/triinpen_004_c45dd63fd5a8806b.json b/data/solutions/generated/triinpen_004_c45dd63fd5a8806b.json
index a5fe948a2b467d575424e6107780a7f9ce6123bc..97ab457f8354b1374eae27c6ff1904b877d4aa41 100644
--- a/data/solutions/generated/triinpen_004_c45dd63fd5a8806b.json
+++ b/data/solutions/generated/triinpen_004_c45dd63fd5a8806b.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.199,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/triinpen_005_a99f063702c9d4e8.json b/data/solutions/generated/triinpen_005_a99f063702c9d4e8.json
index bf83d267c85e7e957554983afc78853008520782..4fb4c1a75035a5cc96c0ab2e0e1de37fe1e5a6a8 100644
--- a/data/solutions/generated/triinpen_005_a99f063702c9d4e8.json
+++ b/data/solutions/generated/triinpen_005_a99f063702c9d4e8.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.24,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triinpen_006_8d12939187f41554.json b/data/solutions/generated/triinpen_006_8d12939187f41554.json
index bd1fa112d1c58c26099b341da52c1dc5285d2297..cdd510ca146639e0c10d1b947fd09a174f4c9528 100644
--- a/data/solutions/generated/triinpen_006_8d12939187f41554.json
+++ b/data/solutions/generated/triinpen_006_8d12939187f41554.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.060796548531019554,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.393,
     "source_image_url": "https://erich-friedman.github.io/packing/triinpen/6.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinpen_007_d149692a95cde76c.json b/data/solutions/generated/triinpen_007_d149692a95cde76c.json
index 692d7a8a384ce0970e83bb981e7d2889f8b1a91c..fd103e8126c0483e06f94b214aa155e52be6bd46 100644
--- a/data/solutions/generated/triinpen_007_d149692a95cde76c.json
+++ b/data/solutions/generated/triinpen_007_d149692a95cde76c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.581,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/triinpen_008_2ac4629603f9ce00.json b/data/solutions/generated/triinpen_008_2ac4629603f9ce00.json
index 58c56bc19308e92ad445fecdda5f55b29e10b37f..cb4aacd93a957c13acc24e8678f69b6f46760cce 100644
--- a/data/solutions/generated/triinpen_008_2ac4629603f9ce00.json
+++ b/data/solutions/generated/triinpen_008_2ac4629603f9ce00.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.659,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/triinpen_009_72279a3b92ae69ca.json b/data/solutions/generated/triinpen_009_72279a3b92ae69ca.json
index fbb41f2078aeda8107602baad6cefa0f0e1db182..93b38a3762cfffb09718d816caae09947f8da59e 100644
--- a/data/solutions/generated/triinpen_009_72279a3b92ae69ca.json
+++ b/data/solutions/generated/triinpen_009_72279a3b92ae69ca.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.06850558764225709,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.767,
     "source_image_url": "https://erich-friedman.github.io/packing/triinpen/9.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinpen_010_f05f442bda1c650b.json b/data/solutions/generated/triinpen_010_f05f442bda1c650b.json
index a885c3c4c8f17f694a72c123e7d0b03ac9f47d23..b716e538e51bb7a932acfb3b7418f5f308ea901f 100644
--- a/data/solutions/generated/triinpen_010_f05f442bda1c650b.json
+++ b/data/solutions/generated/triinpen_010_f05f442bda1c650b.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.03611864790170327,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.815,
     "source_image_url": "https://erich-friedman.github.io/packing/triinpen/10.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinpen_011_ca41afc6c9b25b21.json b/data/solutions/generated/triinpen_011_ca41afc6c9b25b21.json
index b658ebd34f7cac04bbd0edaa9d715ba978739d9f..2e0697221b09ec5c5f3380106dce98e423832dad 100644
--- a/data/solutions/generated/triinpen_011_ca41afc6c9b25b21.json
+++ b/data/solutions/generated/triinpen_011_ca41afc6c9b25b21.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.871,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Timo Berthold et al"
diff --git a/data/solutions/generated/triinpen_012_bf7ddcc735398246.json b/data/solutions/generated/triinpen_012_bf7ddcc735398246.json
index c665c43554886759536701c7dbc14c2abcbc2964..ab11647ae2b244608532d7752fbefc91b447e279 100644
--- a/data/solutions/generated/triinpen_012_bf7ddcc735398246.json
+++ b/data/solutions/generated/triinpen_012_bf7ddcc735398246.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.973,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinpen_013_ff07ea08219353cb.json b/data/solutions/generated/triinpen_013_ff07ea08219353cb.json
index 0b5a8f2457c299c4e5621fac1fd9086efe4f3fcc..f69e83b7cff200aa1f13c6eb6f5d566a544097ca 100644
--- a/data/solutions/generated/triinpen_013_ff07ea08219353cb.json
+++ b/data/solutions/generated/triinpen_013_ff07ea08219353cb.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.01664347421335975,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.017,
     "source_image_url": "https://erich-friedman.github.io/packing/triinpen/13.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinpen_014_bc900c323229ee0c.json b/data/solutions/generated/triinpen_014_bc900c323229ee0c.json
index 639d7d7d8df9f2f95c4e0276cbf29e4bd92e3584..826a35eb70278827c9a8136fa79de4ae0d06b3a6 100644
--- a/data/solutions/generated/triinpen_014_bc900c323229ee0c.json
+++ b/data/solutions/generated/triinpen_014_bc900c323229ee0c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.088,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinpen_015_39b13eec51bf2ea6.json b/data/solutions/generated/triinpen_015_39b13eec51bf2ea6.json
index fc45587dba957a202411393b3a86f2dd961a2b54..3b32cd0e1d5783b8d0165ab01c1e367e42d7fda6 100644
--- a/data/solutions/generated/triinpen_015_39b13eec51bf2ea6.json
+++ b/data/solutions/generated/triinpen_015_39b13eec51bf2ea6.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.11289025481407901,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.123,
     "source_image_url": "https://erich-friedman.github.io/packing/triinpen/15.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinpen_016_852225bc33edeebe.json b/data/solutions/generated/triinpen_016_852225bc33edeebe.json
index 8b24c33ec895090638c0b68ff0d6059671550e51..30b3a3db1007c1411db684be2ad1ec7926f4b8b9 100644
--- a/data/solutions/generated/triinpen_016_852225bc33edeebe.json
+++ b/data/solutions/generated/triinpen_016_852225bc33edeebe.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.17598,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ian Watson"
diff --git a/data/solutions/generated/triinpen_017_a8618eee7fdaba2a.json b/data/solutions/generated/triinpen_017_a8618eee7fdaba2a.json
index f1e45b3ff56df427ec170effadafe329d6be4ee1..ab616f82fae812190d96e7f2630a5032927db350 100644
--- a/data/solutions/generated/triinpen_017_a8618eee7fdaba2a.json
+++ b/data/solutions/generated/triinpen_017_a8618eee7fdaba2a.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.01121388039917119,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.23658,
     "source_image_url": "https://erich-friedman.github.io/packing/triinpen/17.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinpen_018_6bf4f9b0915d39ee.json b/data/solutions/generated/triinpen_018_6bf4f9b0915d39ee.json
index d0134d36bc3ce644d48c27ed6e31c60816c00960..d748a2a8e2d61d1ef72c6fcab778437867009b88 100644
--- a/data/solutions/generated/triinpen_018_6bf4f9b0915d39ee.json
+++ b/data/solutions/generated/triinpen_018_6bf4f9b0915d39ee.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.024962265936740738,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.29382,
     "source_image_url": "https://erich-friedman.github.io/packing/triinpen/18.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinpen_020_760faebc4d0b131b.json b/data/solutions/generated/triinpen_020_760faebc4d0b131b.json
index 001dc04786848785d458a78887c592d18c79d5ad..0719f15c241ed49018ed61961caf545ad7e25bcb 100644
--- a/data/solutions/generated/triinpen_020_760faebc4d0b131b.json
+++ b/data/solutions/generated/triinpen_020_760faebc4d0b131b.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.4335,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ian Watson"
diff --git a/data/solutions/generated/triinpen_021_115c20fad199fe9d.json b/data/solutions/generated/triinpen_021_115c20fad199fe9d.json
index 651eab95c7b4dfd7e2c74e247e989219132af34e..1bce8885a4cbafb6b75ff3a15da1d87b480ac42d 100644
--- a/data/solutions/generated/triinpen_021_115c20fad199fe9d.json
+++ b/data/solutions/generated/triinpen_021_115c20fad199fe9d.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.479,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinpen_022_929a1aedb3cfabb6.json b/data/solutions/generated/triinpen_022_929a1aedb3cfabb6.json
index b1074a5e63d2c67afa5073d347e90b967996f53f..d37ab32de3f7786f8e8b5c9b8b85559d4735a830 100644
--- a/data/solutions/generated/triinpen_022_929a1aedb3cfabb6.json
+++ b/data/solutions/generated/triinpen_022_929a1aedb3cfabb6.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.02053744054583269,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.5674,
     "source_image_url": "https://erich-friedman.github.io/packing/triinpen/22.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinpen_023_c0d3905a26f7ef33.json b/data/solutions/generated/triinpen_023_c0d3905a26f7ef33.json
index 9c07722654aa6cd04b6796bc05de4678d1005dd4..cb555430703c9e138aaed5e9324de16ea3c11460 100644
--- a/data/solutions/generated/triinpen_023_c0d3905a26f7ef33.json
+++ b/data/solutions/generated/triinpen_023_c0d3905a26f7ef33.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.04053979977311972,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.61831,
     "source_image_url": "https://erich-friedman.github.io/packing/triinpen/23.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinpen_026_f991467944e6e634.json b/data/solutions/generated/triinpen_026_f991467944e6e634.json
index dcb4f1eeb6473e88f3e397673bb8d1b5c7eb875e..80a1a6376972915df477ff4647bb9e9eafff9ada 100644
--- a/data/solutions/generated/triinpen_026_f991467944e6e634.json
+++ b/data/solutions/generated/triinpen_026_f991467944e6e634.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.16670194484103726,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.771,
     "source_image_url": "https://erich-friedman.github.io/packing/triinpen/26.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinpen_027_d6f1d3073209f163.json b/data/solutions/generated/triinpen_027_d6f1d3073209f163.json
index 681985df64f1fe98b20dabb9b35add496e41d9a4..bbd9e0fad108ef4e113a77d498d4b1a57a6a6c2b 100644
--- a/data/solutions/generated/triinpen_027_d6f1d3073209f163.json
+++ b/data/solutions/generated/triinpen_027_d6f1d3073209f163.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.029041273698152757,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.81761,
     "source_image_url": "https://erich-friedman.github.io/packing/triinpen/27.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinpen_028_2caa877f5aa08139.json b/data/solutions/generated/triinpen_028_2caa877f5aa08139.json
index b1d3f71361725ee8773ca3c858a17db1e3f3f271..b7138996f347e4397e5b1576e59052776675c17f 100644
--- a/data/solutions/generated/triinpen_028_2caa877f5aa08139.json
+++ b/data/solutions/generated/triinpen_028_2caa877f5aa08139.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.18637867606681333,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.868,
     "source_image_url": "https://erich-friedman.github.io/packing/triinpen/28.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T03:19:00+00:00",
diff --git a/data/solutions/generated/triinpen_031_44a0bb3f581e92e2.json b/data/solutions/generated/triinpen_031_44a0bb3f581e92e2.json
index 351e162c53c8481364c811f0ffd5d9d42bb2ea40..5d5f3358f0b4412398f03dfb3d9d155302e87e8b 100644
--- a/data/solutions/generated/triinpen_031_44a0bb3f581e92e2.json
+++ b/data/solutions/generated/triinpen_031_44a0bb3f581e92e2.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.018022977390182646,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.992,
     "source_image_url": "https://erich-friedman.github.io/packing/triinpen/31.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinpen_032_310badf403ba4fce.json b/data/solutions/generated/triinpen_032_310badf403ba4fce.json
index f2ffd8f067888fc8b458f7d02b721002055f7943..5c8b413d2a3d369f4ad86e376713e3ca4a8ed618 100644
--- a/data/solutions/generated/triinpen_032_310badf403ba4fce.json
+++ b/data/solutions/generated/triinpen_032_310badf403ba4fce.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.011952682168381908,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.029,
     "source_image_url": "https://erich-friedman.github.io/packing/triinpen/32.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinpen_033_2cf1b1f38810795d.json b/data/solutions/generated/triinpen_033_2cf1b1f38810795d.json
index cda2c80b621a1102ff7fa52815d6cff4cb4e1111..8c6c4e0641a9507d037616fe001ca8cf916115e5 100644
--- a/data/solutions/generated/triinpen_033_2cf1b1f38810795d.json
+++ b/data/solutions/generated/triinpen_033_2cf1b1f38810795d.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.01854101751570289,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.078,
     "source_image_url": "https://erich-friedman.github.io/packing/triinpen/33.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinpen_035_8fe5da1df972c0b3.json b/data/solutions/generated/triinpen_035_8fe5da1df972c0b3.json
index 98ab2cc2f8eab51a6711baf208863861e657dcdb..453eb687e3849f0cd6168a2da5d887c899c3b056 100644
--- a/data/solutions/generated/triinpen_035_8fe5da1df972c0b3.json
+++ b/data/solutions/generated/triinpen_035_8fe5da1df972c0b3.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.016589303394093757,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.15,
     "source_image_url": "https://erich-friedman.github.io/packing/triinpen/35.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinpen_039_67a6bbf24108966a.json b/data/solutions/generated/triinpen_039_67a6bbf24108966a.json
index b6de0628fc5a8a270b1019fe013354d010b08076..5ee60c23cab469b0975256efd576c91ccbf9e95b 100644
--- a/data/solutions/generated/triinpen_039_67a6bbf24108966a.json
+++ b/data/solutions/generated/triinpen_039_67a6bbf24108966a.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.295,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/triinpen_19_16349db1062e3f6e.json b/data/solutions/generated/triinpen_19_16349db1062e3f6e.json
new file mode 100644
index 0000000000000000000000000000000000000000..623d6400eefa5824ff2cc0fbfc852a43bc4fe8f4
--- /dev/null
+++ b/data/solutions/generated/triinpen_19_16349db1062e3f6e.json
@@ -0,0 +1,181 @@
+{
+  "case": "triinpen@19",
+  "container": {
+    "circumradius": 1.994849109033647,
+    "orientation_radians": 0.0,
+    "side_length": 2.345085773677515,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@19",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "",
+    "metric_expression": "2.344+",
+    "metric_symbol": "s",
+    "metric_value": 2.344,
+    "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "19.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@19",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "",
+      "metric_expression": "2.344+",
+      "metric_symbol": "s",
+      "metric_value": 2.344,
+      "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "19.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "sa_escape",
+    "image_seed_recovery_log": "bench_outputs/current_best_recovery/current_best_recovery_20260501_near_deepx4_deep.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.344,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/triinpen_019_20260501_near_deepx4_sa_escape.state",
+    "source_url": "https://erich-friedman.github.io/packing/triinpen/",
+    "submitted_at": "2026-05-01T17:16:20+00:00",
+    "submitted_by": "Ignacio Vallejo"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.0466332418646862,
+      "x": -1.029245406103516,
+      "y": 0.9565281215781034
+    },
+    {
+      "id": 2,
+      "rotation_radians": -0.00018105846271675085,
+      "x": -0.4587961044692008,
+      "y": -0.04001635458418696
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.8377836706179262,
+      "x": 0.052527229633798064,
+      "y": 1.410430467170363
+    },
+    {
+      "id": 4,
+      "rotation_radians": 1.046737616760658,
+      "x": -0.1632209413793545,
+      "y": 0.4562008480406909
+    },
+    {
+      "id": 5,
+      "rotation_radians": 1.0471198009403149,
+      "x": -1.0362491518763137,
+      "y": -0.03981400430051956
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.34079371820468485,
+      "x": 0.7331317347912998,
+      "y": -1.1790155572172527
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.42624803171878495,
+      "x": 1.3338679178302473,
+      "y": -0.4123759561697349
+    },
+    {
+      "id": 8,
+      "rotation_radians": 1.0417402770719386,
+      "x": -0.07026694195208974,
+      "y": -0.48769726605262154
+    },
+    {
+      "id": 9,
+      "rotation_radians": 1.4248477465001446,
+      "x": 0.7534514842804939,
+      "y": -0.5799961758724699
+    },
+    {
+      "id": 10,
+      "rotation_radians": 2.0943532542046692,
+      "x": -1.3251546059421935,
+      "y": -0.5397382463275521
+    },
+    {
+      "id": 11,
+      "rotation_radians": 2.0890275462097696,
+      "x": 0.5105020822229773,
+      "y": 0.13715231398911415
+    },
+    {
+      "id": 12,
+      "rotation_radians": 1.6755124863926234,
+      "x": 1.4558321364026998,
+      "y": 0.2507560211096041
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.96140226748872,
+      "x": 0.8430813336863185,
+      "y": 0.6569735908472353
+    },
+    {
+      "id": 14,
+      "rotation_radians": 2.088937581343829,
+      "x": -0.36098778057775166,
+      "y": -0.9865159602299328
+    },
+    {
+      "id": 15,
+      "rotation_radians": 1.8849812844177278,
+      "x": 0.6087955236143662,
+      "y": 1.2504465351384009
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.0468059362080002,
+      "x": -0.9408964907568064,
+      "y": -0.9847996819442173
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.256640497052912,
+      "x": 0.14658476687089994,
+      "y": -1.441001557681813
+    },
+    {
+      "id": 18,
+      "rotation_radians": 2.094101686801884,
+      "x": -1.3249919615429757,
+      "y": 0.46031580673534783
+    },
+    {
+      "id": 19,
+      "rotation_radians": 2.0939351165269295,
+      "x": -0.4518155574893887,
+      "y": 0.9562564650934554
+    }
+  ],
+  "problem": "19 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/19.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_19_7110ea9122a5788e.json b/data/solutions/generated/triinpen_19_7110ea9122a5788e.json
new file mode 100644
index 0000000000000000000000000000000000000000..ad6b22839c8cef547acba71cb131971b8440f2d0
--- /dev/null
+++ b/data/solutions/generated/triinpen_19_7110ea9122a5788e.json
@@ -0,0 +1,181 @@
+{
+  "case": "triinpen@19",
+  "container": {
+    "circumradius": 1.996348109987661,
+    "orientation_radians": 0.0,
+    "side_length": 2.3468479549853987,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@19",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "",
+    "metric_expression": "2.344+",
+    "metric_symbol": "s",
+    "metric_value": 2.344,
+    "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "19.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@19",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "",
+      "metric_expression": "2.344+",
+      "metric_symbol": "s",
+      "metric_value": 2.344,
+      "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "19.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "cg_precise",
+    "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_20260501_systematic_broad.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.344,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/triinpen_019_20260501_systematic_cg_precise.state",
+    "source_url": "https://erich-friedman.github.io/packing/triinpen/",
+    "submitted_at": "2026-05-01T16:24:14+00:00",
+    "submitted_by": "Ignacio Vallejo"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.8312891178299343,
+      "x": 0.055636707675133894,
+      "y": -1.409331080886062
+    },
+    {
+      "id": 2,
+      "rotation_radians": -1.8737441020643768,
+      "x": 0.6146649661199185,
+      "y": -1.25268799772173
+    },
+    {
+      "id": 3,
+      "rotation_radians": -0.8351615295374215,
+      "x": -0.898551580955059,
+      "y": -1.101330296469593
+    },
+    {
+      "id": 4,
+      "rotation_radians": -1.8823541214750457,
+      "x": -0.33394093742373127,
+      "y": -0.9805644208473681
+    },
+    {
+      "id": 5,
+      "rotation_radians": -0.8265440059469552,
+      "x": 0.7869054620172002,
+      "y": -0.7016008266299458
+    },
+    {
+      "id": 6,
+      "rotation_radians": -1.8762037188794207,
+      "x": -1.2250015018976879,
+      "y": -0.6139060402181786
+    },
+    {
+      "id": 7,
+      "rotation_radians": -0.8289707644456836,
+      "x": -0.16404286399770107,
+      "y": -0.4247953225792019
+    },
+    {
+      "id": 8,
+      "rotation_radians": -1.6755268354309658,
+      "x": 1.3720522616881528,
+      "y": -0.36811878812105836
+    },
+    {
+      "id": 9,
+      "rotation_radians": -1.8737430007521911,
+      "x": 0.39577878354246376,
+      "y": -0.27689694959490824
+    },
+    {
+      "id": 10,
+      "rotation_radians": -0.8152285030367039,
+      "x": -1.0531673757979683,
+      "y": -0.05549339268965022
+    },
+    {
+      "id": 11,
+      "rotation_radians": -1.862418224353083,
+      "x": -0.49125786545702665,
+      "y": 0.07724649397842118
+    },
+    {
+      "id": 12,
+      "rotation_radians": -0.6283304911719632,
+      "x": 1.3638262525772447,
+      "y": 0.21330329931269476
+    },
+    {
+      "id": 13,
+      "rotation_radians": -0.8676328172463972,
+      "x": 0.24920829989147594,
+      "y": 0.452670427495019
+    },
+    {
+      "id": 14,
+      "rotation_radians": -2.0943940443143947,
+      "x": -1.3263937752050738,
+      "y": 0.5772710001931617
+    },
+    {
+      "id": 15,
+      "rotation_radians": -1.7854334610579992,
+      "x": 0.8710145338161583,
+      "y": 0.6076494248474186
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.15043185659612995,
+      "x": -0.3462562674388503,
+      "y": 0.8968039770247034
+    },
+    {
+      "id": 17,
+      "rotation_radians": -1.1976214171504738,
+      "x": -0.9039093053640039,
+      "y": 1.070484419176908
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.41714816650909203,
+      "x": 0.6849991756371147,
+      "y": 1.3123119642163306
+    },
+    {
+      "id": 19,
+      "rotation_radians": -1.2740286645557553,
+      "x": 0.01904662500872402,
+      "y": 1.3917417996553887
+    }
+  ],
+  "problem": "19 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/19.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_19_875caebde6570989.json b/data/solutions/generated/triinpen_19_875caebde6570989.json
new file mode 100644
index 0000000000000000000000000000000000000000..ced31bee470fbc2cbecdea53f716a0bd17d71cca
--- /dev/null
+++ b/data/solutions/generated/triinpen_19_875caebde6570989.json
@@ -0,0 +1,181 @@
+{
+  "case": "triinpen@19",
+  "container": {
+    "circumradius": 1.9960191497081092,
+    "orientation_radians": 0.0,
+    "side_length": 2.3464612389835775,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@19",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "",
+    "metric_expression": "2.344+",
+    "metric_symbol": "s",
+    "metric_value": 2.344,
+    "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "19.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@19",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "",
+      "metric_expression": "2.344+",
+      "metric_symbol": "s",
+      "metric_value": 2.344,
+      "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "19.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "cg_precise",
+    "image_seed_recovery_log": "bench_outputs/current_best_recovery/current_best_recovery_20260501_currentbest_deep_deep.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.344,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/triinpen_019_20260501_currentbest_deep_cg_precise.state",
+    "source_url": "https://erich-friedman.github.io/packing/triinpen/",
+    "submitted_at": "2026-05-01T17:13:54+00:00",
+    "submitted_by": "Ignacio Vallejo"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.8292006822007054,
+      "x": 0.054695422679350666,
+      "y": 1.4041674572405791
+    },
+    {
+      "id": 2,
+      "rotation_radians": 1.8766783243158354,
+      "x": 0.6126845326787379,
+      "y": 1.252805828636187
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.8316445672052594,
+      "x": -0.8997040401085926,
+      "y": 1.0988375593619484
+    },
+    {
+      "id": 4,
+      "rotation_radians": 1.8788417223121812,
+      "x": -0.33569480929680684,
+      "y": 0.9753415266583808
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.8294864829845428,
+      "x": 0.7865453896071749,
+      "y": 0.7022293471858784
+    },
+    {
+      "id": 6,
+      "rotation_radians": 1.8763873507115973,
+      "x": -1.2248172634398045,
+      "y": 0.6122848230683937
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.8279945585950615,
+      "x": -0.16342610096845123,
+      "y": 0.42234918952122497
+    },
+    {
+      "id": 8,
+      "rotation_radians": 1.6764463969846912,
+      "x": 1.3719451642647242,
+      "y": 0.3670324642232695
+    },
+    {
+      "id": 9,
+      "rotation_radians": 1.8766838500163592,
+      "x": 0.3964114583848773,
+      "y": 0.27661835634312454
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.8161595259981741,
+      "x": -1.052786424357969,
+      "y": 0.05433062424463462
+    },
+    {
+      "id": 11,
+      "rotation_radians": 1.8633564237860993,
+      "x": -0.49076377086194006,
+      "y": -0.07787716889777745
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.6292488671878557,
+      "x": 1.362048697504897,
+      "y": -0.21462925682861603
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.8691966891804842,
+      "x": 0.24903483237209897,
+      "y": -0.4529081183707143
+    },
+    {
+      "id": 14,
+      "rotation_radians": 2.0943988426119247,
+      "x": -1.3261319732913457,
+      "y": -0.5779037444284963
+    },
+    {
+      "id": 15,
+      "rotation_radians": 1.7796589360598796,
+      "x": 0.8739211113742065,
+      "y": -0.6100485208405761
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.14608396731364554,
+      "x": -0.34459938619761127,
+      "y": -0.8959774535356875
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.1928568818643481,
+      "x": -0.9030851315284298,
+      "y": -1.0680611287479065
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.4188761482505648,
+      "x": 0.6861048641277869,
+      "y": -1.3118027697391117
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.2697718929729374,
+      "x": 0.018166476250002003,
+      "y": -1.3928516173040908
+    }
+  ],
+  "problem": "19 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/19.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_19_e25d367759fc397e.json b/data/solutions/generated/triinpen_19_e25d367759fc397e.json
new file mode 100644
index 0000000000000000000000000000000000000000..d4399665c0628d77d8a2dde083bbe1474899e435
--- /dev/null
+++ b/data/solutions/generated/triinpen_19_e25d367759fc397e.json
@@ -0,0 +1,181 @@
+{
+  "case": "triinpen@19",
+  "container": {
+    "circumradius": 1.9948244487823792,
+    "orientation_radians": 0.0,
+    "side_length": 2.345056783813489,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@19",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "",
+    "metric_expression": "2.344+",
+    "metric_symbol": "s",
+    "metric_value": 2.344,
+    "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "19.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@19",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "",
+      "metric_expression": "2.344+",
+      "metric_symbol": "s",
+      "metric_value": 2.344,
+      "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "19.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "finite_diff_polish",
+    "image_seed_recovery_log": "bench_outputs/current_best_recovery/current_best_recovery_20260501_near_fdiffx6_finite-diff.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.344,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/triinpen_019_20260501_near_fdiffx6_finite_diff_polish.state",
+    "source_url": "https://erich-friedman.github.io/packing/triinpen/",
+    "submitted_at": "2026-05-01T17:17:49+00:00",
+    "submitted_by": "Ignacio Vallejo"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.0466428373110512,
+      "x": -1.0292243279823787,
+      "y": 0.9565027254924129
+    },
+    {
+      "id": 2,
+      "rotation_radians": -0.0001993777940115258,
+      "x": -0.4587930470428032,
+      "y": -0.04003215161350446
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.8377834036488128,
+      "x": 0.052516438556113994,
+      "y": 1.4104095841208166
+    },
+    {
+      "id": 4,
+      "rotation_radians": 1.0466992342900625,
+      "x": -0.16323031868900828,
+      "y": 0.45618347463039577
+    },
+    {
+      "id": 5,
+      "rotation_radians": 1.0471163861267356,
+      "x": -1.036224852487193,
+      "y": -0.03981114345744155
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.3407864247177903,
+      "x": 0.7331108362803258,
+      "y": -1.179008864087128
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.4262443556893314,
+      "x": 1.3338443002017206,
+      "y": -0.4123811347469655
+    },
+    {
+      "id": 8,
+      "rotation_radians": 1.041703779893808,
+      "x": -0.07027664231128412,
+      "y": -0.48768843110404025
+    },
+    {
+      "id": 9,
+      "rotation_radians": 1.4248331321567906,
+      "x": 0.7534276161553246,
+      "y": -0.5799992805515283
+    },
+    {
+      "id": 10,
+      "rotation_radians": 2.0943316933791754,
+      "x": -1.3251301027399518,
+      "y": -0.53971429626091
+    },
+    {
+      "id": 11,
+      "rotation_radians": 2.0890349650381888,
+      "x": 0.5105005473565881,
+      "y": 0.13714492488979022
+    },
+    {
+      "id": 12,
+      "rotation_radians": 1.6755125903754864,
+      "x": 1.4558185122823748,
+      "y": 0.25074527650193057
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.9614078437216754,
+      "x": 0.8430730652284746,
+      "y": 0.6569643454111526
+    },
+    {
+      "id": 14,
+      "rotation_radians": 2.088901372272836,
+      "x": -0.3609979737032685,
+      "y": -0.9865037272154208
+    },
+    {
+      "id": 15,
+      "rotation_radians": 1.884980890679839,
+      "x": 0.6087815096166009,
+      "y": 1.2504330819168097
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.0467821769471437,
+      "x": -0.9408993121006942,
+      "y": -0.9847789605192587
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.2566385516657632,
+      "x": 0.14657035322192316,
+      "y": -1.4409819503332981
+    },
+    {
+      "id": 18,
+      "rotation_radians": 2.0941025635515853,
+      "x": -1.324958172172872,
+      "y": 0.46030398985384924
+    },
+    {
+      "id": 19,
+      "rotation_radians": 2.0938967599969627,
+      "x": -0.4518219280323147,
+      "y": 0.9562322404643984
+    }
+  ],
+  "problem": "19 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/19.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_19_eaa1430599d74148.json b/data/solutions/generated/triinpen_19_eaa1430599d74148.json
index 2af475d11f77dd078157ea4fcca3d3069fd07375..cec29b39aa207a3e864cc54c9be05b2eef195059 100644
--- a/data/solutions/generated/triinpen_19_eaa1430599d74148.json
+++ b/data/solutions/generated/triinpen_19_eaa1430599d74148.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.19191760684266418,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.344,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinpen_24_7bc3466b163ec849.json b/data/solutions/generated/triinpen_24_7bc3466b163ec849.json
index e327c477c124bb34164de4e681b1ec93964051de..4a52e8b14f592c245560f60589f8a07f2fe82daf 100644
--- a/data/solutions/generated/triinpen_24_7bc3466b163ec849.json
+++ b/data/solutions/generated/triinpen_24_7bc3466b163ec849.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.018608034921599067,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.66641,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Ian Watson"
diff --git a/data/solutions/generated/triinpen_25_0f20f89eba855e21.json b/data/solutions/generated/triinpen_25_0f20f89eba855e21.json
index a918ea845a3624f354dad7c3927d083222e6acfc..3e8a7e78ee6d1884114a6c9c408f29f0aa022535 100644
--- a/data/solutions/generated/triinpen_25_0f20f89eba855e21.json
+++ b/data/solutions/generated/triinpen_25_0f20f89eba855e21.json
@@ -49,7 +49,10 @@
     "generator_profile": "sa_escape",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_current_broad_broad.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.72,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T13:47:12+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinpen_29_9730db96941e5b52.json b/data/solutions/generated/triinpen_29_9730db96941e5b52.json
index 55992759a23e8cd8da1784554e81ac23c1a41270..671c1db40261129368b6e94c5c9bb8ed50bdb90b 100644
--- a/data/solutions/generated/triinpen_29_9730db96941e5b52.json
+++ b/data/solutions/generated/triinpen_29_9730db96941e5b52.json
@@ -49,7 +49,10 @@
     "generator_profile": "sa_escape",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_20260501T070815Z_broad.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.903,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T07:13:53+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinpen_29_9da834ae740d1c15.json b/data/solutions/generated/triinpen_29_9da834ae740d1c15.json
new file mode 100644
index 0000000000000000000000000000000000000000..2eaf36aff6f79e560264acca952d285bc053ea45
--- /dev/null
+++ b/data/solutions/generated/triinpen_29_9da834ae740d1c15.json
@@ -0,0 +1,241 @@
+{
+  "case": "triinpen@29",
+  "container": {
+    "circumradius": 2.471129197065864,
+    "orientation_radians": 0.0,
+    "side_length": 2.904986597089311,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@29",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "",
+    "metric_expression": "2.903+",
+    "metric_symbol": "s",
+    "metric_value": 2.903,
+    "reference_text": "s = 2.903+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "29.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/29.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@29",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "",
+      "metric_expression": "2.903+",
+      "metric_symbol": "s",
+      "metric_value": 2.903,
+      "reference_text": "s = 2.903+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "29.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/29.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "sa_escape",
+    "image_seed_recovery_log": "bench_outputs/current_best_recovery/current_best_recovery_20260501_currentbest_deep_deep.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.903,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/triinpen_029_20260501_currentbest_deep_sa_escape.state",
+    "source_url": "https://erich-friedman.github.io/packing/triinpen/",
+    "submitted_at": "2026-05-01T17:13:54+00:00",
+    "submitted_by": "Ignacio Vallejo"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.8581219001594801,
+      "x": 0.5683424425602822,
+      "y": -1.8029566025216632
+    },
+    {
+      "id": 2,
+      "rotation_radians": 1.2566360900317277,
+      "x": -0.291938999146842,
+      "y": -1.703678572092261
+    },
+    {
+      "id": 3,
+      "rotation_radians": 1.256572418884671,
+      "x": -1.2430736480498976,
+      "y": -1.3945902031048236
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.20938530558188206,
+      "x": -0.6782923829593897,
+      "y": -1.2745817690870358
+    },
+    {
+      "id": 5,
+      "rotation_radians": 1.905043996194581,
+      "x": 0.37882197057794154,
+      "y": -1.2574206696748065
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.41887439723918557,
+      "x": 1.2086447816827235,
+      "y": -1.2465238991956082
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.1970455813452068,
+      "x": -1.61820558821218,
+      "y": -0.9474433744317148
+    },
+    {
+      "id": 8,
+      "rotation_radians": 1.2523922961998912,
+      "x": -0.2928912511564119,
+      "y": -0.79147609575058
+    },
+    {
+      "id": 9,
+      "rotation_radians": 1.4660706667811179,
+      "x": 1.2501883549106227,
+      "y": -0.670336957137898
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.8244847365277446,
+      "x": 0.4972638405974209,
+      "y": -0.5735412865654372
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.4179990244448404,
+      "x": 1.7818397095719642,
+      "y": -0.43591621989454193
+    },
+    {
+      "id": 12,
+      "rotation_radians": 1.2442425755253,
+      "x": -1.253488522504092,
+      "y": -0.4613790202984123
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.20514023276855184,
+      "x": -0.6802027674526382,
+      "y": -0.3632350634761098
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.1970304597870439,
+      "x": -1.6182077853136947,
+      "y": -0.013260576788450202
+    },
+    {
+      "id": 15,
+      "rotation_radians": 1.674515845529392,
+      "x": 0.9261792714902977,
+      "y": 0.1541146671952633
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.2558709183197625,
+      "x": -0.4151075497769203,
+      "y": 0.15918758127985774
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.6745437686984905,
+      "x": 1.9405699521649582,
+      "y": 0.2307802705642333
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.577316305227555,
+      "x": 0.3168300737817886,
+      "y": 0.2659445620536
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.6273553470729722,
+      "x": 1.4132537921433632,
+      "y": 0.465971433260853
+    },
+    {
+      "id": 20,
+      "rotation_radians": 1.25578253577531,
+      "x": -1.3272172272175886,
+      "y": 0.503849465519698
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.2086685053746797,
+      "x": -0.7623093477594333,
+      "y": 0.6234285251222239
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.624378448578175,
+      "x": 0.2858201736854658,
+      "y": 0.8425744543931168
+    },
+    {
+      "id": 23,
+      "rotation_radians": 1.6746598676318258,
+      "x": 1.3576010995051655,
+      "y": 1.040765856119004
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.208576744217489,
+      "x": -1.6132220336549974,
+      "y": 1.023095942406656
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.5772008631930872,
+      "x": 0.7582209279258405,
+      "y": 1.175208203280933
+    },
+    {
+      "id": 26,
+      "rotation_radians": 1.887183950450755,
+      "x": -0.4002704672879991,
+      "y": 1.3645826761605064
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.8405045806268839,
+      "x": -0.9656858276801874,
+      "y": 1.4833129715880224
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.624386333491156,
+      "x": 0.7272373198161824,
+      "y": 1.7517621301677126
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.8394382841904766,
+      "x": -0.013172958500125412,
+      "y": 1.7933547100365343
+    }
+  ],
+  "problem": "29 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/29.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_30_29e4e0e684891d8a.json b/data/solutions/generated/triinpen_30_29e4e0e684891d8a.json
index dc1567684c781147f72caa44aeebcb665c701f3c..18802e29cbd9a55600748dbc86cd59bc58abbcac 100644
--- a/data/solutions/generated/triinpen_30_29e4e0e684891d8a.json
+++ b/data/solutions/generated/triinpen_30_29e4e0e684891d8a.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.02712819042244896,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.952,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Ignacio Vallejo"
diff --git a/data/solutions/generated/triinpen_34_6034a27a1d11d106.json b/data/solutions/generated/triinpen_34_6034a27a1d11d106.json
new file mode 100644
index 0000000000000000000000000000000000000000..0c32823f8ba41a8794cae2b5eee2fd5ed19262c7
--- /dev/null
+++ b/data/solutions/generated/triinpen_34_6034a27a1d11d106.json
@@ -0,0 +1,271 @@
+{
+  "case": "triinpen@34",
+  "container": {
+    "circumradius": 2.6513814239288034,
+    "orientation_radians": 0.0,
+    "side_length": 3.1168857983751366,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@34",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "",
+    "metric_expression": "3.114+",
+    "metric_symbol": "s",
+    "metric_value": 3.114,
+    "reference_text": "s = 3.114+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "34.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/34.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@34",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "",
+      "metric_expression": "3.114+",
+      "metric_symbol": "s",
+      "metric_value": 3.114,
+      "reference_text": "s = 3.114+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "34.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/34.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "sa_tight",
+    "image_seed_recovery_log": "bench_outputs/current_best_recovery/current_best_recovery_20260501_currentbest_deep_deep.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.114,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/triinpen_034_20260501_currentbest_deep_sa_tight.state",
+    "source_url": "https://erich-friedman.github.io/packing/triinpen/",
+    "submitted_at": "2026-05-01T17:13:54+00:00",
+    "submitted_by": "Emerson Connelly"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.7920337389044144,
+      "x": 0.2398507880141021,
+      "y": 2.0060866357827787
+    },
+    {
+      "id": 2,
+      "rotation_radians": 1.6755275961574385,
+      "x": 0.8957035408964309,
+      "y": 1.9253357947470275
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.7920123394319467,
+      "x": -0.6649874910788314,
+      "y": 1.6822570171416873
+    },
+    {
+      "id": 4,
+      "rotation_radians": 1.83922924160726,
+      "x": -0.09486862482953433,
+      "y": 1.5252351789800476
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.7928170087742641,
+      "x": -1.5862307795272546,
+      "y": 1.374626869868127
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.6283158968045797,
+      "x": 0.9560546948717598,
+      "y": 1.3511201963966795
+    },
+    {
+      "id": 7,
+      "rotation_radians": 1.8400168401926287,
+      "x": -1.0276629145582927,
+      "y": 1.228492929626543
+    },
+    {
+      "id": 8,
+      "rotation_radians": 1.6755147480475623,
+      "x": 1.4835135372294528,
+      "y": 1.1162948189527464
+    },
+    {
+      "id": 9,
+      "rotation_radians": 0.6402520734675402,
+      "x": 0.1816410680190574,
+      "y": 0.9275096524319643
+    },
+    {
+      "id": 10,
+      "rotation_radians": 1.6798568114234476,
+      "x": 0.7144672689987964,
+      "y": 0.6954563092546088
+    },
+    {
+      "id": 11,
+      "rotation_radians": 2.0151790805994048,
+      "x": -1.8118162731175114,
+      "y": 0.7100970181906969
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.9319511085083658,
+      "x": -0.7055515122433367,
+      "y": 0.6662536936814811
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.6283187075442305,
+      "x": 1.5438670130219003,
+      "y": 0.5420904321387873
+    },
+    {
+      "id": 14,
+      "rotation_radians": 1.6755114130321807,
+      "x": 2.0713196018266293,
+      "y": 0.3072481264594486
+    },
+    {
+      "id": 15,
+      "rotation_radians": 2.076114185745864,
+      "x": -0.12598948474915533,
+      "y": 0.24274596895152717
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.9791499920395377,
+      "x": -0.9910117283594475,
+      "y": 0.15907233325437428
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.9319616305703471,
+      "x": -1.571480296718342,
+      "y": 0.16556459813967386
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.24708454523282333,
+      "x": 0.9463166239960763,
+      "y": -0.03834413386242857
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.294281975702899,
+      "x": 0.39733620821162685,
+      "y": -0.22256943769296658
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.45461257959209983,
+      "x": 2.0183330639540755,
+      "y": -0.35010421481767384
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.03180245063858988,
+      "x": -1.8330523657208104,
+      "y": -0.4432710774490925
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.3023209247502074,
+      "x": 1.3523725406846496,
+      "y": -0.45442505977556935
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.20961498493179653,
+      "x": -0.5340767997971133,
+      "y": -0.5539629566578851
+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.2564962443952024,
+      "x": -1.0989812285792415,
+      "y": -0.6740488720444472
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.24708725467938175,
+      "x": 0.4287331472262821,
+      "y": -0.8316433753341037
+    },
+    {
+      "id": 26,
+      "rotation_radians": 1.2568119043571264,
+      "x": -0.14765981462290564,
+      "y": -0.9829562938349173
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.25512477944958034,
+      "x": 1.4198566285006127,
+      "y": -1.0718114724429761
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.3012549637991908,
+      "x": 0.8614634447894477,
+      "y": -1.220710945938545
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.21024124543579345,
+      "x": -1.0157146865060993,
+      "y": -1.3084518677387886
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.2574462797532848,
+      "x": -1.5803658884554503,
+      "y": -1.4289405779825899
+    },
+    {
+      "id": 31,
+      "rotation_radians": 0.21024709031195477,
+      "x": -0.07240889658355286,
+      "y": -1.623958739801609
+    },
+    {
+      "id": 32,
+      "rotation_radians": 1.2574430149394356,
+      "x": -0.6370614502092143,
+      "y": -1.7444477231732594
+    },
+    {
+      "id": 33,
+      "rotation_radians": 0.25405852801278656,
+      "x": 0.8734821722162244,
+      "y": -1.8230234087454449
+    },
+    {
+      "id": 34,
+      "rotation_radians": 1.2590250543818875,
+      "x": 0.31513870720797926,
+      "y": -2.0529997811915504
+    }
+  ],
+  "problem": "34 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/34.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_34_faff9872314d8b1a.json b/data/solutions/generated/triinpen_34_faff9872314d8b1a.json
index 69180625a63b2d9dfc70c30c1655a0fd27640901..d889442e0889f8840063b8f9461506e18d050717 100644
--- a/data/solutions/generated/triinpen_34_faff9872314d8b1a.json
+++ b/data/solutions/generated/triinpen_34_faff9872314d8b1a.json
@@ -49,7 +49,10 @@
     "generator_profile": "cg_deep",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_current_heavy_heavy.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.114,
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "submitted_at": "2026-05-01T14:34:18+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/triinsqu_001_d0da9c9aae58c37e.json b/data/solutions/generated/triinsqu_001_d0da9c9aae58c37e.json
index 2b042b05017a3aba4ddfe4182d62f86c36193075..5565cdacea056d4eb3b39266e889f8d9b33d5376 100644
--- a/data/solutions/generated/triinsqu_001_d0da9c9aae58c37e.json
+++ b/data/solutions/generated/triinsqu_001_d0da9c9aae58c37e.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 0.9659258262890683,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triinsqu_002_536a8bec14614050.json b/data/solutions/generated/triinsqu_002_536a8bec14614050.json
index 1dd68758460db988c1373dcef316e4ae6f67584a..e39c98100e2866109720b1923c66fce8c607fd71 100644
--- a/data/solutions/generated/triinsqu_002_536a8bec14614050.json
+++ b/data/solutions/generated/triinsqu_002_536a8bec14614050.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.224744871391589,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Trivial"
diff --git a/data/solutions/generated/triinsqu_003_85d51e7a9d3c3790.json b/data/solutions/generated/triinsqu_003_85d51e7a9d3c3790.json
index a043e432fc68e948164a8d23af3d708eadc9310c..ffc3c6988fc760170992c8af170cc2b513c75ee3 100644
--- a/data/solutions/generated/triinsqu_003_85d51e7a9d3c3790.json
+++ b/data/solutions/generated/triinsqu_003_85d51e7a9d3c3790.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.478397839480233,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triinsqu_004_10004832454b0f3c.json b/data/solutions/generated/triinsqu_004_10004832454b0f3c.json
index 10eb05c6f2bcbbb0ed9b1bd37188ee958bcd99f4..7900a46b8711d8d06865305cfd218d9984aa870a 100644
--- a/data/solutions/generated/triinsqu_004_10004832454b0f3c.json
+++ b/data/solutions/generated/triinsqu_004_10004832454b0f3c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.5773502691896257,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triinsqu_005_f41eeaee150f1c15.json b/data/solutions/generated/triinsqu_005_f41eeaee150f1c15.json
index 1d55145d191968c9584c0955ff2fb0512e778f99..fc1ca2e534831b20eaf4494284827c40f88172f0 100644
--- a/data/solutions/generated/triinsqu_005_f41eeaee150f1c15.json
+++ b/data/solutions/generated/triinsqu_005_f41eeaee150f1c15.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.803,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triinsqu_006_47de8ba8f0c9310c.json b/data/solutions/generated/triinsqu_006_47de8ba8f0c9310c.json
index b0baf51e44f679b8196a036bc9057821fe59203f..a4bc3cbc0f1eca62df493744e4c856c051799f29 100644
--- a/data/solutions/generated/triinsqu_006_47de8ba8f0c9310c.json
+++ b/data/solutions/generated/triinsqu_006_47de8ba8f0c9310c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.901923788646684,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triinsqu_007_d4eecc11473f7bf7.json b/data/solutions/generated/triinsqu_007_d4eecc11473f7bf7.json
index edf4aa25b0f237f9e8d2422370d9875dd2d6ae5f..b4e823bee57c3802a815d0ecb5d63a4ceedc25fe 100644
--- a/data/solutions/generated/triinsqu_007_d4eecc11473f7bf7.json
+++ b/data/solutions/generated/triinsqu_007_d4eecc11473f7bf7.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triinsqu_008_bd28b88a6ba9b99d.json b/data/solutions/generated/triinsqu_008_bd28b88a6ba9b99d.json
index f296952656021fe08764a84d65ac34c7904d0716..1421303a4d1e15d2fa0bbf88006e531f555c63eb 100644
--- a/data/solutions/generated/triinsqu_008_bd28b88a6ba9b99d.json
+++ b/data/solutions/generated/triinsqu_008_bd28b88a6ba9b99d.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.098076211353316,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triinsqu_009_458e49fec5e5573c.json b/data/solutions/generated/triinsqu_009_458e49fec5e5573c.json
index d38846293e739a983cde07e4fef007e6256f58f7..5aec2f43570ab534a2c1a30facb59f2c9c35efa4 100644
--- a/data/solutions/generated/triinsqu_009_458e49fec5e5573c.json
+++ b/data/solutions/generated/triinsqu_009_458e49fec5e5573c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.287,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/triinsqu_011_b95fbc7e7009bb63.json b/data/solutions/generated/triinsqu_011_b95fbc7e7009bb63.json
index 9acc8d4712c064a2d7f800f5cdd375e156a3113f..bfeb42ae52fc4eb8a58a79e64b8ad1ff3284ba58 100644
--- a/data/solutions/generated/triinsqu_011_b95fbc7e7009bb63.json
+++ b/data/solutions/generated/triinsqu_011_b95fbc7e7009bb63.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.49,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/triinsqu_012_297283972e34795d.json b/data/solutions/generated/triinsqu_012_297283972e34795d.json
index e8779b2225cb76a65c389bcfbc97f7b2048a0cee..78be08a0472aaf22b704b3f3307b47b0d5a940fd 100644
--- a/data/solutions/generated/triinsqu_012_297283972e34795d.json
+++ b/data/solutions/generated/triinsqu_012_297283972e34795d.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.558,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Dominik Kamp"
diff --git a/data/solutions/generated/triinsqu_014_601dc4458719752d.json b/data/solutions/generated/triinsqu_014_601dc4458719752d.json
index 9be930d501367262aa4c966c548af4ea98729959..7a10139babbf0b476f2dd4c4da3172b5f13480dc 100644
--- a/data/solutions/generated/triinsqu_014_601dc4458719752d.json
+++ b/data/solutions/generated/triinsqu_014_601dc4458719752d.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 2.7290649131274217e-16,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.726,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t14.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_015_430e70d954ae3759.json b/data/solutions/generated/triinsqu_015_430e70d954ae3759.json
index 516a30846011af841b129812d4133f2e6d35369a..dc95f3eb12d24ce02bd7671ca551ba14e1e19b38 100644
--- a/data/solutions/generated/triinsqu_015_430e70d954ae3759.json
+++ b/data/solutions/generated/triinsqu_015_430e70d954ae3759.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 5.734100018249896e-16,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.8299,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t15.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_016_2350476c07d7060c.json b/data/solutions/generated/triinsqu_016_2350476c07d7060c.json
index 1e9075fbf06948812ace60682faeb3fe823a2e3b..9869999091f098d45ef2bfd568994d6d24410c26 100644
--- a/data/solutions/generated/triinsqu_016_2350476c07d7060c.json
+++ b/data/solutions/generated/triinsqu_016_2350476c07d7060c.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.9,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Ian Watson"
diff --git a/data/solutions/generated/triinsqu_017_79a5506fa7f0974c.json b/data/solutions/generated/triinsqu_017_79a5506fa7f0974c.json
index 2c64007c4a2751a45ad2de1bc847793c31d7fe78..4bdfa038a19cde754feab79843d9027f7221adbb 100644
--- a/data/solutions/generated/triinsqu_017_79a5506fa7f0974c.json
+++ b/data/solutions/generated/triinsqu_017_79a5506fa7f0974c.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.00901772363830736,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.982,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t17.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_018_0d24ad1cca3bbb64.json b/data/solutions/generated/triinsqu_018_0d24ad1cca3bbb64.json
index 1d33d9488d8646353f0d068ca198856ad82a6713..391a334a9f8f584b276317b82cf3e52dedfa2202 100644
--- a/data/solutions/generated/triinsqu_018_0d24ad1cca3bbb64.json
+++ b/data/solutions/generated/triinsqu_018_0d24ad1cca3bbb64.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 2.0939615251162484e-16,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.051,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t18.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_019_def5af7572515998.json b/data/solutions/generated/triinsqu_019_def5af7572515998.json
index 6d8408968ddf6262168961e57fa0ba469503fe86..e15c7f696aee99b4b455d9de37cc49cab64bfad9 100644
--- a/data/solutions/generated/triinsqu_019_def5af7572515998.json
+++ b/data/solutions/generated/triinsqu_019_def5af7572515998.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.00952193624958715,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.1293,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t19.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_020_43e53f43942a4488.json b/data/solutions/generated/triinsqu_020_43e53f43942a4488.json
index b52ca7de327a384ab49eecdb66e65210f07fcc02..6a0fefdd6a4418050a759e578e249c6d0afb6fb9 100644
--- a/data/solutions/generated/triinsqu_020_43e53f43942a4488.json
+++ b/data/solutions/generated/triinsqu_020_43e53f43942a4488.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.025942461837545262,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.2305,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t20.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_021_986572060ddb345a.json b/data/solutions/generated/triinsqu_021_986572060ddb345a.json
index 6845c5991d4e55170f9ff87afa3a3615e603b4e5..b368be6dec16f2192fe0b76233e495e79c836346 100644
--- a/data/solutions/generated/triinsqu_021_986572060ddb345a.json
+++ b/data/solutions/generated/triinsqu_021_986572060ddb345a.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.024586924320562056,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.3111,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t21.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_022_4d69d20a7a35e585.json b/data/solutions/generated/triinsqu_022_4d69d20a7a35e585.json
index d272303df9c4365fc9b2f9346be7202e351fac66..e31c9d53614895a0d9828c9922359a0025942206 100644
--- a/data/solutions/generated/triinsqu_022_4d69d20a7a35e585.json
+++ b/data/solutions/generated/triinsqu_022_4d69d20a7a35e585.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.01783528991020488,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.3757,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t22.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_023_959574dda9a01133.json b/data/solutions/generated/triinsqu_023_959574dda9a01133.json
index 99b542ff6d209ca2375dce3b635c2e23e9296446..b25ed336f4d9d008860fccdf1508fe42282d125c 100644
--- a/data/solutions/generated/triinsqu_023_959574dda9a01133.json
+++ b/data/solutions/generated/triinsqu_023_959574dda9a01133.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.010375825478000167,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.4311,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t23.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_024_d96b5ad8b1001b9a.json b/data/solutions/generated/triinsqu_024_d96b5ad8b1001b9a.json
index 53e468d8762d4db9571ea93c3fe5e9fe8a8af5f4..b427abc7565aaae256e99f55446dca672594e479 100644
--- a/data/solutions/generated/triinsqu_024_d96b5ad8b1001b9a.json
+++ b/data/solutions/generated/triinsqu_024_d96b5ad8b1001b9a.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 5.095968879607056e-16,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.468,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t24.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_025_8da962f4a2ed3f11.json b/data/solutions/generated/triinsqu_025_8da962f4a2ed3f11.json
index c5ec34c432f2d8fa056b9f2a1ec3ea4971ec21c4..29201671d7af725f168005336390118dff3527ee 100644
--- a/data/solutions/generated/triinsqu_025_8da962f4a2ed3f11.json
+++ b/data/solutions/generated/triinsqu_025_8da962f4a2ed3f11.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.015239320506215747,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.537,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t25.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_026_c36ce120aca7c2e7.json b/data/solutions/generated/triinsqu_026_c36ce120aca7c2e7.json
index 622865803884ac1c3881aa92ea5ffb3cf9cd9023..d0218f966f83803e59df8723e90db98f710fc15d 100644
--- a/data/solutions/generated/triinsqu_026_c36ce120aca7c2e7.json
+++ b/data/solutions/generated/triinsqu_026_c36ce120aca7c2e7.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 4.543168905090693e-16,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.575,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t26.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_027_4c91417b38b8be95.json b/data/solutions/generated/triinsqu_027_4c91417b38b8be95.json
index bf543df1cf1517023fb6fe84f373bd0cf7c694b9..cf1a994c216a0c3e2455a04351d7e537a2ca4757 100644
--- a/data/solutions/generated/triinsqu_027_4c91417b38b8be95.json
+++ b/data/solutions/generated/triinsqu_027_4c91417b38b8be95.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.01574522607957463,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.6726,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t27.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_028_9b7285926a894eec.json b/data/solutions/generated/triinsqu_028_9b7285926a894eec.json
index 7cf001828c9d64f6a8b2fc75474cf17bbf7c169b..ccaf6f1ec62ddc517cbaaa5f4aa5ae245a678d58 100644
--- a/data/solutions/generated/triinsqu_028_9b7285926a894eec.json
+++ b/data/solutions/generated/triinsqu_028_9b7285926a894eec.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.019825472773182515,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.7571,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t28.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_029_a02ae61c838755d7.json b/data/solutions/generated/triinsqu_029_a02ae61c838755d7.json
index 974eeebc1f8ac5654bd5d455da067e77a9ae6693..f0b2eaaa8c0584934e35b9fc807e252c565d4ace 100644
--- a/data/solutions/generated/triinsqu_029_a02ae61c838755d7.json
+++ b/data/solutions/generated/triinsqu_029_a02ae61c838755d7.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.019948347549317774,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.818,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t29.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_030_d3cf7ea5ce255135.json b/data/solutions/generated/triinsqu_030_d3cf7ea5ce255135.json
index 390d0bccc93ae95d9ecf77eeb230386d609a7f36..7c386e112a8f21b9373d39537285bdc923be7264 100644
--- a/data/solutions/generated/triinsqu_030_d3cf7ea5ce255135.json
+++ b/data/solutions/generated/triinsqu_030_d3cf7ea5ce255135.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.011706033460104534,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.8662,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t30.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_031_90f4b9b8010910a7.json b/data/solutions/generated/triinsqu_031_90f4b9b8010910a7.json
index 30e4b6c8e0c97bb8fac25537582a14ba73f30845..cdf8d5aeb3af5b17fb8dc41c1a5aad8c3bde4d62 100644
--- a/data/solutions/generated/triinsqu_031_90f4b9b8010910a7.json
+++ b/data/solutions/generated/triinsqu_031_90f4b9b8010910a7.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.011714648897274603,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.936,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t31.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_035_ab6aa3f219e08b42.json b/data/solutions/generated/triinsqu_035_ab6aa3f219e08b42.json
index 3419a121b60d89c3e70a1413e6748d32b2f1842c..ed3377ce3aea69b1495d256c481c78b953412664 100644
--- a/data/solutions/generated/triinsqu_035_ab6aa3f219e08b42.json
+++ b/data/solutions/generated/triinsqu_035_ab6aa3f219e08b42.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 1.021894416409633e-15,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.176914536239791,
     "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t35.gif",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triinsqu_040_ccf2360cc8917adc.json b/data/solutions/generated/triinsqu_040_ccf2360cc8917adc.json
index 2ceab08fb9a87f9da6ef960f5639618dd4c7532c..de321b90b02c5e7f044349817280d3effb44b486 100644
--- a/data/solutions/generated/triinsqu_040_ccf2360cc8917adc.json
+++ b/data/solutions/generated/triinsqu_040_ccf2360cc8917adc.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.437,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/triinsqu_10_5b0eaf84f54fe48c.json b/data/solutions/generated/triinsqu_10_5b0eaf84f54fe48c.json
index b55825fa22ce7c43b139c9eb88b8180fc3d3cdd9..d8afd92584a28aa672031c03eab8d3b45776c1b5 100644
--- a/data/solutions/generated/triinsqu_10_5b0eaf84f54fe48c.json
+++ b/data/solutions/generated/triinsqu_10_5b0eaf84f54fe48c.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 2.707242505775539e-16,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.377,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/triinsqu_13_7628e283de25ee68.json b/data/solutions/generated/triinsqu_13_7628e283de25ee68.json
index af57e29dffcada1c9fa46fc35f2d56ee187aa96c..7bfc044005291460465c923968f19b8b6021d6b3 100644
--- a/data/solutions/generated/triinsqu_13_7628e283de25ee68.json
+++ b/data/solutions/generated/triinsqu_13_7628e283de25ee68.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 2.327997847980024e-16,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.595,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/triinsqu_32_300596cf09652b9a.json b/data/solutions/generated/triinsqu_32_300596cf09652b9a.json
new file mode 100644
index 0000000000000000000000000000000000000000..dd10b229e141adab62dfc04e461fb98518d7a01a
--- /dev/null
+++ b/data/solutions/generated/triinsqu_32_300596cf09652b9a.json
@@ -0,0 +1,259 @@
+{
+  "case": "triinsqu@32",
+  "container": {
+    "circumradius": 2.813776279002818,
+    "orientation_radians": 0.0,
+    "side_length": 3.979280575249487,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triinsqu@32",
+    "credit": "Maurizio Morandi",
+    "date": "May 2026",
+    "family_updated": "",
+    "metric_expression": "6\u20137\u221a3/6 = 3.979+",
+    "metric_symbol": "s",
+    "metric_value": 3.9792740578363097,
+    "reference_text": "32. | | s = 6\u20137\u221a3/6 = 3.979+ | Found by Maurizio Morandi | in May 2026.",
+    "source_image": "t32.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t32.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triinsqu@32",
+      "credit": "Maurizio Morandi",
+      "date": "May 2026",
+      "family_updated": "",
+      "metric_expression": "6\u20137\u221a3/6 = 3.979+",
+      "metric_symbol": "s",
+      "metric_value": 3.9792740578363097,
+      "reference_text": "32. | | s = 6\u20137\u221a3/6 = 3.979+ | Found by Maurizio Morandi | in May 2026.",
+      "source_image": "t32.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t32.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "generator": "friedman_image_seed_rigorous_recovery",
+    "generator_profile": "cg_precise",
+    "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_20260501_systematic_broad.jsonl",
+    "metric_recovery_tolerance_rel": 0.001,
+    "notes": "Image-seeded from the Friedman source image and refined with a rigorous polygon-packer-c recovery pass.",
+    "original_submitted_by": "polygon-packer-c image seed",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.9792740578363097,
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/triinsqu_032_20260501_systematic_cg_precise.state",
+    "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
+    "submitted_at": "2026-05-01T16:24:14+00:00",
+    "submitted_by": "Maurizio Morandi"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.3197908309587827,
+      "x": -0.1434072972321184,
+      "y": 2.2544959147571872
+    },
+    {
+      "id": 2,
+      "rotation_radians": 1.8325939379079113,
+      "x": 0.5653129375923301,
+      "y": 1.8401975715768506
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.2725890073944397,
+      "x": -0.28681576262262004,
+      "y": 1.695210797257185
+    },
+    {
+      "id": 4,
+      "rotation_radians": 1.3197867960068201,
+      "x": -0.8462100010936372,
+      "y": 1.5516953097904969
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.7851666612476609,
+      "x": 0.5193319910789941,
+      "y": 1.2300636831199432
+    },
+    {
+      "id": 6,
+      "rotation_radians": 1.8323581262445576,
+      "x": 1.0770559836512854,
+      "y": 1.0806996706954262
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.27258707080711636,
+      "x": -0.9896193349108963,
+      "y": 0.9924111505657147
+    },
+    {
+      "id": 8,
+      "rotation_radians": 1.3096697428001558,
+      "x": -0.2244293472166145,
+      "y": 0.9334591910931157
+    },
+    {
+      "id": 9,
+      "rotation_radians": 1.308996716692682,
+      "x": -1.5549284035103763,
+      "y": 0.8505839273455018
+    },
+    {
+      "id": 10,
+      "rotation_radians": 1.832589118711603,
+      "x": 1.8365491349262648,
+      "y": 0.5689655734045375
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.7851735750958612,
+      "x": 1.2263631713159198,
+      "y": 0.5229542397427409
+    },
+    {
+      "id": 12,
+      "rotation_radians": 1.8327099822645545,
+      "x": 0.46697558241283343,
+      "y": 0.4657246341441907
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.2628242575697567,
+      "x": -0.3734386067926528,
+      "y": 0.37545907602485296
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.2564442261881065,
+      "x": -1.6903973617380708,
+      "y": 0.28637140269674716
+    },
+    {
+      "id": 15,
+      "rotation_radians": 1.3117664715978437,
+      "x": -0.9316985162919753,
+      "y": 0.22473478332476515
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.2946350783285527,
+      "x": -2.2538996156625184,
+      "y": 0.1413184288833288
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.26179322590897025,
+      "x": 2.2560897932817583,
+      "y": -0.14942500714829723
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.26178883397790426,
+      "x": 0.9396528499094635,
+      "y": -0.22416034909037338
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.308987372421238,
+      "x": 1.69482213274998,
+      "y": -0.2855323151532553
+    },
+    {
+      "id": 20,
+      "rotation_radians": 1.3030080304843767,
+      "x": 0.3786183605002285,
+      "y": -0.37268838124014997
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.7831468842582568,
+      "x": -0.4647387464708879,
+      "y": -0.4658064674525685
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.8312366708930488,
+      "x": -1.2261826406261354,
+      "y": -0.5199390598233956
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.7853966268939372,
+      "x": -1.8375272756194039,
+      "y": -0.567980813512568
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.2617935044902805,
+      "x": 1.5453847617589724,
+      "y": -0.843232474983817
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.25569444741604586,
+      "x": 0.22575796853720925,
+      "y": -0.9295208371510357
+    },
+    {
+      "id": 26,
+      "rotation_radians": 1.3089927197446733,
+      "x": 0.9876860959806714,
+      "y": -0.9926624748683119
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.7831139426381194,
+      "x": -1.078058923347734,
+      "y": -1.0798243569823567
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.8303425884570514,
+      "x": -0.5201411924118268,
+      "y": -1.2285321107587721
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.2618001193459705,
+      "x": 0.8515871766959657,
+      "y": -1.5539351704328883
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.3210366740010568,
+      "x": 0.2853995003832546,
+      "y": -1.6948745108181202
+    },
+    {
+      "id": 31,
+      "rotation_radians": 0.785391339592867,
+      "x": -0.5662004022095602,
+      "y": -1.8393077704961072
+    },
+    {
+      "id": 32,
+      "rotation_radians": 0.27384832314632535,
+      "x": 0.1426928882518604,
+      "y": -2.2543298253694792
+    }
+  ],
+  "problem": "32 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t32.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_32_f42801b713b9238d.json b/data/solutions/generated/triinsqu_32_f42801b713b9238d.json
index 1580f41abf078e59a39ac186d846862ad919c82a..1afcb85cde7ad7eeafa65a4087fb8060d264969e 100644
--- a/data/solutions/generated/triinsqu_32_f42801b713b9238d.json
+++ b/data/solutions/generated/triinsqu_32_f42801b713b9238d.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 4.34913614441221e-16,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.9792740578363097,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/triinsqu_33_a6f49f2f24228d1b.json b/data/solutions/generated/triinsqu_33_a6f49f2f24228d1b.json
index 38669885ca0099234134c03f07829290fe1a6bfc..409e7696e40ea5e6c0b91879abdd1b795881779f 100644
--- a/data/solutions/generated/triinsqu_33_a6f49f2f24228d1b.json
+++ b/data/solutions/generated/triinsqu_33_a6f49f2f24228d1b.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 4.776843691548918e-16,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.058,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/triinsqu_34_61b4d5d6bf22a206.json b/data/solutions/generated/triinsqu_34_61b4d5d6bf22a206.json
index 0026afee31b3302e450be87590964723eb5919d4..bad086dcd1e6cabbb8d4c9fa38acdbca6a2c7c2a 100644
--- a/data/solutions/generated/triinsqu_34_61b4d5d6bf22a206.json
+++ b/data/solutions/generated/triinsqu_34_61b4d5d6bf22a206.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 9.292012346988251e-16,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.098,
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Emerson Connelly"
diff --git a/data/solutions/generated/triintri_001_b09a5ce4a2c03ad3.json b/data/solutions/generated/triintri_001_b09a5ce4a2c03ad3.json
index f281ff8b51f0fa1b6026a6681bbc18801626740f..02547c9dd2439364787816a8fcc8af004837a441 100644
--- a/data/solutions/generated/triintri_001_b09a5ce4a2c03ad3.json
+++ b/data/solutions/generated/triintri_001_b09a5ce4a2c03ad3.json
@@ -46,9 +46,12 @@
     },
     "generator": "exact_triangular_subdivision",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Exact triangular subdivision coordinate JSON.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 1.0,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
-    "submitted_at": "2026-05-01T15:42:49+00:00",
+    "submitted_at": "2026-05-01T18:08:37+00:00",
     "submitted_by": "Trivial"
   },
   "placements": [
diff --git a/data/solutions/generated/triintri_002_2d6f654db11412d8.json b/data/solutions/generated/triintri_002_2d6f654db11412d8.json
index 1dd658187ce447fd0f1fae8a674c208c087c4670..9c5b56e8b9dc841df2a6dc27bdc2f8a97f8921fa 100644
--- a/data/solutions/generated/triintri_002_2d6f654db11412d8.json
+++ b/data/solutions/generated/triintri_002_2d6f654db11412d8.json
@@ -46,9 +46,12 @@
     },
     "generator": "exact_triangular_subdivision",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Exact triangular subdivision coordinate JSON.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
-    "submitted_at": "2026-05-01T15:42:49+00:00",
+    "submitted_at": "2026-05-01T18:08:37+00:00",
     "submitted_by": "Trivial"
   },
   "placements": [
diff --git a/data/solutions/generated/triintri_003_76381d42f8f17f41.json b/data/solutions/generated/triintri_003_76381d42f8f17f41.json
index 004e6304f3c4348f01f437ee7c3e520dc3976eab..8baeec11e6672b44209322ef0dc5cf814e9e32e7 100644
--- a/data/solutions/generated/triintri_003_76381d42f8f17f41.json
+++ b/data/solutions/generated/triintri_003_76381d42f8f17f41.json
@@ -46,9 +46,12 @@
     },
     "generator": "exact_triangular_subdivision",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Exact triangular subdivision coordinate JSON.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
-    "submitted_at": "2026-05-01T15:42:49+00:00",
+    "submitted_at": "2026-05-01T18:08:37+00:00",
     "submitted_by": "Trivial"
   },
   "placements": [
diff --git a/data/solutions/generated/triintri_004_be1b0b4b1802d8fa.json b/data/solutions/generated/triintri_004_be1b0b4b1802d8fa.json
index 1fdbacbb0d35ec08ee9e820be18c683e397a01e6..155406b8db87dd36ef5077db793afe5e6433ce73 100644
--- a/data/solutions/generated/triintri_004_be1b0b4b1802d8fa.json
+++ b/data/solutions/generated/triintri_004_be1b0b4b1802d8fa.json
@@ -46,9 +46,12 @@
     },
     "generator": "exact_triangular_subdivision",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Exact triangular subdivision coordinate JSON.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.0,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
-    "submitted_at": "2026-05-01T15:42:49+00:00",
+    "submitted_at": "2026-05-01T18:08:37+00:00",
     "submitted_by": "Trivial"
   },
   "placements": [
diff --git a/data/solutions/generated/triintri_005_b4ac2c13e986485e.json b/data/solutions/generated/triintri_005_b4ac2c13e986485e.json
index 6f92b0abff77dc38d47e0db4e89bf883e564807d..95fcae08c1c329949133df998b1b53521c877a44 100644
--- a/data/solutions/generated/triintri_005_b4ac2c13e986485e.json
+++ b/data/solutions/generated/triintri_005_b4ac2c13e986485e.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.732050807568877,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triintri_006_df20f3104adbd6a1.json b/data/solutions/generated/triintri_006_df20f3104adbd6a1.json
index 712939b44d52c66db79e88f7b39f5a0997cec531..31bcf1087a95c9dcc1fbbb14f81f1a1fbcef3abc 100644
--- a/data/solutions/generated/triintri_006_df20f3104adbd6a1.json
+++ b/data/solutions/generated/triintri_006_df20f3104adbd6a1.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.977081728298996,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/triintri_007_355f218b5ea40614.json b/data/solutions/generated/triintri_007_355f218b5ea40614.json
index 8abf82c0a55be0c63e08306158b3db960d7eb9b4..4d86c2fb5b805dd89362bc85dcef4702d6f5a600 100644
--- a/data/solutions/generated/triintri_007_355f218b5ea40614.json
+++ b/data/solutions/generated/triintri_007_355f218b5ea40614.json
@@ -46,9 +46,12 @@
     },
     "generator": "exact_triangular_subdivision",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Exact triangular subdivision coordinate JSON.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.0,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
-    "submitted_at": "2026-05-01T15:42:49+00:00",
+    "submitted_at": "2026-05-01T18:08:37+00:00",
     "submitted_by": "Trivial"
   },
   "placements": [
diff --git a/data/solutions/generated/triintri_008_43e3200cf32d77a9.json b/data/solutions/generated/triintri_008_43e3200cf32d77a9.json
index f967a801365b83dab8f238f56c150b01ba524812..65416af63d964bdc6038ce46c3d12d7d80f7b316 100644
--- a/data/solutions/generated/triintri_008_43e3200cf32d77a9.json
+++ b/data/solutions/generated/triintri_008_43e3200cf32d77a9.json
@@ -46,9 +46,12 @@
     },
     "generator": "exact_triangular_subdivision",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Exact triangular subdivision coordinate JSON.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.0,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
-    "submitted_at": "2026-05-01T15:42:49+00:00",
+    "submitted_at": "2026-05-01T18:08:37+00:00",
     "submitted_by": "Trivial"
   },
   "placements": [
diff --git a/data/solutions/generated/triintri_009_4242c6a66848e1ea.json b/data/solutions/generated/triintri_009_4242c6a66848e1ea.json
index ed5063586abe4a4ed11067ac653f5e2fb72430d5..30a471c35f72ffb492a79110840047ac38e6cf97 100644
--- a/data/solutions/generated/triintri_009_4242c6a66848e1ea.json
+++ b/data/solutions/generated/triintri_009_4242c6a66848e1ea.json
@@ -46,9 +46,12 @@
     },
     "generator": "exact_triangular_subdivision",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Exact triangular subdivision coordinate JSON.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.0,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
-    "submitted_at": "2026-05-01T15:42:49+00:00",
+    "submitted_at": "2026-05-01T18:08:37+00:00",
     "submitted_by": "Trivial"
   },
   "placements": [
diff --git a/data/solutions/generated/triintri_010_bcf7fa93627e2e22.json b/data/solutions/generated/triintri_010_bcf7fa93627e2e22.json
index 71fdd65826b2a07b4e723dfe0a8ce680f7d09a64..aee29320c5d2793f87cef8b6e9a8777017455642 100644
--- a/data/solutions/generated/triintri_010_bcf7fa93627e2e22.json
+++ b/data/solutions/generated/triintri_010_bcf7fa93627e2e22.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "steepest",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.5,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triintri_013_afe3e3dc6de1bc36.json b/data/solutions/generated/triintri_013_afe3e3dc6de1bc36.json
index b5e0ddaf4fe12e7b4ca82c3043ea11ef7695b4e8..8fddfddccefb96363634a1c1a2505e6d5620b7de 100644
--- a/data/solutions/generated/triintri_013_afe3e3dc6de1bc36.json
+++ b/data/solutions/generated/triintri_013_afe3e3dc6de1bc36.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.013904885100651864,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.992,
     "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt13.gif",
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triintri_014_8676384ad0301449.json b/data/solutions/generated/triintri_014_8676384ad0301449.json
index bbdd420e485490a20456e70f7640f99300cee0dc..23bbf3f964c00aa7eda38b445300e336bee491ae 100644
--- a/data/solutions/generated/triintri_014_8676384ad0301449.json
+++ b/data/solutions/generated/triintri_014_8676384ad0301449.json
@@ -46,9 +46,12 @@
     },
     "generator": "exact_triangular_subdivision",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Exact triangular subdivision coordinate JSON.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.0,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
-    "submitted_at": "2026-05-01T15:42:49+00:00",
+    "submitted_at": "2026-05-01T18:08:37+00:00",
     "submitted_by": "Trivial"
   },
   "placements": [
diff --git a/data/solutions/generated/triintri_015_31db3ec76cc0421f.json b/data/solutions/generated/triintri_015_31db3ec76cc0421f.json
index 284555fc4642e6a79fdc95fe8b492ba304447738..897323ab6de3aea22fcbb58b22d868a3208d8ab2 100644
--- a/data/solutions/generated/triintri_015_31db3ec76cc0421f.json
+++ b/data/solutions/generated/triintri_015_31db3ec76cc0421f.json
@@ -46,9 +46,12 @@
     },
     "generator": "exact_triangular_subdivision",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Exact triangular subdivision coordinate JSON.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.0,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
-    "submitted_at": "2026-05-01T15:42:49+00:00",
+    "submitted_at": "2026-05-01T18:08:37+00:00",
     "submitted_by": "Trivial"
   },
   "placements": [
diff --git a/data/solutions/generated/triintri_016_2ffa329b602032d6.json b/data/solutions/generated/triintri_016_2ffa329b602032d6.json
index cddd114e7f4332c02de2554bd2f72c73e27650d4..94a72b828658618d8e29a754135f924190f34095 100644
--- a/data/solutions/generated/triintri_016_2ffa329b602032d6.json
+++ b/data/solutions/generated/triintri_016_2ffa329b602032d6.json
@@ -46,9 +46,12 @@
     },
     "generator": "exact_triangular_subdivision",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Exact triangular subdivision coordinate JSON.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.0,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
-    "submitted_at": "2026-05-01T15:42:49+00:00",
+    "submitted_at": "2026-05-01T18:08:37+00:00",
     "submitted_by": "Trivial"
   },
   "placements": [
diff --git a/data/solutions/generated/triintri_017_ad8aac0e4c06f7d0.json b/data/solutions/generated/triintri_017_ad8aac0e4c06f7d0.json
index 179bdd126c743407bd3bf874ff336eb5402b3c40..231b1887bd2d8f3648f6b7a19de2cde94636fad5 100644
--- a/data/solutions/generated/triintri_017_ad8aac0e4c06f7d0.json
+++ b/data/solutions/generated/triintri_017_ad8aac0e4c06f7d0.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.465,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/triintri_018_b4cfb14015aca75a.json b/data/solutions/generated/triintri_018_b4cfb14015aca75a.json
index 6f00c06850049007a3ba9fa2a87ae95c9e4dbf28..78cc357aa3b317d9c0f265321e9235df510c0df2 100644
--- a/data/solutions/generated/triintri_018_b4cfb14015aca75a.json
+++ b/data/solutions/generated/triintri_018_b4cfb14015aca75a.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.5,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triintri_019_bf4e89c9b4dd8ae2.json b/data/solutions/generated/triintri_019_bf4e89c9b4dd8ae2.json
index f056aef17b3f9d12fe9e8c0699c487b1351c7178..c0558b37b8d4f512ff9cd454fa48be7ddea0b3ff 100644
--- a/data/solutions/generated/triintri_019_bf4e89c9b4dd8ae2.json
+++ b/data/solutions/generated/triintri_019_bf4e89c9b4dd8ae2.json
@@ -52,8 +52,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.666666666666667,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T01:05:47+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/triintri_020_4dff2c76e1273753.json b/data/solutions/generated/triintri_020_4dff2c76e1273753.json
index adf920f56e26498ec078b28b63a63d2b421211e9..d382065758b65845e47c72c69e8d5e63be50d34c 100644
--- a/data/solutions/generated/triintri_020_4dff2c76e1273753.json
+++ b/data/solutions/generated/triintri_020_4dff2c76e1273753.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.025641210469582294,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.861485379546474,
     "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt20.gif",
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triintri_021_4dc62e9e9421c0aa.json b/data/solutions/generated/triintri_021_4dc62e9e9421c0aa.json
index dea7528a59e35e6997e7c519c79359fecae1624c..447e91ddb5de426ecf2213d22aa5c9a6e84a264a 100644
--- a/data/solutions/generated/triintri_021_4dc62e9e9421c0aa.json
+++ b/data/solutions/generated/triintri_021_4dc62e9e9421c0aa.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.051134640135780535,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.923,
     "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt21.gif",
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triintri_022_2122d833c6fcab70.json b/data/solutions/generated/triintri_022_2122d833c6fcab70.json
index 69e98ba4ebd1e3d8d2e13f2f23259fd025b8da67..76bc1672b264131c81048873a66bbfa9990300b0 100644
--- a/data/solutions/generated/triintri_022_2122d833c6fcab70.json
+++ b/data/solutions/generated/triintri_022_2122d833c6fcab70.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.996,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/generated/triintri_023_4f1bdd5d6c07f589.json b/data/solutions/generated/triintri_023_4f1bdd5d6c07f589.json
index 4b39d888d829d5c7f626df13d0e970c607136e40..2ea52b4a9160762d6abd32c690a19a685200d638 100644
--- a/data/solutions/generated/triintri_023_4f1bdd5d6c07f589.json
+++ b/data/solutions/generated/triintri_023_4f1bdd5d6c07f589.json
@@ -46,9 +46,12 @@
     },
     "generator": "exact_triangular_subdivision",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Exact triangular subdivision coordinate JSON.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.0,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
-    "submitted_at": "2026-05-01T15:42:49+00:00",
+    "submitted_at": "2026-05-01T18:08:37+00:00",
     "submitted_by": "Trivial"
   },
   "placements": [
diff --git a/data/solutions/generated/triintri_024_64d77fbf13ae0be7.json b/data/solutions/generated/triintri_024_64d77fbf13ae0be7.json
index 3152098ff47fe34a8d1416b3d0dfa39a1f2136c4..1118173a3f008d5d2dcc4fe8c277cecbf9980efe 100644
--- a/data/solutions/generated/triintri_024_64d77fbf13ae0be7.json
+++ b/data/solutions/generated/triintri_024_64d77fbf13ae0be7.json
@@ -46,9 +46,12 @@
     },
     "generator": "exact_triangular_subdivision",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Exact triangular subdivision coordinate JSON.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.0,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
-    "submitted_at": "2026-05-01T15:42:49+00:00",
+    "submitted_at": "2026-05-01T18:08:37+00:00",
     "submitted_by": "Trivial"
   },
   "placements": [
diff --git a/data/solutions/generated/triintri_025_9c4806b8b37c5d37.json b/data/solutions/generated/triintri_025_9c4806b8b37c5d37.json
index fe46234221d6c656e27b09bdb832979e93f07c64..9b5f673f25302eab07cbd4ca292b780ed7ea2b40 100644
--- a/data/solutions/generated/triintri_025_9c4806b8b37c5d37.json
+++ b/data/solutions/generated/triintri_025_9c4806b8b37c5d37.json
@@ -46,9 +46,12 @@
     },
     "generator": "exact_triangular_subdivision",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Exact triangular subdivision coordinate JSON.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.0,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
-    "submitted_at": "2026-05-01T15:42:49+00:00",
+    "submitted_at": "2026-05-01T18:08:37+00:00",
     "submitted_by": "Trivial"
   },
   "placements": [
diff --git a/data/solutions/generated/triintri_026_0af5a3765ecc4828.json b/data/solutions/generated/triintri_026_0af5a3765ecc4828.json
index 2a2d5fdd0f6701fd9001a66c1b5f41aba30c6403..b6b899cd923b1919072a9f46feace2a2edb416cf 100644
--- a/data/solutions/generated/triintri_026_0af5a3765ecc4828.json
+++ b/data/solutions/generated/triintri_026_0af5a3765ecc4828.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.02182683239868679,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.406,
     "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt26.gif",
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triintri_027_f1c2be61e829f1e2.json b/data/solutions/generated/triintri_027_f1c2be61e829f1e2.json
index d932512d34e8c5152192fa25324c96123004903d..830db02b1bc1544c95b52260347dc80a0a561e56 100644
--- a/data/solutions/generated/triintri_027_f1c2be61e829f1e2.json
+++ b/data/solutions/generated/triintri_027_f1c2be61e829f1e2.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.5,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triintri_028_9562d7d6e075a347.json b/data/solutions/generated/triintri_028_9562d7d6e075a347.json
index 5706cf77ea11fdcb9b04f781025f5da809e98fd2..0a34908aa4efa047fb59a1c0c63b4bd9cfb22eda 100644
--- a/data/solutions/generated/triintri_028_9562d7d6e075a347.json
+++ b/data/solutions/generated/triintri_028_9562d7d6e075a347.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.5,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triintri_031_c729ec2b23a32942.json b/data/solutions/generated/triintri_031_c729ec2b23a32942.json
index e99a07f856aaa402978797e263473f0eaab19420..df0d92c12e0c9756c6754d4d5822a44ea7d10d6b 100644
--- a/data/solutions/generated/triintri_031_c729ec2b23a32942.json
+++ b/data/solutions/generated/triintri_031_c729ec2b23a32942.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.02386981745117243,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.912,
     "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt31.gif",
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T02:51:36+00:00",
diff --git a/data/solutions/generated/triintri_032_fa640909a0850f97.json b/data/solutions/generated/triintri_032_fa640909a0850f97.json
index e1c12c4b3ab93efa24f419169cec1823fae2ab49..b914bf3e374c4e65be7672757b375b6334a6925d 100644
--- a/data/solutions/generated/triintri_032_fa640909a0850f97.json
+++ b/data/solutions/generated/triintri_032_fa640909a0850f97.json
@@ -50,7 +50,10 @@
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/bulk_recovery_after_quant_fix.jsonl",
     "image_seed_transform_error": 0.008427084130114499,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.951,
     "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt32.gif",
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T02:29:44+00:00",
diff --git a/data/solutions/generated/triintri_033_34a5032aebc12aff.json b/data/solutions/generated/triintri_033_34a5032aebc12aff.json
index 684898fe4044f67227e0d00e9bd397485436f676..91990b50eb928a19ce598502c6c973ce7e9cc9f9 100644
--- a/data/solutions/generated/triintri_033_34a5032aebc12aff.json
+++ b/data/solutions/generated/triintri_033_34a5032aebc12aff.json
@@ -46,9 +46,12 @@
     },
     "generator": "exact_triangular_subdivision",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Exact triangular subdivision coordinate JSON.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.0,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
-    "submitted_at": "2026-05-01T15:42:49+00:00",
+    "submitted_at": "2026-05-01T18:08:37+00:00",
     "submitted_by": "Trivial"
   },
   "placements": [
diff --git a/data/solutions/generated/triintri_034_a2ccd0a19cfa1b75.json b/data/solutions/generated/triintri_034_a2ccd0a19cfa1b75.json
index 0b8a9b73b7584760a1f617a361af8b535bed03fb..eb00562e077e142f93663b93cf6a68fd4f23cda6 100644
--- a/data/solutions/generated/triintri_034_a2ccd0a19cfa1b75.json
+++ b/data/solutions/generated/triintri_034_a2ccd0a19cfa1b75.json
@@ -46,9 +46,12 @@
     },
     "generator": "exact_triangular_subdivision",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Exact triangular subdivision coordinate JSON.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.0,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
-    "submitted_at": "2026-05-01T15:42:49+00:00",
+    "submitted_at": "2026-05-01T18:08:37+00:00",
     "submitted_by": "Trivial"
   },
   "placements": [
diff --git a/data/solutions/generated/triintri_035_6325f936448cdf94.json b/data/solutions/generated/triintri_035_6325f936448cdf94.json
index b86ec548e6821af24b6747e564fc58ca5a624279..38462af5d18ca5f185f4f6bfc75c1f83eca5cd8f 100644
--- a/data/solutions/generated/triintri_035_6325f936448cdf94.json
+++ b/data/solutions/generated/triintri_035_6325f936448cdf94.json
@@ -46,9 +46,12 @@
     },
     "generator": "exact_triangular_subdivision",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Exact triangular subdivision coordinate JSON.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.0,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
-    "submitted_at": "2026-05-01T15:42:49+00:00",
+    "submitted_at": "2026-05-01T18:08:37+00:00",
     "submitted_by": "Trivial"
   },
   "placements": [
diff --git a/data/solutions/generated/triintri_036_4b90836bf07f8a65.json b/data/solutions/generated/triintri_036_4b90836bf07f8a65.json
index f5c8557db260600579b8086116577cd27c8ca0da..52f496f57bb0e80e50b4753840b4c2c7976228c4 100644
--- a/data/solutions/generated/triintri_036_4b90836bf07f8a65.json
+++ b/data/solutions/generated/triintri_036_4b90836bf07f8a65.json
@@ -46,9 +46,12 @@
     },
     "generator": "exact_triangular_subdivision",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Exact triangular subdivision coordinate JSON.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.0,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
-    "submitted_at": "2026-05-01T15:42:49+00:00",
+    "submitted_at": "2026-05-01T18:08:37+00:00",
     "submitted_by": "Trivial"
   },
   "placements": [
diff --git a/data/solutions/generated/triintri_037_a824891b660555f5.json b/data/solutions/generated/triintri_037_a824891b660555f5.json
index 5a7474f2a699b38773162da1bd265fe42f2a0ff5..0e3007f3631106a408d071f707b67736a8fbf1a9 100644
--- a/data/solutions/generated/triintri_037_a824891b660555f5.json
+++ b/data/solutions/generated/triintri_037_a824891b660555f5.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.333333333333333,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Ian Watson"
diff --git a/data/solutions/generated/triintri_039_5ff069bd30790b7f.json b/data/solutions/generated/triintri_039_5ff069bd30790b7f.json
index 4b19386c6d9280c3c48c87c5d71d60695cb9bcaf..1e8083acb5ca5ec39f78486a2655285a8df12257 100644
--- a/data/solutions/generated/triintri_039_5ff069bd30790b7f.json
+++ b/data/solutions/generated/triintri_039_5ff069bd30790b7f.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "cg",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.5,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triintri_040_7890a1da940c9143.json b/data/solutions/generated/triintri_040_7890a1da940c9143.json
index 8557172a6045bae19058d2f89e4fa63b4d4acaf8..2b878e2672ba73456e4a38dd78ce23fce7e33cf5 100644
--- a/data/solutions/generated/triintri_040_7890a1da940c9143.json
+++ b/data/solutions/generated/triintri_040_7890a1da940c9143.json
@@ -48,8 +48,11 @@
     "generator": "coordinate_reconstruction",
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
     "profile": "sa",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.5,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T01:47:21+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triintri_11_8c37202a929dc807.json b/data/solutions/generated/triintri_11_8c37202a929dc807.json
index 3a3f010fd29b45a45fc8e86ba8800775e0099f55..1d7c51109c1be1f140e451403596a23892296bc2 100644
--- a/data/solutions/generated/triintri_11_8c37202a929dc807.json
+++ b/data/solutions/generated/triintri_11_8c37202a929dc807.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.0610756975609028,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.7229707590929486,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Erich Friedman"
diff --git a/data/solutions/generated/triintri_12_7642b05605706588.json b/data/solutions/generated/triintri_12_7642b05605706588.json
index ef07937e1b58a3130dff899c3b4bafdd71c4b180..2f2652e4bb52b2cee70805a7988911ffc87bceea 100644
--- a/data/solutions/generated/triintri_12_7642b05605706588.json
+++ b/data/solutions/generated/triintri_12_7642b05605706588.json
@@ -49,7 +49,10 @@
     "generator_profile": "sa_escape",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_20260501T070815Z_broad.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.879385241571817,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T07:13:53+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/triintri_29_38c7a009f9059275.json b/data/solutions/generated/triintri_29_38c7a009f9059275.json
index e3edb54f1fd6ff868a3ff1ddba439884f0be1ca6..c18535f8dc844ceb01f378107b4f2540b1a5908f 100644
--- a/data/solutions/generated/triintri_29_38c7a009f9059275.json
+++ b/data/solutions/generated/triintri_29_38c7a009f9059275.json
@@ -49,7 +49,10 @@
     "generator_profile": "sa_escape",
     "image_seed_recovery_log": "bench_outputs/friedman_image_seeds/rigorous_orange_recovery_current_broad_broad.jsonl",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.666666666666667,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T13:47:12+00:00",
     "submitted_by": "David W. Cantrell"
diff --git a/data/solutions/generated/triintri_30_149a91e0248df04e.json b/data/solutions/generated/triintri_30_149a91e0248df04e.json
index fa328035344e44e29dba98a38ad97a8736287b97..daed25c8caec89c8018b20e18a1de17f51c2f175 100644
--- a/data/solutions/generated/triintri_30_149a91e0248df04e.json
+++ b/data/solutions/generated/triintri_30_149a91e0248df04e.json
@@ -49,7 +49,10 @@
     "generator_profile": "best of cg/steepest/sa seed profiles",
     "image_seed_transform_error": 0.014633043011461478,
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.75,
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "submitted_at": "2026-05-01T02:08:58+00:00",
     "submitted_by": "Maurizio Morandi"
diff --git a/data/solutions/record_hunt/squinhex_36_b7083884dfb200c3.json b/data/solutions/record_hunt/squinhex_36_b7083884dfb200c3.json
index ab59e0c2706aae6e6952ac9363388e97c89565f0..13d9e72cc972b040fe0135ae74a68a0e58c73493 100644
--- a/data/solutions/record_hunt/squinhex_36_b7083884dfb200c3.json
+++ b/data/solutions/record_hunt/squinhex_36_b7083884dfb200c3.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "tight",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.02072594216369,
     "seed": "163676",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/squinhex_36.state",
diff --git a/data/solutions/record_hunt/squinhex_38_657f5bc54656101d.json b/data/solutions/record_hunt/squinhex_38_657f5bc54656101d.json
index b9e889f58e4d81a6cb5a389c01bcafb352dd3779..396e17ebb27edfd49f996a198a4059fadcb305fb 100644
--- a/data/solutions/record_hunt/squinhex_38_657f5bc54656101d.json
+++ b/data/solutions/record_hunt/squinhex_38_657f5bc54656101d.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "tight",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.18476,
     "seed": "159640",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/squinhex_38.state",
diff --git a/data/solutions/record_hunt/squinhex_40_9859865bba74b499.json b/data/solutions/record_hunt/squinhex_40_9859865bba74b499.json
index 0812ae9bc566e18a14c464d10763a365c3bcd2cf..0c024ded2fec18b46ae9aec033ed8448e4e2ba86 100644
--- a/data/solutions/record_hunt/squinhex_40_9859865bba74b499.json
+++ b/data/solutions/record_hunt/squinhex_40_9859865bba74b499.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "tight",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.31157,
     "seed": "138451",
     "source_url": "https://erich-friedman.github.io/packing/squinhex/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/squinhex_40.state",
diff --git a/data/solutions/record_hunt/squinpen_36_e43d96c031faf38c.json b/data/solutions/record_hunt/squinpen_36_e43d96c031faf38c.json
index a7eac62faeb634ec4b33854907bf29038d9a5dd7..d3663eed265e79f27a6a8787dbe88f9858b6882d 100644
--- a/data/solutions/record_hunt/squinpen_36_e43d96c031faf38c.json
+++ b/data/solutions/record_hunt/squinpen_36_e43d96c031faf38c.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "cg",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.93902,
     "seed": "152577",
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/squinpen_36.state",
diff --git a/data/solutions/record_hunt/squinpen_38_00496638a2011285.json b/data/solutions/record_hunt/squinpen_38_00496638a2011285.json
index bc424ea363dc567189a4c094ac597772a70d16ce..2cb13fd3e7f094182887ec9e3a306d13ef28121a 100644
--- a/data/solutions/record_hunt/squinpen_38_00496638a2011285.json
+++ b/data/solutions/record_hunt/squinpen_38_00496638a2011285.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "cg",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.05233,
     "seed": "141478",
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/squinpen_38.state",
diff --git a/data/solutions/record_hunt/squinpen_39_b01313a4744f0eda.json b/data/solutions/record_hunt/squinpen_39_b01313a4744f0eda.json
index c9624c14f1ef39792abfd80ae4dc112ee93d49f2..3656b1f47ba6c3f4f4d7c1aff01071d8396d4e64 100644
--- a/data/solutions/record_hunt/squinpen_39_b01313a4744f0eda.json
+++ b/data/solutions/record_hunt/squinpen_39_b01313a4744f0eda.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "tight",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.13846,
     "seed": "97082",
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/squinpen_39.state",
diff --git a/data/solutions/record_hunt/squinpen_40_153dbd88227e7083.json b/data/solutions/record_hunt/squinpen_40_153dbd88227e7083.json
index 902c2afa13fb56847de8ab1b91268487a844beba..41ec6df92398525728a04e1b10cb4faa1880c4d7 100644
--- a/data/solutions/record_hunt/squinpen_40_153dbd88227e7083.json
+++ b/data/solutions/record_hunt/squinpen_40_153dbd88227e7083.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "cg",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 5.1725,
     "seed": "173766",
     "source_url": "https://erich-friedman.github.io/packing/squinpen/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/squinpen_40.state",
diff --git a/data/solutions/record_hunt/squintri_39_c0988e1f3bf189d9.json b/data/solutions/record_hunt/squintri_39_c0988e1f3bf189d9.json
index 7fd5d3041eb1de104ca212d2440ebfb4a212048a..e2009412066eb1e40d563d68daafd7a890548414 100644
--- a/data/solutions/record_hunt/squintri_39_c0988e1f3bf189d9.json
+++ b/data/solutions/record_hunt/squintri_39_c0988e1f3bf189d9.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "cg",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 10.31,
     "seed": "149550",
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/squintri_39.state",
diff --git a/data/solutions/record_hunt/squintri_40_13b03f25af76ce87.json b/data/solutions/record_hunt/squintri_40_13b03f25af76ce87.json
index 1be2959c19b989c44b1dc048c9c8e2e2b85e3ec7..c4ee127fadff8266ec99863551cb935b8eb90d3b 100644
--- a/data/solutions/record_hunt/squintri_40_13b03f25af76ce87.json
+++ b/data/solutions/record_hunt/squintri_40_13b03f25af76ce87.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "cg",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 10.46426,
     "seed": "101118",
     "source_url": "https://erich-friedman.github.io/packing/squintri/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/squintri_40.state",
diff --git a/data/solutions/record_hunt/triinhex_36_d30ec5c19b8369f3.json b/data/solutions/record_hunt/triinhex_36_d30ec5c19b8369f3.json
index 444f2c94a8810a5b364f5654abb2c37997942bb8..987038eb0b8c2b10a41f2172b2c4591c7f2ee1b7 100644
--- a/data/solutions/record_hunt/triinhex_36_d30ec5c19b8369f3.json
+++ b/data/solutions/record_hunt/triinhex_36_d30ec5c19b8369f3.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "tight",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.59123,
     "seed": "122307",
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/triinhex_36.state",
diff --git a/data/solutions/record_hunt/triinhex_37_c791d76ac960cbca.json b/data/solutions/record_hunt/triinhex_37_c791d76ac960cbca.json
index bf34b4649eb0cc5040dd1d995e6000d24e25cdbc..8d7c53d6d106cea0b94af37f7cb542c359da563a 100644
--- a/data/solutions/record_hunt/triinhex_37_c791d76ac960cbca.json
+++ b/data/solutions/record_hunt/triinhex_37_c791d76ac960cbca.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "tight",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.61943,
     "seed": "91028",
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/triinhex_37.state",
diff --git a/data/solutions/record_hunt/triinhex_40_8b6d682b66356562.json b/data/solutions/record_hunt/triinhex_40_8b6d682b66356562.json
index f7053706e59686cccc4ad60c75d60b4578b7b06f..ca12dda7135a2bd4dab0605a94d48b4b72c780c8 100644
--- a/data/solutions/record_hunt/triinhex_40_8b6d682b66356562.json
+++ b/data/solutions/record_hunt/triinhex_40_8b6d682b66356562.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "tight",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 2.71622,
     "seed": "98091",
     "source_url": "https://erich-friedman.github.io/packing/triinhex/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/triinhex_40.state",
diff --git a/data/solutions/record_hunt/triinpen_36_5183a03ffc16bcf9.json b/data/solutions/record_hunt/triinpen_36_5183a03ffc16bcf9.json
index ac7d7ddafead2e418789a5e133c4aea710367852..2e34af0ad2c26594f0fc4a5a18d1b41ffb9d7596 100644
--- a/data/solutions/record_hunt/triinpen_36_5183a03ffc16bcf9.json
+++ b/data/solutions/record_hunt/triinpen_36_5183a03ffc16bcf9.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "tight",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.177,
     "seed": "127352",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/triinpen_36.state",
diff --git a/data/solutions/record_hunt/triinpen_37_08996b45ff04652c.json b/data/solutions/record_hunt/triinpen_37_08996b45ff04652c.json
index 62681b6251733bbffb9d9e2306feeaad0d0a7f0a..ed8e06379dc6984e84d8f73dca1e9b53af79542c 100644
--- a/data/solutions/record_hunt/triinpen_37_08996b45ff04652c.json
+++ b/data/solutions/record_hunt/triinpen_37_08996b45ff04652c.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "cg",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.21529,
     "seed": "112217",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/triinpen_37.state",
diff --git a/data/solutions/record_hunt/triinpen_38_cca381f54ee9b299.json b/data/solutions/record_hunt/triinpen_38_cca381f54ee9b299.json
index 5260e4b66f6ea0f1c2cb2245d20545471cba0ac2..14440e542111af2547b728f015944636996f9ada 100644
--- a/data/solutions/record_hunt/triinpen_38_cca381f54ee9b299.json
+++ b/data/solutions/record_hunt/triinpen_38_cca381f54ee9b299.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "cg",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.25877,
     "seed": "104145",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/triinpen_38.state",
diff --git a/data/solutions/record_hunt/triinpen_40_032ceee4e789eff6.json b/data/solutions/record_hunt/triinpen_40_032ceee4e789eff6.json
index 1776c466077af3fd10125753b78600b73813055a..53e9850307590d491ab1c6ae6b923b8e19bc1f1e 100644
--- a/data/solutions/record_hunt/triinpen_40_032ceee4e789eff6.json
+++ b/data/solutions/record_hunt/triinpen_40_032ceee4e789eff6.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "tight",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 3.32786,
     "seed": "91028",
     "source_url": "https://erich-friedman.github.io/packing/triinpen/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/triinpen_40.state",
diff --git a/data/solutions/record_hunt/triinsqu_36_aae755b2130a7a83.json b/data/solutions/record_hunt/triinsqu_36_aae755b2130a7a83.json
index 1e595426dab81f156a5b7b016fe15b0b9b632f8c..484bc8956094e30dce7f3393852bdad32a9ae398 100644
--- a/data/solutions/record_hunt/triinsqu_36_aae755b2130a7a83.json
+++ b/data/solutions/record_hunt/triinsqu_36_aae755b2130a7a83.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "tight",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.214,
     "seed": "167712",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/triinsqu_36.state",
diff --git a/data/solutions/record_hunt/triinsqu_37_46406dc33c9746a7.json b/data/solutions/record_hunt/triinsqu_37_46406dc33c9746a7.json
index 41177dd03a4759dcfbd5f9b3efe3e4f65f8d93af..e3f81e8cf252c567996b36323c2ce406e896fa62 100644
--- a/data/solutions/record_hunt/triinsqu_37_46406dc33c9746a7.json
+++ b/data/solutions/record_hunt/triinsqu_37_46406dc33c9746a7.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "tight",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.27233,
     "seed": "103136",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/triinsqu_37.state",
diff --git a/data/solutions/record_hunt/triinsqu_38_f44a4bd75616bc73.json b/data/solutions/record_hunt/triinsqu_38_f44a4bd75616bc73.json
index 618d16bc74bd6e34fc0a48e8c556cd3344fa6787..2f68099f8b4d509ca013a27c5980d0b57f870058 100644
--- a/data/solutions/record_hunt/triinsqu_38_f44a4bd75616bc73.json
+++ b/data/solutions/record_hunt/triinsqu_38_f44a4bd75616bc73.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "tight",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.327,
     "seed": "131388",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/triinsqu_38.state",
diff --git a/data/solutions/record_hunt/triinsqu_39_263f7876a25d297b.json b/data/solutions/record_hunt/triinsqu_39_263f7876a25d297b.json
index b1816a8c675d74007ffaae6c6a7416117b8fdb78..35db42e521d833b635f5c6097767f7f0176540de 100644
--- a/data/solutions/record_hunt/triinsqu_39_263f7876a25d297b.json
+++ b/data/solutions/record_hunt/triinsqu_39_263f7876a25d297b.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "sa",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 4.383,
     "seed": "122307",
     "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/triinsqu_39.state",
diff --git a/data/solutions/record_hunt/triintri_38_b1563d97c893e28d.json b/data/solutions/record_hunt/triintri_38_b1563d97c893e28d.json
index cde3dbb5a336ad4db704ea48cf654a7fa2027288..60b83ec0c0a9e446c9b8b8249d3498d5d4194b48 100644
--- a/data/solutions/record_hunt/triintri_38_b1563d97c893e28d.json
+++ b/data/solutions/record_hunt/triintri_38_b1563d97c893e28d.json
@@ -54,7 +54,10 @@
     "generator": "coordinate_record_hunt",
     "generator_profile": "sa",
     "leaderboard_status": "current_best_coordinate",
+    "metric_recovery_tolerance_rel": 0.001,
     "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "public_credit_policy": "@1 cases are credited as Trivial; Nathan Roll is credited only for non-image-seeded coordinate improvements above 0.15% relative to the Friedman reference metric.",
+    "reference_side": 6.43454,
     "seed": "126343",
     "source_url": "https://erich-friedman.github.io/packing/triintri/",
     "state_path": "bench_outputs/record_hunt_frontier/certified_best_states_live/triintri_38.state",
diff --git a/data/svg/0b33929541015a68.svg b/data/svg/0b33929541015a68.svg
new file mode 100644
index 0000000000000000000000000000000000000000..7bd606a77bfc754551e3a294ffa8cd18fcaa7072
--- /dev/null
+++ b/data/svg/0b33929541015a68.svg
@@ -0,0 +1,33 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-3.34742266649 -3.87330963234 7.40194059773 7.74661926469" width="900" height="900">
+  <title>squinpen@27</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="1.91109623845,-2.23682625088 1.10207861084,-1.64904187017 1.68986299155,-0.840024242554 2.49888061917,-1.42780862327" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="0.56504482479,2.28131448235 -0.386087860525,1.97253201049 -0.694870332382,2.9236646958 0.256262352933,3.23244716766" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="1.05724959903,-1.00593313341 0.05736293902,-0.990877664932 0.072418407495,0.00900899507905 1.07230506751,-0.00604647339598" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="0.0102483098708,0.974178313963 -0.989742594289,0.969913152951 -0.994007755301,1.96990405711 0.00598314885847,1.97416921812" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="0.0235855103279,-1.02583839249 -0.976405391755,-1.03010404038 -0.980671039646,-0.0301131383004 0.0193198624363,-0.0258474904088" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="2.60746599786,-1.50664486254 1.79844838264,-0.918860464765 2.38623278041,-0.109842849546 3.19525039563,-0.69762724732" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="2.35578894777,1.85340768084 1.54677028233,1.26562472859 0.95898733007,2.07464339403 1.76800599551,2.66242634629" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="0.0658136872318,-0.0256217924338 -0.934177215319,-0.029887330487 -0.938442753373,0.970103572064 0.0615481491787,0.974369110117" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="-1.99507424694,-1.17594221692 -2.99507423229,-1.17577107778 -2.99490309315,-0.175771092421 -1.9949031078,-0.17594223156" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="2.85574504207,0.978204042002 2.04751337324,0.389339397538 1.45864872877,1.19757106637 2.2668803976,1.78643571083" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="-0.995231737786,-1.50168670843 -1.99523139358,-1.50085700158 -1.99440168673,-0.500857345787 -0.994402030934,-0.501687052639" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="1.76408445126,2.65969081768 0.952337742051,2.07568116015 0.368328084514,2.88742786935 1.18007479372,3.47143752689" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="-0.995997142515,-2.50407089829 -1.99599209058,-2.50089224472 -1.99281343701,-1.50089729665 -0.992818488939,-1.50407595023" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="-1.99518022162,0.824906439271 -2.99518021977,0.824967233013 -2.99511942603,1.82496723116 -1.99511942787,1.82490643742" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="-1.9952792627,-2.17617747513 -2.99527926269,-2.17617821205 -2.99527999962,-1.17617821205 -1.99527999962,-1.17617747513" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="1.00924791469,-2.00537304868 0.00936126826944,-1.99031667751 0.0244176394373,-0.990430031092 1.02430428586,-1.00548640226" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="1.43201784553,-3.12487877692 0.623000228533,-2.53709438159 1.21078462386,-1.72807676459 2.01980224086,-2.31586115992" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="1.22358912017,-0.00824160019012 0.223701938766,0.00677920055554 0.238722739512,1.00666638196 1.23860992092,0.991645581218" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="1.8780687219,-0.80868629792 1.06924629457,-0.220633340227 1.65729925226,0.588189087101 2.46612167959,0.000136129408116" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="-1.98983149876,-0.1757484913 -2.98983141357,-0.175335727237 -2.98941864951,0.824664187576 -1.98941873469,0.824251423513" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="-0.97877419783,-0.491550512668 -1.97873112189,-0.500832216704 -1.98801282592,0.499124707354 -0.988055901866,0.508406411389" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="0.009465180274,-2.02593386838 -0.990525720576,-2.03019980513 -0.994791657327,-1.03020890428 0.00519924352324,-1.02594296753" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="3.5337756017,0.232054813305 2.72476095477,-0.355733669954 2.13697247151,0.453280976976 2.94598711844,1.04106946024" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="-0.985529758536,0.50846757682 -1.98548667709,0.499185280244 -1.99476897367,1.4991421988 -0.994812055113,1.50842449538" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="-0.992086453906,1.5084875862 -1.99204336236,1.49920420095 -2.00132674761,2.4991611094 -1.00136983916,2.50844449465" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="1.01015124924,1.01000387925 0.0101603389415,1.0057401577 0.00589661738771,2.00573106799 1.00588752769,2.00999478955" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="0.625023223768,-3.0233423903 -0.37496767694,-3.02760836038 -0.379233647024,-2.02761745967 0.620757253684,-2.02335148959" fill="#cdf7d6" stroke-width="0.0270860813381"/>
+    <polygon points="3.70239887285,-0 1.14410417167,-3.52119057395 -2.99530360809,-2.17621545557 -2.99530360809,2.17621545557 1.14410417167,3.52119057395" fill="none" stroke-width="0.070423811479"/>
+  </g>
+</svg>
diff --git a/data/svg/16349db1062e3f6e.svg b/data/svg/16349db1062e3f6e.svg
new file mode 100644
index 0000000000000000000000000000000000000000..284015bb4a1e0ed5707844b1b9cf65e957c38b38
--- /dev/null
+++ b/data/svg/16349db1062e3f6e.svg
@@ -0,0 +1,25 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-1.80358825584 -2.08693566959 3.98815879029 4.17387133918" width="900" height="900">
+  <title>triinpen@19</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="-0.740288162821,-1.4563651399 -1.60659558337,-0.956853925705 -0.740852472123,-0.456365299126" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="0.118554155257,0.0401208887358 -0.747380705101,-0.460035904296 -0.747561763563,0.539964079313" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="0.438838968681,-1.83949523339 -0.512209627301,-1.53045386386 0.230952347522,-0.861342304268" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="0.125684129892,-0.956068023525 -0.740571149503,-0.456466391302 0.125224195472,0.0439318707049" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="-0.747535143026,-0.460163549623 -1.61359941932,0.0397691151692 -0.747612893282,0.539836447355" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="1.27727840168,0.986044734944 0.29394076707,0.804256131445 0.628176035626,1.74674580526" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="1.85955886765,0.173666177123 0.864293710135,0.0764691286108 1.27775117571,0.986992562775" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="0.221132517533,-0.0107199169828 -0.647608613886,0.484546523007 0.215675270497,0.989265192134" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="0.837416105717,0.00878406493611 0.216784974542,0.792886736158 1.20615337258,0.938317726524" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="-1.61380881619,0.0397261662339 -1.61385066438,1.03972616536 -0.747804337258,0.53976240739" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="0.224514871283,-0.638694583905 0.219147340874,0.3612910108 1.08784403451,-0.134053368862" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="1.3954846645,-0.8249437221 0.988744736755,0.0886002731064 1.98326700795,-0.0159246143353" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="1.1735397096,-1.13039791967 0.267854650199,-0.706446774874 1.08784964126,-0.134076078" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="-0.646929869177,0.484947963543 -0.652387363135,1.48493307131 0.216353890578,0.989666845836" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="0.430370371351,-1.79953468687 0.222483811428,-0.821381744738 1.17353238806,-1.13042317381" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="-0.652025570809,0.484912769791 -1.51824671567,0.984573582931 -0.652417185787,1.48491269311" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="0.324993925284,0.891908209035 -0.418148601312,1.56104136855 0.532908976641,1.87005509546" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="-1.61352037592,-0.960400486996 -1.6138137915,0.0395994699574 -0.747641717206,-0.460146403167" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="-0.740260668619,-1.45638919867 -0.740720654469,-0.456389304467 0.12553465062,-0.955990892139" fill="#cdf7d6" stroke-width="0.0145939557244"/>
+    <polygon points="1.99484910903,-0 0.616442275905,-1.89721424417 -1.61386683042,-1.17254288684 -1.61386683042,1.17254288684 0.616442275905,1.89721424417" fill="none" stroke-width="0.0379442848834"/>
+  </g>
+</svg>
diff --git a/data/svg/300596cf09652b9a.svg b/data/svg/300596cf09652b9a.svg
new file mode 100644
index 0000000000000000000000000000000000000000..953361480176b1f1102283fc0165cdb27d011a23
--- /dev/null
+++ b/data/svg/300596cf09652b9a.svg
@@ -0,0 +1,38 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-3.0951539079 -3.0951539079 6.19030781581 6.19030781581" width="900" height="900">
+  <title>triinsqu@32</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="-6.15083088881e-06,-2.81375385573 -0.699439454586,-2.09905597998 0.26922371372,-1.85067790855" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="0.415884683049,-2.39787537289 0.1570639218,-1.43195000644 1.12299020793,-1.6907673354" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="0.269217058822,-1.85064835645 -0.699445048312,-2.09903056637 -0.430219298378,-1.13595346895" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="-0.702806598115,-2.11095267214 -1.40224278564,-1.39625761858 -0.433580619531,-1.14787563864" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="0.927674780959,-1.63821745229 -0.0383109366111,-1.37962202802 0.668632128889,-0.672351569047" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="0.927759240191,-1.63841269343 0.668710709673,-0.672548386791 1.63469800109,-0.931137931868" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="-0.433586212448,-1.14784763296 -1.40224783857,-1.39623171877 -1.13302395372,-0.433154099972" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="-0.0753753432154,-1.49123713725 -0.782006220264,-0.783654772013 0.18409352183,-0.525485664011" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="-1.40549903418,-1.40826142995 -2.11260597255,-0.701154805958 -1.1466802038,-0.442335546127" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="1.68712356794,-1.12664409484 1.42829815171,-0.160719975707 2.39422568512,-0.419532649671" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="1.63470313927,-0.931110832121 0.668719209615,-0.672508729185 1.37566716506,0.034756842078" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="0.317482613514,-1.0233850914 0.0587739441953,-0.0574296967646 1.02467018953,-0.316359114271" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="0.184085490662,-0.525459789657 -0.782105084112,-0.783288750827 -0.522296226929,0.182371312409" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="-1.13192760843,-0.432812066358 -2.09645357327,-0.696800064476 -1.84281090351,0.270497922744" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="-0.783814348157,-0.782824029009 -1.4889600647,-0.073761606905 -0.522321136018,0.18238128594" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="-2.09647676917,-0.696792443339 -2.81366564657,8.63941446262e-05 -1.85155643125,0.272750762544" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="2.81376824986,-8.01862477084e-07 1.84784401841,-0.258825798889 2.10665711158,0.707101622196" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="1.49733196275,0.0747369893664 0.531408868048,-0.18409224993 0.790217718927,0.781836307835" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="1.84425671317,-0.27214379112 1.13714316742,0.434956225444 2.10306651766,0.693784511136" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="0.531384785854,-0.184084240768 -0.179944086967,0.518775087043 0.784414382614,0.783374297446" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="-0.0555724104768,0.0584782916256 -1.02207846241,0.315122114022 -0.316565366525,1.02381899671" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="-1.37485384008,-0.0379410417989 -1.63498538117,0.927632146173 -0.668708700628,0.670126075096" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="-1.42927835788,0.159733150324 -2.39520458185,0.418550711278 -1.68809888713,1.12565857894" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="2.10306317671,0.693806510614 1.13713887315,0.434981782676 1.39595223541,1.40090913166" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="0.784337362959,0.783498943378 -0.17999039819,0.518787838438 0.0729269408425,1.48627572964" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="1.13711769432,0.434985569528 0.430007929681,1.14208936725 1.39593266394,1.40091248783" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="-0.668879169526,0.672509659978 -1.6353936752,0.92912164396 -0.929903925319,1.63784176701" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="-0.66831354171,0.670519307826 -0.929308280739,1.63585953086 0.0371982452139,1.37921749359" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="1.40926460321,1.4045055171 0.443338587579,1.14568717862 0.702158339302,2.11161281557" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="0.428103788062,1.13543834859 -0.270438571744,1.85100705357 0.698533284831,2.09817813029" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="-0.157949325949,1.43106226585 -1.12387691835,1.68987471966 -0.416774962334,2.39698632598" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="0.698529523882,2.09819216872 -0.27044460671,1.85103000688 -6.25241679408e-06,2.8137673005" fill="#cdf7d6" stroke-width="0.0216444329154"/>
+    <polygon points="2.813776279,-0 1.7229410568e-16,-2.813776279 -2.813776279,-3.4458821136e-16 -5.1688231704e-16,2.813776279" fill="none" stroke-width="0.0562755255801"/>
+  </g>
+</svg>
diff --git a/data/svg/3fb669c73e695ac9.svg b/data/svg/3fb669c73e695ac9.svg
new file mode 100644
index 0000000000000000000000000000000000000000..84b56861e06130db25c1ba62b4137b716d3d2286
--- /dev/null
+++ b/data/svg/3fb669c73e695ac9.svg
@@ -0,0 +1,27 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-3.5620926982 -3.12824730657 7.12418539639 6.25649461314" width="900" height="900">
+  <title>squinhex@21</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="-1.87704782791,0.0768268682818 -2.74322226461,0.576568646818 -2.24348048607,1.44274308351 -1.37730604937,0.943001304978" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="-1.49863969307,1.01303582192 -2.36467999664,1.51301001384 -1.86470580471,2.37905031741 -0.998665501142,1.87907612549" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="0.00135431644284,1.69857775814 -0.998645683523,1.69856943614 -0.99865400552,2.69856943611 0.00134599444556,2.6985777581" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="1.00137426833,1.80435430705 0.00137426834667,1.80436012743 0.00138008872597,2.80436012741 1.00138008871,2.80435430703" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="1.89320106959,1.06276698973 0.906364324386,1.22448661844 1.0680839531,2.21132336365 2.0549206983,2.04960373494" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="-1.75313507452,-0.572249019637 -2.61915247186,-1.07226288694 -3.11916633916,-0.206245489599 -2.25314894182,0.293768377706" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="-0.44953702802,0.249917261138 -1.43671759776,0.409524662969 -1.27711019593,1.39670523271 -0.289929626188,1.23709783088" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="0.611755223565,0.548469969914 -0.375087380222,0.710153844656 -0.21340350548,1.69699644844 0.773439098307,1.5353125737" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="1.552499542,0.105239017424 0.565661240053,0.266949146381 0.72737136901,1.25378744833 1.71420967096,1.09207731937" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="2.53937627798,-0.0564849594852 1.5525391311,0.105232218141 1.71425630873,1.09206936502 2.70109345561,0.930352187394" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="-1.2487920389,-1.43582811517 -2.11481177503,-1.93583793171 -2.61482159157,-1.06981819558 -1.74880185544,-0.569808379045" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="-0.729349467829,-0.716253339891 -1.72397206249,-0.612687446899 -1.6204061695,0.381935147761 -0.625783574837,0.27836925477" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="0.173087618045,-0.736510409047 -0.671215597551,-0.20064467947 -0.135349867974,0.643658536126 0.708953347621,0.107792806549" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="1.55852442721,-0.90913365363 0.571687111611,-0.747417505572 0.733403259669,0.239419810027 1.72024057527,0.0777036619681" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="2.45912090377,-1.34940884902 1.59308915802,-0.84941983379 2.09307817324,0.0166119119632 2.959109919,-0.483377103264" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="-0.75309075588,-2.30440423611 -1.61911640648,-2.8044038086 -2.11911597898,-1.938378158 -1.25309032838,-1.4383785855" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="-0.096353395805,-1.7275616491 -1.09619934898,-1.71000972818 -1.07864742805,-0.710163775005 -0.0788014748761,-0.727715695934" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="0.902497728727,-1.80438972438 -0.0973475341533,-1.786798525 -0.0797563347692,-0.786953262116 0.920088928111,-0.804544461501" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="1.24699462131,-2.80440981183 0.246994621344,-2.804401351 0.247003082178,-1.80440135104 1.24700308214,-1.80440981187" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="1.9590561482,-2.21549770626 1.09304377975,-1.71547512908 1.59306635694,-0.849462760628 2.45907872539,-1.34948533781" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="0.246943436645,-2.80296465138 -0.753056563194,-2.80294669785 -0.753038609661,-1.80294669801 0.246961390178,-1.80296465154" fill="#cdf7d6" stroke-width="0.0249097391412"/>
+    <polygon points="3.23826608836,-0 1.61913304418,-2.80442069673 -1.61913304418,-2.80442069673 -3.23826608836,-3.9657321999e-16 -1.61913304418,2.80442069673 1.61913304418,2.80442069673" fill="none" stroke-width="0.0647653217672"/>
+  </g>
+</svg>
diff --git a/data/svg/545ef4899aee40a3.svg b/data/svg/545ef4899aee40a3.svg
new file mode 100644
index 0000000000000000000000000000000000000000..f58f9ed7b16199c11801b3edc8501d4db42ad194
--- /dev/null
+++ b/data/svg/545ef4899aee40a3.svg
@@ -0,0 +1,25 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-2.15005648053 -1.88819016354 4.30011296105 3.77638032708" width="900" height="900">
+  <title>triinhex@19</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="1.42113545861,-0.82327040664 0.421151102705,-0.817676844427 0.925987447633,0.0455382300703" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="1.43182737769,-0.826643977092 0.931816522162,0.0393751591582 1.93181652208,0.0393876940905" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="-0.909081133591,0.0787975224461 -1.90908113336,0.078776124133 -1.40909966496,0.944812226876" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="-0.333965648184,0.823417131187 -1.33392770548,0.814705990752 -0.841490745745,1.68505410541" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="-6.99975053564e-06,-1.65332941052 -1.00000699966,-1.65334322966 -0.500018967433,-0.787310916387" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="1.93184334461,0.0394050843889 0.931843344685,0.0393928068337 1.43183271197,0.90542434933" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="-0.333722913457,0.823329277277 -0.839570147988,1.68595235564 0.160406969027,1.692717372" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="0.343788201989,0.281361810995 -0.652002742236,0.373015481951 -0.0747328627252,1.18956890103" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="0.977300011727,-1.69270167576 0.477303377194,-0.826674328933 1.47730337719,-0.826678215035" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="1.01724101028,0.187387893692 0.15430924407,0.692708353273 1.02339548222,1.18736895475" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="0.977281639195,-1.69271453094 -0.0227183607618,-1.69272388007 0.477273542635,-0.826693801757" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="-0.567653994343,-0.511756568769 -0.969100170632,0.404126047915 0.0248005304452,0.293847326491" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="0.414242498185,-0.610402646139 0.0248624409517,0.310674533596 1.01722870607,0.187348965019" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="0.424552260062,-0.636150850338 -0.56775215698,-0.512328623262 0.0356332457421,0.285121096646" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="-0.108355105502,-1.45992963754 -0.486510394847,-0.534187461149 0.504283491931,-0.669566462194" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="-1.40908516107,-0.787269926941 -1.90910372498,0.0787447586976 -0.909103725212,0.0787661945922" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="1.02338192844,1.18738935384 0.154295841037,0.692728487502 0.160450008235,1.69270955044" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="-1.00002419718,-1.65333431026 -1.50003620276,-0.787315838013 -0.500036202852,-0.78730197511" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="-0.409062183874,-0.787264356055 -1.40906218365,-0.787285586288 -0.909080569682,0.0787504324175" fill="#cdf7d6" stroke-width="0.0150353599967"/>
+    <polygon points="1.95459679957,-0 0.977298399785,-1.69273048258 -0.977298399785,-1.69273048258 -1.95459679957,-2.39369071422e-16 -0.977298399785,1.69273048258 0.977298399785,1.69273048258" fill="none" stroke-width="0.0390919359914"/>
+  </g>
+</svg>
diff --git a/data/svg/5bbf9f2ba5ab11a2.svg b/data/svg/5bbf9f2ba5ab11a2.svg
new file mode 100644
index 0000000000000000000000000000000000000000..778c21a1720d036a27b5e1f6755ebc0306d02a6d
--- /dev/null
+++ b/data/svg/5bbf9f2ba5ab11a2.svg
@@ -0,0 +1,47 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-5.50004761843 -3.00002597414 11.0000952369 6.00005194829" width="900" height="900">
+  <title>squindom@41</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="2.82017780655,-1.25257316242 2.8201684,-2.25257316238 1.82016840005,-2.25256375583 1.82017780659,-1.25256375588" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="4.97641327901,2.50001175241 4.97641100824,1.50001175242 3.97641100824,1.50001402319 3.97641327902,2.50001402319" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="1.82013347707,-2.50001159323 0.820133477083,-2.50001612523 0.820128945078,-1.50001612524 1.82012894507,-1.50001159324" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="0.691358550644,-0.499990021323 -0.308641449344,-0.499994916926 -0.308646344947,0.500005083062 0.691353655041,0.500009978665" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-0.191848641937,-2.50001783423 -1.19184864194,-2.50001944741 -1.19185025512,-1.50001944742 -0.191850255124,-1.50001783423" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="2.86651067856,0.920808518849 2.29427251788,0.100721031159 1.47418503019,0.672959191835 2.04642319087,1.49304667953" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-4.81760267932,-2.50001657342 -4.81760132919,-1.50001657343 -3.81760132919,-1.50001792356 -3.81760267932,-2.50001792356" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="0.654087129871,1.24520556117 1.22632538096,2.06529298577 2.04641280556,1.49305473468 1.47417455447,0.672967310078" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-1.33854361616,-1.50002064996 -1.33854462885,-2.50002064996 -2.33854462885,-2.50001963726 -2.33854361616,-1.50001963726" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="3.9911179673,1.35564715128 3.41888250849,0.535557778294 2.59879313551,1.1077932371 3.17102859432,1.92788261009" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-3.3460113045,-0.500009070446 -2.3460113045,-0.500008783507 -2.34601101756,-1.50000878351 -3.34601101756,-1.50000907045" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-1.33941486882,-1.50000721202 -1.33941644188,-0.500007212019 -0.33941644188,-0.500005638962 -0.339414868823,-1.50000563896" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-1.34594762841,1.50000485606 -0.345947628407,1.50000629506 -0.345946189406,0.500006295066 -1.34594618941,0.500004856066" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="3.17094625167,1.92778503953 2.59871075657,1.10769569186 1.77862140891,1.67993118696 2.350856904,2.50002053462" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-4.36050326862,-1.5000078983 -4.36050162703,-0.500007898305 -3.36050162704,-0.500009539892 -3.36050326862,-1.50000953989" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-1.34596629388,0.500005180663 -2.34596629388,0.500005171282 -2.34596630326,1.50000517128 -1.34596630326,1.50000518066" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="3.05295014183,-0.428530758117 2.48083096548,-1.2487012575 1.6606604661,-0.676582081145 2.23277964245,0.143588418234" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="0.660640947702,-1.50000187293 0.660632278368,-0.500001872967 1.66063227833,-0.499993203634 1.66064094766,-1.4999932036" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-1.34596631875,0.499997612198 -1.34596673668,-0.500002387802 -2.34596673668,-0.500001969868 -2.34596631875,0.499998030132" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-2.2337348567,2.50001847549 -1.2337348567,2.500018426 -1.23373490619,1.500018426 -2.23373490619,1.50001847549" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-4.24296040856,1.50002061133 -4.24295896496,2.50002061133 -3.24295896496,2.50001916774 -3.24296040856,1.50001916774" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="1.72422874533,0.498458604819 1.69082010537,-0.500983170762 0.691378329785,-0.467574530797 0.72478696975,0.531867244783" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-0.345942007527,-0.499999692833 -1.34594200753,-0.500001182932 -1.34594349763,0.499998817066 -0.345943497626,0.500000307166" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="2.79208549363,-0.803980318453 3.48811156399,-0.085963807936 4.20612807451,-0.781989878299 3.51010200415,-1.50000638882" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="0.660609787106,-0.500001950601 0.660611864558,-1.5000019506 -0.33938813544,-1.50000402805 -0.339390212891,-0.500004028053" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="2.82019091417,-2.50001535555 2.82019568673,-1.50001535556 3.82019568672,-1.50002012812 3.82019091416,-2.5000201281" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="4.00398291344,1.49999550472 5.00004306326,1.41131530431 4.91136286285,0.415255154492 3.91530271303,0.503935354904" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-3.36020016313,-2.500017933 -3.36020114425,-1.500017933 -2.36020114425,-1.50001695188 -2.36020016313,-2.50001695188" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="0.654069133451,1.5000110657 0.65407431088,0.500011065718 -0.345925689107,0.500005888289 -0.345930866536,1.50000588828" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="2.29435740267,0.100820872929 2.86659550426,0.920908401848 3.68668303318,0.348670300257 3.11444493159,-0.471417228662" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-1.23362983954,1.50001774607 -1.23363174862,2.50001774607 -0.233631748623,2.50001965515 -0.233629839543,1.50001965515" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-2.34598132683,-1.50001017624 -2.34598031142,-0.500010176238 -1.34598031142,-0.500011191651 -1.34598132683,-1.50001119165" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-2.34600042519,0.499998958795 -2.34599990408,-0.500001041205 -3.34599990408,-0.500001562308 -3.34600042519,0.499998437692" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-0.179901560451,-1.500018198 0.820098439547,-1.50001633647 0.820100301078,-2.50001633647 -0.17989969892,-2.500018198" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-4.35417724477,-0.499999002089 -4.35417640454,0.500000997911 -3.35417640454,0.500000157681 -3.35417724477,-0.499999842318" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-2.24195548258,2.50001921275 -2.24195441065,1.50001921275 -3.24195441065,1.50001814082 -3.24195548258,2.50001814082" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="4.00397581001,0.496024277984 5.00003544488,0.407338293839 4.91134946074,-0.58872134103 3.91528982587,-0.500035356886" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-3.3459867388,1.50000544124 -2.3459867388,1.50000620977 -2.34598597026,0.500006209775 -3.34598597026,0.500005441236" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="0.770593742174,2.50001990513 0.770598621276,1.50001990514 -0.229401378712,1.50001502604 -0.229406257814,2.50001502603" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-3.98360893741,1.50001027768 -3.98361028515,0.500010277683 -4.98361028515,0.500011625429 -4.98360893741,1.50001162543" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="4.69617989447,-0.955471718615 5.00003007608,-1.90819154476 4.04731024993,-2.21204172637 3.74346006832,-1.25932190022" fill="#cdf7d6" stroke-width="0.0384618714506"/>
+    <polygon points="-5.00004328857,2.50002164429 5.00004328857,2.50002164429 5.00004328857,-2.50002164429 -5.00004328857,-2.50002164429" fill="none" stroke-width="0.100000865771"/>
+  </g>
+</svg>
diff --git a/data/svg/6034a27a1d11d106.svg b/data/svg/6034a27a1d11d106.svg
new file mode 100644
index 0000000000000000000000000000000000000000..268d03d23747a8e7ea466e782d32f9f5baf7b56c
--- /dev/null
+++ b/data/svg/6034a27a1d11d106.svg
@@ -0,0 +1,40 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-2.39717398957 -2.77377493945 5.30071677254 5.54754987891" width="900" height="900">
+  <title>triinpen@34</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="0.645381148271,-2.41703488099 -0.318806012109,-2.15181210717 0.39297722788,-1.44941291919" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="0.835347393161,-2.49952258384 0.428621268896,-1.58597244299 1.42314196063,-1.69051235742" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="-0.259448336839,-2.09319658412 -1.22364117263,-1.82799444345 -0.511872963772,-1.12558002385" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="-0.247993924352,-2.08190920925 -0.500399826911,-1.1142877645 0.463787876775,-1.37950856319" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="-1.18102242701,-1.7858926287 -2.14500155064,-1.51991471755 -1.43266836093,-0.818073263351" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="1.42314176819,-1.69047693977 0.428619597507,-1.58595109598 1.01640271892,-0.776932553437" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="-1.18122660222,-1.78504618599 -1.43287032929,-0.817226246831 -0.46889181216,-1.08320635606" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="1.42316476671,-1.69048238346 1.01642690509,-0.776937468347 2.01094893988,-0.881464605055" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="0.644644342388,-1.27241732306 -0.348559373888,-1.15602841476 0.248838235558,-0.35408321948" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="0.651625916415,-1.26937642368 0.248858546458,-0.354074044297 1.24291734412,-0.462918459789" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="-2.06001953797,-1.23137283064 -2.13915273665,-0.234508779296 -1.23627654473,-0.664409444633" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="-0.361295561285,-1.12974174484 -1.27907191437,-0.732644067038 -0.476287061072,-0.13637526917" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="2.0109531325,-0.881448488369 1.01643125561,-0.776919849243 1.60421665096,0.0320970411957" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="2.01097274624,-0.881435892224 1.60423183793,0.0321076664032 2.59875422132,-0.0724161535576" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="-0.405476435019,-0.747939375443 -0.42375633346,0.251893533254 0.451264314232,-0.232192064665" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="-1.22027688551,-0.688950452308 -1.3352670618,0.304416176564 -0.417491237776,-0.0926827240185" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="-1.22722922263,-0.629056271551 -2.14500139738,-0.231948936876 -1.34221027015,0.364311414008" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="1.50613253337,-0.102863093084 0.544119623574,-0.375867051628 0.788697715041,0.593762546299" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="0.554955184221,-0.332848955714 -0.162479718213,0.363776597054 0.799533158627,0.636780671739" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="2.53704256919,0.09658146926 1.53942117325,0.0276499788809 1.97853544943,0.926081196312" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="-1.25599403676,0.424913018921 -2.13748007525,-0.0472970656305 -2.10568298515,0.952197279056" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="1.50552149161,-0.102242464124 0.793709848064,0.600127939663 1.75788628238,0.865389703788" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="0.0306359084909,0.433825991359 -0.920474817824,0.12497588809 -0.712391490058,1.10308699052" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="-0.920492863848,0.124981265106 -1.66373190695,0.794007217376 -0.712718914941,1.10315813365" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="0.988548674008,0.690434631597 0.0265350245229,0.417433279577 0.271115743148,1.38706221483" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="0.0306552225592,0.433832372622 -0.71237259881,1.10309290236 0.238737932382,1.41194360652" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="1.97851911628,0.926107807134 1.01434230903,0.660847398541 1.26670846019,1.62847921165" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="1.01520569443,0.664206989073 0.302645756015,1.36581823054 1.26653888392,1.6321076182" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="-0.45107732599,1.18796126876 -1.4023812864,0.879706869098 -1.19368544713,1.85768746536" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="-1.40239923783,0.879703648598 -2.14500234731,1.54943540221 -1.19369608022,1.85768268314" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="0.49222775967,1.50346484059 -0.459078002432,1.19521600119 -0.250376446988,2.17319537763" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="-0.459093006433,1.19521137482 -1.20169830245,1.86494070397 -0.250393041741,2.17319109073" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="1.43229969914,1.67791550083 0.46840627421,1.41162718831 0.719740543302,2.3795275371" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="0.492238015066,1.50348256718 -0.249306813868,2.1743858886 0.702484920425,2.48113088779" fill="#cdf7d6" stroke-width="0.0193970275416"/>
+    <polygon points="2.65138142393,-0 0.819321918564,-2.52161358041 -2.14501263053,-1.55844289919 -2.14501263053,1.55844289919 0.819321918564,2.52161358041" fill="none" stroke-width="0.0504322716082"/>
+  </g>
+</svg>
diff --git a/data/svg/6d45a6352a0ed4b0.svg b/data/svg/6d45a6352a0ed4b0.svg
new file mode 100644
index 0000000000000000000000000000000000000000..1fa93c1bc4be30b3b27c331612cd7ffd5d071853
--- /dev/null
+++ b/data/svg/6d45a6352a0ed4b0.svg
@@ -0,0 +1,36 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-3.50407873535 -4.0545766909 7.74834409426 8.10915338181" width="900" height="900">
+  <title>squinpen@30</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="1.49560212307,1.5644171614 2.08815885841,0.758888443473 1.28263014048,0.166331708137 0.690073405141,0.971860426065" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="1.17634177859,3.67902992722 1.76412878646,2.87001420835 0.955113067588,2.28222720048 0.367326059717,3.09124291935" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="3.41833554561,-0.629436856285 2.82970319374,-1.43783771869 2.02130233134,-0.849205366826 2.6099346832,-0.0408045044204" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="-1.87537495066,-1.63190113372 -2.18440475462,-2.58295348783 -3.13545710873,-2.27392368387 -2.82642730477,-1.32287132976" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="-1.13514019231,1.59931721293 -1.13541226604,0.599317249942 -2.13541222903,0.599589323666 -2.1351401553,1.59958928665" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="-0.887004646226,-0.904988664419 -1.20040526573,-1.85460966866 -2.15002626997,-1.54120904916 -1.83662565047,-0.591588044916" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="0.97670712225,-2.56272497554 0.66767473698,-3.51377649089 -0.283376778372,-3.20474410562 0.0256556068971,-2.25369259027" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="2.95700730003,1.26439636046 3.54480253821,0.455386621348 2.7357927991,-0.132408616832 2.14799756092,0.676601122276" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="1.90886610617,0.626946523023 2.51942988448,-0.165020567586 1.72746279387,-0.775584345902 1.11689901556,0.0163827447072" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="0.801065941361,-0.402620035885 0.490830425318,-1.35327976712 -0.459829305914,-1.04304425107 -0.149593789871,-0.092384519843" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="0.0169344622261,0.906938405783 -0.293302244154,-0.0437209369965 -1.24396158693,0.266515769383 -0.933724880554,1.21717511216" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="-2.13545763336,1.27542591626 -2.13545937524,0.275425916258 -3.13545937524,0.275427658144 -3.13545763336,1.27542765814" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="-1.10015754641,0.218452994137 -1.41685353507,-0.730074101295 -2.3653806305,-0.413378112638 -2.04868464184,0.535148982794" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="0.0401612148143,2.0436478275 -0.154264348972,1.06273055263 -1.13518162385,1.25715611641 -0.94075606006,2.23807339129" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="0.0256126389007,-2.25367720096 -0.283419346323,-3.2047288463 -1.23447099167,-2.89569686108 -0.925439006442,-1.94464521574" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="0.0743919077614,-1.21788716369 -0.235577190796,-2.16863379552 -1.18632382263,-1.85866469697 -0.87635472407,-0.907918065133" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="-2.13462876354,2.27547757659 -2.13545728986,1.27547791982 -3.13545694663,1.27630644614 -3.13462842031,2.27630610291" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="1.07754651624,-1.54397123232 0.768514895584,-2.49502299613 -0.18253686822,-2.18599137547 0.126494752437,-1.23493961167" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="2.82871959428,-1.43715149144 2.24008593673,-2.24555140311 1.43168602506,-1.65691774556 2.02031968261,-0.848517833886" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="1.94159058198,-0.924808223984 1.37001158144,-1.74535526477 0.549464540656,-1.17377626422 1.1210435412,-0.35322922344" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="1.05894268198,2.15525478489 0.947728041316,1.16145837531 -0.0460683682679,1.27267301597 0.0651462723991,2.26646942556" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="-1.85160341731,-0.587922275075 -2.17318894476,-1.53480281059 -3.12006948027,-1.21321728313 -2.79848395282,-0.266336747622" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="-0.149807093873,-0.0928845255619 -0.462099252227,-1.04287063484 -1.41208536151,-0.730578476491 -1.09979320316,0.219407632792" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="-1.16938190497,2.71901154129 -1.04221027438,1.7271308144 -2.03409100127,1.59995918381 -2.16126263186,2.5918399107" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="2.369191262,2.07344372747 2.9569825429,1.26443111317 2.1479699286,0.67663983227 1.5601786477,1.48565244657" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="0.967130479649,0.595134663483 0.65689509988,-0.35552511222 -0.293764675823,-0.0452897324505 0.016470703946,0.905370043252" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="-0.925293187592,-1.94405624621 -1.23432329365,-2.89510850217 -2.1853755496,-2.5860783961 -1.87634544354,-1.63502614015" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="1.7770959989,2.87938297571 2.36488567583,2.07036919604 1.55587189616,1.48257951911 0.968082219234,2.29159329878" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="0.271781663642,3.38512521143 0.580797673938,2.43406837539 -0.370259162103,2.12505236509 -0.6792751724,3.07610920113" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="2.2418331772,-2.24699105799 1.65310959187,-3.0553254814 0.844775168452,-2.46660189607 1.43349875378,-1.65826747266" fill="#cdf7d6" stroke-width="0.0283536831462"/>
+    <polygon points="3.87566747701,-0 1.19764711494,-3.685978809 -3.13548085345,-2.27806018578 -3.13548085345,2.27806018578 1.19764711494,3.685978809" fill="none" stroke-width="0.0737195761801"/>
+  </g>
+</svg>
diff --git a/data/svg/7110ea9122a5788e.svg b/data/svg/7110ea9122a5788e.svg
new file mode 100644
index 0000000000000000000000000000000000000000..953ca1b2db961de029756c6e5ebe2b64972c46b0
--- /dev/null
+++ b/data/svg/7110ea9122a5788e.svg
@@ -0,0 +1,25 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-1.80494353655 -2.08850386768 3.99115563542 4.17700773535" width="900" height="900">
+  <title>triinpen@19</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="0.444726863772,1.83587789398 0.230492005671,0.859095714796 -0.508308746417,1.53301963388" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="0.442421152825,1.80374643574 1.17801747906,1.12632629667 0.223556266471,0.827991260752" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="-0.511116102914,1.52938062492 -0.721566861437,0.551776165932 -1.46297177851,1.22283409855" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="-0.510922931558,1.53011942909 0.230478657559,0.859057819659 -0.721378538272,0.552516013793" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="1.17801524248,1.12629656826 0.959147872912,0.150541950263 0.223553270655,0.827963961369" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="-1.39860018541,1.16453915802 -0.661339891962,0.488930351308 -1.61506442832,0.188248611331" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="0.226035131828,0.850438941709 0.00953632521494,-0.125843940828 -0.727700049036,0.549790966856" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="1.31169655075,0.942305623124 1.89949050279,0.133294949554 0.904969731525,0.028755791685" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="0.223535577135,0.82795557731 0.959131157323,0.150534628116 0.00466961617023,-0.147799356641" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="-0.657277090682,0.47573643604 -0.887171367051,-0.497479173007 -1.61505366966,0.188222915036" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="-0.65724954449,0.47572737143 0.0706273891324,-0.209980415823 -0.887151441013,-0.497486437542" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="1.83090837315,0.126060260863 1.42418265652,-0.78749006147 0.83638772806,0.021519902669" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="0.622542639937,-0.0122674258292 0.443941317214,-0.996188950912 -0.318859057477,-0.349554905744" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="-1.61506838076,-0.0772706947524 -0.749043506016,-0.577271611075 -1.61506943884,-1.07727069475" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="0.748043023932,-0.0435471813755 1.42102716194,-0.783204095082 0.44397341558,-0.996196998085" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="0.224573667556,-0.81027930628 -0.556738672018,-1.43441953734 -0.706603797855,-0.445713087451" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="-0.693422604898,-0.532870540766 -0.543565379465,-1.52157818814 -1.47473993173,-1.15700452862" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="1.21284055685,-1.07839571935 0.623655895441,-1.88639413195 0.218501074619,-0.972146041349" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="0.187881567237,-0.839629405649 0.412772512849,-1.81401334568 -0.54351420506,-1.52158264764" fill="#cdf7d6" stroke-width="0.0146049221446"/>
+    <polygon points="1.99634810999,-0 0.616905492674,-1.8986398788 -1.61507954767,-1.17342397749 -1.61507954767,1.17342397749 0.616905492674,1.8986398788" fill="none" stroke-width="0.0379727975759"/>
+  </g>
+</svg>
diff --git a/data/svg/7dafd61dbd636b00.svg b/data/svg/7dafd61dbd636b00.svg
new file mode 100644
index 0000000000000000000000000000000000000000..13b0008d914803b093bbe72894121b2de1fe3020
--- /dev/null
+++ b/data/svg/7dafd61dbd636b00.svg
@@ -0,0 +1,40 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-3.71400070615 -4.29747783384 8.21253105626 8.59495566769" width="900" height="900">
+  <title>squinpen@34</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="-1.56958319901,2.9430675203 -1.21524755903,2.00794921 -2.15036586933,1.65361357003 -2.5047015093,2.58873188032" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="-0.630547490929,3.28713647768 -0.276211549249,2.35201828171 -1.21132974522,1.99768234003 -1.5656656869,2.932800536" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="0.32085250779,3.59857506244 0.675186979616,2.66345630952 -0.259931773311,2.30912183769 -0.614266245137,3.24424059062" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="1.63225019253,2.95994907882 0.697132010898,2.60561309931 0.342796031383,3.54073128094 1.27791421302,3.89506726046" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="2.93891379523,1.60887180691 2.13356591591,1.01606931596 1.54076342497,1.82141719528 2.34611130429,2.41421968623" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="3.52673241327,0.799800782023 2.72151578609,0.206820020681 2.12853502475,1.01203664786 2.93375165192,1.6050174092" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="-2.03385930767,1.34607322847 -2.96897689078,0.991735669408 -3.32331444984,1.92685325252 -2.38819686673,2.28119081158" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="-0.61894617815,2.19665105628 -0.297273398629,1.24980015835 -1.24412429656,0.928127378828 -1.56579707608,1.87497827676" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="0.330853781349,2.50982835301 0.652596230375,1.56300112669 -0.294230995942,1.24125867766 -0.615973444968,2.18808590398" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="1.63106504292,1.88794917567 0.694820037607,1.53660135651 0.34347221845,2.47284636183 1.27971722376,2.82419418098" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="2.16749429179,0.95823981039 1.35806740339,0.371019142897 0.770846735897,1.1804460313 1.5802736243,1.76766669879" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="4.10664490512,-0.00161865465561 3.39730233024,-0.706482550362 2.69243843453,0.00286002451304 3.40178100941,0.707723920219" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="-2.32330446868,0.983835346084 -2.32329766192,-0.0161646538932 -3.32329766189,-0.016171460654 -3.32330446865,0.983828539323" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="-1.44348068907,1.51478387284 -1.13765947559,0.562694914085 -2.08974843435,0.256873700608 -2.39556964782,1.20896265937" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="-0.304604785053,1.23908693069 0.01007952273,0.289890540876 -0.939116867084,-0.0247937669068 -1.25380117487,0.924402622907" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="0.963347201644,0.610611169755 0.0159726468795,0.290483924765 -0.304154598111,1.23785847953 0.643219956653,1.55798572452" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="1.69769715254,-0.0900580492083 0.8938553828,-0.684901229568 0.29901220244,0.118940540172 1.10285397218,0.713783720532" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="2.77128823394,0.139284264701 1.96662374083,-0.454445516865 1.37289395926,0.35021897625 2.17755845238,0.943948757817" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="-2.32329752368,-0.0162190824277 -2.323296337,-1.01621908243 -3.323296337,-1.0162202691 -3.32329752368,-0.0162202691043" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="-1.32324315957,0.256808795969 -1.32324875665,-0.743191204016 -2.32324875663,-0.743185606939 -2.32324315955,0.256814393046" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="-0.131569437299,-0.274641511564 -0.427011137564,-1.23000228203 -1.38237190803,-0.934560581765 -1.08693020776,0.0208001887006" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="0.822057962404,-0.587974907769 0.523142281808,-1.5422544349 -0.431137245319,-1.2433387543 -0.132221564724,-0.289059227173" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="2.14094834981,-1.00128370678 1.39271511412,-1.66471947987 0.729279341034,-0.91648624418 1.47751257672,-0.25305047109" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="3.46255048069,-0.772301592449 2.75316512098,-1.47712242885 2.04834428458,-0.767737069142 2.75772964429,-0.0629162327384" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="-2.32327651599,-2.0250488778 -3.32324887006,-2.01761307927 -3.31581307153,-1.0176407252 -2.31584071747,-1.02507652373" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="-1.03444953671,-1.04819459202 -1.33937153025,-2.00057192157 -2.29174885981,-1.69564992803 -1.98682686626,-0.743272598474" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="-0.0777404468538,-1.35838811844 -0.387160472367,-2.30931358755 -1.33808594148,-1.99989356204 -1.02866591597,-1.04896809292" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="0.877519739861,-1.66037340481 0.572187223041,-2.61261919985 -0.380058572,-2.30728668303 -0.0747260551795,-1.35504088799" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="1.84229904098,-1.98267246561 1.52064279614,-2.9295289807 0.573786281053,-2.60787273585 0.895442525896,-1.66101622077" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="2.9128975447,-1.64467524444 2.20020085216,-2.34614757065 1.49872852595,-1.63345087811 2.21142521849,-0.931978551897" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="-1.27234569237,-2.0275075386 -1.58191517852,-2.97838436198 -2.5327920019,-2.66881487583 -2.22322251575,-1.71793805245" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="-0.319427217379,-2.33141273433 -0.628771306163,-3.28236290902 -1.57972148085,-2.97301882024 -1.27037739206,-2.02206864555" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="0.323662483068,-3.58749773498 -0.627305589326,-3.2782086707 -0.318016525037,-2.3272405983 0.632951547357,-2.63652966259" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="1.27340363524,-3.90120684013 0.323778209191,-3.58781961927 0.637165430051,-2.63819419322 1.5867908561,-2.95158141408" fill="#cdf7d6" stroke-width="0.0300522925374"/>
+    <polygon points="4.10785054612,-0 1.2693956291,-3.90679802986 -3.32332090217,-2.41453396963 -3.32332090217,2.41453396963 1.2693956291,3.90679802986" fill="none" stroke-width="0.0781359605972"/>
+  </g>
+</svg>
diff --git a/data/svg/875caebde6570989.svg b/data/svg/875caebde6570989.svg
new file mode 100644
index 0000000000000000000000000000000000000000..0403ccd8bb6a4027f935e12a36f7170421f10270
--- /dev/null
+++ b/data/svg/875caebde6570989.svg
@@ -0,0 +1,25 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-1.80464611611 -2.08815972188 3.99049796872 4.17631944376" width="900" height="900">
+  <title>triinpen@19</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="0.44467554517,-1.82990075098 -0.508990486178,-1.52903350342 0.228401209046,-0.853568117325" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="0.438824535253,-1.80335649354 0.222823669513,-0.82696332171 1.17640539327,-1.12809767066" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="-0.510765524387,-1.52552264736 -1.46369342359,-1.22232565049 -0.724653172346,-0.548664380237" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="-0.510745459142,-1.52551477512 -0.724633494024,-0.548656592713 0.228294525276,-0.851853212142" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="1.17640382126,-1.12807408016 0.222823816958,-0.826934286394 0.960408530601,-0.151679675006" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="-1.3985170578,-1.16288605334 -1.61480201903,-0.186555773389 -0.661132713493,-0.487412642479" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="0.227067224714,-0.847611809476 -0.72696099597,-0.547895019594 0.00961546835049,0.128459260506" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="1.31106147878,-0.941163555678 0.905174896703,-0.0272401001922 1.89959911731,-0.132693736799" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="0.222548418783,-0.827168060542 0.00655294830309,0.149226304831 0.960133008068,-0.151913313318" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="-0.657287566688,-0.474942068353 -1.61479604891,-0.1865369601 -0.886275657472,0.498487155719" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="-0.657274176532,-0.474940719866 -0.886262903363,0.498488354584 0.0712457673087,0.210083871975" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="1.82881895779,-0.125163117191 0.834394739446,-0.0197094593037 1.42293239527,0.788760346981" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="0.621679982273,0.0119218083921 -0.319193089741,0.350681106949 0.444617604584,0.996121439771" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="-1.61480897799,0.0779048241401 -1.61480523777,1.07790482413 -0.748781704106,0.577901585012" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="0.754209056138,0.0452455842649 0.444643447786,0.996123670102 1.4229108302,0.788776308155" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="0.226601351784,0.811935498164 -0.702982223524,0.443324081469 -0.557417286853,1.43267278097" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="-0.690039349564,0.531456219974 -1.4743215053,1.15186052378 -0.544894539717,1.52086664249" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="1.2135412545,1.07697477429 0.219019659362,0.972443454526 0.625753678525,1.8859900804" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="0.189350098079,0.841462915071 -0.544941958159,1.5202966032 0.410091288829,1.81679533364" fill="#cdf7d6" stroke-width="0.0146025155306"/>
+    <polygon points="1.99601914971,-0 0.616803838358,-1.89832701898 -1.61481341321,-1.17323061949 -1.61481341321,1.17323061949 0.616803838358,1.89832701898" fill="none" stroke-width="0.0379665403796"/>
+  </g>
+</svg>
diff --git a/data/svg/8da86e16a42a7ee1.svg b/data/svg/8da86e16a42a7ee1.svg
new file mode 100644
index 0000000000000000000000000000000000000000..35a9608ea629d8d650cccc19dffba8ed1cc0c82b
--- /dev/null
+++ b/data/svg/8da86e16a42a7ee1.svg
@@ -0,0 +1,42 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-4.43281924353 -3.89292363615 8.86563848705 7.7858472723" width="900" height="900">
+  <title>squinhex@36</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="1.01279776663,3.48992870703 1.01279941678,2.48992870703 0.0127994167801,2.48992705688 0.0127977666275,3.48992705688" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="2.01618598581,3.48770294479 2.01396263356,2.48770541644 1.01396510521,2.48992876869 1.01618845747,3.48992629704" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="0.00583936075916,2.98992130247 -0.494160208937,2.12389565025 -1.36018586116,2.62389521995 -0.860186291461,3.48992087217" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="-1.14938712639,2.98906490678 -1.64938727956,2.12303959143 -2.51541259491,2.6230397446 -2.01541244174,3.48906505995" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="1.66403022415,2.48845508888 1.66258198111,1.48845613758 0.662583029812,1.48990438063 0.664031272859,2.48990333192" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="-0.494180793067,2.12387458311 -0.994180156676,1.2578488119 -1.86020592788,1.75784817551 -1.36020656427,2.62387394671" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="0.656816700397,2.11735677774 0.156792819833,1.25134516184 -0.709218796063,1.75136904241 -0.209194915499,2.6173806583" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="-1.64989979267,2.12215607719 -2.14989826175,1.25612978953 -3.01592454941,1.75612825861 -2.51592608033,2.62215454627" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="2.52952300638,2.59859174705 3.02952257673,1.7325660952 2.16349692489,1.23256652486 1.66349735454,2.0985921767" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="-0.994193363685,1.25782414235 -1.4941903522,0.391796999889 -2.36021749466,0.8917939884 -1.86022050615,1.75782113086" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="0.156406433736,1.25068471845 -0.343591558926,0.384658155729 -1.20961812164,0.884656148392 -0.709620128982,1.75068271111" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="-2.15061955667,1.25487829443 -2.65061722506,0.388851544488 -3.516643975,0.888849212872 -3.01664630661,1.75487596281" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="3.02953702575,1.73254102665 3.52953717,0.866515706147 2.6635118495,0.366515561892 2.16351170525,1.23254088239" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="1.25256920881,1.14922220051 0.752544041243,0.283211327717 -0.113466831555,0.78323649528 0.386558336009,1.64924736808" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="2.01878849121,1.47801321394 2.51978365667,0.612563132085 1.65433357481,0.111567966624 1.15333840935,0.97701804848" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="-1.49419964939,0.391768713126 -1.99419554279,-0.474259061594 -2.86022331751,0.0257368318026 -2.36022742411,0.891764606523" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="-0.338796349377,0.381612642144 -0.838974665153,-0.484309786499 -1.7048970938,0.0158685292774 -1.20471877802,0.88179095792" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="-2.65073314724,0.388646930911 -3.15073290851,-0.477378610706 -4.01675845013,0.0226211505625 -3.51675868886,0.888646692179" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="3.52965615894,0.866310056277 4.02965672512,0.000284979375948 3.16363164822,-0.499715586802 2.66363108204,0.366309490099" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="2.52161515087,0.612231114698 3.02161582385,-0.253793900542 2.15559080861,-0.75379457352 1.65559013563,0.11223044172" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="1.09512884049,0.610251647498 1.78563760685,-0.113072376427 1.06231358292,-0.803581142781 0.371804816568,-0.0802571188556" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="-2.73729383646,-0.238719473216 -2.23729496001,-1.10474552568 -3.10332101248,-1.60474440213 -3.60331988893,-0.738718349664" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="-0.237236099873,-0.484347148529 -0.237235157851,-1.48434714853 -1.23723515785,-1.48434809055 -1.23723609987,-0.484348090551" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="-1.23726329169,-0.474290535222 -1.23726245468,-1.47429053522 -2.23726245468,-1.47429137224 -2.23726329169,-0.474291372237" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="0.762792972174,-0.489871597758 0.762791395665,-1.48987159776 -0.237208604334,-1.48987002125 -0.237207027825,-0.489870021249" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="2.36090281642,-0.89065684787 1.8608717623,-1.75666432181 0.994864288359,-1.25663326768 1.49489534248,-0.390625793748" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="3.44807368136,-1.0076370155 2.94807134476,-1.87366107024 2.08204729002,-1.37365873365 2.58204962661,-0.507634678903" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="1.39881097525,-1.48990289336 1.39880906532,-2.48990289336 0.398809065321,-2.48990098343 0.398810975255,-1.48990098343" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="0.398783804759,-1.48989880594 0.398782627352,-2.48989880594 -0.601217372647,-2.48989762853 -0.60121619524,-1.48989762853" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="-0.601241843106,-1.48499192652 -0.601243556339,-2.48499192652 -1.60124355634,-2.48499021329 -1.6012418431,-1.48499021329" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="-1.6012698988,-1.47431863322 -1.6012677551,-2.47431863321 -2.6012677551,-2.47432077691 -2.6012698988,-1.47432077692" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="2.94685612693,-1.87576031505 2.44684176977,-2.74177742956 1.58082465525,-2.24176307241 2.08083901241,-1.37574595789" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="-1.01702343434,-2.48611994025 -1.01691165942,-3.486119934 -2.01691165318,-3.48623170892 -2.0170234281,-2.48623171517" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="2.00316753817,-2.48992651922 2.0031684071,-3.48992651922 1.0031684071,-3.48992738815 1.00316753817,-2.48992738815" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="0.988420405988,-2.48992686677 0.988421446395,-3.48992686676 -0.0115785536045,-3.48992790717 -0.0115795940112,-2.48992790717" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="-0.0157238355053,-2.4899261769 -0.0157245149987,-3.4899261769 -1.015724515,-3.48992549741 -1.01572383551,-2.48992549741" fill="#cdf7d6" stroke-width="0.0309987359617"/>
+    <polygon points="4.02983567502,-0 2.01491783751,-3.48994006765 -2.01491783751,-3.48994006765 -4.02983567502,-4.93512536051e-16 -2.01491783751,3.48994006765 2.01491783751,3.48994006765" fill="none" stroke-width="0.0805967135005"/>
+  </g>
+</svg>
diff --git a/data/svg/8e846defa45411b2.svg b/data/svg/8e846defa45411b2.svg
new file mode 100644
index 0000000000000000000000000000000000000000..c844cfe43caecde3639e363759077f9f169c251d
--- /dev/null
+++ b/data/svg/8e846defa45411b2.svg
@@ -0,0 +1,40 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-3.9969261898 -3.9969261898 7.9938523796 7.9938523796" width="900" height="900">
+  <title>squincir@34</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="3.52768955859,-0.0564287864127 2.52786498893,-0.0751592406131 2.50913453473,0.924665329042 3.50895910439,0.943395783242" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="3.02183112043,1.00393065292 2.02183270974,1.00571352162 2.02361557844,2.00571193231 3.02361398913,2.00392906361" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="2.97313292627,-1.08691249883 1.97313574847,-1.08928829431 1.97075995299,-0.0892911165125 2.97075713079,-0.0869153210318" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="2.97384943135,-2.08726732556 1.97385913859,-2.09167350266 1.96945296148,-1.09168320991 2.96944325424,-1.0872770328" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="2.52638731881,0.00180476198736 1.52656264597,-0.0169201838133 1.50783770017,0.982904489019 2.50766237301,1.00162943482" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="2.02679071002,2.02576453524 1.02693528373,2.00876081464 1.00993156314,3.00861624094 2.00978698943,3.02561996153" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="2.02084965499,0.992761119376 1.02084968555,0.992513914057 1.02060248023,1.9925138835 2.02060244967,1.99276108882" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="1.96029015477,-1.0228028836 0.960316050846,-1.02999951399 0.953119420455,-0.0300254100705 1.95309352437,-0.0228287796788" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="1.97054296195,-2.02819913176 0.970570024969,-2.03555612163 0.963213035102,-1.03558318465 1.96318597209,-1.02822619478" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="1.99381554405,-3.03735682099 0.994039967094,-3.05854162037 0.97285516771,-2.05876604342 1.97263074466,-2.03758124403" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="1.5264576352,-0.0131817746342 0.526632819168,-0.0318990726091 0.507915521193,0.967925743424 1.50774033723,0.986643041399" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="1.00965619803,2.49412382608 0.00974001456189,2.48117677869 -0.00320703282421,3.48109296216 0.996709150645,3.49404000955" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="1.01999190158,1.49334579461 0.0200659899836,1.48117323045 0.00789342583126,2.48109914205 1.00781933743,2.4932717062" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="0.961279965814,-1.50250309874 -0.0383922175955,-1.52810633519 -0.0639954540408,-0.528434151776 0.935676729369,-0.502830915331" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="0.982052500857,-2.50261333087 -0.017626382803,-2.52795360641 -0.0429666583349,-1.52827472275 0.956712225325,-1.50293444721" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="0.963291619713,-3.5034750115 -0.0363366591281,-3.53073861621 -0.0636002638383,-2.53111033737 0.936028015003,-2.50384673266" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="0.513522690891,0.486824554098 -0.486408551217,0.475098043301 -0.498135062015,1.47502928541 0.501796180093,1.48675579621" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="0.538680474261,-0.512905963406 -0.461000100143,-0.538179450693 -0.48627358743,0.461501123711 0.513406986974,0.486774610998" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="0.00907831993143,2.5137264897 -0.99056073579,2.48686093039 -1.0174262951,3.48649998611 -0.0177872393792,3.51336554542" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="0.0186648824271,1.48301193724 -0.981217273883,1.46766027631 -0.996568934819,2.46754243262 0.0033132214903,2.48289409355" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="-0.035110048382,-1.95397008487 -1.03493574304,-1.97264039019 -1.05360604836,-0.972814695531 -0.0537803536977,-0.954144390216" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="-0.0564654081801,-2.97525268112 -1.05630549129,-2.99313586313 -1.0741886733,-1.99329578001 -0.0743485901827,-1.97541259801" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="-0.48150584814,0.04844836655 -1.48143797857,0.0367978498069 -1.49308849531,1.03672998023 -0.493156364883,1.04838049698" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="-0.452488815258,-0.951306745697 -1.452211984,-0.974835151312 -1.47574038962,0.0248880174348 -0.476017220873,0.0484164230498" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="-0.990232229055,2.0455525195 -1.99010645239,2.02969258518 -2.00596638671,3.02956680851 -1.00609216337,3.04542674283" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="-0.98528461022,1.0447209055 -1.98517000164,1.02958141958 -2.00030948756,2.02946681099 -1.00042409614,2.04460629691" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="-1.03530571164,-1.96950501302 -2.03513626273,-1.98791341093 -2.05354466064,-0.988082859843 -1.05371410955,-0.969674461937" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="-1.05734451465,-2.97192064889 -2.05707972387,-2.99493176469 -2.08009083966,-1.99519655547 -1.08035563044,-1.97218543967" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="-1.4814725403,0.0348323130722 -2.48140508641,0.0232175287263 -2.49301987076,1.02315007484 -1.49308732464,1.03476485919" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="-1.48171012611,-0.977406607701 -2.48171002473,-0.976956313899 -2.48125973092,0.0230435847186 -1.48125983231,0.022593290917" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="-1.98796768678,1.0503963593 -2.98787792299,1.0369978702 -3.00127641209,2.03690810642 -2.00136617588,2.05030659552" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="-2.03545548193,-1.97905903481 -3.03528719104,-1.99740442822 -3.05363258446,-0.997572719114 -2.05380087535,-0.979227325697" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="-2.48131251995,0.0130485355423 -3.48124510435,0.00143704721821 -3.49285659267,1.00136963162 -2.49292400827,1.01298111994" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <polygon points="-2.48801357919,-0.987154802845 -3.48794604503,-0.998776495879 -3.49956773807,0.00115596996584 -2.49963527222,0.0127776629997" fill="#cdf7d6" stroke-width="0.0279505327888"/>
+    <circle cx="0" cy="-0" r="3.63356926255" fill="none" stroke-width="0.0726713852509"/>
+  </g>
+</svg>
diff --git a/data/svg/9da834ae740d1c15.svg b/data/svg/9da834ae740d1c15.svg
new file mode 100644
index 0000000000000000000000000000000000000000..1a504ab41d938a8ab818f1b827caa6c1f283503d
--- /dev/null
+++ b/data/svg/9da834ae740d1c15.svg
@@ -0,0 +1,35 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-2.23420386927 -2.58520187902 4.94035141988 5.17040375805" width="900" height="900">
+  <title>triinpen@29</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="0.945848470564,1.36612421801 0.00128148637955,1.69444298444 0.757897370737,2.34830260511" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="-0.113527420869,1.1545860097 -0.856672896343,1.82371589417 0.0943833197716,2.1327338124" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="-1.06462710878,0.8455090015 -1.80781518702,1.51459156768 -0.856778648354,1.82367004013" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="-0.113552096587,1.1545745098 -1.06459186132,0.84550596419 -0.856733190967,1.82366483327" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="0.189417267962,0.712022473895 0.00119562916232,1.69414905163 0.94585301461,1.3660904835" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="1.73608158324,1.01169682729 0.74156017114,0.907163766111 1.14829259067,1.82071110418" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="-1.05202747855,0.834413814259 -1.99918111353,0.513633528484 -1.80340817256,1.49428278055" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="-0.112151050819,0.243145617558 -0.85812947511,0.90911572987 0.0916067724592,1.22216693982" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="1.31054128183,0.0961498294997 0.72275125239,0.905163353051 1.71727253051,1.00969768886" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="0.889247354132,0.149651845259 -0.0658269407367,0.446018326633 0.668371108397,1.1249536878" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="2.30948187025,0.201550941729 1.31505234458,0.0961473437237 1.72098491389,1.01005037423" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="-1.06828563356,-0.0854602826609 -1.81966669513,0.5744082651 -0.872513238824,0.895189078456" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="-0.11495813154,0.245626241931 -1.06467731258,-0.0674767398043 -0.860972858241,0.911555688302" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="-1.05202796653,-0.0997604218759 -1.99917675071,-0.420555030053 -1.8034186387,0.560097182295" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="0.866404088391,-0.728362227764 0.458753887526,0.184775940168 1.45337983855,0.0812422860095" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="-0.236275873673,-0.708143467445 -0.979933130805,-0.0395824127043 -0.0291136448527,0.27016313631" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="1.88077873428,-0.805026161796 1.47315403128,0.108123388665 2.46777709093,0.00456196143816" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="0.800609395538,-0.58104914973 -0.197948164873,-0.527357450682 0.34782899068,0.310572914251" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="1.88066661896,-0.804879359783 0.886044504822,-0.701308852078 1.47305025265,0.108273912079" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="-1.14833703369,-1.05278954394 -1.89205337705,-0.384294218133 -0.94126127091,-0.0744646344836" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="-0.197483185248,-0.743030947656 -1.14830116528,-1.05278111931 -0.941143692746,-0.0744735083982" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="0.254899322061,-1.41909612291 -0.198001811269,-0.527535377122 0.800563010265,-0.581091863149" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="1.29774321269,-1.61500480178 0.890224528126,-0.701807932684 1.8848355577,-0.805484833889" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="-1.04838489866,-1.14264653534 -1.99917445166,-1.45248395384 -1.79210675064,-0.47415733804" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="1.24203662277,-1.49025694039 0.243472870737,-1.43668051721 0.789153290267,-0.59868715224" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="-0.579904643558,-1.91327648517 -0.785636156657,-0.934668011616 0.164729398352,-1.24580353169" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="-0.58054296381,-1.91342726773 -1.5307471666,-1.60179932772 -0.785767352628,-0.93471231932" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="0.696311922369,-2.32828355486 0.243417818933,-1.43671923801 1.24198221815,-1.49028359763" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="0.372428315673,-2.22305808527 -0.578107634633,-1.91244352158 0.166160443459,-1.24456252325" fill="#cdf7d6" stroke-width="0.0180783348114"/>
+    <polygon points="2.47112919707,-0 0.763620917189,-2.35018352548 -1.99918551572,-1.45249329854 -1.99918551572,1.45249329854 0.763620917189,2.35018352548" fill="none" stroke-width="0.0470036705095"/>
+  </g>
+</svg>
diff --git a/data/svg/9ed000ff11bd8b55.svg b/data/svg/9ed000ff11bd8b55.svg
new file mode 100644
index 0000000000000000000000000000000000000000..01e2a9063084abc99c34bfa052b2742a21551c06
--- /dev/null
+++ b/data/svg/9ed000ff11bd8b55.svg
@@ -0,0 +1,47 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-5.42103823056 -2.9569299444 10.8420764611 5.91385988879" width="900" height="900">
+  <title>squindom@41</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="-3.16931157407,2.03693391433 -3.59647074076,1.13275746788 -4.50064718721,1.55991663456 -4.07348802052,2.46409308101" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-2.06876586697,2.02547565537 -2.49574187829,1.12121270371 -3.40000482996,1.54818871503 -2.97302881864,2.4524516667" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-0.945365510419,2.04246308725 -1.36698545195,1.13569044491 -2.27375809429,1.55731038644 -1.85213815276,2.46408302878" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="1.31799079238,2.04615701902 0.900060600815,1.13767787508 -0.00841854312576,1.55560806665 0.409511648443,2.46408721059" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="2.42147433442,2.04411483861 2.00148809094,1.13658436789 1.09395762022,1.55657061136 1.51394386369,2.46410108209" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="3.52339993577,2.04410278328 3.10341326541,1.13657251011 2.19588299224,1.55655918047 2.6158696626,2.46408945364" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="4.92612994629,2.43193466725 4.89545767706,1.43240517198 3.89592818179,1.46307744121 3.92660045102,2.46260693647" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-3.59687859321,1.13291602389 -4.02403873315,0.228740037239 -4.92821471981,0.655900177188 -4.50105457986,1.56007616384" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-2.49781439727,1.11602252241 -2.92427434847,0.211516076869 -3.82878079401,0.637976028062 -3.40232084282,1.5424824736" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-1.38219623325,1.1367173988 -1.80829259822,0.232039617625 -2.7129703794,0.658135982601 -2.28687401443,1.56281376378" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="0.203234956099,2.02877818341 -0.232070491682,1.12849535722 -1.13235331787,1.563800805 -0.697047870091,2.46408363119" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="2.00147827986,1.1365628037 1.58149089679,0.229032860358 0.673960953445,0.649020243424 1.09394833651,1.55655018677" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="3.10340016787,1.13654205265 2.68341356229,0.229011749505 1.77588325914,0.648998355088 2.19586986472,1.55652865824" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="4.27481365747,1.28669053238 3.85482689008,0.379160304115 2.94729666181,0.799147071505 3.3672834292,1.70667729977" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-2.93112191805,0.193217800659 -3.36516611777,-0.707673775883 -4.26605769431,-0.273629576157 -3.83201349459,0.627262000385" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-1.80733240778,0.221749052908 -2.24137649515,-0.679142577769 -3.14226812583,-0.245098490404 -2.70822403846,0.655793140273" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-0.254768151412,1.13942806583 -0.689415649166,0.238827403667 -1.59001631133,0.673474901422 -1.15536881358,1.57407556359" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="0.879022945645,1.12909832374 0.445881078709,0.227772565143 -0.455444679886,0.660914432079 -0.0223028129502,1.56224019067" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="2.71319029639,0.214433421053 2.2925763441,-0.692806295418 1.38533662763,-0.272192343133 1.80595057992,0.635047373339" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="3.91636713606,0.344475314976 3.49791332609,-0.563762764452 2.58967524666,-0.145308954485 3.00812905663,0.762929124943" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="4.92820772428,0.537635184668 4.9281972508,-0.462364815277 3.92819725086,-0.462354341795 3.92820772434,0.53764565815" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-3.89777856897,-0.454372993704 -3.91385075648,-1.45424382776 -4.91372159053,-1.43817164025 -4.89764940302,-0.438300806196" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-2.24190466771,-0.680239819566 -2.67594898711,-1.58113133845 -3.57684050599,-1.14708701905 -3.14279618659,-0.246195500168" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-0.689139815948,0.238653452952 -1.12318391348,-0.662238172828 -2.02407553926,-0.2281940753 -1.59003144173,0.67269755048" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="0.420911508193,0.238651629779 -0.0131325405741,-0.662240019493 -0.914024189847,-0.228195970726 -0.479980141079,0.672695678547" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="1.5560919497,0.229229332415 1.12640697338,-0.673749527321 0.223428113646,-0.244064551006 0.65311308996,0.658914308729" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="3.46232455289,-0.5475308697 3.0495600933,-1.45836867135 2.13872229166,-1.04560421176 2.55148675124,-0.134766410118" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="4.570608164,-0.463265761752 4.56924722823,-1.46326483568 3.56924815431,-1.46190389991 3.57060909008,-0.46190482598" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-3.92604345028,-2.45982078966 -4.92604328577,-2.4592471737 -4.9254696698,-1.45924733821 -3.92546983431,-1.45982095418" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-1.12319733802,-0.66227191196 -1.55724137059,-1.56316356904 -2.45813302766,-1.12911953647 -2.0240889951,-0.228227879394" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-0.0131483983261,-0.662271513841 -0.447192414987,-1.56316317858 -1.34808407973,-1.12911916192 -0.914040063068,-0.22822749718" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="1.09788555763,-0.660203263075 0.668199896929,-1.56318179714 -0.234778637137,-1.13349613644 0.194907023568,-0.23051760237" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="2.23701238068,-0.667081732577 1.81639820757,-1.57432134667 0.909158593476,-1.15370717355 1.32977276659,-0.246467559461" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="3.91557369064,-2.4637750804 2.91557565912,-2.46179090239 2.91755983713,-1.46179287087 3.91755786865,-1.46377704888" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="4.91659290011,-2.46377662038 3.91659382619,-2.4624156794 3.91795476717,-1.46241660548 4.91795384109,-1.46377754646" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-2.92308165873,-1.46269166782 -2.92478646519,-2.46269021464 -3.924785012,-2.46098540818 -3.92308020555,-1.46098686136" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-1.5572574081,-1.56319550357 -1.99130163801,-2.46408706557 -2.89219320001,-2.03004283566 -2.4581489701,-1.12915127366" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-0.447203762041,-1.56319626946 -0.881247790688,-2.46408792843 -1.78213944965,-2.03004389979 -1.34809542101,-1.12915224082" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="0.663822239353,-1.56112328886 0.234136644473,-2.46410185424 -0.668841920916,-2.03441625936 -0.239156326036,-1.13143769398" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="1.77864143071,-1.55685162975 1.35802733143,-2.46409127807 0.450787683107,-2.04347717879 0.871401782387,-1.13623753047" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="2.78115883392,-2.46408639721 1.79042177744,-2.32829212295 1.9262160517,-1.33755506647 2.91695310818,-1.47334934073" fill="#cdf7d6" stroke-width="0.0379093582487"/>
+    <polygon points="-4.92821657233,2.46410828616 4.92821657233,2.46410828616 4.92821657233,-2.46410828616 -4.92821657233,-2.46410828616" fill="none" stroke-width="0.0985643314466"/>
+  </g>
+</svg>
diff --git a/data/svg/a3f4dd7d0b94e803.svg b/data/svg/a3f4dd7d0b94e803.svg
new file mode 100644
index 0000000000000000000000000000000000000000..3b2c532225ae59cf6643df943565c0af73c4c60f
--- /dev/null
+++ b/data/svg/a3f4dd7d0b94e803.svg
@@ -0,0 +1,40 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-3.70538176665 -4.28750484127 8.19347254929 8.57500968253" width="900" height="900">
+  <title>squinpen@34</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="-2.11438862708,1.66121432131 -3.08818725451,1.4338022873 -3.31559928852,2.40760091474 -2.34180066109,2.63501294874" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="-1.402161451,2.98787780673 -1.13203145375,2.02505394714 -2.09485531334,1.75492394989 -2.36498531059,2.71774780948" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="-0.450314309025,3.29723085085 -0.180156926584,2.33441467488 -1.14297310256,2.06425729244 -1.413130485,3.02707346841" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="0.569905058019,3.15088808088 1.14578157648,2.33335139334 0.328244888938,1.75747487488 -0.247631629526,2.57501156242" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="1.84429182912,3.08157683727 1.02814962447,2.50372573034 0.450298517537,3.319867935 1.26644072219,3.89771904193" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="2.42284667256,2.26590116903 1.6067058315,1.6880481362 1.02885279867,2.50418897726 1.84499363973,3.08204201009" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="-1.86642625622,0.683478516764 -2.84210782165,0.464285718325 -3.06130062008,1.43996728375 -2.08561905466,1.65916008219" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="-1.14852203646,2.02038615252 -0.875567263666,1.05835928595 -1.83759413024,0.785404513157 -2.11054890303,1.74743137973" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="-0.180166187586,2.33438202456 0.0899911523608,1.37156583666 -0.872825035534,1.10140849672 -1.14298237548,2.06422468461" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="0.414046370949,1.60097819915 0.991921505565,0.784853007292 0.175796313703,0.206977872675 -0.402078820914,1.02310306454" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="1.13795555884,2.32779373889 1.71383204383,1.51025702777 0.896295332705,0.93438054278 0.320418847715,1.7519172539" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="2.44213447306,2.27952652066 3.02000961998,1.46340133751 2.20388443683,0.885526190589 1.62600928991,1.70165137374" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="-2.24974178561,-0.503779193812 -3.24813485888,-0.56044727335 -3.30480293842,0.437945799924 -2.30640986515,0.494613879462" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="-1.25433692643,0.363827976275 -1.24482519482,-0.636126786183 -2.24477995727,-0.6456385178 -2.25429168889,0.354316244657" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="-0.447499910012,1.18111884586 -0.171741205994,0.219891954246 -1.13296809761,-0.0558667497725 -1.40872680162,0.905360141839" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="1.60836399798,-0.00399953507339 0.792238885275,-0.581874781488 0.21436363886,0.234250331212 1.03048875156,0.812125577627" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="2.32347610902,0.716580443133 1.50735094924,0.138705263208 0.929475769318,0.954830422988 1.7456009291,1.53270560291" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="3.59790894681,0.647260221594 2.78178325349,0.069385795174 2.20390882707,0.88551148849 3.02003452039,1.46338591491" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="-1.98020933554,-1.77940583241 -2.93425038667,-1.47972988618 -2.63457444044,-0.525688835047 -1.68053338931,-0.825364781279" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="-0.0146614106529,-0.314611765242 -0.321012942412,-1.2665302171 -1.27293139427,-0.960178685342 -0.966579862511,-0.00826023348312" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="0.953159908342,-0.637273443798 0.62781896459,-1.58287022378 -0.317777815396,-1.25752928003 0.00756312835643,-0.311932500046" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="1.58447207032,-1.75262491838 0.776252696355,-1.16374339927 1.36513421546,-0.355524025304 2.17335358943,-0.944405544408" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="2.76749321004,-0.130334927406 2.17840560332,-0.938404102419 1.37033642831,-0.349316495698 1.95942403503,0.458752679316" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="3.86025637402,-0.327648424535 3.27246449225,-1.13666060227 2.46345231452,-0.548868720508 3.05124419628,0.260143457231" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="-2.36158180044,-2.70790722911 -3.31559693577,-2.40814879041 -3.01583849707,-1.45413365508 -2.06182336174,-1.75389209378" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="-0.729489385503,-1.13522961568 -1.02926349366,-2.08923982741 -1.98327370539,-1.78946571925 -1.68349959723,-0.835455507526" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="0.221962466847,-1.4433088655 -0.0777412716766,-2.39734118629 -1.03177359247,-2.09763744777 -0.732069853945,-1.14360512698" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="1.1776753256,-1.7565395604 0.876536165588,-2.71011976484 -0.0770440388562,-2.40898060483 0.224095121155,-1.45540040039" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="2.68402734133,-1.94533707343 2.09624857048,-2.75435877681 1.2872268671,-2.16658000596 1.87500563795,-1.35755830258" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="3.27179040005,-1.13621766413 2.68399850469,-1.94522983199 1.87498633682,-1.35743793663 2.46277823218,-0.548425768772" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="-1.11073549867,-2.06388328016 -1.41068212402,-3.01783926549 -2.36463810935,-2.71789264013 -2.06469148399,-1.76393665481" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="-0.15913906475,-2.37233283143 -0.459347492651,-3.32620646029 -1.4132211215,-3.02599803239 -1.1130126936,-2.07212440353" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="0.792311695048,-2.683546524 0.491172910813,-3.63712684711 -0.4624074123,-3.33598806288 -0.161268628066,-2.38240773976" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="2.09674732509,-2.75489428126 1.5089685441,-3.56391597728 0.699946848089,-2.97613719629 1.28772562907,-2.16711550028" fill="#cdf7d6" stroke-width="0.0299825513305"/>
+    <polygon points="4.09831761434,-0 1.26644979118,-3.89773167297 -3.31560859835,-2.40893065292 -3.31560859835,2.40893065292 1.26644979118,3.89773167297" fill="none" stroke-width="0.0779546334594"/>
+  </g>
+</svg>
diff --git a/data/svg/aa2ddbda942a0ffd.svg b/data/svg/aa2ddbda942a0ffd.svg
new file mode 100644
index 0000000000000000000000000000000000000000..34e58ecafa27135b9656e510efb535ced92b28f8
--- /dev/null
+++ b/data/svg/aa2ddbda942a0ffd.svg
@@ -0,0 +1,40 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-3.99467534862 -3.99467534862 7.98935069724 7.98935069724" width="900" height="900">
+  <title>squincir@34</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="-3.52664845611,0.0677110812641 -2.52678954841,0.0845088400136 -2.50999178967,-0.915350067683 -3.50985069736,-0.932147826433" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-3.02537091676,-0.996887413137 -2.02538930631,-1.00295196308 -2.03145385626,-2.00293357353 -3.03143546671,-1.99686902358" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-2.96099050729,1.07933406987 -1.96106457039,1.09150455533 -1.94889408493,0.0915786184272 -2.94882002183,0.0794081329698" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-2.97693580011,2.07925288531 -1.97700992621,2.09142854539 -1.96483426613,1.09150267149 -2.96476014003,1.0793270114" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-2.52543328203,0.00469790642028 -1.52557436839,0.0214953116867 -1.50877696313,-0.978363601949 -2.50863587676,-0.995161007215" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-2.02611248614,-2.0050415446 -1.02618747849,-1.99279495015 -1.01394088404,-2.9927199578 -2.01386589169,-3.00496655225" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-2.02537596931,-0.998163152273 -1.02539292126,-0.992340471257 -1.01957024024,-1.99232351931 -2.01955328829,-1.99814620032" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-1.95333651842,1.02665230213 -0.953404591231,1.0383202493 -0.941736644057,0.0383883221141 -1.94166857124,0.0267203749393" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-1.97309955945,2.02654796633 -0.973188050378,2.03985112495 -0.95988489175,1.03993961588 -1.95979640082,1.02663645726" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-1.99337573159,3.02666256171 -0.993529556039,3.04420181015 -0.975990307603,2.0443556346 -1.97583648315,2.02681638616" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-1.52536267303,0.0101850799783 -0.525503795066,0.0269846082016 -0.508704266843,-0.972874269766 -1.50856314481,-0.98967379799" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-1.00450994389,-2.49142127263 -0.00452534348068,-2.48587159372 0.00102433542367,-3.48585619414 -0.99896026499,-3.49140587304" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-1.01938268661,-1.49145652018 -0.0193980849786,-1.48590706081 -0.0138486256104,-2.48589166244 -1.01383322724,-2.49144112181" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-0.963518346634,1.50145221117 0.0362070265108,1.5248867645 0.0596415798491,0.525161391359 -0.940083793296,0.501726838021" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-0.983965021041,2.50127653053 0.0157603776533,2.52470999388 0.0391938410053,1.52498459518 -0.960531557689,1.50155113183" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-0.960710987584,3.50212881581 0.0389921795895,3.52649226268 0.0633556264661,2.52678909551 -0.936347540707,2.50242564863" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-0.515174422072,-0.488642872857 0.484735853893,-0.475247350443 0.498131376306,-1.47515762641 -0.501778899658,-1.48855314882" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-0.535171445926,0.511188076518 0.464627737432,0.531227860855 0.484667521769,-0.468571322503 -0.515131661589,-0.48861110684" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-0.0045254791641,-2.48206414436 0.995423332703,-2.47194615809 1.00554131897,-3.47189496996 0.00559250709976,-3.48201295622" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="-0.0175241398335,-1.48210482441 0.982420077756,-1.4715425468 0.992982355364,-2.47148676439 -0.00696186222572,-2.482049042" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="0.0303268642804,1.9483304249 1.03010578244,1.96935695125 1.05113230879,0.969578033094 0.051353390633,0.948551506742" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="0.0549846812263,2.95491790977 1.05479188571,2.97455343517 1.07442741111,1.97474623068 0.0746202066218,1.95511070528" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="0.479068501869,-0.0459461624924 1.47897961327,-0.0326131474058 1.49231262836,-1.03252425881 0.492401516956,-1.0458572739" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="0.458324881938,0.954250469641 1.45814928193,0.972989977941 1.47688879024,-0.0268344220553 0.477064390239,-0.0455739303556" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="0.990722394232,-2.04109328277 1.99066188789,-2.0300928722 2.00166229846,-3.03003236585 1.00172280481,-3.04103277643" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="0.985894596251,-1.04104316744 1.98582877167,-1.02956950976 1.99730242935,-2.02950368518 0.997368253927,-2.04097734286" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="1.03018618055,1.96739747869 2.02996512918,1.98842255581 2.05099020631,0.988643607177 1.05121125767,0.967618530056" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="1.06036226569,2.97511522744 2.0602628035,2.98921893257 2.07436650863,1.98931839476 1.07446597082,1.97521468963" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="1.47896336535,-0.0301756813883 2.47887451041,-0.0168451909029 2.4922050009,-1.01675633597 1.49229385583,-1.03008682645" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="1.46308349316,0.971660830955 2.46297221983,0.986578413839 2.47788980272,-0.0133103128303 1.47800107605,-0.0282278957148" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="1.98838859165,-1.05216303622 2.98811735187,-1.02887342517 3.01140696292,-2.0286021854 2.01167820269,-2.05189179644" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="2.03016379316,1.98078700967 3.0299427497,2.00181171095 3.05096745098,1.00203275442 2.05118849445,0.981008053133" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="2.47880768884,-0.0101841424272 3.47871883051,0.00314660228263 3.49204957522,-0.996764539392 2.49213843355,-1.0100952841" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <polygon points="2.47539113208,0.989893773882 3.47530220637,1.00322957255 3.48863800503,0.00331849826331 2.48872693075,-0.0100173004009" fill="#cdf7d6" stroke-width="0.0279347926407"/>
+    <circle cx="0" cy="-0" r="3.63152304329" fill="none" stroke-width="0.0726304608658"/>
+  </g>
+</svg>
diff --git a/data/svg/abcbdd03f9f27f35.svg b/data/svg/abcbdd03f9f27f35.svg
new file mode 100644
index 0000000000000000000000000000000000000000..ed7ef9781cd0c578da0c8f58b0866d1883e5dd98
--- /dev/null
+++ b/data/svg/abcbdd03f9f27f35.svg
@@ -0,0 +1,36 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-3.50424552245 -4.05476968061 7.74871289987 8.10953936122" width="900" height="900">
+  <title>squinpen@30</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="1.49192914047,-1.56500865501 0.688059309303,-0.970203397349 1.28286456696,-0.166333566182 2.08673439813,-0.761138823843" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="1.17651126194,-3.67924935212 0.365607535252,-3.09406976767 0.950787119697,-2.28316604099 1.76169084638,-2.86834562544" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="3.41868673578,0.629221334899 2.61014098142,0.0407880225349 2.02170766905,0.849333776899 2.83025342342,1.43776708926" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="-1.87553566628,1.63443333439 -2.82659033574,1.3254106561 -3.13561301403,2.27646532556 -2.18455834457,2.58548800385" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="-1.13557654895,-1.60214021568 -2.13557654894,-1.6021446554 -2.13558098866,-0.60214465541 -1.13558098867,-0.602140215692" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="-0.894377661553,0.903411576329 -1.84473180259,0.592241194356 -2.15590218456,1.54259533539 -1.20554804353,1.85376571736" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="0.9772300409,2.56305286452 0.0261763856731,2.25402706482 -0.282849414026,3.20508072004 0.668204241201,3.51410651974" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="2.95709012607,-1.26454392916 2.14807780368,-0.676752246474 2.73586948637,0.132260075908 3.54488180875,-0.455531606778" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="1.90933447785,-0.629840095877 1.12074038986,-0.0149259844786 1.73565450126,0.773668103505 2.52424858925,0.158753992107" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="0.802016160889,0.403120141063 -0.148957141448,0.0938471576939 -0.458230124817,1.04482046003 0.49274317752,1.3540934434" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="0.0153152941885,-0.907479257027 -0.935658104077,-1.21675194543 -1.24493079248,-0.265778547163 -0.293957394213,0.0434941412388" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="-2.13561389959,-1.27810988145 -3.13561389958,-1.27811395567 -3.1356179738,-0.278113955676 -2.13561797381,-0.27810988146" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="-1.09980400331,-0.216030639175 -2.04584380362,-0.540081092372 -2.36989425682,0.405958707945 -1.4238544565,0.730009161141" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="0.0385769864635,-2.04440662087 -0.94264236509,-2.23730188814 -1.13553763236,-1.25608253659 -0.154318280809,-1.06318726932" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="0.0261448373399,2.25401458314 -0.924909119128,1.94498971053 -1.23393399173,2.896043667 -0.282880035263,3.2050685396" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="0.0729875568599,1.21771915177 -0.878065185165,0.908690541626 -1.18709379531,1.85974328365 -0.236041053285,2.16877189379" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="-2.13561002814,-2.27814778879 -3.13561002813,-2.27815139741 -3.13561363675,-1.27815139742 -2.13561363676,-1.2781477888" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="1.08415512841,1.54629271977 0.133101655819,1.23726635799 -0.175924705969,2.18831983057 0.775128766618,2.49734619236" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="2.82962540003,1.43857732893 2.02167175438,0.84933127975 1.4324257052,1.65728492541 2.24037935086,2.24653097458" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="1.94245663661,0.916066029721 1.11873133803,0.349076935937 0.551742244244,1.17280223452 1.37546754283,1.73979132831" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="1.05719075039,-2.15506163811 0.0633711979982,-2.26606928325 -0.0476364471394,-1.27224973085 0.946183105255,-1.16124208571" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="-1.86157647252,0.58252431835 -2.80771063936,0.258749491747 -3.13148546596,1.20488365858 -2.18535129913,1.52865848519" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="-0.149061534433,0.0940603451924 -1.09958799875,-0.216583245826 -1.41023158976,0.733943218486 -0.459705125452,1.04458680951" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="-1.1749464018,-2.72689245276 -2.16597044119,-2.59320867154 -2.03228665997,-1.60218463216 -1.04126262058,-1.73586841337" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="2.36928150767,-2.07358519809 1.56026914216,-1.48579357476 2.1480607655,-0.676781209256 2.957073131,-1.26457283259" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="0.965389642309,-0.595334834219 0.014416084408,-0.904607031761 -0.294856113134,0.04636652614 0.656117444767,0.355638723682" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="-0.92494204226,1.94498324406 -1.87599622233,1.63595905962 -2.18502040677,2.58701323969 -1.2339662267,2.89603742413" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="1.7810911232,-2.88234621487 0.971001029806,-2.29604079908 1.5573064456,-1.48595070569 2.36739653899,-2.07225612148" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="0.271021096159,-3.38504193551 -0.680036086942,-3.07602699336 -0.371021144794,-2.12496981026 0.580036038308,-2.43398475241" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="2.24249436146,2.24809770593 1.43454159471,1.65885045163 0.845294340413,2.46680321838 1.65324710716,3.05605047268" fill="#cdf7d6" stroke-width="0.0283550327245"/>
+    <polygon points="3.87585195099,-0 1.19770412054,-3.68615425419 -3.13563009604,-2.27816861686 -3.13563009604,2.27816861686 1.19770412054,3.68615425419" fill="none" stroke-width="0.0737230850838"/>
+  </g>
+</svg>
diff --git a/data/svg/c6682411cb8007fa.svg b/data/svg/c6682411cb8007fa.svg
new file mode 100644
index 0000000000000000000000000000000000000000..f4b594a17c2e09ea4feed358cce1ece6d771a270
--- /dev/null
+++ b/data/svg/c6682411cb8007fa.svg
@@ -0,0 +1,27 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-3.56025127588 -3.12663016044 7.12050255175 6.25326032088" width="900" height="900">
+  <title>squinhex@21</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="0.455697338893,-0.212407250343 -0.380003533259,-0.761592148427 -0.929188431343,0.0741087237251 -0.0934875591909,0.623293621809" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="1.02634302697,-1.28469132004 0.185261304234,-1.82559938586 -0.35564676159,-0.984517663122 0.48543496115,-0.443609597298" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="-0.249218406469,-1.1742947077 -1.1213170237,-1.66362486396 -1.61064717996,-0.791526246728 -0.738548562729,-0.302196090469" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="0.248041885987,-2.04199981241 -0.62404717126,-2.53134700636 -1.11339436521,-1.65925794911 -0.241305307965,-1.16991075516" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="-0.0995829503871,0.619461512858 -0.941908469262,0.0804923854938 -1.48087759663,0.922817904369 -0.638552077752,1.46178703173" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="1.7541450208,-0.567556458276 0.9130632398,-1.10846443351 0.372155264569,-0.267382652505 1.21323704557,0.273525322725" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="1.65140870491,0.553940793325 0.809083221378,0.0149716107184 0.270114038771,0.857297094246 1.1124395223,1.39626627685" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="-0.739469016021,-0.236881340111 -1.58206358459,-0.775429752989 -2.12061199747,0.0671648155829 -1.2780174289,0.605713228461" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="1.92301212893,-2.19266711167 1.05705132055,-1.69255524582 1.5571631864,-0.826594437447 2.42312399477,-1.32670630329" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="0.742169198355,1.15939278055 -0.100156333775,0.620423673898 -0.639125440424,1.46274920603 0.203200091706,2.00171831268" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="-1.75231551103,-0.570807451854 -2.61833800529,-1.07081249125 -3.11834304469,-0.204789996988 -2.25232055043,0.295215042412" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="-1.24995288146,-1.43552854332 -2.11597812555,-1.93552881991 -2.61597840214,-1.06950357581 -1.74995315805,-0.569503299222" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="1.24804273691,-2.80295256533 0.248042739241,-2.80288430498 0.248110999595,-1.80288430731 1.24811099726,-1.80295256766" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="-1.99578593874,0.147148101015 -2.86178663014,0.647190901676 -2.36174382948,1.51319159308 -1.49574313808,1.01314879242" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="2.45880597221,-1.34713261457 1.59278724358,-0.847121053045 2.0927988051,0.0188976755889 2.95881753373,-0.481113885933" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="-1.4966076802,1.01369762802 -2.36260821399,1.51374070164 -1.86256514036,2.37974123543 -0.996564606575,1.87969816181" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="0.138904119617,1.96062452973 -0.703421393325,1.4216553931 -1.24239052996,2.26398090604 -0.40006501702,2.80295004267" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="2.93964732779,0.510578838186 2.07482256869,0.00850500292603 1.57274873343,0.873329762023 2.43757349253,1.37540359728" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="-0.752262292946,-2.30294194938 -1.61828812732,-2.80294120357 -2.11828738151,-1.93691536919 -1.25226154714,-1.436916115" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="2.42069555714,1.37231414101 1.55883202294,0.865173875985 1.05169175791,1.72703741019 1.91355529211,2.23417767522" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="1.4167182544,1.96063706267 0.574392642521,1.42166808065 0.0354236605061,2.26399369253 0.877749272384,2.80296267455" fill="#cdf7d6" stroke-width="0.0248968620621"/>
+    <polygon points="3.23659206807,-0 1.61829603403,-2.80297095263 -1.61829603403,-2.80297095263 -3.23659206807,-3.96368211631e-16 -1.61829603403,2.80297095263 1.61829603403,2.80297095263" fill="none" stroke-width="0.0647318413614"/>
+  </g>
+</svg>
diff --git a/data/svg/c7e14ee67108e002.svg b/data/svg/c7e14ee67108e002.svg
new file mode 100644
index 0000000000000000000000000000000000000000..c51a15f4e78df232c5551780178614f0b0ea53bb
--- /dev/null
+++ b/data/svg/c7e14ee67108e002.svg
@@ -0,0 +1,36 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-3.50039545347 -4.05031475789 7.74019948978 8.10062951578" width="900" height="900">
+  <title>squinpen@30</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="-2.08377559129,1.32553340162 -3.08260840211,1.27723209703 -3.1309097067,2.27606490786 -2.13207689588,2.32436621245" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="-0.953140795341,1.93219440582 -1.9041949514,1.62317014748 -2.21321920974,2.57422430354 -1.26216505368,2.88324856188" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="-0.00205245777004,2.24123446686 -0.953106614405,1.9322102103 -1.26213087097,2.88326436693 -0.311076714338,3.1922886235" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="0.949041257036,2.55025880641 -0.00201302999279,2.24123495115 -0.311036885261,3.19228923817 0.640017401767,3.50131309344" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="2.23695550335,2.24985531586 1.42793230149,1.66207860753 0.840155593158,2.47110180939 1.64917879501,3.05887851772" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="2.82475595096,1.44080678711 2.01573274948,0.853030078251 1.42795604062,1.66205327972 2.2369792421,2.24982998858" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="-2.13217844815,0.277207006207 -3.13217844813,0.277201364352 -3.13218408999,1.27720136434 -2.13218409,1.27720700619" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="-1.28456042607,0.325481304921 -2.13214979796,0.856133975368 -1.60149712752,1.70372334726 -0.753907755622,1.17307067681" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="0.264080909105,1.27621447201 -0.686961027193,0.967152608618 -0.996022890585,1.91819454492 -0.044980954287,2.22725640831" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="1.49251378145,1.57313544758 0.683487754983,0.985362627102 0.0957149345044,1.79438865357 0.904740960975,2.38216147405" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="2.08030345918,0.76407928542 1.27127739333,0.176306519144 0.683504627056,0.985332584994 1.49253069291,1.57310535127" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="3.41255427344,0.631756484637 2.60353099473,0.043979882078 2.01575439217,0.853003160781 2.82477767088,1.44077976334" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="-1.55484042075,-0.685159062738 -2.40242975077,-0.154506325398 -1.87177701343,0.693083004616 -1.02418768341,0.162430267276" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="-0.639642552464,-1.10338911011 -1.44865613603,-0.515599163273 -0.860866189201,0.293414420298 -0.0518526056304,-0.294375526535" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="-0.0510416373141,-0.294924051288 -0.860055168097,0.2928659682 -0.272265148609,1.10187949898 0.536748382174,0.514089479495" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="0.851124902811,-0.754559205277 0.0421112679151,-0.166769329087 0.629901144105,0.642244305809 1.438914779,0.054454429619" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="2.03508116444,-0.826352827693 1.22606670365,-0.23856408824 1.8138554431,0.570450372553 2.6228699039,-0.0173383668999" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="2.96008895713,-1.25455018732 2.15107445833,-0.666761500189 2.73886314546,0.142252998619 3.54787764426,-0.445535688512" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="-2.17021302043,-1.43295293028 -3.13216242802,-1.15972530129 -2.85893479903,-0.197775893699 -1.89698539144,-0.47100352269" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="-1.24961450049,-1.83583571851 -2.20067047607,-1.52681705999 -1.89165181755,-0.575761084407 -0.940595841971,-0.884779742924" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="-1.22720498198,-2.89461494496 -2.17826095311,-2.58559627274 -1.86924228089,-1.63454030161 -0.918186309764,-1.94355897383" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="0.263313744562,-1.56360641115 -0.545699896686,-0.975816543702 0.0420899707623,-0.166802902454 0.85110361201,-0.754592769903" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="1.4125330467,-1.68321264998 0.60351822031,-1.09542441372 1.19130645657,-0.28640958733 2.00032128296,-0.874197823588" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="2.37227999662,-2.06359795408 1.56326504484,-1.47580989041 2.15105310851,-0.666794938629 2.96006806029,-1.2545830023" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="-2.17829934127,-2.58558481193 -3.12935528722,-2.27656606223 -2.82033653753,-1.32551011627 -1.86928059157,-1.63452886597" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="0.208384357541,-3.33652358953 -0.600348548162,-2.74834752131 -0.0121724799374,-1.93961461561 0.796560425766,-2.52779068383" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="1.19650833339,-3.68190862076 0.38749330074,-3.09412066839 0.975281253107,-2.28510563574 1.78429628576,-2.87289358811" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="-0.333627508878,-2.37410065994 -1.13876916811,-1.78101811208 -0.545686620253,-0.97587645285 0.259455038978,-1.56895900071" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="0.809770855152,-2.51285455822 0.0007550358642,-1.92506768857 0.588541905523,-1.11605186928 1.39755772481,-1.70383873894" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="1.78447282926,-2.87264788951 0.975457047819,-2.28486096776 1.56324396957,-1.47584518632 2.37225975101,-2.06363210807" fill="#cdf7d6" stroke-width="0.0283238794188"/>
+    <polygon points="3.87159360286,-0 1.1963882186,-3.68210432445 -3.13218502003,-2.27566562263 -3.13218502003,2.27566562263 1.1963882186,3.68210432445" fill="none" stroke-width="0.073642086489"/>
+  </g>
+</svg>
diff --git a/data/svg/cbc24f56627bdbaa.svg b/data/svg/cbc24f56627bdbaa.svg
new file mode 100644
index 0000000000000000000000000000000000000000..038ea005544f7bcffa84856121b19482e912ee25
--- /dev/null
+++ b/data/svg/cbc24f56627bdbaa.svg
@@ -0,0 +1,42 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-4.4226878853 -3.88402622758 8.8453757706 7.76805245517" width="900" height="900">
+  <title>squinhex@36</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="-1.11471377594,3.48151297941 -0.114770710946,3.47084214221 -0.12544154815,2.47089907721 -1.12538461315,2.48156991442" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="1.14159259816,2.98660262692 2.01032459383,3.48188509149 2.5056070584,2.61315309582 1.63687506273,2.11787063125" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-0.0083136963092,2.99458240784 0.864876350404,3.4819622826 1.35225622516,2.60877223588 0.47906617845,2.12139236112" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-1.97363634183,3.48144415528 -1.12038701154,2.95994096223 -1.64189020459,2.10669163194 -2.49513953488,2.62819482499" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-0.686273909672,2.1573879866 0.186916137841,2.64476785993 0.674296011168,1.77157781242 -0.198894036344,1.28419793909" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="1.64455689769,2.11416954313 2.51108078641,2.61330514624 3.01021638951,1.74678125752 2.1436925008,1.24764565442" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="0.479966795072,2.12187851307 1.35315683986,2.60925839128 1.84053671807,1.73606834649 0.967346673284,1.24868846828" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-2.51405511296,2.60943197708 -1.64803027339,2.10943099984 -2.14803125063,1.24340616027 -3.0140560902,1.74340713751" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-1.42532788179,2.46050439788 -0.568085322482,1.94559159506 -1.0829981253,1.08834903575 -1.94024068461,1.60326183857" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-0.197129273092,1.28230701294 0.681423772508,1.75995180362 1.15906856319,0.881398758025 0.280515517591,0.403753967341" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="2.14583473734,1.24718600791 3.0118666586,1.74717471914 3.51185536983,0.881142797883 2.64582344858,0.381154086648" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="0.978404630895,1.25484275563 1.85159467452,1.74222263593 2.33897455481,0.869032592307 1.46578451119,0.381652712011" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-3.01907016601,1.73463926017 -2.15304906587,1.23463180612 -2.65305651991,0.368610705977 -3.51907762006,0.868618160023" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-1.92537508874,1.59430964902 -1.06813252669,1.07939685076 -1.58304532495,0.222154288715 -2.440287887,0.737067086975" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-0.845178535352,1.41918689174 0.00984113455592,0.900591322856 -0.508754434333,0.0455716529485 -1.36377410424,0.564167221837" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="0.301692841326,0.414265944011 1.18136739495,0.88984209954 1.65694355048,0.0101675459168 0.777268996855,-0.465408609612" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-3.51198900756,0.864231866535 -2.65018082375,0.356997547595 -3.15741514269,-0.504810636219 -4.0192233265,0.00242368272132" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="2.64754995482,0.376241229791 3.52911257381,0.848308331792 4.00117967581,-0.0332542872029 3.11961705682,-0.505321389203" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="1.48481235546,0.392254678674 2.35800239865,0.879634559731 2.84538227971,0.00644451653228 1.97219223651,-0.480935364524" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-2.42046232859,0.725136698792 -1.56321976927,0.210223895984 -2.07813257208,-0.647018663333 -2.9353751314,-0.132105860524" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-1.34961400667,0.554999116439 -0.494543657407,0.0364871129088 -1.01305566094,-0.818583236358 -1.8681260102,-0.300071232828" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-2.93402515025,-0.132937656332 -2.07678259499,-0.647850465887 -2.59169540454,-1.50509302115 -3.44893795981,-0.990180211597" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-1.87014948357,-0.3038604834 -1.01290692739,-0.818773291426 -1.52781973542,-1.67601584761 -2.3850622916,-1.16110303958" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="2.70939257426,-0.270559709197 3.57487708481,-0.771495395692 3.07394139831,-1.63697990624 2.20845688777,-1.13604421974" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-0.781880034151,-0.441030425067 0.217714920617,-0.469489630976 0.189255714708,-1.46908458574 -0.81033924006,-1.44062537984" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="1.21862547622,-0.468487043548 2.21848859626,-0.485032169228 2.20194347058,-1.48489528927 1.20208035054,-1.46835016359" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="0.218343576615,-0.456289238823 1.21819153263,-0.473726694103 1.20075407735,-1.47357465012 0.200906121335,-1.45613719484" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="1.59890041368,-1.47495458566 2.59876415538,-1.49146209969 2.58225664135,-2.4913258414 1.58239289964,-2.47481832736" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="0.598930929658,-1.4640286025 1.59879467138,-1.48053611558 1.58228715831,-2.4803998573 0.582423416582,-2.46389234422" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-0.401153990703,-1.46012770725 0.59870975113,-1.47663521364 0.582202244744,-2.47649895547 -0.41766149709,-2.45999144909" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-1.40139259184,-1.46556491311 -0.401528849877,-1.48207241149 -0.418036348249,-2.48193615345 -1.41790009021,-2.46542865508" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-2.93717448924,-1.84118131439 -2.0637407406,-1.35423831287 -1.57679773908,-2.22767206151 -2.45023148772,-2.71461506303" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-2.01602268169,-2.47265041471 -1.01602275485,-2.47226788266 -1.0156402228,-3.47226780949 -2.01564014963,-3.47265034154" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="-1.01556051772,-2.48195357198 -0.0155605177203,-2.48195555379 -0.0155624995274,-3.48195555379 -1.01556249953,-3.48195357198" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="1.01251261522,-2.47879302417 2.01250760599,-2.48195821702 2.00934241313,-3.48195320779 1.00934742236,-3.47878801493" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="0.0121312054556,-2.47379226143 1.0121073819,-2.48069490924 1.00520473409,-3.48067108569 0.00522855764439,-3.47376843788" fill="#cdf7d6" stroke-width="0.0309278873028"/>
+    <polygon points="4.02062534936,-0 2.01031267468,-3.48196369165 -2.01031267468,-3.48196369165 -4.02062534936,-4.92384596467e-16 -2.01031267468,3.48196369165 2.01031267468,3.48196369165" fill="none" stroke-width="0.0804125069873"/>
+  </g>
+</svg>
diff --git a/data/svg/d93824a50e5c0a99.svg b/data/svg/d93824a50e5c0a99.svg
new file mode 100644
index 0000000000000000000000000000000000000000..5930ffdc9ceab764e4746f089527c307ff62809a
--- /dev/null
+++ b/data/svg/d93824a50e5c0a99.svg
@@ -0,0 +1,39 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-3.6620318223 -4.23734453176 8.09761560353 8.47468906351" width="900" height="900">
+  <title>squinpen@33</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="1.03812238638,2.73127684574 0.0870671217068,2.42225599929 -0.221953724737,3.37331126397 0.729101539937,3.68233211041" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="0.0870960190745,2.42202173116 -0.863959392852,2.1130013379 -1.1729797861,3.06405674983 -0.221924374178,3.37307714308" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="2.28058025466,2.42392867944 1.48711194541,1.81531711019 0.878500376163,2.60878541944 1.67196868541,3.21739698869" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="-0.863475002273,2.11136160294 -1.8145309441,1.80234284053 -2.1235497065,2.75339878236 -1.17249376468,3.06241754476" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="-1.81518854174,1.80417841142 -2.766248885,1.49517319549 -3.07525410093,2.44623353875 -2.12419375767,2.75523875468" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="1.43749951305,1.86263061426 0.640052952848,1.2592410356 0.0366633741967,2.0566875958 0.834109934397,2.66007717446" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="2.87527867818,1.61734597257 2.08063543451,1.01026927618 1.47355873812,1.80491251984 2.26820198179,2.41198921624" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="-0.0713705444618,1.31899349711 -1.02139235996,1.00680997725 -1.33357587983,1.95683179275 -0.383554064327,2.26901531261" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="-1.0207092392,1.00045174487 -1.96867807122,0.682088597638 -2.28704121845,1.63005742966 -1.33907238643,1.94842057689" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="2.06076608347,1.03610085139 1.26608242725,0.429077057351 0.659058633212,1.22376071358 1.45374228944,1.83078450761" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="-2.22692272076,0.505181529397 -3.22674336401,0.486242645359 -3.24568224804,1.48606328861 -2.24586160479,1.50500217265" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="0.955716646992,0.821984169595 0.151300641564,0.227917767405 -0.442765760626,1.03233377283 0.361650244802,1.62640017502" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="3.3827434044,0.746584578979 2.59245503698,0.133849484242 1.97971994224,0.924137851661 2.77000830966,1.5368729464" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="-0.169272941099,0.234246618214 -1.11524818125,-0.0899922520864 -1.43948705155,0.855982988069 -0.493511811399,1.18022185837" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="4.04872241186,-0.00223257156914 3.26020161391,-0.617240661923 2.64519352356,0.171280136027 3.43371432151,0.786288226381" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="-2.25802050188,-0.495607060963 -3.25784107031,-0.514549894767 -3.27678390411,0.485270673658 -2.27696333569,0.504213507463" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="1.07813945385,-0.660842757707 0.259661681067,-0.0863045644913 0.834199874282,0.73217320829 1.65267764706,0.157635015074" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="-1.25526986605,-0.626046493427 -2.25508943718,-0.645041892102 -2.27408483586,0.354777679035 -1.27426526472,0.37377307771" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="2.19530393012,-0.810206415601 1.37666290712,-0.235900856289 1.95096846643,0.582740166714 2.76960948943,0.00843460740213" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="-0.246123598818,-1.07343957275 -1.24593693623,-1.09276029555 -1.26525765903,-0.0929469581396 -0.265444321617,-0.0736262353409" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="0.66149572953,-1.52812688102 -0.296218945608,-1.24040722402 -0.00849928860674,-0.28269254888 0.949215386532,-0.570412205881" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="2.88000678294,-1.57892432508 2.07424597604,-0.986683223784 2.66648707734,-0.180922416885 3.47224788424,-0.773163518182" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="1.62249961748,-1.63353235109 0.801529838648,-1.06256070359 1.37250148614,-0.241590924761 2.19347126498,-0.812562572256" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="-2.24199317168,-1.4955068152 -3.24181374601,-1.51444933762 -3.26075626843,-0.514628763298 -2.2609356941,-0.495686240876" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="-1.23182264014,-1.63499408997 -2.23148069151,-1.66114328353 -2.25762988508,-0.661485232157 -1.2579718337,-0.635336038594" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="2.30326900025,-2.39612888714 1.49719673334,-1.80431176968 2.0890138508,-0.998239502772 2.89508611771,-1.59005662023" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="-0.144525403426,-2.34289081252 -1.09614258961,-2.03560473904 -0.788856516128,-1.08398755285 0.162760670057,-1.39127362634" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="0.826865892534,-2.63286795125 -0.12779125799,-2.33516050265 0.169916190609,-1.38050335212 1.12457334113,-1.67821080072" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="-2.09425168626,-2.76496188779 -3.04531543269,-2.4559671464 -2.7363206913,-1.50490339996 -1.78525694486,-1.81389814135" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="-1.14294419941,-3.07345069747 -2.09401714548,-2.76448427331 -1.78505072132,-1.81341132724 -0.833977775254,-2.1223777514" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="1.6422987831,-3.18141722536 0.851570481749,-2.56924996599 1.46373774111,-1.77852166464 2.25446604247,-2.390688924" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="-0.189763439558,-3.38026335511 -1.14123573162,-3.07252892831 -0.833501304815,-2.12105663625 0.117970987246,-2.42879106305" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="0.766978484759,-3.6945880712 -0.183759653683,-3.38459292267 0.126235494846,-2.43385478422 1.07697363329,-2.74384993275" fill="#cdf7d6" stroke-width="0.0296317799354"/>
+    <polygon points="4.05037064107,-0 1.25163336161,-3.8521313916 -3.27681868214,-2.38074812914 -3.27681868214,2.38074812914 1.25163336161,3.8521313916" fill="none" stroke-width="0.0770426278319"/>
+  </g>
+</svg>
diff --git a/data/svg/e25d367759fc397e.svg b/data/svg/e25d367759fc397e.svg
new file mode 100644
index 0000000000000000000000000000000000000000..a2cad3715b3604645b7314e3df73541775ccf786
--- /dev/null
+++ b/data/svg/e25d367759fc397e.svg
@@ -0,0 +1,25 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-1.80356595995 -2.08690987097 3.98810948882 4.17381974193" width="900" height="900">
+  <title>triinpen@19</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="-0.740271880873,-1.45634251647 -1.60657450834,-0.956822989687 -0.74082659473,-0.456342670322" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="0.118557210672,0.0401472624358 -0.747368487004,-0.46002539386 -0.747567864796,0.539974586264" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="0.43882829215,-1.8394742472 -0.512220386337,-1.53043313157 0.230941409855,-0.861321373584" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="0.125693938507,-0.956039560856 -0.740580516195,-0.456471178019 0.125195621621,0.0439603149838" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="-0.747509136308,-0.460165424558 -1.61357511978,0.0397642827826 -0.747590301378,0.539834572148" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="1.27725891058,0.986042010545 0.293922601873,0.804246235091 0.628150996385,1.74673834662" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="1.85953612752,0.173673288157 0.864271327313,0.0764725810216 1.27772544577,0.986997535062" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="0.221141007801,-0.0107181163414 -0.647618198868,0.484516616719 0.215647264133,0.989266792935" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="0.837400585473,0.00878839676397 0.216757995218,0.792881997785 1.20612426777,0.938327447105" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="-1.61377353225,0.0396959926604 -1.61383694126,1.03969599065 -0.747779834711,0.539750905472" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="0.224509615569,-0.638685073102 0.219149503881,0.361300561396 1.08784252262,-0.134050262964" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="1.39547098068,-0.824932971217 0.988731147922,0.0886110662831 1.98325340825,-0.0159139245719" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="1.17352880122,-1.13039051694 0.267846105876,-0.706434321839 1.08784428859,-0.134068197457" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="-0.646921900804,0.48492537716 -0.65241560329,1.48491028666 0.216343582984,0.989675517825" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="0.43035657355,-1.7995213039 0.222469628492,-0.821368443622 1.17351832681,-1.13040949823" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="-0.652016515291,0.484898911867 -1.51824953148,0.984539144091 -0.652431889528,1.4848988256" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="0.324980579834,0.891888948763 -0.418163248484,1.56102066258 0.532893728316,1.87003623966" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="-1.613487025,-0.960388417147 -1.61377956383,0.0396115400631 -0.747607927688,-0.460135092477" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="-0.740247855594,-1.45637603743 -0.740746197969,-0.456376161603 0.125528269466,-0.95594452236" fill="#cdf7d6" stroke-width="0.0145937753145"/>
+    <polygon points="1.99482444878,-0 0.616434655468,-1.89719079088 -1.61384687986,-1.17252839191 -1.61384687986,1.17252839191 0.616434655468,1.89719079088" fill="none" stroke-width="0.0379438158176"/>
+  </g>
+</svg>
diff --git a/data/svg/f5757609f28a7743.svg b/data/svg/f5757609f28a7743.svg
new file mode 100644
index 0000000000000000000000000000000000000000..3cddd95c23a2a06b6495ebf58502fbd20d63286d
--- /dev/null
+++ b/data/svg/f5757609f28a7743.svg
@@ -0,0 +1,25 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-4.0642345093 -6.60021581619 11.5926839073 13.2004316324" width="900" height="900">
+  <title>hexintri@19</title>
+  <g stroke="black" stroke-linejoin="round">
+    <polygon points="1.73205457008,-2.00000064626 0.866034224973,-2.50000940805 3.76259767287e-06,-2.00001816989 -6.35467296206e-06,-1.00001816994 0.866013990432,-0.500009408155 1.73204445281,-1.00000064632" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="-1.73214877041,-5.00016967734 -2.59817764148,-5.50016367178 -3.46419957794,-5.00015766624 -3.46419264332,-4.00015766627 -2.59816377225,-3.50016367183 -1.7321418358,-4.00016967737" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="2.59827925825,0.499993126345 1.73225478259,0.999994733895 1.73225663883,1.99999473389 2.59828297073,2.49999312634 3.46430744639,1.99999151879 3.46430559015,0.999991518793" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="0.865857821559,2.50020870847 -0.000170994028367,2.00021461793 -0.86619298597,2.50022052737 -0.866186162324,3.50022052735 -0.000157346737301,4.00021461789 0.865864645204,3.50020870845" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="-0.866067678278,-3.50016564954 -1.73209958016,-4.00015439435 -2.5981184857,-3.50014313923 -2.59810548937,-2.50014313932 -1.73207358749,-2.00015439452 -0.866054681944,-2.50016564963" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="6.06236287301,-0.500000355782 5.1963372653,-1.00000000257 4.33031206545,-0.49999964935 4.3303124733,0.50000035065 5.19633808102,0.999999997434 6.06236328087,0.499999644218" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="-0.866090989086,0.499952439579 -0.866089599487,-0.50004756042 -1.73211430847,-1.00004876385 -2.59814040705,-0.500049967277 -2.59814179665,0.499950032722 -1.73211708767,0.99995123615" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="-0.866239513325,2.50005780543 -1.73226158002,2.00005202547 -2.59829032086,2.50004624548 -2.59829699499,3.50004624546 -1.7322749283,4.00005202542 -0.866246187462,3.5000578054" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="0.866057925439,-3.50008831974 3.48447996455e-05,-4.00009234352 -0.865992882111,-3.50009636732 -0.865997528383,-2.50009636733 2.55522566316e-05,-2.00009234355 0.866053279167,-2.50008831975" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="-1.73215060841,4.00018160075 -2.59817350315,3.50017725498 -3.46420141596,4.0001729092 -3.46420643402,5.00017290919 -2.59818353928,5.50017725495 -1.73215562648,5.00018160073" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="2.59815186093,-0.499999783835 1.73212789819,-1.00000227979 0.866101053371,-0.500004775739 0.866098171294,0.499995224257 1.73212213404,0.999997720207 2.59814897886,0.500000216161" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="-5.88521138132e-05,1.00009655165 -0.866085567045,0.500098822632 -1.73210965968,1.00010109361 -1.73210703738,2.00010109361 -0.866080322446,2.50009882263 -5.62298144469e-05,2.00009655165" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="0.86603892226,-0.499927934361 2.16521447383e-05,-0.999942022024 -0.866011885079,-0.49995610982 -0.866028152188,0.500043890048 -1.08820723091e-05,1.00005797771 0.866022655152,0.500072065506" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="1.7321839916,1.00032533124 0.866148907678,0.500342098107 0.000133184359611,1.00035886479 0.000152544966601,2.0003588646 0.866187628892,2.50034209773 1.73220335221,2.00032533105" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="-1.73214621752,1.99995987678 -1.73214260881,0.999959876788 -2.59816620824,0.499956751558 -3.46419341637,0.999953626322 -3.46419702508,1.99995362632 -2.59817342565,2.49995675155" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="3.46413475687,-2.00008106956 2.598113137,-2.50008762344 1.73208394935,-2.00009417735 1.73207638157,-1.00009417738 2.59809800143,-0.500087623499 3.46412718909,-1.00008106959" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="-3.31298227203e-05,-2.00008883396 -0.866059943705,-2.50008639159 -1.73208393738,-2.00008394922 -1.73208111718,-1.00008394923 -0.8660543033,-0.500086391597 -3.03096200115e-05,-1.00008883396" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="-1.73214968504,-1.00011168428 -1.73215299017,-2.00011168427 -2.59818004651,-2.50010882194 -3.46420379773,-2.00010595962 -3.4642004926,-1.00010595963 -2.59817343626,-0.500108821955" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="4.33027337427,-0.500109581311 3.46424463353,-1.0001038015 2.59822256674,-0.500098021718 2.59822924067,0.499901978259 3.4642579814,0.999896198452 4.3302800482,0.499890418666" fill="#cdf7d6" stroke-width="0.046155355351"/>
+    <polygon points="6.92842977747,-0 -3.46421488873,-6.00019619562 -3.46421488873,6.00019619562" fill="none" stroke-width="0.120003923912"/>
+  </g>
+</svg>