Credit Friedman authors and show image recovery status

app.py

@@ -941,9 +941,13 @@ def visual_provenance(record: dict[str, Any], visual_record: dict[str, Any]) ->
     if visual_record.get("frontend_seed"):
         visual_metric = metric_value(visual_record)
         shown_metric = metric_value(record)
+        notes = str(visual_record.get("notes") or "").lower()
         suffix = ""
         if visual_metric != shown_metric:
-            suffix = f" Rendering metric: {esc(metric_symbol(visual_record))} = {esc(visual_metric)}; displayed record metric: {esc(metric_symbol(record))} = {esc(shown_metric)}."
+            suffix = f" Verified coordinate metric: {esc(metric_symbol(visual_record))} = {esc(visual_metric)}; Friedman reported metric: {esc(metric_symbol(record))} = {esc(shown_metric)}."
+        if "image-seeded" in notes or "image seeded" in notes:
+            status = "recovered within tolerance" if not needs_recovery(record, visual_record) else "still outside recovery tolerance"
+            return f"Image-seeded from the Friedman source image and verified ({status})." + suffix
         return "Generated feasible coordinate rendering, not recovered from the Friedman source image." + suffix
 
     return "Coordinate rendering attached to this case."

data/solutions/generated/cirincir_10_be14c55679a54b28.json

@@ -0,0 +1,119 @@
+{
+  "case": "cirincir@10",
+  "container": {
+    "radius": 3.813115539124243,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "cirincir@10",
+    "credit": "Pirl",
+    "date": "1969",
+    "family_updated": "6/27/05",
+    "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "cirincir@10",
+      "credit": "Pirl",
+      "date": "1969",
+      "family_updated": "6/27/05",
+      "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"
+    },
+    "generator": "friedman_image_seed",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "image_seed": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/site_images/cirincir_010.gif",
+    "image_seed_transform_error": 0.06260662900137194,
+    "notes": "Image-seeded from the Friedman source image and refined with polygon-packer-c.",
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/cirincir_010_image_refined.state",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T02:08:58+00:00",
+    "submitted_by": "polygon-packer-c image seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 4.250841583787497,
+      "x": -1.5495894413068694,
+      "y": 2.347809976552831
+    },
+    {
+      "id": 2,
+      "rotation_radians": 1.2049245946973615,
+      "x": 2.475977848974938,
+      "y": -1.3352782482689725
+    },
+    {
+      "id": 3,
+      "rotation_radians": 3.324535391146819,
+      "x": 0.9628155378992221,
+      "y": -2.6431837470626016
+    },
+    {
+      "id": 4,
+      "rotation_radians": 2.235924865008793,
+      "x": -2.7181525310229597,
+      "y": 0.724620859045127
+    },
+    {
+      "id": 5,
+      "rotation_radians": 5.015462004334633,
+      "x": 0.4022919298430151,
+      "y": 2.7841965332540686
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.28911623382725804,
+      "x": -1.0370560344683115,
+      "y": -2.614970847945628
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.652847074253164,
+      "x": 2.7375524795110038,
+      "y": 0.6476129213608892
+    },
+    {
+      "id": 8,
+      "rotation_radians": 2.753751059344826,
+      "x": 0.7444079617997427,
+      "y": 0.813627221395956
+    },
+    {
+      "id": 9,
+      "rotation_radians": 5.720342076194702,
+      "x": -0.6056692970283514,
+      "y": -0.6619913272422999
+    },
+    {
+      "id": 10,
+      "rotation_radians": 2.794472784545188,
+      "x": -2.512698883945597,
+      "y": -1.2648690591199467
+    }
+  ],
+  "problem": "10 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc10.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirinsqu_10_522948d614943781.json

@@ -0,0 +1,122 @@
+{
+  "case": "cirinsqu@10",
+  "container": {
+    "circumradius": 4.771259329856722,
+    "orientation_radians": 0.0,
+    "side_length": 6.74757965388254,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "cirinsqu@10",
+    "credit": "De Groot",
+    "date": "1990",
+    "family_updated": "10/9/10",
+    "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "cirinsqu@10",
+      "credit": "De Groot",
+      "date": "1990",
+      "family_updated": "10/9/10",
+      "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"
+    },
+    "generator": "friedman_image_seed",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "image_seed": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/site_images/cirinsqu_010.gif",
+    "image_seed_transform_error": 1.0052492910490174e-15,
+    "notes": "Image-seeded from the Friedman source image and refined with polygon-packer-c.",
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/cirinsqu_010_image_refined.state",
+    "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
+    "submitted_at": "2026-05-01T02:08:58+00:00",
+    "submitted_by": "polygon-packer-c image seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.6631201483233983,
+      "x": -1.452583219963529,
+      "y": -1.9044085825632537
+    },
+    {
+      "id": 2,
+      "rotation_radians": 3.460415277605134,
+      "x": -0.038322427094046985,
+      "y": -3.3186863548500445
+    },
+    {
+      "id": 3,
+      "rotation_radians": 5.175384480811934,
+      "x": 1.4137529043718686,
+      "y": -1.9432788926909437
+    },
+    {
+      "id": 4,
+      "rotation_radians": 1.210268797097649,
+      "x": 2.828002842573363,
+      "y": -0.5289911772412871
+    },
+    {
+      "id": 5,
+      "rotation_radians": 1.2733469800666406,
+      "x": -3.357028277502991,
+      "y": -1.8343155996848248e-06
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.7406471839276207,
+      "x": -1.3591735215093275,
+      "y": 0.09348660293620727
+    },
+    {
+      "id": 7,
+      "rotation_radians": 5.70981309480042,
+      "x": 0.6312250856386635,
+      "y": -0.10267057200586589
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.7817877980872996,
+      "x": 2.045418000705354,
+      "y": 1.3116253947392875
+    },
+    {
+      "id": 9,
+      "rotation_radians": 3.1295383626226756,
+      "x": -1.2656324453185372,
+      "y": 2.091369376176176
+    },
+    {
+      "id": 10,
+      "rotation_radians": 1.2491990785030422,
+      "x": 0.6311280446094484,
+      "y": 2.7258703870584085
+    }
+  ],
+  "problem": "10 equal items for Circles in Squares",
+  "setup": "cirinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/cirinsqu/cs10.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinsqu/"
+}

data/solutions/generated/triincir_16_8bb5531a7df45934.json

@@ -0,0 +1,157 @@
+{
+  "case": "triincir@16",
+  "container": {
+    "radius": 1.6880356342518776,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triincir@16",
+    "credit": "Maurizio Morandi",
+    "date": "April 2008",
+    "family_updated": "8/31/19",
+    "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"
+  },
+  "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": "triincir@16",
+      "credit": "Maurizio Morandi",
+      "date": "April 2008",
+      "family_updated": "8/31/19",
+      "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"
+    },
+    "generator": "friedman_image_seed",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "image_seed": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/site_images/triincir_016.gif",
+    "image_seed_transform_error": 0.027220545981561973,
+    "notes": "Image-seeded from the Friedman source image and refined with polygon-packer-c.",
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/triincir_016_image_refined.state",
+    "source_url": "https://erich-friedman.github.io/packing/triincir/",
+    "submitted_at": "2026-05-01T02:08:58+00:00",
+    "submitted_by": "polygon-packer-c image seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 3.664836111795197,
+      "x": 0.17784122734082114,
+      "y": -1.2571047992820488
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+    {
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+    },
+    {
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+      "y": -0.38778615596180166
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+    {
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+    {
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+      "rotation_radians": 4.714609969432941,
+      "x": -0.002953549079464715,
+      "y": 1.323563676623352
+    }
+  ],
+  "problem": "16 equal items for Triangles in Circles",
+  "setup": "triincir",
+  "source_image": "https://erich-friedman.github.io/packing/triincir/tc16.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triincir/"
+}

data/solutions/generated/triincir_24_e1de703df3a339d6.json

@@ -0,0 +1,205 @@
+{
+  "case": "triincir@24",
+  "container": {
+    "radius": 2.0003198331040326,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triincir@24",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "8/31/19",
+    "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"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triincir@24",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "8/31/19",
+      "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"
+    },
+    "generator": "friedman_image_seed",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "image_seed": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/site_images/triincir_024.gif",
+    "image_seed_transform_error": 0.007191923516456017,
+    "notes": "Image-seeded from the Friedman source image and refined with polygon-packer-c.",
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/triincir_024_image_refined.state",
+    "source_url": "https://erich-friedman.github.io/packing/triincir/",
+    "submitted_at": "2026-05-01T02:08:58+00:00",
+    "submitted_by": "polygon-packer-c image seed"
+  },
+  "placements": [
+    {
+      "id": 1,
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+  "problem": "24 equal items for Triangles in Circles",
+  "setup": "triincir",
+  "source_image": "https://erich-friedman.github.io/packing/triincir/tc24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triincir/"
+}

data/solutions/generated/triincir_26_8245fa6b2a472124.json

@@ -0,0 +1,217 @@
+{
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+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triincir@26",
+    "credit": "Maurizio Morandi",
+    "date": "April 2008",
+    "family_updated": "8/31/19",
+    "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"
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+      "case": "triincir@26",
+      "credit": "Maurizio Morandi",
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+      "family_updated": "8/31/19",
+      "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"
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+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/triincir_026_image_refined.state",
+    "source_url": "https://erich-friedman.github.io/packing/triincir/",
+    "submitted_at": "2026-05-01T02:08:58+00:00",
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+  "problem": "26 equal items for Triangles in Circles",
+  "setup": "triincir",
+  "source_image": "https://erich-friedman.github.io/packing/triincir/tc26.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triincir/"
+}

data/solutions/generated/triinhex_28_3435500023858121.json

@@ -0,0 +1,232 @@
+{
+  "case": "triinhex@28",
+  "container": {
+    "circumradius": 2.3245501826518793,
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+    "side_length": 2.324550182651879,
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+    "type": "regular_polygon"
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+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinhex@28",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "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"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
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+  "metadata": {
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+    "friedman_reference": {
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+      "case": "triinhex@28",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "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"
+    },
+    "generator": "friedman_image_seed",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "image_seed": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/site_images/triinhex_028.gif",
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+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/triinhex_028_image_refined.state",
+    "source_url": "https://erich-friedman.github.io/packing/triinhex/",
+    "submitted_at": "2026-05-01T02:08:58+00:00",
+    "submitted_by": "polygon-packer-c image seed"
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+  "placements": [
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+      "x": -0.45636221370125063,
+      "y": -1.6055697730710883
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+  ],
+  "problem": "28 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/28.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}

data/solutions/generated/triinhex_29_4339d1ebd3160f94.json

@@ -0,0 +1,238 @@
+{
+  "case": "triinhex@29",
+  "container": {
+    "circumradius": 2.3335122751747748,
+    "orientation_radians": 0.0,
+    "side_length": 2.3335122751747743,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triinhex@29",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "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"
+  },
+  "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": "triinhex@29",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "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"
+    },
+    "generator": "friedman_image_seed",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "image_seed": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/site_images/triinhex_029.gif",
+    "image_seed_transform_error": 0.07906520028491007,
+    "notes": "Image-seeded from the Friedman source image and refined with polygon-packer-c.",
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/triinhex_029_image_refined.state",
+    "source_url": "https://erich-friedman.github.io/packing/triinhex/",
+    "submitted_at": "2026-05-01T02:08:58+00:00",
+    "submitted_by": "polygon-packer-c image seed"
+  },
+  "placements": [
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+}

data/solutions/generated/triinhex_30_7274d354e73d8050.json

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+{
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+}

data/solutions/generated/triinhex_31_cae7087451040120.json

@@ -0,0 +1,250 @@
+{
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+    "source_image": "31.gif",
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+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/31.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}

data/solutions/generated/triinhex_35_ec49778cf450c37b.json

@@ -0,0 +1,274 @@
+{
+  "case": "triinhex@35",
+  "container": {
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+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "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/",
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+      "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"
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+    "source_url": "https://erich-friedman.github.io/packing/triinhex/",
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+  "setup": "triinhex",
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+}

data/solutions/generated/triinhex_39_a314b4bb8467e5e8.json

@@ -0,0 +1,298 @@
+{
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+    "case": "triinhex@39",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "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/",
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+      "credit": "Emerson Connelly",
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+      "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.",
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+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
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+    "source_url": "https://erich-friedman.github.io/packing/triinhex/",
+    "submitted_at": "2026-05-01T02:08:58+00:00",
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+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/39.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}

data/solutions/generated/triinoct_16_640352ab60961c58.json

@@ -0,0 +1,160 @@
+{
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+    "source_page": "https://erich-friedman.github.io/packing/triinoct/",
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+}

data/solutions/generated/triinoct_27_c7748eb19b34ff2e.json

@@ -0,0 +1,226 @@
+{
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+    "source_page": "https://erich-friedman.github.io/packing/triinoct/",
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+}

data/solutions/generated/triinoct_29_0575780ea85d68dd.json

@@ -0,0 +1,238 @@
+{
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+  "problem": "29 equal items for Triangles in Octagons",
+  "setup": "triinoct",
+  "source_image": "https://erich-friedman.github.io/packing/triinoct/29.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinoct/"
+}

data/solutions/generated/triinpen_19_eaa1430599d74148.json

@@ -0,0 +1,178 @@
+{
+  "case": "triinpen@19",
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+    "case": "triinpen@19",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "4/29/26",
+    "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/",
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+      "credit": "Ignacio Vallejo",
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+      "family_updated": "4/29/26",
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+      "metric_value": 2.344,
+      "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.",
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+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
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+    "generator": "friedman_image_seed",
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+    "source_url": "https://erich-friedman.github.io/packing/triinpen/",
+    "submitted_at": "2026-05-01T02:08:58+00:00",
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+  "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/"
+}

data/solutions/generated/triinpen_24_7bc3466b163ec849.json

@@ -0,0 +1,208 @@
+{
+  "case": "triinpen@24",
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+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@24",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "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"
+  },
+  "item": {
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+      "case": "triinpen@24",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "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"
+    },
+    "generator": "friedman_image_seed",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "image_seed": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/site_images/triinpen_024.gif",
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+    "source_url": "https://erich-friedman.github.io/packing/triinpen/",
+    "submitted_at": "2026-05-01T02:08:58+00:00",
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+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}

data/solutions/generated/triinpen_25_d7a41b31b48a9cd4.json

@@ -0,0 +1,214 @@
+{
+  "case": "triinpen@25",
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+  "friedman_reference": {
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+    "case": "triinpen@25",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "4/29/26",
+    "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/",
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+      "family_updated": "4/29/26",
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+      "metric_value": 2.72,
+      "reference_text": "s = 2.720+ | Found by Ignacio Vallejo | in March 2026.",
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+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/25.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
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+  "problem": "25 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/25.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}

data/solutions/generated/triinpen_30_29e4e0e684891d8a.json

@@ -0,0 +1,244 @@
+{
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+    "metric_symbol": "s",
+    "metric_value": 2.952,
+    "reference_text": "s = 2.952+ | Found by Ignacio Vallejo | in April 2026.",
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+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/30.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
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+      "credit": "Ignacio Vallejo",
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+      "metric_expression": "2.952+",
+      "metric_symbol": "s",
+      "metric_value": 2.952,
+      "reference_text": "s = 2.952+ | Found by Ignacio Vallejo | in April 2026.",
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+      "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"
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+    "source_url": "https://erich-friedman.github.io/packing/triinpen/",
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+  "problem": "30 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/30.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}

data/solutions/generated/triinsqu_10_5b0eaf84f54fe48c.json

@@ -0,0 +1,124 @@
+{
+  "case": "triinsqu@10",
+  "container": {
+    "circumradius": 1.6809609047175382,
+    "orientation_radians": 0.0,
+    "side_length": 2.3772377092704904,
+    "sides": 4,
+    "type": "regular_polygon"
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+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@10",
+    "credit": "David W",
+    "date": "July 2002",
+    "family_updated": "4/29/26",
+    "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"
+  },
+  "item": {
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+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
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+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@10",
+      "credit": "David W",
+      "date": "July 2002",
+      "family_updated": "4/29/26",
+      "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"
+    },
+    "generator": "friedman_image_seed",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "image_seed": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/site_images/triinsqu_010.gif",
+    "image_seed_transform_error": 2.707242505775539e-16,
+    "notes": "Image-seeded from the Friedman source image and refined with polygon-packer-c.",
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/triinsqu_010_image_refined.state",
+    "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
+    "submitted_at": "2026-05-01T02:08:58+00:00",
+    "submitted_by": "polygon-packer-c image seed"
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+  "placements": [
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+  "problem": "10 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t10.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}

data/solutions/generated/triinsqu_13_7628e283de25ee68.json

@@ -0,0 +1,142 @@
+{
+  "case": "triinsqu@13",
+  "container": {
+    "circumradius": 1.8353309359550882,
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+    "side_length": 2.595549901070592,
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+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@13",
+    "credit": "David W",
+    "date": "July 2002",
+    "family_updated": "4/29/26",
+    "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"
+  },
+  "item": {
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+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
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+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
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+      "case": "triinsqu@13",
+      "credit": "David W",
+      "date": "July 2002",
+      "family_updated": "4/29/26",
+      "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"
+    },
+    "generator": "friedman_image_seed",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "image_seed": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/site_images/triinsqu_013.gif",
+    "image_seed_transform_error": 2.327997847980024e-16,
+    "notes": "Image-seeded from the Friedman source image and refined with polygon-packer-c.",
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/triinsqu_013_image_refined.state",
+    "source_url": "https://erich-friedman.github.io/packing/triinsqu/",
+    "submitted_at": "2026-05-01T02:08:58+00:00",
+    "submitted_by": "polygon-packer-c image seed"
+  },
+  "placements": [
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+    {
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+      "x": 0.5578745042273364,
+      "y": 0.8669705100795495
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+    {
+      "id": 13,
+      "rotation_radians": 3.4038845577375336,
+      "x": -0.14914994230393525,
+      "y": 1.2775613124288179
+    }
+  ],
+  "problem": "13 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t13.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}

data/solutions/generated/triinsqu_32_f42801b713b9238d.json

@@ -0,0 +1,256 @@
+{
+  "case": "triinsqu@32",
+  "container": {
+    "circumradius": 2.8258720673212823,
+    "orientation_radians": 0.0,
+    "side_length": 3.996386603137053,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@32",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.997+",
+    "metric_symbol": "s",
+    "metric_value": 3.997,
+    "reference_text": "32. | | s = 3.997+ | Found by Emerson Connelly | in April 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": {
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+    "side_length": 1.0,
+    "sides": 3,
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+}

data/solutions/generated/triinsqu_33_a6f49f2f24228d1b.json

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+{
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+}

data/solutions/generated/triinsqu_34_61b4d5d6bf22a206.json

@@ -0,0 +1,268 @@
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+    "reference_text": "34. | | s = 4.098+ | Found by Emerson Connelly | in April 2026.",
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+      "reference_text": "34. | | s = 4.098+ | Found by Emerson Connelly | in April 2026.",
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+  "setup": "triinsqu",
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+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}

data/solutions/generated/triintri_11_8c37202a929dc807.json

@@ -0,0 +1,130 @@
+{
+  "case": "triintri@11",
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+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triintri@11",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "2/29/26",
+    "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"
+  },
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+      "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"
+    },
+    "generator": "friedman_image_seed",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "image_seed": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/site_images/triintri_011.gif",
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+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/triintri_011_image_refined.state",
+    "source_url": "https://erich-friedman.github.io/packing/triintri/",
+    "submitted_at": "2026-05-01T02:08:58+00:00",
+    "submitted_by": "polygon-packer-c image seed"
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+  "problem": "11 equal items for Triangles in Triangles",
+  "setup": "triintri",
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+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}

data/solutions/generated/triintri_29_f2204c752005e940.json

@@ -0,0 +1,238 @@
+{
+  "case": "triintri@29",
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+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triintri@29",
+    "credit": "David W",
+    "date": "July 2007",
+    "family_updated": "2/29/26",
+    "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"
+  },
+  "item": {
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+    "friedman_reference": {
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+      "case": "triintri@29",
+      "credit": "David W",
+      "date": "July 2007",
+      "family_updated": "2/29/26",
+      "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"
+    },
+    "generator": "friedman_image_seed",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "image_seed": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/site_images/triintri_029.gif",
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+    "notes": "Image-seeded from the Friedman source image and refined with polygon-packer-c.",
+    "refined_state": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/states/triintri_029_image_refined.state",
+    "source_url": "https://erich-friedman.github.io/packing/triintri/",
+    "submitted_at": "2026-05-01T02:08:58+00:00",
+    "submitted_by": "polygon-packer-c image seed"
+  },
+  "placements": [
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+    {
+      "id": 29,
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+      "x": -1.3493083169194713,
+      "y": 2.3370798624357567
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+  ],
+  "problem": "29 equal items for Triangles in Triangles",
+  "setup": "triintri",
+  "source_image": "https://erich-friedman.github.io/packing/triintri/tt29.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}

data/solutions/generated/triintri_30_149a91e0248df04e.json

@@ -0,0 +1,244 @@
+{
+  "case": "triintri@30",
+  "container": {
+    "circumradius": 3.3220967081077366,
+    "orientation_radians": 0.0,
+    "side_length": 5.754040286099913,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triintri@30",
+    "credit": "Maurizio Morandi",
+    "date": "May 2008",
+    "family_updated": "2/29/26",
+    "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"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triintri@30",
+      "credit": "Maurizio Morandi",
+      "date": "May 2008",
+      "family_updated": "2/29/26",
+      "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"
+    },
+    "generator": "friedman_image_seed",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "image_seed": "/Users/nathanroll/Documents/polygon-packer-c/bench_outputs/friedman_image_seeds/site_images/triintri_030.gif",
+    "image_seed_transform_error": 0.014633043011461478,
+    "notes": "Image-seeded from the Friedman source image and refined with polygon-packer-c.",
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+}