Use exact evaluator metrics for public records

app.py

@@ -958,7 +958,7 @@ MONTHS = (
     "December",
 )
 
-RECOVERY_TOLERANCE_ABS = 1.0e-2
+RECOVERY_TOLERANCE_ABS = DEFAULT_TOLERANCE
 
 
 def esc(value: Any) -> str:
@@ -1082,13 +1082,6 @@ def metric_value(record: dict[str, Any]) -> str:
         return str(value)
 
 
-def formatted_float(value: Any) -> str:
-    try:
-        return f"{float(value):.5f}"
-    except (TypeError, ValueError):
-        return str(value)
-
-
 def numeric_metric(record: dict[str, Any]) -> float | None:
     value = record.get("metric_value")
     if value is None:
@@ -1230,9 +1223,9 @@ def visual_provenance(record: dict[str, Any], visual_record: dict[str, Any]) ->
         notes = str(visual_record.get("notes") or "").lower()
         suffix = ""
         if visual_metric != 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)}."
+            suffix = f" Coordinate JSON evaluator 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"
+            status = "matches or beats the reference" if not needs_recovery(record, visual_record) else "worse than the reference"
             return f"Image-seeded from the Friedman source image and verified ({status})." + suffix
         if visual_record is record or visual_record.get("id") == record.get("id"):
             return "Verified coordinate layout credited under the public attribution policy." + suffix
@@ -1247,8 +1240,6 @@ def visual_provenance(record: dict[str, Any], visual_record: dict[str, Any]) ->
 
 
 def display_metric_record(record: dict[str, Any], visual_record: dict[str, Any]) -> dict[str, Any]:
-    if visual_record.get("verified") and visual_record.get("solution_path"):
-        return visual_record
     return record
 
 
@@ -1265,14 +1256,13 @@ def needs_recovery(record: dict[str, Any], visual_record: dict[str, Any]) -> boo
 def record_detail_rows(record: dict[str, Any], visual_record: dict[str, Any], source: str, image_name: str, expression: str, analytical: Any) -> list[str]:
     rows: list[str] = []
     rows.append(detail_row("Rendering", esc(visual_provenance(record, visual_record))))
-    raw_metric = record.get("verified_coordinate_metric_value")
-    if raw_metric is not None:
-        raw_symbol = str(record.get("verified_coordinate_metric_symbol") or metric_symbol(record))
-        raw_text = f"{esc(raw_symbol)} = {esc(formatted_float(raw_metric))} from the stored coordinate JSON"
-        if record.get("public_metric_source") == "friedman_reference_verified_coordinate_recovery":
-            raw_text += "; public metric shown from the recovered Friedman reference"
-        rows.append(detail_row("Evaluator metric", raw_text))
     if record.get("record_type") == "reference" and visual_record.get("verified"):
+        rows.append(
+            detail_row(
+                "Coordinate JSON",
+                f"{esc(metric_symbol(visual_record))} = {esc(metric_value(visual_record))} from the stored evaluator",
+            )
+        )
         rows.append(
             detail_row(
                 "Friedman reference",
@@ -1449,7 +1439,7 @@ def family_description(summary: dict[str, Any]) -> str:
         f"inside a {esc(container)}. The number shown on each card is the verified coordinate metric "
         f"for the rendering; click a card to view the Friedman reference value and source information. "
         f"Orange cards need more recovery work because the verified coordinate JSON does not yet match "
-        f"the listed reference within {RECOVERY_TOLERANCE_ABS:.2f}.{updated}"
+        f"or beat the listed reference under the evaluator tolerance.{updated}"
     )
 
 

data/solutions/generated/cirincir_001_d8dddd0385fd067c.json

@@ -0,0 +1,68 @@
+{
+  "case": "cirincir@1",
+  "comparison": {
+    "friedman_displayed_expression": "1",
+    "friedman_displayed_metric": 1.0
+  },
+  "container": {
+    "radius": 1.000000501742324,
+    "type": "circle"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.0001000045001205,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Trivial"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 4.234594617131402,
+      "x": -2.7008070190548483e-07,
+      "y": -2.7008070190548483e-07
+    }
+  ],
+  "problem": "1 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc1.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_002_ab9a33067266df01.json

@@ -0,0 +1,74 @@
+{
+  "case": "cirincir@2",
+  "comparison": {
+    "friedman_displayed_expression": "2",
+    "friedman_displayed_metric": 2.0
+  },
+  "container": {
+    "radius": 2.0000398062108586,
+    "type": "circle"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Trivial"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 5.063717356374632,
+      "x": -0.9971454746265687,
+      "y": -0.0759875446196585
+    },
+    {
+      "id": 2,
+      "rotation_radians": 1.684152167661818,
+      "x": 0.9975783904801367,
+      "y": 0.06987921434558285
+    }
+  ],
+  "problem": "2 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc2.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_003_fe973ff9a23dc34c.json

@@ -0,0 +1,80 @@
+{
+  "case": "cirincir@3",
+  "comparison": {
+    "friedman_displayed_expression": "1 + 2 / \u221a3 = 2.154+",
+    "friedman_displayed_metric": 2.154
+  },
+  "container": {
+    "radius": 2.1547631783850805,
+    "type": "circle"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Trivial"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.0,
+      "x": -0.8165322703616158,
+      "y": -0.8165322703616158
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.0,
+      "x": 1.1154073607268733,
+      "y": -0.2988709096476672
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.0,
+      "x": -0.2988709096476672,
+      "y": 1.1154073607268733
+    }
+  ],
+  "problem": "3 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc3.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_004_9d3e9e7ea6ba298b.json

@@ -0,0 +1,86 @@
+{
+  "case": "cirincir@4",
+  "comparison": {
+    "friedman_displayed_expression": "1 + \u221a2 = 2.414+",
+    "friedman_displayed_metric": 2.414
+  },
+  "container": {
+    "radius": 2.4142505021963334,
+    "type": "circle"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Trivial"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.7275266288784918,
+      "x": -1.0000233024542953,
+      "y": -1.0000233024542953
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.24880554922931425,
+      "x": 1.0000233024542953,
+      "y": -1.0000233024542953
+    },
+    {
+      "id": 3,
+      "rotation_radians": 3.5733904421699134,
+      "x": -1.0000233024542953,
+      "y": 1.0000233024542953
+    },
+    {
+      "id": 4,
+      "rotation_radians": 5.807896804639159,
+      "x": 1.0000233024542953,
+      "y": 1.0000233024542953
+    }
+  ],
+  "problem": "4 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc4.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_005_9c2ab1f687c06eec.json

@@ -0,0 +1,92 @@
+{
+  "case": "cirincir@5",
+  "comparison": {
+    "friedman_displayed_expression": "2.701+",
+    "friedman_displayed_metric": 2.701
+  },
+  "container": {
+    "radius": 2.701351400102724,
+    "type": "circle"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "steepest",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Graham"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 6.080102518711922,
+      "x": -1.4809559456422146,
+      "y": -0.8374700997307101
+    },
+    {
+      "id": 2,
+      "rotation_radians": 2.340306634445139,
+      "x": 0.33882857375183867,
+      "y": -1.6672677884746763
+    },
+    {
+      "id": 3,
+      "rotation_radians": 2.366511830109195,
+      "x": 1.6903659093835475,
+      "y": -0.19296659095478694
+    },
+    {
+      "id": 4,
+      "rotation_radians": 1.6161147764289103,
+      "x": -1.2541176897946924,
+      "y": 1.1496790130183168
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.04997995565748884,
+      "x": 0.7058682708582166,
+      "y": 1.5480016026359158
+    }
+  ],
+  "problem": "5 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc5.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_006_5d3d5beee3c5f33c.json

@@ -0,0 +1,98 @@
+{
+  "case": "cirincir@6",
+  "comparison": {
+    "friedman_displayed_expression": "3",
+    "friedman_displayed_metric": 3.0
+  },
+  "container": {
+    "radius": 3.0000562636711883,
+    "type": "circle"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Graham"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 3.694109714466408,
+      "x": -1.7321071150801597,
+      "y": -0.9999963350902086
+    },
+    {
+      "id": 2,
+      "rotation_radians": 4.243508589899284,
+      "x": 0.0,
+      "y": -2.000042225188291
+    },
+    {
+      "id": 3,
+      "rotation_radians": 6.257899385712383,
+      "x": 1.7321071150801597,
+      "y": -0.9999963350902086
+    },
+    {
+      "id": 4,
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+    {
+      "id": 5,
+      "rotation_radians": 3.7280572279819015,
+      "x": 0.0,
+      "y": 1.5812728282175974e-05
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+    {
+      "id": 6,
+      "rotation_radians": 3.7202276520027064,
+      "x": 1.732066930978596,
+      "y": 1.000078575282282
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+  ],
+  "problem": "6 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc6.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_007_2b1985e4094e6893.json

@@ -0,0 +1,104 @@
+{
+  "case": "cirincir@7",
+  "comparison": {
+    "friedman_displayed_expression": "3",
+    "friedman_displayed_metric": 3.0
+  },
+  "container": {
+    "radius": 3.000070013511673,
+    "type": "circle"
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+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
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+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Graham"
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+  "placements": [
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+      "y": -1.2315244129967613
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+  "problem": "7 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc7.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_008_0193661647fd3854.json

@@ -0,0 +1,110 @@
+{
+  "case": "cirincir@8",
+  "comparison": {
+    "friedman_displayed_expression": "3.304+",
+    "friedman_displayed_metric": 3.304
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+  "container": {
+    "radius": 3.304841442551775,
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+  "friedman_reference": {
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+    "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
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+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
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+      "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
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+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Braaksma"
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+  "problem": "8 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc8.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_009_b51df67181f6833b.json

@@ -0,0 +1,116 @@
+{
+  "case": "cirincir@9",
+  "comparison": {
+    "friedman_displayed_expression": "3.613+",
+    "friedman_displayed_metric": 3.613
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+  "friedman_reference": {
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+    "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
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+    "friedman_reference": {
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+      "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "steepest",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Pirl"
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+  "placements": [
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+      "x": 0.2383705413706959,
+      "y": 0.056229761746810436
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+      "x": 2.612959821914608,
+      "y": -0.03185196970417412
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+      "rotation_radians": -0.12944339330746094,
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+      "y": 1.8701747720791053
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+      "rotation_radians": -0.19113443555400586,
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+  "problem": "9 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc9.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_011_e624f391927921fb.json

@@ -0,0 +1,128 @@
+{
+  "case": "cirincir@11",
+  "comparison": {
+    "friedman_displayed_expression": "3.923+",
+    "friedman_displayed_metric": 3.923
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+  "container": {
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+  "friedman_reference": {
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+    "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"
+  },
+  "item": {
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+    "type": "circle"
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+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
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+      "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"
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+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
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+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
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+  "problem": "11 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc11.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_012_0d7fc8a14b1c4e0e.json

@@ -0,0 +1,134 @@
+{
+  "case": "cirincir@12",
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+    "friedman_displayed_expression": "4.029+",
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+  "friedman_reference": {
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+    "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"
+  },
+  "item": {
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+    "type": "circle"
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+      "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
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+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Kravitz"
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+  "problem": "12 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc12.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_013_a118f33872e0cb30.json

@@ -0,0 +1,140 @@
+{
+  "case": "cirincir@13",
+  "comparison": {
+    "friedman_displayed_expression": "2 + \u221a5 = 4.236+",
+    "friedman_displayed_metric": 4.236
+  },
+  "container": {
+    "radius": 4.236183785796592,
+    "type": "circle"
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+  "friedman_reference": {
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+    "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
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+    "friedman_reference": {
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+      "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
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+  "problem": "13 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc13.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_014_b2ec44e582e5ab93.json

@@ -0,0 +1,146 @@
+{
+  "case": "cirincir@14",
+  "comparison": {
+    "friedman_displayed_expression": "4.328+",
+    "friedman_displayed_metric": 4.328
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+    "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
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+  "metadata": {
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+    "friedman_reference": {
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+      "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Goldberg"
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+  "placements": [
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+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_015_eeff7b918e6d6618.json

@@ -0,0 +1,150 @@
+{
+  "case": "cirincir@15",
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+    "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"
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+  "item": {
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+    "type": "circle"
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+  "metadata": {
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+    "friedman_reference": {
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+      "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"
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+    "leaderboard_status": "current_best_coordinate",
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+    "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",
+    "submitted_by": "Kravitz"
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+  "placements": [
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+  "problem": "15 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc15.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_016_7824261a02b5ed90.json

@@ -0,0 +1,158 @@
+{
+  "case": "cirincir@16",
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+    "friedman_displayed_expression": "4.615+",
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+    "case": "cirincir@16",
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+    "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"
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+  "item": {
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+    "type": "circle"
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+      "case": "cirincir@16",
+      "credit": "Goldberg",
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+      "family_updated": "",
+      "metric_expression": "4.615+",
+      "metric_symbol": "r",
+      "metric_value": 4.615,
+      "reference_text": "r = 4.615+ | Found by Goldberg in 1971.",
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+      "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
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+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Goldberg"
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+  "problem": "16 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc16.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_017_68c41c427924b99a.json

@@ -0,0 +1,164 @@
+{
+  "case": "cirincir@17",
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+    "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"
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+  "item": {
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+      "case": "cirincir@17",
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+      "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"
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+    "generator_profile": "best of cg/steepest/sa seed profiles",
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+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
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+  "problem": "17 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc17.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_018_6acc78721c0b4ca1.json

@@ -0,0 +1,170 @@
+{
+  "case": "cirincir@18",
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+    "friedman_displayed_expression": "1 + \u221a2 + \u221a6 = 4.863+",
+    "friedman_displayed_metric": 4.863
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+    "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"
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+  "item": {
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+    "friedman_reference": {
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+      "case": "cirincir@18",
+      "credit": "Kravitz",
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+      "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"
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+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
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+  "problem": "18 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc18.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_019_8325b5bff319f74f.json

@@ -0,0 +1,176 @@
+{
+  "case": "cirincir@19",
+  "comparison": {
+    "friedman_displayed_expression": "1 + \u221a2 + \u221a6 = 4.863+",
+    "friedman_displayed_metric": 4.863
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+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
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+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
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+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "F. Fodor"
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+  ],
+  "problem": "19 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc19.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_020_f0718319f5a05220.json

@@ -0,0 +1,182 @@
+{
+  "case": "cirincir@20",
+  "comparison": {
+    "friedman_displayed_expression": "5.122+",
+    "friedman_displayed_metric": 5.122
+  },
+  "container": {
+    "radius": 5.122422626807949,
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+  "friedman_reference": {
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+    "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Goldberg"
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+      "id": 5,
+      "rotation_radians": 4.932050447724145,
+      "x": 2.775281547173684,
+      "y": -3.0482983529705208
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+    {
+      "id": 6,
+      "rotation_radians": 5.063811942457424,
+      "x": -3.8736878185458172,
+      "y": -1.4102272906807423
+    },
+    {
+      "id": 7,
+      "rotation_radians": 3.4340542577388273,
+      "x": -1.8187599661915754,
+      "y": -1.2995981767221878
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+    {
+      "id": 8,
+      "rotation_radians": 3.8167853720718408,
+      "x": 0.03655453077142027,
+      "y": -0.23668838098225195
+    },
+    {
+      "id": 9,
+      "rotation_radians": 2.6661983254815094,
+      "x": 1.7372268791180883,
+      "y": -1.338730925810945
+    },
+    {
+      "id": 10,
+      "rotation_radians": 5.147700061464448,
+      "x": 3.883388880991557,
+      "y": -1.3832828169577045
+    },
+    {
+      "id": 11,
+      "rotation_radians": 1.6239521143911027,
+      "x": -4.081551113538968,
+      "y": 0.5789823471898708
+    },
+    {
+      "id": 12,
+      "rotation_radians": 4.788836556730196,
+      "x": -2.084195330534861,
+      "y": 0.6827618178654932
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.40448330634827756,
+      "x": -0.6464520039977862,
+      "y": 2.073113868647903
+    },
+    {
+      "id": 14,
+      "rotation_radians": 1.9521740985712233,
+      "x": 2.077532987326301,
+      "y": 0.6321470395657008
+    },
+    {
+      "id": 15,
+      "rotation_radians": 2.0817265552958197,
+      "x": 4.07742827273042,
+      "y": 0.607327291681712
+    },
+    {
+      "id": 16,
+      "rotation_radians": 2.3686497318476234,
+      "x": -3.328665431295852,
+      "y": 2.4319082715307525
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.3168259841767753,
+      "x": -1.792278655159194,
+      "y": 3.712409725361867
+    },
+    {
+      "id": 18,
+      "rotation_radians": 2.8569722607665446,
+      "x": 0.16598513157280884,
+      "y": 4.119075181983351
+    },
+    {
+      "id": 19,
+      "rotation_radians": 4.958631180549401,
+      "x": 1.3118114373171361,
+      "y": 2.479800755076375
+    },
+    {
+      "id": 20,
+      "rotation_radians": 3.3167624129180617,
+      "x": 3.311695266736384,
+      "y": 2.4549858855373747
+    }
+  ],
+  "problem": "20 equal items for Circles in Circles",
+  "setup": "cirincir",
+  "source_image": "https://erich-friedman.github.io/packing/cirincir/ccc20.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirincir/"
+}

data/solutions/generated/cirincir_10_be14c55679a54b28.json

@@ -0,0 +1,118 @@
+{
+  "case": "cirincir@10",
+  "container": {
+    "radius": 3.813115539124243,
+    "type": "circle"
+  },
+  "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"
+  },
+  "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": "",
+      "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_transform_error": 0.06260662900137194,
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "source_url": "https://erich-friedman.github.io/packing/cirincir/",
+    "submitted_at": "2026-05-01T02:08:58+00:00",
+    "submitted_by": "Pirl"
+  },
+  "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/cirinhex_001_37d86bed2252b572.json

@@ -0,0 +1,71 @@
+{
+  "case": "cirinhex@1",
+  "comparison": {
+    "friedman_displayed_expression": "2/\u221a3 = 1.154+",
+    "friedman_displayed_metric": 1.154
+  },
+  "container": {
+    "circumradius": 1.1547129204441555,
+    "orientation_radians": 0.0,
+    "side_length": 1.1547129204441553,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Trivial"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.0,
+      "x": -3.3642843089735496e-06,
+      "y": 5.8286230715229394e-06
+    }
+  ],
+  "problem": "1 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc1.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_002_4ba45a45587fd527.json

@@ -0,0 +1,77 @@
+{
+  "case": "cirinhex@2",
+  "comparison": {
+    "friedman_displayed_expression": "1 + 2/\u221a3 = 2.154+",
+    "friedman_displayed_metric": 2.154
+  },
+  "container": {
+    "circumradius": 2.154717337638839,
+    "orientation_radians": 0.0,
+    "side_length": 2.1547173376388384,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Trivial"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 2.523989452646143,
+      "x": -1.000006450069848,
+      "y": 8.853987435255486e-06
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.06931346388856387,
+      "x": 1.0000064500698516,
+      "y": 8.85398745435216e-06
+    }
+  ],
+  "problem": "2 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc2.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_003_fa4a26f729d80904.json

@@ -0,0 +1,83 @@
+{
+  "case": "cirinhex@3",
+  "comparison": {
+    "friedman_displayed_expression": "4/\u221a3 = 2.309+",
+    "friedman_displayed_metric": 2.309
+  },
+  "container": {
+    "circumradius": 2.3094165045351462,
+    "orientation_radians": 0.0,
+    "side_length": 2.309416504535146,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Trivial"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 2.7714344980141687,
+      "x": -0.5773605964391968,
+      "y": -1.0000061615569955
+    },
+    {
+      "id": 2,
+      "rotation_radians": 2.3297843107726157,
+      "x": 1.1547110379633796,
+      "y": -5.862598425327664e-06
+    },
+    {
+      "id": 3,
+      "rotation_radians": 1.4202046395216328,
+      "x": -0.5773504416254885,
+      "y": 1.0000120240541113
+    }
+  ],
+  "problem": "3 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc3.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_004_4ea68db180a8d4c4.json

@@ -0,0 +1,89 @@
+{
+  "case": "cirinhex@4",
+  "comparison": {
+    "friedman_displayed_expression": "2/\u221a3 + 4/\u221a7 = 2.666+",
+    "friedman_displayed_metric": 2.666
+  },
+  "container": {
+    "circumradius": 2.666604151094754,
+    "orientation_radians": 0.0,
+    "side_length": 2.6666041510947536,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "steepest",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Shahriar Manzoor"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 4.913920354826519,
+      "x": -0.7559377282330951,
+      "y": 1.3093368370487763
+    },
+    {
+      "id": 2,
+      "rotation_radians": 1.2350486872441646,
+      "x": 0.7559374079525333,
+      "y": -1.309336259503437
+    },
+    {
+      "id": 3,
+      "rotation_radians": 4.88464061898282,
+      "x": 1.1339316077753712,
+      "y": 0.6546660375899639
+    },
+    {
+      "id": 4,
+      "rotation_radians": 5.650804693041064,
+      "x": -1.133931166846577,
+      "y": -0.6546667842601672
+    }
+  ],
+  "problem": "4 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc4.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_005_eb88c54ef20a6355.json

@@ -0,0 +1,95 @@
+{
+  "case": "cirinhex@5",
+  "comparison": {
+    "friedman_displayed_expression": "2.999+",
+    "friedman_displayed_metric": 2.999
+  },
+  "container": {
+    "circumradius": 2.999411672594878,
+    "orientation_radians": 0.0,
+    "side_length": 2.9994116725948774,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Erich Friedman"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 2.9855794555288115,
+      "x": -1.267343408793683,
+      "y": -0.9999992364252375
+    },
+    {
+      "id": 2,
+      "rotation_radians": 3.6854466510071515,
+      "x": 0.6413588226133865,
+      "y": -1.5975607589374838
+    },
+    {
+      "id": 3,
+      "rotation_radians": 1.3680105147223782,
+      "x": 1.8446947581837059,
+      "y": -1.1228266052288168e-05
+    },
+    {
+      "id": 4,
+      "rotation_radians": 5.679727207063267,
+      "x": -1.2673105470107882,
+      "y": 1.0000592201616798
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.9733695316624005,
+      "x": 0.641407553155326,
+      "y": 1.597566441183687
+    }
+  ],
+  "problem": "5 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc5.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_006_9b7724fab73c49c1.json

@@ -0,0 +1,101 @@
+{
+  "case": "cirinhex@6",
+  "comparison": {
+    "friedman_displayed_expression": "2 + 2/\u221a3 = 3.154+",
+    "friedman_displayed_metric": 3.154
+  },
+  "container": {
+    "circumradius": 3.154774248194912,
+    "orientation_radians": 0.0,
+    "side_length": 3.1547742481949115,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Trivial"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.2943068376938401,
+      "x": -2.0000542175592595,
+      "y": -2.434388357199348e-05
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+    {
+      "id": 2,
+      "rotation_radians": 3.489350737838448,
+      "x": 1.0000116633911356,
+      "y": -1.7321093435163895
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+    {
+      "id": 3,
+      "rotation_radians": -0.004820447227597302,
+      "x": 2.0000533472422615,
+      "y": -8.855132703193272e-06
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.2515430581427518,
+      "x": -1.000033363102193,
+      "y": 1.7320902265107787
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+    {
+      "id": 5,
+      "rotation_radians": 2.1251713193533788,
+      "x": -5.63827793453996e-06,
+      "y": -1.6381034914830075e-05
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+    {
+      "id": 6,
+      "rotation_radians": 2.1078016329665368,
+      "x": 1.0000255876284736,
+      "y": 1.7320931329244282
+    }
+  ],
+  "problem": "6 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc6.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_007_7368090471750227.json

@@ -0,0 +1,107 @@
+{
+  "case": "cirinhex@7",
+  "comparison": {
+    "friedman_displayed_expression": "2 + 2/\u221a3 = 3.154+",
+    "friedman_displayed_metric": 3.154
+  },
+  "container": {
+    "circumradius": 3.1547526785063353,
+    "orientation_radians": 0.0,
+    "side_length": 3.154752678506335,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "steepest",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Trivial"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.23322506594830267,
+      "x": -1.0000309000324779,
+      "y": -1.7320801817404443
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+    {
+      "id": 2,
+      "rotation_radians": -0.045304852292609214,
+      "x": 1.0000097039055962,
+      "y": -1.7320929631920046
+    },
+    {
+      "id": 3,
+      "rotation_radians": -0.25463607947563405,
+      "x": 2.000042262428875,
+      "y": -1.2974602376825998e-05
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+    {
+      "id": 4,
+      "rotation_radians": 0.20046369676565526,
+      "x": -2.0000412968186594,
+      "y": 1.176064020196015e-05
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.0417618583579787,
+      "x": -5.888372798050501e-07,
+      "y": -1.9188932050271395e-06
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.023035387174397022,
+      "x": 1.0000323094283496,
+      "y": 1.7320814401895983
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+    {
+      "id": 7,
+      "rotation_radians": 0.10517500977787747,
+      "x": -1.0000106658541326,
+      "y": 1.7320933724905183
+    }
+  ],
+  "problem": "7 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc7.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_008_afebd04e4720460b.json

@@ -0,0 +1,113 @@
+{
+  "case": "cirinhex@8",
+  "comparison": {
+    "friedman_displayed_expression": "3.709+",
+    "friedman_displayed_metric": 3.709
+  },
+  "container": {
+    "circumradius": 3.709450333181874,
+    "orientation_radians": 0.0,
+    "side_length": 3.7094503331818736,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "David W. Cantrell"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 3.367018875700228,
+      "x": -1.7226457757776057,
+      "y": -1.4412327535311795
+    },
+    {
+      "id": 2,
+      "rotation_radians": 4.850409331687075,
+      "x": 0.12269763243544175,
+      "y": -2.2124772246267894
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+    {
+      "id": 3,
+      "rotation_radians": 3.0099139191390254,
+      "x": 1.8547524268187494,
+      "y": -1.2124309644556657
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+    {
+      "id": 4,
+      "rotation_radians": 2.411106504172674,
+      "x": -2.277420820397278,
+      "y": 0.48031882573957607
+    },
+    {
+      "id": 5,
+      "rotation_radians": 4.046799140966074,
+      "x": -0.10985306119838227,
+      "y": -0.14645322992931653
+    },
+    {
+      "id": 6,
+      "rotation_radians": 2.802884848849016,
+      "x": 2.1094303917058035,
+      "y": 0.771309929499181
+    },
+    {
+      "id": 7,
+      "rotation_radians": 2.447224413838566,
+      "x": -1.2773949642880942,
+      "y": 2.2124108779044818
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.741586795760499,
+      "x": 0.72263301214482,
+      "y": 2.2124707635802228
+    }
+  ],
+  "problem": "8 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc8.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_009_64b59a5605599f8e.json

@@ -0,0 +1,119 @@
+{
+  "case": "cirinhex@9",
+  "comparison": {
+    "friedman_displayed_expression": "20/7 + 2/\u221a3 = 4.011+",
+    "friedman_displayed_metric": 4.011
+  },
+  "container": {
+    "circumradius": 4.011901159340442,
+    "orientation_radians": 0.0,
+    "side_length": 4.011901159340441,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "David W. Cantrell"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.0,
+      "x": -1.857168504318097,
+      "y": -1.732082720025819
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.0,
+      "x": 5.135473370559955e-06,
+      "y": -2.474399704160964
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.0,
+      "x": 1.8571713461309614,
+      "y": -1.7320757933228896
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.0,
+      "x": -2.8571824644529364,
+      "y": -1.3918017550433788e-06
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.0,
+      "x": 0.0,
+      "y": 0.0
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.0,
+      "x": 2.8571843024332804,
+      "y": 5.885512926623855e-06
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.0,
+      "x": -1.857171194858483,
+      "y": 1.732081016692529
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.0,
+      "x": -9.257559637270259e-07,
+      "y": 2.474400829614805
+    },
+    {
+      "id": 9,
+      "rotation_radians": 0.0,
+      "x": 1.8571685583664075,
+      "y": 1.73208721379758
+    }
+  ],
+  "problem": "9 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc9.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_010_cd79fdfeb9e3f24b.json

@@ -0,0 +1,125 @@
+{
+  "case": "cirinhex@10",
+  "comparison": {
+    "friedman_displayed_expression": "4.119+",
+    "friedman_displayed_metric": 4.119
+  },
+  "container": {
+    "circumradius": 4.119415972587211,
+    "orientation_radians": 0.0,
+    "side_length": 4.11941597258721,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "David W. Cantrell"
+  },
+  "placements": [
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+      "rotation_radians": -0.27307936564548985,
+      "x": 0.14745469929120136,
+      "y": 2.567495389368784
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+  ],
+  "problem": "10 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc10.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_011_cda2ccbbf4de67aa.json

@@ -0,0 +1,131 @@
+{
+  "case": "cirinhex@11",
+  "comparison": {
+    "friedman_displayed_expression": "2 + 4/\u221a3 = 4.309+",
+    "friedman_displayed_metric": 4.309
+  },
+  "container": {
+    "circumradius": 4.309479847631291,
+    "orientation_radians": 0.0,
+    "side_length": 4.30947984763129,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Erich Friedman"
+  },
+  "placements": [
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+    {
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+      "rotation_radians": 1.3830654844668049,
+      "x": 1.5773793880940932,
+      "y": 2.732110688051179
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+  ],
+  "problem": "11 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc11.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_012_c3d795864cfeb74c.json

@@ -0,0 +1,137 @@
+{
+  "case": "cirinhex@12",
+  "comparison": {
+    "friedman_displayed_expression": "2 + 4/\u221a3 = 4.309+",
+    "friedman_displayed_metric": 4.309
+  },
+  "container": {
+    "circumradius": 4.3094818532104355,
+    "orientation_radians": 0.0,
+    "side_length": 4.309481853210435,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "steepest",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Erich Friedman"
+  },
+  "placements": [
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+      "id": 1,
+      "rotation_radians": 4.210707352496977,
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+      "y": -1.0000238246159827
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+      "x": 2.1547496135297255,
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+      "x": 1.1547250229060404,
+      "y": 4.189493212716789e-06
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+      "x": 3.154767338003531,
+      "y": 5.484177013404955e-06
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+      "rotation_radians": 6.485558806611068,
+      "x": 0.4226575410548005,
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+      "id": 12,
+      "rotation_radians": 2.6575209197021117,
+      "x": 2.1547444363979906,
+      "y": 1.7320986624781614
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+  ],
+  "problem": "12 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc12.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_013_62c003d981fbe524.json

@@ -0,0 +1,141 @@
+{
+  "case": "cirinhex@13",
+  "container": {
+    "circumradius": 4.618967820933494,
+    "orientation_radians": 0.0,
+    "side_length": 4.618967820933493,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "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"
+    },
+    "generator": "friedman_image_seed_quant_fix",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "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",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "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",
+    "submitted_by": "Erich Friedman"
+  },
+  "placements": [
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+      "id": 1,
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+      "x": -2.5761303891208434e-05,
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+      "rotation_radians": 3.133775615477552,
+      "x": 1.7320987737724693,
+      "y": 0.9999939432867946
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+    {
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+      "rotation_radians": 3.1403020417518435,
+      "x": 7.072885573634517e-06,
+      "y": 2.0000784513162317
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+      "rotation_radians": 3.133374279295559,
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+      "rotation_radians": 3.13973310159971,
+      "x": 1.7321553500487126,
+      "y": 3.000070079307269
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+  ],
+  "problem": "13 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc13.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_014_d3d8d6f246feeaad.json

@@ -0,0 +1,149 @@
+{
+  "case": "cirinhex@14",
+  "comparison": {
+    "friedman_displayed_expression": "2 + 2/\u221a3 + 4/\u221a7 = 4.666+",
+    "friedman_displayed_metric": 4.666
+  },
+  "container": {
+    "circumradius": 4.666653968376352,
+    "orientation_radians": 0.0,
+    "side_length": 4.666653968376351,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "steepest",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "David W. Cantrell"
+  },
+  "placements": [
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+      "id": 1,
+      "rotation_radians": 3.916094721328099,
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+  ],
+  "problem": "14 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc14.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_015_d923ba7fbcb56e93.json

@@ -0,0 +1,155 @@
+{
+  "case": "cirinhex@15",
+  "comparison": {
+    "friedman_displayed_expression": "4.961+",
+    "friedman_displayed_metric": 4.961
+  },
+  "container": {
+    "circumradius": 4.9615756365508545,
+    "orientation_radians": 0.0,
+    "side_length": 4.961575636550854,
+    "sides": 6,
+    "type": "regular_polygon"
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+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "David W. Cantrell"
+  },
+  "placements": [
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+  ],
+  "problem": "15 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc15.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_016_b6a042d1d6eee5a4.json

@@ -0,0 +1,161 @@
+{
+  "case": "cirinhex@16",
+  "comparison": {
+    "friedman_displayed_expression": "4.999+",
+    "friedman_displayed_metric": 4.999
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+  "container": {
+    "circumradius": 4.999508954626882,
+    "orientation_radians": 0.0,
+    "side_length": 4.999508954626881,
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+    "type": "regular_polygon"
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+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
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+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
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+      "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
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+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "David W. Cantrell"
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+  "placements": [
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+      "x": 1.2325380759100986,
+      "y": 3.3296830313106933
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+  ],
+  "problem": "16 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc16.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_017_4927714d5d50ab2b.json

@@ -0,0 +1,167 @@
+{
+  "case": "cirinhex@17",
+  "comparison": {
+    "friedman_displayed_expression": "5.133+",
+    "friedman_displayed_metric": 5.133
+  },
+  "container": {
+    "circumradius": 5.133274584209645,
+    "orientation_radians": 0.0,
+    "side_length": 5.133274584209644,
+    "sides": 6,
+    "type": "regular_polygon"
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+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "David W. Cantrell"
+  },
+  "placements": [
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+      "x": -3.0105420957957567,
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+    {
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+      "rotation_radians": -0.00028693533240482056,
+      "x": 1.9892747566527176,
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+      "id": 15,
+      "rotation_radians": 0.08931005434530255,
+      "x": 2.989305945663474,
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+      "id": 16,
+      "rotation_radians": -0.11740775222711178,
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+      "y": 3.4087555787392128
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+      "rotation_radians": 0.2087708477896544,
+      "x": -0.01078882603263054,
+      "y": 3.44551921828235
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+  ],
+  "problem": "17 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc17.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_018_223b1a3f7b7d0e67.json

@@ -0,0 +1,173 @@
+{
+  "case": "cirinhex@18",
+  "comparison": {
+    "friedman_displayed_expression": "4 + 2/\u221a3 = 5.154+",
+    "friedman_displayed_metric": 5.154
+  },
+  "container": {
+    "circumradius": 5.154759899456761,
+    "orientation_radians": 0.0,
+    "side_length": 5.15475989945676,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.0000200001000001,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Trivial"
+  },
+  "placements": [
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+  "problem": "18 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc18.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_019_78f9327e80d8ab20.json

@@ -0,0 +1,179 @@
+{
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+  "comparison": {
+    "friedman_displayed_expression": "4 + 2/\u221a3 = 5.154+",
+    "friedman_displayed_metric": 5.154
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+    "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"
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+      "credit": "Trivial",
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+      "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"
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+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
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+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_020_247c6c06779a7d8b.json

@@ -0,0 +1,185 @@
+{
+  "case": "cirinhex@20",
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+    "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"
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+      "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"
+    },
+    "generator": "coordinate_reconstruction",
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+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
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+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc20.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_021_38040eceeb63c1e3.json

@@ -0,0 +1,187 @@
+{
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+    "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"
+  },
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+      "case": "cirinhex@21",
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+      "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"
+    },
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+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "David W. Cantrell"
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+    {
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+      "rotation_radians": 6.41724804394573,
+      "x": -1.3867925668066305,
+      "y": 3.944575609752429
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+  ],
+  "problem": "21 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc21.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_022_cd7262f9f7d0d279.json

@@ -0,0 +1,193 @@
+{
+  "case": "cirinhex@22",
+  "container": {
+    "circumradius": 5.9518770721265515,
+    "orientation_radians": 0.0,
+    "side_length": 5.951877072126551,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Verified coordinate layout matches or beats the Friedman metric; credited to the Friedman-listed finder.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "David W. Cantrell"
+  },
+  "placements": [
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+  ],
+  "problem": "22 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc22.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_023_de2d2aabdc650ad2.json

@@ -0,0 +1,199 @@
+{
+  "case": "cirinhex@23",
+  "container": {
+    "circumradius": 6.0119964252593965,
+    "orientation_radians": 0.0,
+    "side_length": 6.011996425259396,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "David W. Cantrell"
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+  "placements": [
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+  ],
+  "problem": "23 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc23.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinhex_024_61a86ae12328c1ca.json

@@ -0,0 +1,205 @@
+{
+  "case": "cirinhex@24",
+  "container": {
+    "circumradius": 6.120164603994217,
+    "orientation_radians": 0.0,
+    "side_length": 6.120164603994216,
+    "sides": 6,
+    "type": "regular_polygon"
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+  "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"
+  },
+  "item": {
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+    "type": "circle"
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+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
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+      "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "Rob Pratt"
+  },
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+      "id": 21,
+      "rotation_radians": -0.09701789144025728,
+      "x": -3.298269764141387,
+      "y": 2.887610133398389
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.36753378024609773,
+      "x": -1.8823644499449348,
+      "y": 4.300202073045761
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.17246626897426362,
+      "x": 0.40620727194605777,
+      "y": 4.28333434889399
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.860472800784408,
+      "x": 2.4827213991085153,
+      "y": 4.300214568152071
+    }
+  ],
+  "problem": "24 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}

data/solutions/generated/cirinpen_001_2249439da521383e.json

@@ -0,0 +1,71 @@
+{
+  "case": "cirinpen@1",
+  "comparison": {
+    "friedman_displayed_expression": "1.453+",
+    "friedman_displayed_metric": 1.453
+  },
+  "container": {
+    "circumradius": 1.2360749163506617,
+    "orientation_radians": 0.0,
+    "side_length": 1.4530932131191425,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Trivial"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.05318622067211453,
+      "x": 1.0012350262445666e-06,
+      "y": -7.983199662957441e-09
+    }
+  ],
+  "problem": "1 equal items for Circles in Pentagons",
+  "setup": "cirinpen",
+  "source_image": "https://erich-friedman.github.io/packing/cirinpen/pent.1.png",
+  "source_page": "https://erich-friedman.github.io/packing/cirinpen/"
+}

data/solutions/generated/cirinpen_002_042df6c460b769f5.json

@@ -0,0 +1,77 @@
+{
+  "case": "cirinpen@2",
+  "comparison": {
+    "friedman_displayed_expression": "2.689+",
+    "friedman_displayed_metric": 2.689
+  },
+  "container": {
+    "circumradius": 2.287585116707018,
+    "orientation_radians": 0.0,
+    "side_length": 2.689217589928282,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "Trivial"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.0,
+      "x": -0.8506863314275537,
+      "y": -0.6180292253412032
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.0,
+      "x": 1.0514824069355486,
+      "y": 2.5613590620363354e-05
+    }
+  ],
+  "problem": "2 equal items for Circles in Pentagons",
+  "setup": "cirinpen",
+  "source_image": "https://erich-friedman.github.io/packing/cirinpen/pent.2.png",
+  "source_page": "https://erich-friedman.github.io/packing/cirinpen/"
+}

data/solutions/generated/cirinpen_003_7afe63c4f78d1c3c.json

@@ -0,0 +1,83 @@
+{
+  "case": "cirinpen@3",
+  "comparison": {
+    "friedman_displayed_expression": "3.015+",
+    "friedman_displayed_metric": 3.015
+  },
+  "container": {
+    "circumradius": 2.5654848215169617,
+    "orientation_radians": 0.0,
+    "side_length": 3.0159082861357156,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "steepest",
+    "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "George Sicherman"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 2.9521502076646713,
+      "x": -1.0755184708911585,
+      "y": -0.7814099087741448
+    },
+    {
+      "id": 2,
+      "rotation_radians": 4.371685738605809,
+      "x": 0.9135639218534516,
+      "y": -0.5723605147667044
+    },
+    {
+      "id": 3,
+      "rotation_radians": 2.5676468572552515,
+      "x": -0.26204041999383665,
+      "y": 1.045720046897995
+    }
+  ],
+  "problem": "3 equal items for Circles in Pentagons",
+  "setup": "cirinpen",
+  "source_image": "https://erich-friedman.github.io/packing/cirinpen/pent.3.png",
+  "source_page": "https://erich-friedman.github.io/packing/cirinpen/"
+}

data/solutions/generated/cirinpen_004_3b6f81450d56967c.json

@@ -0,0 +1,89 @@
+{
+  "case": "cirinpen@4",
+  "comparison": {
+    "friedman_displayed_expression": "3.314+",
+    "friedman_displayed_metric": 3.314
+  },
+  "container": {
+    "circumradius": 2.8195112651866383,
+    "orientation_radians": 0.0,
+    "side_length": 3.3145342806983966,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "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"
+    },
+    "generator": "coordinate_reconstruction",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "leaderboard_status": "current_best_coordinate",
+    "notes": "Best available verified coordinate reconstruction, but its evaluator metric is worse than the Friedman reference.",
+    "profile": "steepest",
+    "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
+    "submitted_at": "2026-05-01T01:05:47+00:00",
+    "submitted_by": "George Sicherman"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 4.529129012427202,
+      "x": -1.281021704340876,
+      "y": 0.9307027770085637
+    },
+    {
+      "id": 2,
+      "rotation_radians": 3.2975342630409825,
+      "x": -0.9428960146154225,
+      "y": -1.0405766999612989
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.5707473527477467,
+      "x": 0.6982395930590469,
+      "y": 1.218372527245509
+    },
+    {
+      "id": 4,
+      "rotation_radians": 1.079979650937594,
+      "x": 1.0363912988960218,
+      "y": -0.7529140880814239
+    }
+  ],
+  "problem": "4 equal items for Circles in Pentagons",
+  "setup": "cirinpen",
+  "source_image": "https://erich-friedman.github.io/packing/cirinpen/pent.4.png",
+  "source_page": "https://erich-friedman.github.io/packing/cirinpen/"
+}