Add expandable record details and complete supported renderings

app.py

@@ -331,7 +331,7 @@ gradio-app,
 .shape-container {
   fill: none;
   stroke: #000;
-  stroke-width: 3.5px !important;
+  stroke-width: 2.6px !important;
   stroke-linejoin: round;
   vector-effect: non-scaling-stroke;
 }
@@ -382,6 +382,49 @@ gradio-app,
   color: var(--ink);
 }
 
+.record-author {
+  margin-top: 8px;
+  color: var(--muted);
+  font-size: 12px;
+  line-height: 1.35;
+}
+
+.record-author strong {
+  color: var(--ink);
+}
+
+.record-details {
+  margin-top: 8px;
+  padding-top: 8px;
+  border-top: 1px solid var(--line-soft);
+  color: var(--muted);
+  font-size: 12px;
+  line-height: 1.4;
+}
+
+.record-details summary {
+  cursor: pointer;
+  color: var(--ink);
+  font-weight: 700;
+  list-style-position: outside;
+}
+
+.record-details dl {
+  margin: 7px 0 0;
+}
+
+.record-details dt {
+  margin-top: 6px;
+  color: var(--ink);
+  font-weight: 700;
+}
+
+.record-details dd {
+  margin: 1px 0 0;
+  color: var(--muted);
+  overflow-wrap: anywhere;
+}
+
 .back-link {
   display: inline-block;
   margin-top: 14px;
@@ -792,25 +835,54 @@ def record_visual(record: dict[str, Any], coordinates: dict[str, dict[str, Any]]
     return '<div class="render-stage"><div class="placeholder">coordinate JSON not available yet</div></div>'
 
 
+def detail_row(label: str, value: str) -> str:
+    value = value.strip()
+    if not value:
+        return ""
+    return f"<dt>{esc(label)}</dt><dd>{value}</dd>"
+
+
+def record_details(record: dict[str, Any], source: str, image_name: str, expression: str, analytical: Any) -> str:
+    rows: list[str] = []
+    if record.get("record_type") == "verified":
+        rows.append(detail_row("Submitted", esc(display_date(record))))
+        notes = str(record.get("notes") or "").strip()
+        if notes:
+            rows.append(detail_row("Notes", esc(notes)))
+        previous = (
+            f"{esc(metric_symbol(record))} = {esc(metric_value({'metric_value': record.get('reference_side'), 'side': record.get('reference_side'), 'metric_symbol': metric_symbol(record)}))}"
+            f" by {esc(reference_credit(record))}, {esc(reference_date(record))}"
+            if record.get("reference_side") is not None
+            else ""
+        )
+        rows.append(detail_row("Previous record", previous))
+    else:
+        rows.append(detail_row("Date", esc(reference_date(record))))
+
+    rows.append(detail_row("Formula", esc(expression)))
+    if image_name:
+        rows.append(detail_row("Source image", esc(image_name)))
+    if source:
+        rows.append(detail_row("Source", source))
+    if analytical:
+        rows.append(detail_row("Status", "analytical/proved"))
+    reference_text = str(friedman_reference(record).get("reference_text") or "").strip()
+    rows.append(detail_row("Reference text", esc(reference_text)))
+    return f"""
+        <details class="record-details">
+          <summary>Details</summary>
+          <dl>{''.join(rows)}</dl>
+        </details>
+    """
+
+
 def record_card(record: dict[str, Any], coordinates: dict[str, dict[str, Any]]) -> str:
     verified = record.get("record_type") == "verified"
     source = source_link(record)
     expression = compact_expression(record)
     image_name = source_image_name(record)
     analytical = friedman_reference(record).get("analytical_or_proved")
-    if verified:
-        primary_meta = f"submission: <strong>{esc(author_name(record))}</strong>, {esc(display_date(record))}"
-        reference_meta = f"reference: <strong>{esc(reference_credit(record))}</strong>, {esc(reference_date(record))}"
-    else:
-        primary_meta = f"by <strong>{esc(reference_credit(record))}</strong>"
-        reference_meta = esc(reference_date(record))
-    source_bits = []
-    if image_name:
-        source_bits.append(f"image: {esc(image_name)}")
-    if source:
-        source_bits.append(source)
-    source_line = "<br>" + " · ".join(source_bits) if source_bits else ""
-    analytical_line = "<br>analytical/proved" if analytical else ""
+    visible_author = author_name(record) if verified else reference_credit(record)
     return f"""
     <article class="record-card {'verified' if verified else 'reference'}">
       <div class="record-top">
@@ -820,12 +892,8 @@ def record_card(record: dict[str, Any], coordinates: dict[str, dict[str, Any]])
       <div class="record-body">
         <div class="metric"><strong>{esc(metric_symbol(record))} = {esc(metric_value(record))}</strong><span>n={esc(record.get("n"))}</span></div>
         <div class="expression">{esc(expression)}</div>
-        <div class="meta">
-          {primary_meta}<br>
-          {reference_meta}
-          {source_line}
-          {analytical_line}
-        </div>
+        <div class="record-author">by <strong>{esc(visible_author)}</strong></div>
+        {record_details(record, source, image_name, expression, analytical)}
       </div>
     </article>
     """

data/solutions/generated/cirinhex_021_38040eceeb63c1e3.json

@@ -0,0 +1,186 @@
+{
+  "case": "cirinhex@21",
+  "container": {
+    "circumradius": 5.709519968963224,
+    "orientation_radians": 0.0,
+    "side_length": 5.709519968963223,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "cirinhex@21",
+    "credit": "David W",
+    "date": "July 2012",
+    "family_updated": "7/19/12",
+    "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"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "cirinhex@21",
+      "credit": "David W",
+      "date": "July 2012",
+      "family_updated": "7/19/12",
+      "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"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 6.543485383352783,
+      "x": -2.977418137227549,
+      "y": -2.7321141604437353
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.6677851051964091,
+      "x": -1.3867920552597868,
+      "y": -3.9445800211625603
+    },
+    {
+      "id": 3,
+      "rotation_radians": 4.878686321852387,
+      "x": 0.6132577255879791,
+      "y": -3.9445721885790226
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.30239827960909094,
+      "x": 2.55475202878758,
+      "y": -3.4641926402705816
+    },
+    {
+      "id": 5,
+      "rotation_radians": 4.320834703493851,
+      "x": 3.5547753663028288,
+      "y": -1.7320994594036376
+    },
+    {
+      "id": 6,
+      "rotation_radians": 5.919448672454216,
+      "x": -3.977445211095278,
+      "y": -1.0000219518002595
+    },
+    {
+      "id": 7,
+      "rotation_radians": -0.29055690120803757,
+      "x": -1.977396112282955,
+      "y": -1.0000186736895977
+    },
+    {
+      "id": 8,
+      "rotation_radians": -0.4032918951577629,
+      "x": -0.3867729206450415,
+      "y": -2.212482249102536
+    },
+    {
+      "id": 9,
+      "rotation_radians": -0.7102921751069424,
+      "x": 1.554721776596295,
+      "y": -1.7320969486764575
+    },
+    {
+      "id": 10,
+      "rotation_radians": 5.075464747986945,
+      "x": 4.554799745769319,
+      "y": -6.936982071529475e-06
+    },
+    {
+      "id": 11,
+      "rotation_radians": 2.3772931236757855,
+      "x": -3.9774455896680094,
+      "y": 1.0000181328272364
+    },
+    {
+      "id": 12,
+      "rotation_radians": 3.842461184879661,
+      "x": -1.9773949988624189,
+      "y": 1.0000188577960665
+    },
+    {
+      "id": 13,
+      "rotation_radians": 2.776557717034663,
+      "x": -0.06708025173379516,
+      "y": -0.046183101728368654
+    },
+    {
+      "id": 14,
+      "rotation_radians": 2.627174319074063,
+      "x": 2.5547485506101757,
+      "y": -8.272024163587036e-06
+    },
+    {
+      "id": 15,
+      "rotation_radians": 1.952690627984041,
+      "x": 3.5547807172244523,
+      "y": 1.7320881696604125
+    },
+    {
+      "id": 16,
+      "rotation_radians": 4.824123034318457,
+      "x": -2.977418520889521,
+      "y": 2.7321111807361333
+    },
+    {
+      "id": 17,
+      "rotation_radians": 2.1331867069142443,
+      "x": -0.38676773460277103,
+      "y": 2.212478217016376
+    },
+    {
+      "id": 18,
+      "rotation_radians": 5.983740674349732,
+      "x": 0.613259621201437,
+      "y": 3.944572395436246
+    },
+    {
+      "id": 19,
+      "rotation_radians": 6.084676181192759,
+      "x": 1.5547259083092684,
+      "y": 1.7320846410323407
+    },
+    {
+      "id": 20,
+      "rotation_radians": 1.1379501682026076,
+      "x": 2.5547545551573854,
+      "y": 3.4641812077209866
+    },
+    {
+      "id": 21,
+      "rotation_radians": 6.41724804394573,
+      "x": -1.3867925668066305,
+      "y": 3.944575609752429
+    }
+  ],
+  "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 +1,192 @@
+{
+  "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",
+    "date": "July 2012",
+    "family_updated": "7/19/12",
+    "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",
+      "date": "July 2012",
+      "family_updated": "7/19/12",
+      "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": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.5336903785710856,
+      "x": -3.057843195509521,
+      "y": -3.012572174193485
+    },
+    {
+      "id": 2,
+      "rotation_radians": 5.627618367090928,
+      "x": -1.415825337804449,
+      "y": -4.154467925502052
+    },
+    {
+      "id": 3,
+      "rotation_radians": 1.588642453094273,
+      "x": 0.3261896435058119,
+      "y": -3.1718479790654124
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.6537002391114125,
+      "x": 2.0682052517810035,
+      "y": -4.154470081525163
+    },
+    {
+      "id": 5,
+      "rotation_radians": 3.7913269258110547,
+      "x": 3.3057127668991004,
+      "y": -2.583254154097507
+    },
+    {
+      "id": 6,
+      "rotation_radians": 2.6700645622335104,
+      "x": -4.0578623048112314,
+      "y": -1.2804858241134436
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.8143602476779578,
+      "x": -1.6970911446573878,
+      "y": -1.529109325316158
+    },
+    {
+      "id": 8,
+      "rotation_radians": 2.365761333225855,
+      "x": 0.33144143966232537,
+      "y": -1.1718107775334614
+    },
+    {
+      "id": 9,
+      "rotation_radians": 2.405045407507131,
+      "x": 2.305627353448162,
+      "y": -0.8511919861199759
+    },
+    {
+      "id": 10,
+      "rotation_radians": 1.5287516311548723,
+      "x": 4.305736159332807,
+      "y": -0.8511663633664502
+    },
+    {
+      "id": 11,
+      "rotation_radians": 4.506637422660895,
+      "x": -4.398609846467052,
+      "y": 0.6903063692321826
+    },
+    {
+      "id": 12,
+      "rotation_radians": 5.946477411672315,
+      "x": -2.3757809480744814,
+      "y": 0.3885664046027516
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.48491402793877963,
+      "x": -0.39851076161112026,
+      "y": 0.6902727666972293
+    },
+    {
+      "id": 14,
+      "rotation_radians": 2.297430853304856,
+      "x": 2.137862017249792,
+      "y": 1.141809252572138
+    },
+    {
+      "id": 15,
+      "rotation_radians": 0.1976652809115194,
+      "x": 4.137926722329381,
+      "y": 1.1418203373407287
+    },
+    {
+      "id": 16,
+      "rotation_radians": 2.343841855451056,
+      "x": -3.3985878386902066,
+      "y": 2.422390417126905
+    },
+    {
+      "id": 17,
+      "rotation_radians": 6.046869609924399,
+      "x": -1.3985382639451405,
+      "y": 2.422365842183051
+    },
+    {
+      "id": 18,
+      "rotation_radians": 5.201906471583247,
+      "x": 0.6015255516927154,
+      "y": 2.422372521530647
+    },
+    {
+      "id": 19,
+      "rotation_radians": 3.5211090941163614,
+      "x": 1.6015549723767342,
+      "y": 4.154461433559104
+    },
+    {
+      "id": 20,
+      "rotation_radians": 3.158677610852162,
+      "x": 3.1378984763846116,
+      "y": 2.8739078943281555
+    },
+    {
+      "id": 21,
+      "rotation_radians": 2.3917888936717118,
+      "x": -2.3985542361200842,
+      "y": 4.1544639864895
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.4777643359144321,
+      "x": -0.39849776533211084,
+      "y": 4.154464568713927
+    }
+  ],
+  "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 +1,198 @@
+{
+  "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",
+    "date": "July 2012",
+    "family_updated": "7/19/12",
+    "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",
+      "date": "July 2012",
+      "family_updated": "7/19/12",
+      "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": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.01088585785669998,
+      "x": -3.4286284844130193,
+      "y": -2.4744777907799715
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.013562955445130623,
+      "x": -2.42856178593742,
+      "y": -4.206535438620394
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.007684762682779028,
+      "x": -0.42850107946482296,
+      "y": -4.206530108540232
+    },
+    {
+      "id": 4,
+      "rotation_radians": -0.2096223722215658,
+      "x": 1.1429317953478868,
+      "y": -2.969279686172223
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.05490829208071887,
+      "x": 3.142975626993475,
+      "y": -2.9692619457033222
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.0706102912732397,
+      "x": -4.428656184153742,
+      "y": -0.7423914146316885
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+    {
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+    {
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+      "y": 4.206534222200379
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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 +1,204 @@
+{
+  "case": "cirinhex@24",
+  "container": {
+    "circumradius": 6.120164603994217,
+    "orientation_radians": 0.0,
+    "side_length": 6.120164603994216,
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+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "cirinhex@24",
+    "credit": "Rob Pratt",
+    "date": "March 2020",
+    "family_updated": "7/19/12",
+    "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": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "cirinhex@24",
+      "credit": "Rob Pratt",
+      "date": "March 2020",
+      "family_updated": "7/19/12",
+      "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": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+    {
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+    {
+      "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_021_6869ffb03b036ff3.json

@@ -0,0 +1,186 @@
+{
+  "case": "cirinpen@21",
+  "container": {
+    "circumradius": 6.062450861101137,
+    "orientation_radians": 0.0,
+    "side_length": 7.1268384178061055,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "cirinpen@21",
+    "credit": "David W",
+    "date": "July 2012",
+    "family_updated": "7/10/12",
+    "metric_expression": "7.107+",
+    "metric_symbol": "s",
+    "metric_value": 7.107,
+    "reference_text": "s = 7.107+ | Found by David W. Cantrell | in July 2012.",
+    "source_image": "pent.21.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.21.gif",
+    "source_page": "https://erich-friedman.github.io/packing/cirinpen/",
+    "title": "Circles in Pentagons"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "cirinpen@21",
+      "credit": "David W",
+      "date": "July 2012",
+      "family_updated": "7/10/12",
+      "metric_expression": "7.107+",
+      "metric_symbol": "s",
+      "metric_value": 7.107,
+      "reference_text": "s = 7.107+ | Found by David W. Cantrell | in July 2012.",
+      "source_image": "pent.21.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.21.gif",
+      "source_page": "https://erich-friedman.github.io/packing/cirinpen/",
+      "title": "Circles in Pentagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "x": 0.8213047026883471,
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+  ],
+  "problem": "21 equal items for Circles in Pentagons",
+  "setup": "cirinpen",
+  "source_image": "https://erich-friedman.github.io/packing/cirinpen/pent.21.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinpen/"
+}

data/solutions/generated/cirinpen_022_ebdb05232e56526e.json

@@ -0,0 +1,192 @@
+{
+  "case": "cirinpen@22",
+  "container": {
+    "circumradius": 6.186441627951481,
+    "orientation_radians": 0.0,
+    "side_length": 7.272598306156239,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "cirinpen@22",
+    "credit": "David W",
+    "date": "July 2012",
+    "family_updated": "7/10/12",
+    "metric_expression": "7.271+",
+    "metric_symbol": "s",
+    "metric_value": 7.271,
+    "reference_text": "s = 7.271+ | Found by David W. Cantrell | in July 2012.",
+    "source_image": "pent.22.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.22.gif",
+    "source_page": "https://erich-friedman.github.io/packing/cirinpen/",
+    "title": "Circles in Pentagons"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "cirinpen@22",
+      "credit": "David W",
+      "date": "July 2012",
+      "family_updated": "7/10/12",
+      "metric_expression": "7.271+",
+      "metric_symbol": "s",
+      "metric_value": 7.271,
+      "reference_text": "s = 7.271+ | Found by David W. Cantrell | in July 2012.",
+      "source_image": "pent.22.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.22.gif",
+      "source_page": "https://erich-friedman.github.io/packing/cirinpen/",
+      "title": "Circles in Pentagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+    {
+      "id": 18,
+      "rotation_radians": 0.16139505065608656,
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+      "y": -4.703645521669129
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.7315603974115586,
+      "x": 2.7029040619279256,
+      "y": 0.14303054988656203
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+    {
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+      "y": 2.905909804892462
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+    {
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+      "x": -2.1760253347659906,
+      "y": 1.5696980439706367
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+    {
+      "id": 22,
+      "rotation_radians": 2.0194611309223403,
+      "x": -4.004889553475687,
+      "y": 0.7599856001465126
+    }
+  ],
+  "problem": "22 equal items for Circles in Pentagons",
+  "setup": "cirinpen",
+  "source_image": "https://erich-friedman.github.io/packing/cirinpen/pent.22.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinpen/"
+}

data/solutions/generated/cirinpen_023_0115bd21477c01e6.json

@@ -0,0 +1,198 @@
+{
+  "case": "cirinpen@23",
+  "container": {
+    "circumradius": 6.292543051568551,
+    "orientation_radians": 0.0,
+    "side_length": 7.39732801025494,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "cirinpen@23",
+    "credit": "David W",
+    "date": "July 2012",
+    "family_updated": "7/10/12",
+    "metric_expression": "7.397+",
+    "metric_symbol": "s",
+    "metric_value": 7.397,
+    "reference_text": "s = 7.397+ | Found by David W. Cantrell | in July 2012.",
+    "source_image": "pent.23.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.23.gif",
+    "source_page": "https://erich-friedman.github.io/packing/cirinpen/",
+    "title": "Circles in Pentagons"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "cirinpen@23",
+      "credit": "David W",
+      "date": "July 2012",
+      "family_updated": "7/10/12",
+      "metric_expression": "7.397+",
+      "metric_symbol": "s",
+      "metric_value": 7.397,
+      "reference_text": "s = 7.397+ | Found by David W. Cantrell | in July 2012.",
+      "source_image": "pent.23.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.23.gif",
+      "source_page": "https://erich-friedman.github.io/packing/cirinpen/",
+      "title": "Circles in Pentagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "id": 1,
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+    {
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+      "x": 3.145541439734377,
+      "y": 2.630158995905486
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+    {
+      "id": 21,
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+      "x": -2.184559458549131,
+      "y": 3.5775023321469903
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+    {
+      "id": 22,
+      "rotation_radians": 4.710151075394056,
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+      "y": 4.208158076687209
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+    {
+      "id": 23,
+      "rotation_radians": 1.7316665189773388,
+      "x": 1.6574298463117145,
+      "y": 4.678375375007642
+    }
+  ],
+  "problem": "23 equal items for Circles in Pentagons",
+  "setup": "cirinpen",
+  "source_image": "https://erich-friedman.github.io/packing/cirinpen/pent.23.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinpen/"
+}

data/solutions/generated/cirinpen_024_9eb26a95274f1d1d.json

@@ -0,0 +1,204 @@
+{
+  "case": "cirinpen@24",
+  "container": {
+    "circumradius": 6.409384831954181,
+    "orientation_radians": 0.0,
+    "side_length": 7.534683760979478,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "cirinpen@24",
+    "credit": "David W",
+    "date": "July 2012",
+    "family_updated": "7/10/12",
+    "metric_expression": "7.534+",
+    "metric_symbol": "s",
+    "metric_value": 7.534,
+    "reference_text": "s = 7.534+ | Found by David W. Cantrell | in July 2012.",
+    "source_image": "pent.24.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.24.gif",
+    "source_page": "https://erich-friedman.github.io/packing/cirinpen/",
+    "title": "Circles in Pentagons"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "cirinpen@24",
+      "credit": "David W",
+      "date": "July 2012",
+      "family_updated": "7/10/12",
+      "metric_expression": "7.534+",
+      "metric_symbol": "s",
+      "metric_value": 7.534,
+      "reference_text": "s = 7.534+ | Found by David W. Cantrell | in July 2012.",
+      "source_image": "pent.24.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.24.gif",
+      "source_page": "https://erich-friedman.github.io/packing/cirinpen/",
+      "title": "Circles in Pentagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "id": 1,
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+      "x": -3.379357969116141,
+      "y": -3.3026568261384885
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+    {
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+    {
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+      "y": 3.1733764728250495
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+      "rotation_radians": -0.06215533964713401,
+      "x": 0.04125787789502965,
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+    {
+      "id": 24,
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+      "x": 2.0390419533684594,
+      "y": 4.313118458580701
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+  ],
+  "problem": "24 equal items for Circles in Pentagons",
+  "setup": "cirinpen",
+  "source_image": "https://erich-friedman.github.io/packing/cirinpen/pent.24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinpen/"
+}

data/solutions/generated/cirinsqu_021_65afc927a4d3cb10.json

@@ -0,0 +1,186 @@
+{
+  "case": "cirinsqu@21",
+  "container": {
+    "circumradius": 6.61788806130434,
+    "orientation_radians": 0.0,
+    "side_length": 9.359107050563585,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "cirinsqu@21",
+    "credit": "Erich Friedman Packing Center",
+    "date": "",
+    "family_updated": "10/9/10",
+    "metric_expression": "9.358+",
+    "metric_symbol": "s",
+    "metric_value": 9.358,
+    "reference_text": "s = 9.358+",
+    "source_image": "cs21.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs21.gif",
+    "source_page": "https://erich-friedman.github.io/packing/cirinsqu/",
+    "title": "Circles in Squares"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "cirinsqu@21",
+      "credit": "Erich Friedman Packing Center",
+      "date": "",
+      "family_updated": "10/9/10",
+      "metric_expression": "9.358+",
+      "metric_symbol": "s",
+      "metric_value": 9.358,
+      "reference_text": "s = 9.358+",
+      "source_image": "cs21.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs21.gif",
+      "source_page": "https://erich-friedman.github.io/packing/cirinsqu/",
+      "title": "Circles in Squares"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "id": 1,
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+      "x": -3.6774811073260305,
+      "y": -1.5261713953792755
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+  ],
+  "problem": "21 equal items for Circles in Squares",
+  "setup": "cirinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/cirinsqu/cs21.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinsqu/"
+}

data/solutions/generated/cirinsqu_022_27d48d864449f174.json

@@ -0,0 +1,192 @@
+{
+  "case": "cirinsqu@22",
+  "container": {
+    "circumradius": 6.692079645333952,
+    "orientation_radians": 0.0,
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+    "type": "regular_polygon"
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+  "friedman_reference": {
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+    "case": "cirinsqu@22",
+    "credit": "Erich Friedman Packing Center",
+    "date": "",
+    "family_updated": "10/9/10",
+    "metric_expression": "9.463+",
+    "metric_symbol": "s",
+    "metric_value": 9.463,
+    "reference_text": "s = 9.463+",
+    "source_image": "cs22.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs22.gif",
+    "source_page": "https://erich-friedman.github.io/packing/cirinsqu/",
+    "title": "Circles in Squares"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "cirinsqu@22",
+      "credit": "Erich Friedman Packing Center",
+      "date": "",
+      "family_updated": "10/9/10",
+      "metric_expression": "9.463+",
+      "metric_symbol": "s",
+      "metric_value": 9.463,
+      "reference_text": "s = 9.463+",
+      "source_image": "cs22.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs22.gif",
+      "source_page": "https://erich-friedman.github.io/packing/cirinsqu/",
+      "title": "Circles in Squares"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+  "problem": "22 equal items for Circles in Squares",
+  "setup": "cirinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/cirinsqu/cs22.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinsqu/"
+}

data/solutions/generated/cirinsqu_023_cfa99060ee2203a1.json

@@ -0,0 +1,198 @@
+{
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+  "container": {
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+    "orientation_radians": 0.0,
+    "side_length": 9.732306391434195,
+    "sides": 4,
+    "type": "regular_polygon"
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+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "cirinsqu@23",
+    "credit": "Erich Friedman Packing Center",
+    "date": "",
+    "family_updated": "10/9/10",
+    "metric_expression": "2 + 2\u221a2 + 2\u221a6 = 9.727+",
+    "metric_symbol": "s",
+    "metric_value": 9.727,
+    "reference_text": "s = 2 + 2\u221a2 + 2\u221a6 = 9.727+",
+    "source_image": "cs23.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs23.gif",
+    "source_page": "https://erich-friedman.github.io/packing/cirinsqu/",
+    "title": "Circles in Squares"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "cirinsqu@23",
+      "credit": "Erich Friedman Packing Center",
+      "date": "",
+      "family_updated": "10/9/10",
+      "metric_expression": "2 + 2\u221a2 + 2\u221a6 = 9.727+",
+      "metric_symbol": "s",
+      "metric_value": 9.727,
+      "reference_text": "s = 2 + 2\u221a2 + 2\u221a6 = 9.727+",
+      "source_image": "cs23.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs23.gif",
+      "source_page": "https://erich-friedman.github.io/packing/cirinsqu/",
+      "title": "Circles in Squares"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
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+  "problem": "23 equal items for Circles in Squares",
+  "setup": "cirinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/cirinsqu/cs23.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinsqu/"
+}

data/solutions/generated/cirinsqu_024_e2eca298edbdb88c.json

@@ -0,0 +1,204 @@
+{
+  "case": "cirinsqu@24",
+  "container": {
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+    "orientation_radians": 0.0,
+    "side_length": 9.86391811313438,
+    "sides": 4,
+    "type": "regular_polygon"
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+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "cirinsqu@24",
+    "credit": "Erich Friedman Packing Center",
+    "date": "",
+    "family_updated": "10/9/10",
+    "metric_expression": "6 + \u221a2 + \u221a6 = 9.863+",
+    "metric_symbol": "s",
+    "metric_value": 9.863,
+    "reference_text": "s = 6 + \u221a2 + \u221a6 = 9.863+",
+    "source_image": "cs24.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs24.gif",
+    "source_page": "https://erich-friedman.github.io/packing/cirinsqu/",
+    "title": "Circles in Squares"
+  },
+  "item": {
+    "radius": 1.0,
+    "type": "circle"
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+  "metadata": {
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+    "friedman_reference": {
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+      "case": "cirinsqu@24",
+      "credit": "Erich Friedman Packing Center",
+      "date": "",
+      "family_updated": "10/9/10",
+      "metric_expression": "6 + \u221a2 + \u221a6 = 9.863+",
+      "metric_symbol": "s",
+      "metric_value": 9.863,
+      "reference_text": "s = 6 + \u221a2 + \u221a6 = 9.863+",
+      "source_image": "cs24.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs24.gif",
+      "source_page": "https://erich-friedman.github.io/packing/cirinsqu/",
+      "title": "Circles in Squares"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/cirinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
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+      "id": 22,
+      "rotation_radians": 3.5948153464262655,
+      "x": 1.4142432614436635,
+      "y": 4.1463580698486515
+    },
+    {
+      "id": 23,
+      "rotation_radians": 5.1727923315725945,
+      "x": 4.1463644077221105,
+      "y": -1.4142422052425538
+    },
+    {
+      "id": 24,
+      "rotation_radians": 6.838132625171063,
+      "x": 1.4142424180996134,
+      "y": 1.3178632422959804
+    }
+  ],
+  "problem": "24 equal items for Circles in Squares",
+  "setup": "cirinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/cirinsqu/cs24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinsqu/"
+}

data/solutions/generated/domintri_021_de2eca0c1c28a96d.json

@@ -0,0 +1,187 @@
+{
+  "case": "domintri@21",
+  "container": {
+    "circumradius": 6.477816768931373,
+    "orientation_radians": 0.0,
+    "side_length": 11.219907765910799,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "domintri@21",
+    "credit": "Maurizio Morandi",
+    "date": "April 2026",
+    "family_updated": "4/23/26",
+    "metric_expression": "2+5\u221a3 = 10.66025+",
+    "metric_symbol": "s",
+    "metric_value": 10.66025,
+    "reference_text": "s = 2+5\u221a3 = 10.66025+ | Found by Maurizio Morandi | in April 2026.",
+    "source_image": "21.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/domintri/21.png",
+    "source_page": "https://erich-friedman.github.io/packing/domintri/",
+    "title": "Dominoes in Triangles"
+  },
+  "item": {
+    "height": 1.0,
+    "type": "rectangle",
+    "width": 2.0
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "domintri@21",
+      "credit": "Maurizio Morandi",
+      "date": "April 2026",
+      "family_updated": "4/23/26",
+      "metric_expression": "2+5\u221a3 = 10.66025+",
+      "metric_symbol": "s",
+      "metric_value": 10.66025,
+      "reference_text": "s = 2+5\u221a3 = 10.66025+ | Found by Maurizio Morandi | in April 2026.",
+      "source_image": "21.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/domintri/21.png",
+      "source_page": "https://erich-friedman.github.io/packing/domintri/",
+      "title": "Dominoes in Triangles"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/domintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 4.680915221690283,
+      "x": -0.7075708495529313,
+      "y": -1.7081167148744332
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+    {
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+      "y": 0.8790733356683307
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+    {
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+    {
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+    },
+    {
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+      "x": -2.238859521988467,
+      "y": -2.839650950642868
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+    {
+      "id": 16,
+      "rotation_radians": 4.186111122483624,
+      "x": -0.20877780855667732,
+      "y": 0.3948111307698921
+    },
+    {
+      "id": 17,
+      "rotation_radians": 5.74448393920612,
+      "x": 2.710482927138211,
+      "y": 1.5801042416978601
+    },
+    {
+      "id": 18,
+      "rotation_radians": 5.322673546762745,
+      "x": 3.48798451301135,
+      "y": -0.5247600960112315
+    },
+    {
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+      "rotation_radians": 2.5830563374604467,
+      "x": 1.8800164142248137,
+      "y": 0.8965117265562664
+    },
+    {
+      "id": 20,
+      "rotation_radians": 3.6651879974413157,
+      "x": -0.12268458589224218,
+      "y": -3.233442397766182
+    },
+    {
+      "id": 21,
+      "rotation_radians": 6.121360172546453,
+      "x": -2.1707778589109537,
+      "y": -0.5800805112518915
+    }
+  ],
+  "problem": "21 equal items for Dominoes in Triangles",
+  "setup": "domintri",
+  "source_image": "https://erich-friedman.github.io/packing/domintri/21.png",
+  "source_page": "https://erich-friedman.github.io/packing/domintri/"
+}

data/solutions/generated/domintri_022_6301aae692a9ac9b.json

@@ -0,0 +1,193 @@
+{
+  "case": "domintri@22",
+  "container": {
+    "circumradius": 6.424775861213207,
+    "orientation_radians": 0.0,
+    "side_length": 11.128038218863363,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "domintri@22",
+    "credit": "Maurizio Morandi",
+    "date": "April 2026",
+    "family_updated": "4/23/26",
+    "metric_expression": "4(1+\u221a3) = 10.92820+",
+    "metric_symbol": "s",
+    "metric_value": 10.9282,
+    "reference_text": "s = 4(1+\u221a3) = 10.92820+ | Found by Maurizio Morandi | in April 2026.",
+    "source_image": "22.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/domintri/22.png",
+    "source_page": "https://erich-friedman.github.io/packing/domintri/",
+    "title": "Dominoes in Triangles"
+  },
+  "item": {
+    "height": 1.0,
+    "type": "rectangle",
+    "width": 2.0
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "domintri@22",
+      "credit": "Maurizio Morandi",
+      "date": "April 2026",
+      "family_updated": "4/23/26",
+      "metric_expression": "4(1+\u221a3) = 10.92820+",
+      "metric_symbol": "s",
+      "metric_value": 10.9282,
+      "reference_text": "s = 4(1+\u221a3) = 10.92820+ | Found by Maurizio Morandi | in April 2026.",
+      "source_image": "22.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/domintri/22.png",
+      "source_page": "https://erich-friedman.github.io/packing/domintri/",
+      "title": "Dominoes in Triangles"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "steepest",
+    "source_url": "https://erich-friedman.github.io/packing/domintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 3.665193420477834,
+      "x": 3.0372374447717925,
+      "y": -1.3784343971717528
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+      "x": 0.6935188359199477,
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+    {
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+      "rotation_radians": 4.798983898743175,
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+      "y": -1.5900520756822254
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+    {
+      "id": 18,
+      "rotation_radians": 6.806782417722895,
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+      "y": -3.161732721748257
+    },
+    {
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+      "rotation_radians": 5.75958627712358,
+      "x": -0.3007711658070146,
+      "y": 3.305617334392546
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.5361381663888575,
+      "x": -1.096253299042819,
+      "y": 1.3847297698833205
+    },
+    {
+      "id": 21,
+      "rotation_radians": 4.718436967501354,
+      "x": -2.7063411930411845,
+      "y": 0.6255067060916327
+    },
+    {
+      "id": 22,
+      "rotation_radians": 5.806682862434497,
+      "x": -2.0943905832043486,
+      "y": 4.287445421080233
+    }
+  ],
+  "problem": "22 equal items for Dominoes in Triangles",
+  "setup": "domintri",
+  "source_image": "https://erich-friedman.github.io/packing/domintri/22.png",
+  "source_page": "https://erich-friedman.github.io/packing/domintri/"
+}

data/solutions/generated/domintri_023_7b6e8b12db0049b9.json

@@ -0,0 +1,199 @@
+{
+  "case": "domintri@23",
+  "container": {
+    "circumradius": 6.556092417440949,
+    "orientation_radians": 0.0,
+    "side_length": 11.355485166124788,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "domintri@23",
+    "credit": "Maurizio Morandi",
+    "date": "April 2026",
+    "family_updated": "4/23/26",
+    "metric_expression": "10+2/\u221a3 = 11.15470+",
+    "metric_symbol": "s",
+    "metric_value": 11.1547,
+    "reference_text": "s = 10+2/\u221a3 = 11.15470+ | Found by Maurizio Morandi | in April 2026.",
+    "source_image": "23.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/domintri/23.png",
+    "source_page": "https://erich-friedman.github.io/packing/domintri/",
+    "title": "Dominoes in Triangles"
+  },
+  "item": {
+    "height": 1.0,
+    "type": "rectangle",
+    "width": 2.0
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "domintri@23",
+      "credit": "Maurizio Morandi",
+      "date": "April 2026",
+      "family_updated": "4/23/26",
+      "metric_expression": "10+2/\u221a3 = 11.15470+",
+      "metric_symbol": "s",
+      "metric_value": 11.1547,
+      "reference_text": "s = 10+2/\u221a3 = 11.15470+ | Found by Maurizio Morandi | in April 2026.",
+      "source_image": "23.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/domintri/23.png",
+      "source_page": "https://erich-friedman.github.io/packing/domintri/",
+      "title": "Dominoes in Triangles"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/domintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "x": 2.92055815733062,
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+    },
+    {
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+      "rotation_radians": -0.10587347636396144,
+      "x": -1.230718921808486,
+      "y": 1.5098164615980858
+    },
+    {
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+      "x": -2.142285090089191,
+      "y": -4.444647686400859
+    },
+    {
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+      "x": 1.9590439798814532,
+      "y": -1.4924356940194763
+    },
+    {
+      "id": 19,
+      "rotation_radians": 3.1845284625117616,
+      "x": -1.2521489440944509,
+      "y": -2.8820127656683727
+    },
+    {
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+      "x": -2.778022803867627,
+      "y": 2.100227584566125
+    },
+    {
+      "id": 21,
+      "rotation_radians": 3.668304838661541,
+      "x": 0.8638588474189568,
+      "y": -2.69008528574402
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.5707898451457138,
+      "x": -2.778022693309244,
+      "y": 4.100331558231138
+    },
+    {
+      "id": 23,
+      "rotation_radians": 6.284768266410077,
+      "x": -0.23014401076610144,
+      "y": 0.4007713931615883
+    }
+  ],
+  "problem": "23 equal items for Dominoes in Triangles",
+  "setup": "domintri",
+  "source_image": "https://erich-friedman.github.io/packing/domintri/23.png",
+  "source_page": "https://erich-friedman.github.io/packing/domintri/"
+}

data/solutions/generated/domintri_024_af99e7edd2e30109.json

@@ -0,0 +1,205 @@
+{
+  "case": "domintri@24",
+  "container": {
+    "circumradius": 6.7984944649245795,
+    "orientation_radians": 0.0,
+    "side_length": 11.77533782822516,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "domintri@24",
+    "credit": "Maurizio Morandi",
+    "date": "April 2026",
+    "family_updated": "4/23/26",
+    "metric_expression": "9+4/\u221a3 = 11.30940+",
+    "metric_symbol": "s",
+    "metric_value": 11.3094,
+    "reference_text": "s = 9+4/\u221a3 = 11.30940+ | Found by Maurizio Morandi | in April 2026.",
+    "source_image": "24.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/domintri/24.png",
+    "source_page": "https://erich-friedman.github.io/packing/domintri/",
+    "title": "Dominoes in Triangles"
+  },
+  "item": {
+    "height": 1.0,
+    "type": "rectangle",
+    "width": 2.0
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "domintri@24",
+      "credit": "Maurizio Morandi",
+      "date": "April 2026",
+      "family_updated": "4/23/26",
+      "metric_expression": "9+4/\u221a3 = 11.30940+",
+      "metric_symbol": "s",
+      "metric_value": 11.3094,
+      "reference_text": "s = 9+4/\u221a3 = 11.30940+ | Found by Maurizio Morandi | in April 2026.",
+      "source_image": "24.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/domintri/24.png",
+      "source_page": "https://erich-friedman.github.io/packing/domintri/",
+      "title": "Dominoes in Triangles"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/domintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "id": 1,
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+    {
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+      "x": 1.9772253011575238,
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+    },
+    {
+      "id": 16,
+      "rotation_radians": 2.617988372759859,
+      "x": 4.182414770372991,
+      "y": 0.9330346291831157
+    },
+    {
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+      "x": -1.8960407627282814,
+      "y": 1.7237744541041897
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+    {
+      "id": 18,
+      "rotation_radians": 4.712628503474931,
+      "x": -1.8988276756100098,
+      "y": 3.726647680227827
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+    {
+      "id": 19,
+      "rotation_radians": 3.0842302979076375,
+      "x": -0.3651794901134868,
+      "y": -1.8444643617824752
+    },
+    {
+      "id": 20,
+      "rotation_radians": 5.42564284015502,
+      "x": 0.08166926790043864,
+      "y": 1.2249337456813842
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.5730507204742608,
+      "x": -2.8969857616560777,
+      "y": 1.9424938042922415
+    },
+    {
+      "id": 22,
+      "rotation_radians": 6.80678335111062,
+      "x": 0.4459092571505868,
+      "y": -3.0831103549057177
+    },
+    {
+      "id": 23,
+      "rotation_radians": 3.121535076109764,
+      "x": -2.1734400788181745,
+      "y": -2.8086106625644245
+    },
+    {
+      "id": 24,
+      "rotation_radians": 3.6651905248435552,
+      "x": -1.2831305959292039,
+      "y": -4.088549984427801
+    }
+  ],
+  "problem": "24 equal items for Dominoes in Triangles",
+  "setup": "domintri",
+  "source_image": "https://erich-friedman.github.io/packing/domintri/24.png",
+  "source_page": "https://erich-friedman.github.io/packing/domintri/"
+}

data/solutions/generated/hexincir_021_49a047c29bb184c3.json

@@ -0,0 +1,185 @@
+{
+  "case": "hexincir@21",
+  "container": {
+    "radius": 4.68340545778963,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "hexincir@21",
+    "credit": "Enea Victor",
+    "date": "April 2026",
+    "family_updated": "4/28/26",
+    "metric_expression": "4.68339+",
+    "metric_symbol": "r",
+    "metric_value": 4.68339,
+    "reference_text": "r = 4.68339+ | Found by Enea Victor | in April 2026.",
+    "source_image": "21.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexincir/21.png",
+    "source_page": "https://erich-friedman.github.io/packing/hexincir/",
+    "title": "Hexagons in Circles"
+  },
+  "item": {
+    "circumradius": 1.0000000000000002,
+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "hexincir@21",
+      "credit": "Enea Victor",
+      "date": "April 2026",
+      "family_updated": "4/28/26",
+      "metric_expression": "4.68339+",
+      "metric_symbol": "r",
+      "metric_value": 4.68339,
+      "reference_text": "r = 4.68339+ | Found by Enea Victor | in April 2026.",
+      "source_image": "21.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexincir/21.png",
+      "source_page": "https://erich-friedman.github.io/packing/hexincir/",
+      "title": "Hexagons in Circles"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/hexincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -1.4462898931470023,
+      "x": -2.900670356116669,
+      "y": -2.2408488499670156
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+    {
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+    },
+    {
+      "id": 15,
+      "rotation_radians": -0.08986908629931366,
+      "x": 3.439612373013305,
+      "y": 1.5929917750864595
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.2611887273324643,
+      "x": -2.6819918197411994,
+      "y": 2.6787118204579956
+    },
+    {
+      "id": 17,
+      "rotation_radians": -0.2611838332789637,
+      "x": -1.4099506327026519,
+      "y": 1.5012428613974844
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.17541457942417882,
+      "x": 0.2789445346158778,
+      "y": 2.0411233869851984
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+    {
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+      "y": 3.7324291832889203
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+    {
+      "id": 20,
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+      "x": 2.2393293533348455,
+      "y": 2.916365539251016
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+    {
+      "id": 21,
+      "rotation_radians": -1.2573933622971594,
+      "x": -1.065558943452475,
+      "y": 3.3883282230022225
+    }
+  ],
+  "problem": "21 equal items for Hexagons in Circles",
+  "setup": "hexincir",
+  "source_image": "https://erich-friedman.github.io/packing/hexincir/21.png",
+  "source_page": "https://erich-friedman.github.io/packing/hexincir/"
+}

data/solutions/generated/hexinhex_021_4a431b677be571c9.json

@@ -0,0 +1,188 @@
+{
+  "case": "hexinhex@21",
+  "container": {
+    "circumradius": 5.000067508172298,
+    "orientation_radians": 0.0,
+    "side_length": 5.000067508172297,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "hexinhex@21",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "4/15/26",
+    "metric_expression": "5",
+    "metric_symbol": "s",
+    "metric_value": 5.0,
+    "reference_text": "20-21. | | s = 5 | Trivial. | |",
+    "source_image": "21.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif",
+    "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+    "title": "Hexagons in Hexagons"
+  },
+  "item": {
+    "circumradius": 1.0000000000000002,
+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000200001000001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "hexinhex@21",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "4/15/26",
+      "metric_expression": "5",
+      "metric_symbol": "s",
+      "metric_value": 5.0,
+      "reference_text": "20-21. | | s = 5 | Trivial. | |",
+      "source_image": "21.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif",
+      "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+      "title": "Hexagons in Hexagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "id": 1,
+      "rotation_radians": 7.901581286981117e-07,
+      "x": -0.5000174463538043,
+      "y": 0.8660408791733488
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+      "x": 1.0000192810757436,
+      "y": 1.7876577640023134e-05
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+    {
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+      "y": -1.3886483582868472e-05
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+    {
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+      "y": 2.5981094128802877
+    },
+    {
+      "id": 11,
+      "rotation_radians": -1.9986158879680022e-07,
+      "x": 2.500045944099602,
+      "y": 0.8660744448134621
+    },
+    {
+      "id": 12,
+      "rotation_radians": 5.977223461539629e-08,
+      "x": 2.500039054190333,
+      "y": -0.8660052621280638
+    },
+    {
+      "id": 13,
+      "rotation_radians": -1.3478963937982246e-08,
+      "x": -3.500092072845965,
+      "y": 0.8659632371807578
+    },
+    {
+      "id": 14,
+      "rotation_radians": 4.1132012924842904e-07,
+      "x": -3.50001719472001,
+      "y": -0.8661073175269502
+    },
+    {
+      "id": 15,
+      "rotation_radians": 5.546656121720664e-07,
+      "x": 0.9999791170267553,
+      "y": 3.464158149492293
+    },
+    {
+      "id": 16,
+      "rotation_radians": -4.0502975026486896e-07,
+      "x": 1.0000797359239124,
+      "y": -3.464151263809527
+    },
+    {
+      "id": 17,
+      "rotation_radians": -4.772253186330887e-08,
+      "x": -2.000035262364772,
+      "y": 3.464146559555753
+    },
+    {
+      "id": 18,
+      "rotation_radians": 9.1237704507367e-07,
+      "x": -2.000020084800537,
+      "y": -3.4641558808448685
+    },
+    {
+      "id": 19,
+      "rotation_radians": 2.3453726621205355e-07,
+      "x": 2.500069476967483,
+      "y": -2.5980694889362432
+    },
+    {
+      "id": 20,
+      "rotation_radians": 1.69584433962456e-07,
+      "x": 2.500015099600881,
+      "y": 2.598150980951056
+    },
+    {
+      "id": 21,
+      "rotation_radians": -1.727435234594155e-08,
+      "x": 4.0000566862377624,
+      "y": 1.0128607699719307e-05
+    }
+  ],
+  "problem": "21 equal items for Hexagons in Hexagons",
+  "setup": "hexinhex",
+  "source_image": "https://erich-friedman.github.io/packing/hexinhex/21.gif",
+  "source_page": "https://erich-friedman.github.io/packing/hexinhex/"
+}

data/solutions/generated/hexinhex_022_003a713177cb171c.json

@@ -0,0 +1,194 @@
+{
+  "case": "hexinhex@22",
+  "container": {
+    "circumradius": 5.285900869804883,
+    "orientation_radians": 0.0,
+    "side_length": 5.285900869804882,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "hexinhex@22",
+    "credit": "Maurizio Morandi",
+    "date": "April 2015",
+    "family_updated": "4/15/26",
+    "metric_expression": "(39+8\u221a3)/10 = 5.285+",
+    "metric_symbol": "s",
+    "metric_value": 5.285,
+    "reference_text": "22. | | s = (39+8\u221a3)/10 = 5.285+ | Found by Maurizio Morandi | in April 2015.",
+    "source_image": "22.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/22.gif",
+    "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+    "title": "Hexagons in Hexagons"
+  },
+  "item": {
+    "circumradius": 1.0000000000000002,
+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "hexinhex@22",
+      "credit": "Maurizio Morandi",
+      "date": "April 2015",
+      "family_updated": "4/15/26",
+      "metric_expression": "(39+8\u221a3)/10 = 5.285+",
+      "metric_symbol": "s",
+      "metric_value": 5.285,
+      "reference_text": "22. | | s = (39+8\u221a3)/10 = 5.285+ | Found by Maurizio Morandi | in April 2015.",
+      "source_image": "22.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/22.gif",
+      "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+      "title": "Hexagons in Hexagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
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+      "y": -3.7116633490312636
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.9956310829320324,
+      "x": 4.0460012205776,
+      "y": 0.36589452870687333
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+    {
+      "id": 19,
+      "rotation_radians": 1.0473861046353776,
+      "x": -3.857179015040217,
+      "y": 0.7423189733842023
+    },
+    {
+      "id": 20,
+      "rotation_radians": 1.04718488413327,
+      "x": 0.9999371354762571,
+      "y": 3.711676177264519
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+    {
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+      "rotation_radians": 1.0471929177769443,
+      "x": -2.142935018978356,
+      "y": 3.7116676593171736
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+    {
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+      "rotation_radians": 1.0471911790030466,
+      "x": 3.49712043043339,
+      "y": -1.366192273764231
+    }
+  ],
+  "problem": "22 equal items for Hexagons in Hexagons",
+  "setup": "hexinhex",
+  "source_image": "https://erich-friedman.github.io/packing/hexinhex/22.gif",
+  "source_page": "https://erich-friedman.github.io/packing/hexinhex/"
+}

data/solutions/generated/hexinhex_023_4a3a3fd07554d52b.json

@@ -0,0 +1,200 @@
+{
+  "case": "hexinhex@23",
+  "container": {
+    "circumradius": 5.444854911759239,
+    "orientation_radians": 0.0,
+    "side_length": 5.444854911759238,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "hexinhex@23",
+    "credit": "Alex Kravatsky et al",
+    "date": "February 2026",
+    "family_updated": "4/15/26",
+    "metric_expression": "5.400+",
+    "metric_symbol": "s",
+    "metric_value": 5.4,
+    "reference_text": "23. | | s = 5.400+ | Found by Alex Kravatsky et al | in February 2026.",
+    "source_image": "23.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/23.gif",
+    "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+    "title": "Hexagons in Hexagons"
+  },
+  "item": {
+    "circumradius": 1.0000000000000002,
+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "hexinhex@23",
+      "credit": "Alex Kravatsky et al",
+      "date": "February 2026",
+      "family_updated": "4/15/26",
+      "metric_expression": "5.400+",
+      "metric_symbol": "s",
+      "metric_value": 5.4,
+      "reference_text": "23. | | s = 5.400+ | Found by Alex Kravatsky et al | in February 2026.",
+      "source_image": "23.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/23.gif",
+      "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+      "title": "Hexagons in Hexagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "id": 1,
+      "rotation_radians": 0.006824620830609338,
+      "x": -0.8215524173648067,
+      "y": 0.3833682180057374
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+    {
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+    {
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+      "x": -3.8608575221997232,
+      "y": -1.0086596087949697
+    },
+    {
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+      "y": -3.7244345293755545
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+    {
+      "id": 18,
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+      "x": -4.025784510757465,
+      "y": 0.7230191420718266
+    },
+    {
+      "id": 19,
+      "rotation_radians": -1.5656612716338478e-07,
+      "x": -2.8632020300174506,
+      "y": -2.7394469751405985
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.08382659687829615,
+      "x": 4.11761140979695,
+      "y": -0.4890504818445506
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.6987942242473001,
+      "x": 2.153912426730604,
+      "y": -3.7306479484386914
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.0011007242860997333,
+      "x": 2.2029396625089883,
+      "y": 3.848763430220942
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.008913551807697194,
+      "x": 3.71762600310186,
+      "y": 1.250704344392519
+    }
+  ],
+  "problem": "23 equal items for Hexagons in Hexagons",
+  "setup": "hexinhex",
+  "source_image": "https://erich-friedman.github.io/packing/hexinhex/23.gif",
+  "source_page": "https://erich-friedman.github.io/packing/hexinhex/"
+}

data/solutions/generated/hexinhex_024_c96649ff013a9455.json

@@ -0,0 +1,206 @@
+{
+  "case": "hexinhex@24",
+  "container": {
+    "circumradius": 5.4849837999062,
+    "orientation_radians": 0.0,
+    "side_length": 5.484983799906199,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "hexinhex@24",
+    "credit": "Maurizio Morandi",
+    "date": "April 2015",
+    "family_updated": "4/15/26",
+    "metric_expression": "19\u221a3/6 = 5.484+",
+    "metric_symbol": "s",
+    "metric_value": 5.484,
+    "reference_text": "24. | | s = 19\u221a3/6 = 5.484+ | Found by Maurizio Morandi | in April 2015.",
+    "source_image": "24.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/24.gif",
+    "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+    "title": "Hexagons in Hexagons"
+  },
+  "item": {
+    "circumradius": 1.0000000000000002,
+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "hexinhex@24",
+      "credit": "Maurizio Morandi",
+      "date": "April 2015",
+      "family_updated": "4/15/26",
+      "metric_expression": "19\u221a3/6 = 5.484+",
+      "metric_symbol": "s",
+      "metric_value": 5.484,
+      "reference_text": "24. | | s = 19\u221a3/6 = 5.484+ | Found by Maurizio Morandi | in April 2015.",
+      "source_image": "24.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/24.gif",
+      "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+      "title": "Hexagons in Hexagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.05770485484610239,
+      "x": -4.057623446735772,
+      "y": -0.6852165437808199
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+      "x": 1.2990758104304285,
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+    },
+    {
+      "id": 10,
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+      "x": 0.43305161567370953,
+      "y": -2.250078827625604
+    },
+    {
+      "id": 11,
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+      "x": -1.3900697076117499,
+      "y": 3.7526566453179586
+    },
+    {
+      "id": 12,
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+      "x": 2.177309667774508,
+      "y": 0.7429621970099977
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.521836271286997,
+      "x": 0.4330151943784053,
+      "y": 3.7501227592340087
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.5218364705901408,
+      "x": -1.2990678998632341,
+      "y": -2.250061840005074
+    },
+    {
+      "id": 15,
+      "rotation_radians": 0.041433875740246665,
+      "x": -3.845620204372425,
+      "y": 1.0658486646904968
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.5218365242717001,
+      "x": 2.1651296347539293,
+      "y": 3.7501116724967285
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.23402653645081095,
+      "x": -2.8401030962256724,
+      "y": 2.640004306523297
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.5219394669835438,
+      "x": -2.187682384801012,
+      "y": -0.7369266279736237
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.5218362908220159,
+      "x": -0.43908767298646906,
+      "y": 2.253590019154598
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.9371598173271674,
+      "x": 3.822866311663475,
+      "y": -1.045090705459388
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.3332844683040039,
+      "x": 2.567390333813402,
+      "y": -2.422256981900285
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.5218360782631368,
+      "x": -0.4330124900538102,
+      "y": -3.7501189488205253
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.5218364186693767,
+      "x": 3.031193540896481,
+      "y": 2.250059478350546
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.5218364436698072,
+      "x": -2.1651298754333568,
+      "y": -3.75010602161616
+    }
+  ],
+  "problem": "24 equal items for Hexagons in Hexagons",
+  "setup": "hexinhex",
+  "source_image": "https://erich-friedman.github.io/packing/hexinhex/24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/hexinhex/"
+}

data/solutions/generated/hexinhex_025_4ac680367830872b.json

@@ -0,0 +1,212 @@
+{
+  "case": "hexinhex@25",
+  "container": {
+    "circumradius": 5.626071223468267,
+    "orientation_radians": 0.0,
+    "side_length": 5.626071223468266,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "hexinhex@25",
+    "credit": "Alex Kravatsky et al",
+    "date": "February 2026",
+    "family_updated": "4/15/26",
+    "metric_expression": "5.62390+",
+    "metric_symbol": "s",
+    "metric_value": 5.6239,
+    "reference_text": "25. | | s = 5.62390+ | Found by Alex Kravatsky et al | in February 2026.",
+    "source_image": "25.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/25.gif",
+    "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+    "title": "Hexagons in Hexagons"
+  },
+  "item": {
+    "circumradius": 1.0000000000000002,
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+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "hexinhex@25",
+      "credit": "Alex Kravatsky et al",
+      "date": "February 2026",
+      "family_updated": "4/15/26",
+      "metric_expression": "5.62390+",
+      "metric_symbol": "s",
+      "metric_value": 5.6239,
+      "reference_text": "25. | | s = 5.62390+ | Found by Alex Kravatsky et al | in February 2026.",
+      "source_image": "25.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/25.gif",
+      "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+      "title": "Hexagons in Hexagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "x": 2.2856884807216695,
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+  ],
+  "problem": "25 equal items for Hexagons in Hexagons",
+  "setup": "hexinhex",
+  "source_image": "https://erich-friedman.github.io/packing/hexinhex/25.gif",
+  "source_page": "https://erich-friedman.github.io/packing/hexinhex/"
+}

data/solutions/generated/hexinhex_026_0a420d645748969b.json

@@ -0,0 +1,218 @@
+{
+  "case": "hexinhex@26",
+  "container": {
+    "circumradius": 5.719543411865986,
+    "orientation_radians": 0.0,
+    "side_length": 5.719543411865985,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "hexinhex@26",
+    "credit": "Alex Kravatsky et al",
+    "date": "February 2026",
+    "family_updated": "4/15/26",
+    "metric_expression": "5.70972+",
+    "metric_symbol": "s",
+    "metric_value": 5.70972,
+    "reference_text": "26. | | s = 5.70972+ | Found by Alex Kravatsky et al | in February 2026.",
+    "source_image": "26.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/26.gif",
+    "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+    "title": "Hexagons in Hexagons"
+  },
+  "item": {
+    "circumradius": 1.0000000000000002,
+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "hexinhex@26",
+      "credit": "Alex Kravatsky et al",
+      "date": "February 2026",
+      "family_updated": "4/15/26",
+      "metric_expression": "5.70972+",
+      "metric_symbol": "s",
+      "metric_value": 5.70972,
+      "reference_text": "26. | | s = 5.70972+ | Found by Alex Kravatsky et al | in February 2026.",
+      "source_image": "26.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/26.gif",
+      "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+      "title": "Hexagons in Hexagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
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+  "placements": [
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+  ],
+  "problem": "26 equal items for Hexagons in Hexagons",
+  "setup": "hexinhex",
+  "source_image": "https://erich-friedman.github.io/packing/hexinhex/26.gif",
+  "source_page": "https://erich-friedman.github.io/packing/hexinhex/"
+}

data/solutions/generated/hexinhex_027_4e9628a9f49def85.json

@@ -0,0 +1,224 @@
+{
+  "case": "hexinhex@27",
+  "container": {
+    "circumradius": 5.716567746994859,
+    "orientation_radians": 0.0,
+    "side_length": 5.716567746994858,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "hexinhex@27",
+    "credit": "Alex Kravatsky et al",
+    "date": "February 2026",
+    "family_updated": "4/15/26",
+    "metric_expression": "5.71415+",
+    "metric_symbol": "s",
+    "metric_value": 5.71415,
+    "reference_text": "27. | | s = 5.71415+ | Found by Alex Kravatsky et al | in February 2026.",
+    "source_image": "27.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/27.gif",
+    "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+    "title": "Hexagons in Hexagons"
+  },
+  "item": {
+    "circumradius": 1.0000000000000002,
+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
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+      "case": "hexinhex@27",
+      "credit": "Alex Kravatsky et al",
+      "date": "February 2026",
+      "family_updated": "4/15/26",
+      "metric_expression": "5.71415+",
+      "metric_symbol": "s",
+      "metric_value": 5.71415,
+      "reference_text": "27. | | s = 5.71415+ | Found by Alex Kravatsky et al | in February 2026.",
+      "source_image": "27.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/27.gif",
+      "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+      "title": "Hexagons in Hexagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
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+  "problem": "27 equal items for Hexagons in Hexagons",
+  "setup": "hexinhex",
+  "source_image": "https://erich-friedman.github.io/packing/hexinhex/27.gif",
+  "source_page": "https://erich-friedman.github.io/packing/hexinhex/"
+}

data/solutions/generated/hexinhex_028_59dc7d7850663cbb.json

@@ -0,0 +1,230 @@
+{
+  "case": "hexinhex@28",
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+    "case": "hexinhex@28",
+    "credit": "Alex Kravatsky et al",
+    "date": "February 2026",
+    "family_updated": "4/15/26",
+    "metric_expression": "5.90893+",
+    "metric_symbol": "s",
+    "metric_value": 5.90893,
+    "reference_text": "28. | | s = 5.90893+ | Found by Alex Kravatsky et al | in February 2026.",
+    "source_image": "28.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/28.gif",
+    "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+    "title": "Hexagons in Hexagons"
+  },
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+    "sides": 6,
+    "type": "regular_polygon"
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+    "friedman_reference": {
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+      "metric_expression": "5.90893+",
+      "metric_symbol": "s",
+      "metric_value": 5.90893,
+      "reference_text": "28. | | s = 5.90893+ | Found by Alex Kravatsky et al | in February 2026.",
+      "source_image": "28.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/28.gif",
+      "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+      "title": "Hexagons in Hexagons"
+    },
+    "generator": "polygon_packer_c",
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+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
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+  "problem": "28 equal items for Hexagons in Hexagons",
+  "setup": "hexinhex",
+  "source_image": "https://erich-friedman.github.io/packing/hexinhex/28.gif",
+  "source_page": "https://erich-friedman.github.io/packing/hexinhex/"
+}

data/solutions/generated/hexinhex_029_dba25a591b8992bc.json

@@ -0,0 +1,236 @@
+{
+  "case": "hexinhex@29",
+  "container": {
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+  "friedman_reference": {
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+    "case": "hexinhex@29",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "4/15/26",
+    "metric_expression": "6",
+    "metric_symbol": "s",
+    "metric_value": 6.0,
+    "reference_text": "29-31. | | s = 6 | Trivial. |",
+    "source_image": "31.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif",
+    "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+    "title": "Hexagons in Hexagons"
+  },
+  "item": {
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+    "friedman_reference": {
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+      "case": "hexinhex@29",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "4/15/26",
+      "metric_expression": "6",
+      "metric_symbol": "s",
+      "metric_value": 6.0,
+      "reference_text": "29-31. | | s = 6 | Trivial. |",
+      "source_image": "31.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif",
+      "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+      "title": "Hexagons in Hexagons"
+    },
+    "generator": "polygon_packer_c",
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+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
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+  "problem": "29 equal items for Hexagons in Hexagons",
+  "setup": "hexinhex",
+  "source_image": "https://erich-friedman.github.io/packing/hexinhex/31.gif",
+  "source_page": "https://erich-friedman.github.io/packing/hexinhex/"
+}

data/solutions/generated/hexinhex_030_100db5f9f28894cc.json

@@ -0,0 +1,242 @@
+{
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+  "friedman_reference": {
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+    "case": "hexinhex@30",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "4/15/26",
+    "metric_expression": "6",
+    "metric_symbol": "s",
+    "metric_value": 6.0,
+    "reference_text": "29-31. | | s = 6 | Trivial. |",
+    "source_image": "31.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif",
+    "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+    "title": "Hexagons in Hexagons"
+  },
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+    "friedman_reference": {
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+      "case": "hexinhex@30",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "4/15/26",
+      "metric_expression": "6",
+      "metric_symbol": "s",
+      "metric_value": 6.0,
+      "reference_text": "29-31. | | s = 6 | Trivial. |",
+      "source_image": "31.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif",
+      "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+      "title": "Hexagons in Hexagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
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+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
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+  "problem": "30 equal items for Hexagons in Hexagons",
+  "setup": "hexinhex",
+  "source_image": "https://erich-friedman.github.io/packing/hexinhex/31.gif",
+  "source_page": "https://erich-friedman.github.io/packing/hexinhex/"
+}

data/solutions/generated/hexinhex_031_d503e2b08764a35e.json

@@ -0,0 +1,248 @@
+{
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+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "hexinhex@31",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "4/15/26",
+    "metric_expression": "6",
+    "metric_symbol": "s",
+    "metric_value": 6.0,
+    "reference_text": "29-31. | | s = 6 | Trivial. |",
+    "source_image": "31.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif",
+    "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+    "title": "Hexagons in Hexagons"
+  },
+  "item": {
+    "circumradius": 1.0000000000000002,
+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000200001000001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "hexinhex@31",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "4/15/26",
+      "metric_expression": "6",
+      "metric_symbol": "s",
+      "metric_value": 6.0,
+      "reference_text": "29-31. | | s = 6 | Trivial. |",
+      "source_image": "31.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif",
+      "source_page": "https://erich-friedman.github.io/packing/hexinhex/",
+      "title": "Hexagons in Hexagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/hexinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+    {
+      "id": 31,
+      "rotation_radians": 4.009630559569833e-07,
+      "x": -4.5001329150531655,
+      "y": -0.8659432469098659
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+  ],
+  "problem": "31 equal items for Hexagons in Hexagons",
+  "setup": "hexinhex",
+  "source_image": "https://erich-friedman.github.io/packing/hexinhex/31.gif",
+  "source_page": "https://erich-friedman.github.io/packing/hexinhex/"
+}

data/solutions/generated/hexinsqu_021_5d369a2740fde606.json

@@ -0,0 +1,188 @@
+{
+  "case": "hexinsqu@21",
+  "container": {
+    "circumradius": 5.928045365096002,
+    "orientation_radians": 0.0,
+    "side_length": 8.383522153681731,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "hexinsqu@21",
+    "credit": "Jonathan Viquerat",
+    "date": "April 2026",
+    "family_updated": "4/28/26",
+    "metric_expression": "8.381+",
+    "metric_symbol": "s",
+    "metric_value": 8.381,
+    "reference_text": "s = 8.381+ | Found by Jonathan Viquerat | in April 2026.",
+    "source_image": "21.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/21.png",
+    "source_page": "https://erich-friedman.github.io/packing/hexinsqu/",
+    "title": "Hexagons in Squares"
+  },
+  "item": {
+    "circumradius": 1.0000000000000002,
+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "hexinsqu@21",
+      "credit": "Jonathan Viquerat",
+      "date": "April 2026",
+      "family_updated": "4/28/26",
+      "metric_expression": "8.381+",
+      "metric_symbol": "s",
+      "metric_value": 8.381,
+      "reference_text": "s = 8.381+ | Found by Jonathan Viquerat | in April 2026.",
+      "source_image": "21.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/21.png",
+      "source_page": "https://erich-friedman.github.io/packing/hexinsqu/",
+      "title": "Hexagons in Squares"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+    {
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+    {
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+    {
+      "id": 17,
+      "rotation_radians": 3.3974328745239606,
+      "x": -3.078745425119485,
+      "y": 1.435104626002461
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.2804748333750988,
+      "x": 3.214072686170339,
+      "y": 1.4762201070637124
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.3279380902688882,
+      "x": 1.0942253991854534,
+      "y": 3.59584923187469
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+    {
+      "id": 20,
+      "rotation_radians": 3.4443460849655927,
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+      "y": 0.08118657857232116
+    },
+    {
+      "id": 21,
+      "rotation_radians": 5.507999003647057,
+      "x": -1.4152072713969777,
+      "y": 0.9217617872751641
+    }
+  ],
+  "problem": "21 equal items for Hexagons in Squares",
+  "setup": "hexinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/hexinsqu/21.png",
+  "source_page": "https://erich-friedman.github.io/packing/hexinsqu/"
+}

data/solutions/generated/hexinsqu_022_2f0b0033f0c66708.json

@@ -0,0 +1,194 @@
+{
+  "case": "hexinsqu@22",
+  "container": {
+    "circumradius": 6.064415893285481,
+    "orientation_radians": 0.0,
+    "side_length": 8.576379204155273,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "hexinsqu@22",
+    "credit": "Jonathan Viquerat",
+    "date": "April 2026",
+    "family_updated": "4/28/26",
+    "metric_expression": "8.568+",
+    "metric_symbol": "s",
+    "metric_value": 8.568,
+    "reference_text": "s = 8.568+ | Found by Jonathan Viquerat | in April 2026.",
+    "source_image": "22.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/22.png",
+    "source_page": "https://erich-friedman.github.io/packing/hexinsqu/",
+    "title": "Hexagons in Squares"
+  },
+  "item": {
+    "circumradius": 1.0000000000000002,
+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "hexinsqu@22",
+      "credit": "Jonathan Viquerat",
+      "date": "April 2026",
+      "family_updated": "4/28/26",
+      "metric_expression": "8.568+",
+      "metric_symbol": "s",
+      "metric_value": 8.568,
+      "reference_text": "s = 8.568+ | Found by Jonathan Viquerat | in April 2026.",
+      "source_image": "22.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/22.png",
+      "source_page": "https://erich-friedman.github.io/packing/hexinsqu/",
+      "title": "Hexagons in Squares"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
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+    {
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+      "x": 0.5353872833247472,
+      "y": 3.043558517056281
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+    {
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+    {
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+      "rotation_radians": 3.403309537170139,
+      "x": 0.10527038026378016,
+      "y": 4.734307604755597
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+  ],
+  "problem": "22 equal items for Hexagons in Squares",
+  "setup": "hexinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/hexinsqu/22.png",
+  "source_page": "https://erich-friedman.github.io/packing/hexinsqu/"
+}

data/solutions/generated/hexinsqu_023_31cc17034bd25d7b.json

@@ -0,0 +1,200 @@
+{
+  "case": "hexinsqu@23",
+  "container": {
+    "circumradius": 6.1238264137435126,
+    "orientation_radians": 0.0,
+    "side_length": 8.660398367934667,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "hexinsqu@23",
+    "credit": "Jonathan Viquerat",
+    "date": "April 2026",
+    "family_updated": "4/28/26",
+    "metric_expression": "5\u221a3 = 8.660+",
+    "metric_symbol": "s",
+    "metric_value": 8.66,
+    "reference_text": "s = 5\u221a3 = 8.660+ | Found by Jonathan Viquerat | in April 2026.",
+    "source_image": "23.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/23.png",
+    "source_page": "https://erich-friedman.github.io/packing/hexinsqu/",
+    "title": "Hexagons in Squares"
+  },
+  "item": {
+    "circumradius": 1.0000000000000002,
+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "hexinsqu@23",
+      "credit": "Jonathan Viquerat",
+      "date": "April 2026",
+      "family_updated": "4/28/26",
+      "metric_expression": "5\u221a3 = 8.660+",
+      "metric_symbol": "s",
+      "metric_value": 8.66,
+      "reference_text": "s = 5\u221a3 = 8.660+ | Found by Jonathan Viquerat | in April 2026.",
+      "source_image": "23.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/23.png",
+      "source_page": "https://erich-friedman.github.io/packing/hexinsqu/",
+      "title": "Hexagons in Squares"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+    {
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+    {
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+      "y": 0.05280395901232762
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+    {
+      "id": 20,
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+      "x": -1.1247940160755785,
+      "y": 3.574334667928198
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+    {
+      "id": 21,
+      "rotation_radians": 3.403380916286967,
+      "x": 0.24192493888512073,
+      "y": 4.657141176573033
+    },
+    {
+      "id": 22,
+      "rotation_radians": 4.4505878021011505,
+      "x": -0.09663726729610306,
+      "y": -4.80242259844813
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+    {
+      "id": 23,
+      "rotation_radians": 0.26177728667265426,
+      "x": -4.800373047868109,
+      "y": -0.09867472114638581
+    }
+  ],
+  "problem": "23 equal items for Hexagons in Squares",
+  "setup": "hexinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/hexinsqu/23.png",
+  "source_page": "https://erich-friedman.github.io/packing/hexinsqu/"
+}

data/solutions/generated/hexinsqu_024_941fbce4f50492c6.json

@@ -0,0 +1,206 @@
+{
+  "case": "hexinsqu@24",
+  "container": {
+    "circumradius": 6.219918586523657,
+    "orientation_radians": 0.0,
+    "side_length": 8.796293221918246,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "hexinsqu@24",
+    "credit": "Jonathan Viquerat",
+    "date": "April 2026",
+    "family_updated": "4/28/26",
+    "metric_expression": "8.795+",
+    "metric_symbol": "s",
+    "metric_value": 8.795,
+    "reference_text": "s = 8.795+ | Found by Jonathan Viquerat | in April 2026.",
+    "source_image": "24.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/24.png",
+    "source_page": "https://erich-friedman.github.io/packing/hexinsqu/",
+    "title": "Hexagons in Squares"
+  },
+  "item": {
+    "circumradius": 1.0000000000000002,
+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "hexinsqu@24",
+      "credit": "Jonathan Viquerat",
+      "date": "April 2026",
+      "family_updated": "4/28/26",
+      "metric_expression": "8.795+",
+      "metric_symbol": "s",
+      "metric_value": 8.795,
+      "reference_text": "s = 8.795+ | Found by Jonathan Viquerat | in April 2026.",
+      "source_image": "24.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/24.png",
+      "source_page": "https://erich-friedman.github.io/packing/hexinsqu/",
+      "title": "Hexagons in Squares"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 5.93257010359674,
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+      "y": 4.8742560475230885
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+      "x": 1.9522352413371584,
+      "y": 0.7274180542022084
+    },
+    {
+      "id": 16,
+      "rotation_radians": 2.7753459259304236,
+      "x": -1.174005167136654,
+      "y": -3.6393794921190588
+    },
+    {
+      "id": 17,
+      "rotation_radians": 4.867226430655346,
+      "x": -4.870113971564976,
+      "y": 0.05653988916895529
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.7256380602218475,
+      "x": -3.63839726044839,
+      "y": -1.1753692758016556
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.6790767844405831,
+      "x": -1.0675767818665798,
+      "y": -1.0673738272997746
+    },
+    {
+      "id": 20,
+      "rotation_radians": 2.790529385980945,
+      "x": -0.5116965598563241,
+      "y": 3.193823933294465
+    },
+    {
+      "id": 21,
+      "rotation_radians": 2.7845301281991337,
+      "x": -0.9626439021367643,
+      "y": 1.5112055865123362
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.7262685779144946,
+      "x": -2.2992445356584263,
+      "y": 0.16440599347790744
+    },
+    {
+      "id": 23,
+      "rotation_radians": 5.927284841374064,
+      "x": 0.7196082120177724,
+      "y": 1.960431030200583
+    },
+    {
+      "id": 24,
+      "rotation_radians": 3.8206564458439596,
+      "x": 0.16503554494200573,
+      "y": -2.2983778910790282
+    }
+  ],
+  "problem": "24 equal items for Hexagons in Squares",
+  "setup": "hexinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/hexinsqu/24.png",
+  "source_page": "https://erich-friedman.github.io/packing/hexinsqu/"
+}

data/solutions/generated/hexinsqu_025_d89d09725d796421.json

@@ -0,0 +1,212 @@
+{
+  "case": "hexinsqu@25",
+  "container": {
+    "circumradius": 6.437509629050764,
+    "orientation_radians": 0.0,
+    "side_length": 9.104013425310981,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "hexinsqu@25",
+    "credit": "Jonathan Viquerat",
+    "date": "April 2026",
+    "family_updated": "4/28/26",
+    "metric_expression": "30(4\u221a3\u20133)/13 = 9.065+",
+    "metric_symbol": "s",
+    "metric_value": 9.065,
+    "reference_text": "s = 30(4\u221a3\u20133)/13 = 9.065+ | Found by Jonathan Viquerat | in April 2026.",
+    "source_image": "25.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/25.png",
+    "source_page": "https://erich-friedman.github.io/packing/hexinsqu/",
+    "title": "Hexagons in Squares"
+  },
+  "item": {
+    "circumradius": 1.0000000000000002,
+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "hexinsqu@25",
+      "credit": "Jonathan Viquerat",
+      "date": "April 2026",
+      "family_updated": "4/28/26",
+      "metric_expression": "30(4\u221a3\u20133)/13 = 9.065+",
+      "metric_symbol": "s",
+      "metric_value": 9.065,
+      "reference_text": "s = 30(4\u221a3\u20133)/13 = 9.065+ | Found by Jonathan Viquerat | in April 2026.",
+      "source_image": "25.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/25.png",
+      "source_page": "https://erich-friedman.github.io/packing/hexinsqu/",
+      "title": "Hexagons in Squares"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/hexinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 4.449497435763409,
+      "x": -2.6530181578098566,
+      "y": -0.10938276812361925
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+      "y": -3.8048464160637527
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+  ],
+  "problem": "25 equal items for Hexagons in Squares",
+  "setup": "hexinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/hexinsqu/25.png",
+  "source_page": "https://erich-friedman.github.io/packing/hexinsqu/"
+}

data/solutions/generated/hexintri_021_6cf726ac83ba7d7f.json

@@ -0,0 +1,188 @@
+{
+  "case": "hexintri@21",
+  "container": {
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+    "orientation_radians": 0.0,
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+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "hexintri@21",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "4/5/26",
+    "metric_expression": "7\u221a3 = 12.1243+",
+    "metric_symbol": "s",
+    "metric_value": 12.1243,
+    "reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |",
+    "source_image": "21.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif",
+    "source_page": "https://erich-friedman.github.io/packing/hexintri/",
+    "title": "Hexagons in Triangles"
+  },
+  "item": {
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+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "hexintri@21",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "4/5/26",
+      "metric_expression": "7\u221a3 = 12.1243+",
+      "metric_symbol": "s",
+      "metric_value": 12.1243,
+      "reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |",
+      "source_image": "21.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif",
+      "source_page": "https://erich-friedman.github.io/packing/hexintri/",
+      "title": "Hexagons in Triangles"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/hexintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "x": -1.0000254706526575,
+      "y": 7.949627308408943e-06
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+  ],
+  "problem": "21 equal items for Hexagons in Triangles",
+  "setup": "hexintri",
+  "source_image": "https://erich-friedman.github.io/packing/hexintri/21.gif",
+  "source_page": "https://erich-friedman.github.io/packing/hexintri/"
+}

data/solutions/generated/octinoct_021_92c4bcf9428983c2.json

@@ -0,0 +1,188 @@
+{
+  "case": "octinoct@21",
+  "container": {
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+    "orientation_radians": 0.0,
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+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "octinoct@21",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/27/26",
+    "metric_expression": "5.19715+",
+    "metric_symbol": "s",
+    "metric_value": 5.19715,
+    "reference_text": "s = 5.19715+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "21.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/octinoct/21.gif",
+    "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+    "title": "Octagons in Octagons"
+  },
+  "item": {
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+    "side_length": 1.0,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "octinoct@21",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/27/26",
+      "metric_expression": "5.19715+",
+      "metric_symbol": "s",
+      "metric_value": 5.19715,
+      "reference_text": "s = 5.19715+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "21.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/octinoct/21.gif",
+      "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+      "title": "Octagons in Octagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/octinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "x": 2.3091562449076544,
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+    {
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+      "rotation_radians": 6.978409263442952e-06,
+      "x": -2.228580382872541,
+      "y": 4.560682323177018
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+  ],
+  "problem": "21 equal items for Octagons in Octagons",
+  "setup": "octinoct",
+  "source_image": "https://erich-friedman.github.io/packing/octinoct/21.gif",
+  "source_page": "https://erich-friedman.github.io/packing/octinoct/"
+}

data/solutions/generated/octinoct_022_b8f2befaa2d4a75e.json

@@ -0,0 +1,194 @@
+{
+  "case": "octinoct@22",
+  "container": {
+    "circumradius": 7.000589663177571,
+    "orientation_radians": 0.0,
+    "side_length": 5.358019361768721,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "octinoct@22",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/27/26",
+    "metric_expression": "5.35750+",
+    "metric_symbol": "s",
+    "metric_value": 5.3575,
+    "reference_text": "s = 5.35750+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "22.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/octinoct/22.gif",
+    "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+    "title": "Octagons in Octagons"
+  },
+  "item": {
+    "circumradius": 1.3065629648763766,
+    "side_length": 1.0,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "octinoct@22",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/27/26",
+      "metric_expression": "5.35750+",
+      "metric_symbol": "s",
+      "metric_value": 5.3575,
+      "reference_text": "s = 5.35750+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "22.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/octinoct/22.gif",
+      "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+      "title": "Octagons in Octagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/octinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "id": 1,
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+    {
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+    {
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+      "rotation_radians": -1.2890708267210215e-05,
+      "x": -0.20765600112515012,
+      "y": -5.608000386692329
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+  ],
+  "problem": "22 equal items for Octagons in Octagons",
+  "setup": "octinoct",
+  "source_image": "https://erich-friedman.github.io/packing/octinoct/22.gif",
+  "source_page": "https://erich-friedman.github.io/packing/octinoct/"
+}

data/solutions/generated/octinoct_023_d6528e8801e36ce0.json

@@ -0,0 +1,200 @@
+{
+  "case": "octinoct@23",
+  "container": {
+    "circumradius": 7.074156474460484,
+    "orientation_radians": 0.0,
+    "side_length": 5.414324961468521,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "octinoct@23",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/27/26",
+    "metric_expression": "5.41440+",
+    "metric_symbol": "s",
+    "metric_value": 5.4144,
+    "reference_text": "s = 5.41440+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "23.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/octinoct/23.gif",
+    "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+    "title": "Octagons in Octagons"
+  },
+  "item": {
+    "circumradius": 1.3065629648763766,
+    "side_length": 1.0,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "octinoct@23",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/27/26",
+      "metric_expression": "5.41440+",
+      "metric_symbol": "s",
+      "metric_value": 5.4144,
+      "reference_text": "s = 5.41440+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "23.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/octinoct/23.gif",
+      "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+      "title": "Octagons in Octagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/octinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+    {
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+      "y": 4.620568850100944
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+    {
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+    {
+      "id": 23,
+      "rotation_radians": 3.1416106806734767,
+      "x": 1.8493028780205083,
+      "y": 5.000626067025402
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+  ],
+  "problem": "23 equal items for Octagons in Octagons",
+  "setup": "octinoct",
+  "source_image": "https://erich-friedman.github.io/packing/octinoct/23.gif",
+  "source_page": "https://erich-friedman.github.io/packing/octinoct/"
+}

data/solutions/generated/octinoct_024_a34ac6a3c52f70df.json

@@ -0,0 +1,206 @@
+{
+  "case": "octinoct@24",
+  "container": {
+    "circumradius": 7.257471709325863,
+    "orientation_radians": 0.0,
+    "side_length": 5.554628368034713,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "octinoct@24",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/27/26",
+    "metric_expression": "5.55464+",
+    "metric_symbol": "s",
+    "metric_value": 5.55464,
+    "reference_text": "s = 5.55464+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "24.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/octinoct/24.gif",
+    "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+    "title": "Octagons in Octagons"
+  },
+  "item": {
+    "circumradius": 1.3065629648763766,
+    "side_length": 1.0,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "octinoct@24",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/27/26",
+      "metric_expression": "5.55464+",
+      "metric_symbol": "s",
+      "metric_value": 5.55464,
+      "reference_text": "s = 5.55464+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "24.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/octinoct/24.gif",
+      "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+      "title": "Octagons in Octagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/octinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "id": 1,
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+    {
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+    {
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+      "rotation_radians": 0.7853957059929876,
+      "x": 4.555075737923532,
+      "y": 3.3697662269535447
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+  ],
+  "problem": "24 equal items for Octagons in Octagons",
+  "setup": "octinoct",
+  "source_image": "https://erich-friedman.github.io/packing/octinoct/24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/octinoct/"
+}

data/solutions/generated/octinoct_025_113492960b7e7dce.json

@@ -0,0 +1,212 @@
+{
+  "case": "octinoct@25",
+  "container": {
+    "circumradius": 7.394267573806387,
+    "orientation_radians": 0.0,
+    "side_length": 5.659327389940226,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "octinoct@25",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/27/26",
+    "metric_expression": "5.65593+",
+    "metric_symbol": "s",
+    "metric_value": 5.65593,
+    "reference_text": "s = 5.65593+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "25.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/octinoct/25.gif",
+    "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+    "title": "Octagons in Octagons"
+  },
+  "item": {
+    "circumradius": 1.3065629648763766,
+    "side_length": 1.0,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "octinoct@25",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/27/26",
+      "metric_expression": "5.65593+",
+      "metric_symbol": "s",
+      "metric_value": 5.65593,
+      "reference_text": "s = 5.65593+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "25.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/octinoct/25.gif",
+      "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+      "title": "Octagons in Octagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/octinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "rotation_radians": 2.3329973843458612e-05,
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+    {
+      "id": 25,
+      "rotation_radians": 7.06140528078519e-05,
+      "x": 0.6358013773742742,
+      "y": -3.737851068078261
+    }
+  ],
+  "problem": "25 equal items for Octagons in Octagons",
+  "setup": "octinoct",
+  "source_image": "https://erich-friedman.github.io/packing/octinoct/25.gif",
+  "source_page": "https://erich-friedman.github.io/packing/octinoct/"
+}

data/solutions/generated/octinoct_026_581188c4895e4037.json

@@ -0,0 +1,218 @@
+{
+  "case": "octinoct@26",
+  "container": {
+    "circumradius": 7.504266445326936,
+    "orientation_radians": 0.0,
+    "side_length": 5.743516881359766,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "octinoct@26",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/27/26",
+    "metric_expression": "5.73940+",
+    "metric_symbol": "s",
+    "metric_value": 5.7394,
+    "reference_text": "s = 5.73940+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "26.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/octinoct/26.gif",
+    "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+    "title": "Octagons in Octagons"
+  },
+  "item": {
+    "circumradius": 1.3065629648763766,
+    "side_length": 1.0,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "octinoct@26",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/27/26",
+      "metric_expression": "5.73940+",
+      "metric_symbol": "s",
+      "metric_value": 5.7394,
+      "reference_text": "s = 5.73940+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "26.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/octinoct/26.gif",
+      "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+      "title": "Octagons in Octagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/octinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "id": 1,
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+    {
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+    {
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+    {
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+    {
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+      "y": 0.3887502047479285
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+    {
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+      "rotation_radians": 0.785395382263092,
+      "x": -2.189454752619741,
+      "y": -5.290765587537986
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+    {
+      "id": 26,
+      "rotation_radians": 0.7541278022609171,
+      "x": -4.919882721782195,
+      "y": 2.8634103681353813
+    }
+  ],
+  "problem": "26 equal items for Octagons in Octagons",
+  "setup": "octinoct",
+  "source_image": "https://erich-friedman.github.io/packing/octinoct/26.gif",
+  "source_page": "https://erich-friedman.github.io/packing/octinoct/"
+}

data/solutions/generated/octinoct_027_25c7f85bc0b15209.json

@@ -0,0 +1,224 @@
+{
+  "case": "octinoct@27",
+  "container": {
+    "circumradius": 7.59533034725261,
+    "orientation_radians": 0.0,
+    "side_length": 5.813214174466716,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "octinoct@27",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/27/26",
+    "metric_expression": "5.81238+",
+    "metric_symbol": "s",
+    "metric_value": 5.81238,
+    "reference_text": "s = 5.81238+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "27.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/octinoct/27.gif",
+    "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+    "title": "Octagons in Octagons"
+  },
+  "item": {
+    "circumradius": 1.3065629648763766,
+    "side_length": 1.0,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "octinoct@27",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/27/26",
+      "metric_expression": "5.81238+",
+      "metric_symbol": "s",
+      "metric_value": 5.81238,
+      "reference_text": "s = 5.81238+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "27.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/octinoct/27.gif",
+      "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+      "title": "Octagons in Octagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/octinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "id": 1,
+      "rotation_radians": 5.497788183226797,
+      "x": 0.09492511989680884,
+      "y": -6.249407967499408
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+      "y": -0.776878026654066
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+    {
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+      "rotation_radians": 1.5707935789543368,
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+      "y": -5.392634214861737
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+      "rotation_radians": 1.5760967466755464,
+      "x": 2.5378258433761354,
+      "y": 2.7488513132569423
+    },
+    {
+      "id": 18,
+      "rotation_radians": 4.720929148512929,
+      "x": -2.4542659081461036,
+      "y": -2.8953857484067966
+    },
+    {
+      "id": 19,
+      "rotation_radians": 6.283187276116029,
+      "x": -5.3532674174145845,
+      "y": -2.232770245518803
+    },
+    {
+      "id": 20,
+      "rotation_radians": 3.9270037003705576,
+      "x": -2.196608111460055,
+      "y": 5.362955613503642
+    },
+    {
+      "id": 21,
+      "rotation_radians": 6.283178614369351,
+      "x": 6.192385520359506,
+      "y": -0.23262710822111485
+    },
+    {
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+      "rotation_radians": 5.497792128774849,
+      "x": 2.325063945798523,
+      "y": -5.324637033943778
+    },
+    {
+      "id": 23,
+      "rotation_radians": 3.9269939286257602,
+      "x": -4.432722917950031,
+      "y": 4.452606399166264
+    },
+    {
+      "id": 24,
+      "rotation_radians": 3.141608505242548,
+      "x": 2.32257746105828,
+      "y": 5.326702428525041
+    },
+    {
+      "id": 25,
+      "rotation_radians": 3.16034211742628,
+      "x": 4.22656985891618,
+      "y": -1.7870832729783153
+    },
+    {
+      "id": 26,
+      "rotation_radians": 4.721043752453188,
+      "x": 3.462604221088771,
+      "y": 0.516813984622734
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.8042443034222917,
+      "x": -0.1880545325093968,
+      "y": -3.7434322050456705
+    }
+  ],
+  "problem": "27 equal items for Octagons in Octagons",
+  "setup": "octinoct",
+  "source_image": "https://erich-friedman.github.io/packing/octinoct/27.gif",
+  "source_page": "https://erich-friedman.github.io/packing/octinoct/"
+}

data/solutions/generated/octinoct_028_f8d9c8a9f9a38d45.json

@@ -0,0 +1,230 @@
+{
+  "case": "octinoct@28",
+  "container": {
+    "circumradius": 7.615311619146363,
+    "orientation_radians": 0.0,
+    "side_length": 5.828507177889359,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "octinoct@28",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/27/26",
+    "metric_expression": "3+2\u221a2 = 5.82842+",
+    "metric_symbol": "s",
+    "metric_value": 5.82842,
+    "reference_text": "s = 3+2\u221a2 = 5.82842+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "28.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/octinoct/28.gif",
+    "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+    "title": "Octagons in Octagons"
+  },
+  "item": {
+    "circumradius": 1.3065629648763766,
+    "side_length": 1.0,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000200001000001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "octinoct@28",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/27/26",
+      "metric_expression": "3+2\u221a2 = 5.82842+",
+      "metric_symbol": "s",
+      "metric_value": 5.82842,
+      "reference_text": "s = 3+2\u221a2 = 5.82842+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "28.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/octinoct/28.gif",
+      "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+      "title": "Octagons in Octagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/octinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
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+  "problem": "28 equal items for Octagons in Octagons",
+  "setup": "octinoct",
+  "source_image": "https://erich-friedman.github.io/packing/octinoct/28.gif",
+  "source_page": "https://erich-friedman.github.io/packing/octinoct/"
+}

data/solutions/generated/octinoct_029_30789c6bb8fd99b7.json

@@ -0,0 +1,236 @@
+{
+  "case": "octinoct@29",
+  "container": {
+    "circumradius": 7.915124590620668,
+    "orientation_radians": 0.0,
+    "side_length": 6.0579740918720875,
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+    "type": "regular_polygon"
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+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "octinoct@29",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/27/26",
+    "metric_expression": "6.05746+",
+    "metric_symbol": "s",
+    "metric_value": 6.05746,
+    "reference_text": "s = 6.05746+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "29.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/octinoct/29.gif",
+    "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+    "title": "Octagons in Octagons"
+  },
+  "item": {
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+    "sides": 8,
+    "type": "regular_polygon"
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+      "case": "octinoct@29",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/27/26",
+      "metric_expression": "6.05746+",
+      "metric_symbol": "s",
+      "metric_value": 6.05746,
+      "reference_text": "s = 6.05746+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "29.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/octinoct/29.gif",
+      "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+      "title": "Octagons in Octagons"
+    },
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+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/octinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
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+      "y": 4.95850629054105
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+  ],
+  "problem": "29 equal items for Octagons in Octagons",
+  "setup": "octinoct",
+  "source_image": "https://erich-friedman.github.io/packing/octinoct/29.gif",
+  "source_page": "https://erich-friedman.github.io/packing/octinoct/"
+}

data/solutions/generated/octinoct_030_1a16dc8a4d741008.json

@@ -0,0 +1,242 @@
+{
+  "case": "octinoct@30",
+  "container": {
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+    "orientation_radians": 0.0,
+    "side_length": 6.154794261303532,
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+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "octinoct@30",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/27/26",
+    "metric_expression": "6.15432+",
+    "metric_symbol": "s",
+    "metric_value": 6.15432,
+    "reference_text": "s = 6.15432+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "30.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/octinoct/30.gif",
+    "source_page": "https://erich-friedman.github.io/packing/octinoct/",
+    "title": "Octagons in Octagons"
+  },
+  "item": {
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+      "case": "octinoct@30",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/27/26",
+      "metric_expression": "6.15432+",
+      "metric_symbol": "s",
+      "metric_value": 6.15432,
+      "reference_text": "s = 6.15432+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "30.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/octinoct/30.gif",
+      "source_page": "https://erich-friedman.github.io/packing/octinoct/",
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+    },
+    "generator": "polygon_packer_c",
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+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/octinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
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+      "rotation_radians": -0.7854108039938092,
+      "x": -0.8163657600728035,
+      "y": 4.459996509833742
+    },
+    {
+      "id": 28,
+      "rotation_radians": -1.661503676552794e-05,
+      "x": 1.1794865396797923e-05,
+      "y": 6.7350286820909355
+    },
+    {
+      "id": 29,
+      "rotation_radians": -1.439807534039132e-05,
+      "x": 2.2300198968421148,
+      "y": 5.8099350235240435
+    },
+    {
+      "id": 30,
+      "rotation_radians": -8.538692956654813e-06,
+      "x": 4.461022414535396,
+      "y": 4.887211394230514
+    }
+  ],
+  "problem": "30 equal items for Octagons in Octagons",
+  "setup": "octinoct",
+  "source_image": "https://erich-friedman.github.io/packing/octinoct/30.gif",
+  "source_page": "https://erich-friedman.github.io/packing/octinoct/"
+}

data/solutions/generated/penincir_021_b713bb4909b828e8.json

@@ -0,0 +1,185 @@
+{
+  "case": "penincir@21",
+  "container": {
+    "radius": 3.930338682033069,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "penincir@21",
+    "credit": "Cyril Summerfield",
+    "date": "April 2026",
+    "family_updated": "4/13/26",
+    "metric_expression": "3.90735+",
+    "metric_symbol": "r",
+    "metric_value": 3.90735,
+    "reference_text": "r = 3.90735+ | Found by Cyril Summerfield | in April 2026.",
+    "source_image": "21.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/penincir/21.png",
+    "source_page": "https://erich-friedman.github.io/packing/penincir/",
+    "title": "Pentagons in Circles"
+  },
+  "item": {
+    "circumradius": 0.8506508083520399,
+    "side_length": 1.0,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "penincir@21",
+      "credit": "Cyril Summerfield",
+      "date": "April 2026",
+      "family_updated": "4/13/26",
+      "metric_expression": "3.90735+",
+      "metric_symbol": "r",
+      "metric_value": 3.90735,
+      "reference_text": "r = 3.90735+ | Found by Cyril Summerfield | in April 2026.",
+      "source_image": "21.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/penincir/21.png",
+      "source_page": "https://erich-friedman.github.io/packing/penincir/",
+      "title": "Pentagons in Circles"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/penincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "id": 1,
+      "rotation_radians": -0.024134982253120198,
+      "x": -2.5052356478600597,
+      "y": -1.7899875569344428
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+    {
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+    {
+      "id": 13,
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+      "y": 0.22167079812226745
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+    {
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+      "x": 1.4507386090156857,
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+    {
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+      "rotation_radians": -0.8183032144351778,
+      "x": 2.989299090521316,
+      "y": 0.7848181709730626
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+    {
+      "id": 16,
+      "rotation_radians": 0.31179370118076105,
+      "x": -2.1360109417570254,
+      "y": 2.338483170993703
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.93985356624413,
+      "x": -1.0603545804335173,
+      "y": 1.200655237805827
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.31141187137683607,
+      "x": 0.19390276560845454,
+      "y": 1.7964493716208798
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+    {
+      "id": 19,
+      "rotation_radians": 0.9395442637438224,
+      "x": 0.901213899751428,
+      "y": 2.9845150914689045
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.08302300598622774,
+      "x": 2.3193714821396276,
+      "y": 2.192876911618853
+    },
+    {
+      "id": 21,
+      "rotation_radians": -1.1673746489194439,
+      "x": -0.676949323880265,
+      "y": 3.0707481643152312
+    }
+  ],
+  "problem": "21 equal items for Pentagons in Circles",
+  "setup": "penincir",
+  "source_image": "https://erich-friedman.github.io/packing/penincir/21.png",
+  "source_page": "https://erich-friedman.github.io/packing/penincir/"
+}

data/solutions/generated/peninpen_021_1c71a8b98efbf1a2.json

@@ -0,0 +1,188 @@
+{
+  "case": "peninpen@21",
+  "container": {
+    "circumradius": 4.3933961637073455,
+    "orientation_radians": 0.0,
+    "side_length": 5.164746945011012,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "peninpen@21",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "5.15948+",
+    "metric_symbol": "s",
+    "metric_value": 5.15948,
+    "reference_text": "s = 5.15948+ | Found by Ignacio Vallejo in April 2026.",
+    "source_image": "21.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/peninpen/21.png",
+    "source_page": "https://erich-friedman.github.io/packing/peninpen/",
+    "title": "Pentagons in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.8506508083520399,
+    "side_length": 1.0,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "peninpen@21",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "5.15948+",
+      "metric_symbol": "s",
+      "metric_value": 5.15948,
+      "reference_text": "s = 5.15948+ | Found by Ignacio Vallejo in April 2026.",
+      "source_image": "21.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/peninpen/21.png",
+      "source_page": "https://erich-friedman.github.io/packing/peninpen/",
+      "title": "Pentagons in Pentagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/peninpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.397028218895107e-05,
+      "x": 3.542716728057001,
+      "y": -1.1956123858689668e-06
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+    {
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+      "x": -1.2956626185036004,
+      "y": 2.5895085843890553
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+      "x": -0.09232700751772847,
+      "y": 1.9055009363240227
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+    {
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+      "y": -1.8214336294726978
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+    {
+      "id": 13,
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+      "y": -2.062641297099786
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+    {
+      "id": 14,
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+      "y": -1.333438877633257
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+      "rotation_radians": 1.2638088185675576e-05,
+      "x": 1.0947583408442618,
+      "y": -3.36931972943828
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+    {
+      "id": 16,
+      "rotation_radians": -3.0205189876895802e-05,
+      "x": -0.46507522498454335,
+      "y": -2.8613969604951817
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+    {
+      "id": 17,
+      "rotation_radians": 3.1835662916716426e-06,
+      "x": -2.8661197357775516,
+      "y": -1.1313795165782778
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.6283328470841323,
+      "x": 2.166325843359591,
+      "y": -0.15375892331332083
+    },
+    {
+      "id": 19,
+      "rotation_radians": 2.1761986133661617e-05,
+      "x": -2.8661222132147115,
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+    {
+      "id": 20,
+      "rotation_radians": 0.3745288243736087,
+      "x": 1.064695900254714,
+      "y": 0.9017223055855533
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+    {
+      "id": 21,
+      "rotation_radians": 0.43824537221645077,
+      "x": -1.5303626140563018,
+      "y": 1.1313475656480074
+    }
+  ],
+  "problem": "21 equal items for Pentagons in Pentagons",
+  "setup": "peninpen",
+  "source_image": "https://erich-friedman.github.io/packing/peninpen/21.png",
+  "source_page": "https://erich-friedman.github.io/packing/peninpen/"
+}

data/solutions/generated/peninpen_022_07e217f200bb677e.json

@@ -0,0 +1,194 @@
+{
+  "case": "peninpen@22",
+  "container": {
+    "circumradius": 4.48109149580312,
+    "orientation_radians": 0.0,
+    "side_length": 5.267838990812585,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "peninpen@22",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "5.26740+",
+    "metric_symbol": "s",
+    "metric_value": 5.2674,
+    "reference_text": "s = 5.26740+ | Found by Ignacio Vallejo in April 2026.",
+    "source_image": "22.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/peninpen/22.png",
+    "source_page": "https://erich-friedman.github.io/packing/peninpen/",
+    "title": "Pentagons in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.8506508083520399,
+    "side_length": 1.0,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "peninpen@22",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "5.26740+",
+      "metric_symbol": "s",
+      "metric_value": 5.2674,
+      "reference_text": "s = 5.26740+ | Found by Ignacio Vallejo in April 2026.",
+      "source_image": "22.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/peninpen/22.png",
+      "source_page": "https://erich-friedman.github.io/packing/peninpen/",
+      "title": "Pentagons in Pentagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/peninpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "id": 1,
+      "rotation_radians": 3.5656610694771376e-06,
+      "x": -2.937064016182957,
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+      "x": -2.9232701064214877,
+      "y": -0.5041867041543232
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+    {
+      "id": 12,
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+      "x": -1.3096456636714913,
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+    {
+      "id": 13,
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+      "y": 0.11804475408528063
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+      "y": 1.070122741232727
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+    {
+      "id": 15,
+      "rotation_radians": -1.2544664665159269,
+      "x": 2.851033365522404,
+      "y": 1.0708915888273165
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.5626713206987076,
+      "x": -2.7764363311644593,
+      "y": 0.9719633673950818
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+    {
+      "id": 17,
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+      "x": -1.2603573212771335,
+      "y": 1.4429191807943715
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+    {
+      "id": 18,
+      "rotation_radians": 0.00878890887908165,
+      "x": 0.2091903546551387,
+      "y": 1.6709266377415906
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.0003098729450709277,
+      "x": 0.6663867041104553,
+      "y": 3.3045695683922047
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.007645910609472346,
+      "x": 1.8966654662250435,
+      "y": 2.379827018026491
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.06564601873767298,
+      "x": -2.360991862520845,
+      "y": 2.2881640393900806
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.005382343172488092,
+      "x": -0.8683073599246469,
+      "y": 2.803284077967661
+    }
+  ],
+  "problem": "22 equal items for Pentagons in Pentagons",
+  "setup": "peninpen",
+  "source_image": "https://erich-friedman.github.io/packing/peninpen/22.png",
+  "source_page": "https://erich-friedman.github.io/packing/peninpen/"
+}

data/solutions/generated/peninpen_023_1da2b8cbe37457cd.json

@@ -0,0 +1,200 @@
+{
+  "case": "peninpen@23",
+  "container": {
+    "circumradius": 4.5717171971773904,
+    "orientation_radians": 0.0,
+    "side_length": 5.374375892305501,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "peninpen@23",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "5.34794+",
+    "metric_symbol": "s",
+    "metric_value": 5.34794,
+    "reference_text": "s = 5.34794+ | Found by Ignacio Vallejo in April 2026.",
+    "source_image": "23.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/peninpen/23.png",
+    "source_page": "https://erich-friedman.github.io/packing/peninpen/",
+    "title": "Pentagons in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.8506508083520399,
+    "side_length": 1.0,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "peninpen@23",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "5.34794+",
+      "metric_symbol": "s",
+      "metric_value": 5.34794,
+      "reference_text": "s = 5.34794+ | Found by Ignacio Vallejo in April 2026.",
+      "source_image": "23.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/peninpen/23.png",
+      "source_page": "https://erich-friedman.github.io/packing/peninpen/",
+      "title": "Pentagons in Pentagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/peninpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+  ],
+  "problem": "23 equal items for Pentagons in Pentagons",
+  "setup": "peninpen",
+  "source_image": "https://erich-friedman.github.io/packing/peninpen/23.png",
+  "source_page": "https://erich-friedman.github.io/packing/peninpen/"
+}