diff --git a/app.py b/app.py
index 599fb1e21e58289c71544f6a4c4a6b7d4efd9588..da774462d6731f67301969fb5dce4b1a527bb4b6 100644
--- a/app.py
+++ b/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>
     """
diff --git a/data/records.jsonl b/data/records.jsonl
index 5ab6d2ed90385dc54b65ccd7fec2bdf4bae51569..c9ff16dd0b5ba6e924819c595b694a597dc51778 100644
--- a/data/records.jsonl
+++ b/data/records.jsonl
@@ -38,6 +38,10 @@
 {"case": "cirinhex@18", "density": 0.81913146509039, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc18.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "4 + 2/\u221a3 = 5.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.154, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@18", "credit": "Trivial", "date": "", "family_updated": "7/19/12", "metric_expression": "4 + 2/\u221a3 = 5.154+", "metric_symbol": "s", "metric_value": 5.154, "reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "source_image": "hc18.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc18.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "friedman_source_image": "hc18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "223b1a3f7b7d0e67", "improvement": -0.000759899456760138, "max_boundary_excess": -1.33856736717064e-06, "max_pair_overlap_depth": -1.657857602177515e-05, "metric_expression": "5.15476", "metric_symbol": "s", "metric_value": 5.15475989945676, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.154, "setup": "cirinhex", "side": 5.15475989945676, "solution_path": "data/solutions/generated/cirinhex_018_223b1a3f7b7d0e67.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/223b1a3f7b7d0e67.svg", "tolerance": 1e-08, "verified": true}
 {"case": "cirinhex@19", "density": 0.8646358262071194, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc19.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "4 + 2/\u221a3 = 5.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.154, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@19", "credit": "Trivial", "date": "", "family_updated": "7/19/12", "metric_expression": "4 + 2/\u221a3 = 5.154+", "metric_symbol": "s", "metric_value": 5.154, "reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "source_image": "hc19.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc19.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 4 + 2/\u221a3 = 5.154+ | Trivial. |", "friedman_source_image": "hc19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "78f9327e80d8ab20", "improvement": -0.0007686707015803762, "max_boundary_excess": -6.035946609195264e-07, "max_pair_overlap_depth": -1.6136694912294303e-05, "metric_expression": "5.15477", "metric_symbol": "s", "metric_value": 5.15476867070158, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.154, "setup": "cirinhex", "side": 5.15476867070158, "solution_path": "data/solutions/generated/cirinhex_019_78f9327e80d8ab20.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/78f9327e80d8ab20.svg", "tolerance": 1e-08, "verified": true}
 {"case": "cirinhex@20", "density": 0.7503080962551325, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc20.gif", "friedman_family_updated": "7/19/12", "friedman_metric_expression": "5.676+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.676, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@20", "credit": "David W", "date": "July 2012", "family_updated": "7/19/12", "metric_expression": "5.676+", "metric_symbol": "s", "metric_value": 5.676, "reference_text": "s = 5.676+ | Found by David W. Cantrell | in July 2012.", "source_image": "hc20.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc20.gif", "source_page": "https://erich-friedman.github.io/packing/cirinhex/", "title": "Circles in Hexagons"}, "friedman_reference_text": "s = 5.676+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "hc20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "247c6c06779a7d8b", "improvement": -0.0013304688728235092, "max_boundary_excess": -7.66649728101143e-06, "max_pair_overlap_depth": -2.983410910761819e-05, "metric_expression": "5.67733", "metric_symbol": "s", "metric_value": 5.677330468872824, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.676, "setup": "cirinhex", "side": 5.677330468872824, "solution_path": "data/solutions/generated/cirinhex_020_247c6c06779a7d8b.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/247c6c06779a7d8b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@21", "density": 0.7789652581067265, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc21.gif", "friedman_metric_expression": "5.709+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.709, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@21", "credit": "David W", "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"}, "friedman_reference_text": "s = 5.709+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "hc21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "38040eceeb63c1e3", "improvement": -0.0005199689632231497, "max_boundary_excess": -9.315374129847953e-06, "max_pair_overlap_depth": -3.751451804223649e-05, "metric_expression": "5.70952", "metric_symbol": "s", "metric_value": 5.709519968963223, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.709, "setup": "cirinhex", "side": 5.709519968963223, "solution_path": "data/solutions/generated/cirinhex_021_38040eceeb63c1e3.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/38040eceeb63c1e3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@22", "density": 0.7509530082141859, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc22.gif", "friedman_metric_expression": "5.952+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.952, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@22", "credit": "David W", "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"}, "friedman_reference_text": "s = 5.952+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "hc22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "cd7262f9f7d0d279", "improvement": 0.0001229278734493633, "max_boundary_excess": -6.663138574891647e-06, "max_pair_overlap_depth": -3.268885699680979e-05, "metric_expression": "5.95188", "metric_symbol": "s", "metric_value": 5.951877072126551, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.952, "setup": "cirinhex", "side": 5.951877072126551, "solution_path": "data/solutions/generated/cirinhex_022_cd7262f9f7d0d279.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/cd7262f9f7d0d279.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@23", "density": 0.7694641578789073, "friedman_analytical_or_proved": true, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc23.gif", "friedman_metric_expression": "34/7 + 2/\u221a3 = 6.011+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.011, "friedman_reference": {"analytical_or_proved": true, "case": "cirinhex@23", "credit": "David W", "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"}, "friedman_reference_text": "s = 34/7 + 2/\u221a3 = 6.011+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "hc23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "de2d2aabdc650ad2", "improvement": -0.0009964252593954726, "max_boundary_excess": -6.1931154748950945e-06, "max_pair_overlap_depth": -3.920500316656472e-05, "metric_expression": "6.01200", "metric_symbol": "s", "metric_value": 6.011996425259396, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.011, "setup": "cirinhex", "side": 6.011996425259396, "solution_path": "data/solutions/generated/cirinhex_023_de2d2aabdc650ad2.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/de2d2aabdc650ad2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinhex@24", "density": 0.7747882438352293, "friedman_analytical_or_proved": false, "friedman_credit": "Rob Pratt", "friedman_date": "March 2020", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinhex/hc24.gif", "friedman_metric_expression": "6.117+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.117, "friedman_reference": {"analytical_or_proved": false, "case": "cirinhex@24", "credit": "Rob Pratt", "date": "March 2020", "family_updated": "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"}, "friedman_reference_text": "s = 6.117+ | Found by Rob Pratt | in March 2020.", "friedman_source_image": "hc24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinhex/", "friedman_title": "Circles in Hexagons", "frontend_seed": true, "id": "61a86ae12328c1ca", "improvement": -0.003164603994216364, "max_boundary_excess": -3.4542492504119338e-06, "max_pair_overlap_depth": -2.04098607499148e-05, "metric_expression": "6.12016", "metric_symbol": "s", "metric_value": 6.120164603994216, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.117, "setup": "cirinhex", "side": 6.120164603994216, "solution_path": "data/solutions/generated/cirinhex_024_61a86ae12328c1ca.json", "source_url": "https://erich-friedman.github.io/packing/cirinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/61a86ae12328c1ca.svg", "tolerance": 1e-08, "verified": true}
 {"case": "cirinpen@1", "density": 0.8647965566225578, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.1.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "1.453+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.453, "friedman_reference": {"analytical_or_proved": true, "case": "cirinpen@1", "credit": "Trivial", "date": "", "family_updated": "7/10/12", "metric_expression": "1.453+", "metric_symbol": "s", "metric_value": 1.453, "reference_text": "s = 2tan(36\u00b0) | s = 1.453+ | Trivial.", "source_image": "pent.1.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.1.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 2tan(36\u00b0) | s = 1.453+ | Trivial.", "friedman_source_image": "pent.1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "2249439da521383e", "improvement": -9.321311914245456e-05, "max_boundary_excess": -4.798939718275719e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.45309", "metric_symbol": "s", "metric_value": 1.4530932131191425, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.453, "setup": "cirinpen", "side": 1.4530932131191425, "solution_path": "data/solutions/generated/cirinpen_001_2249439da521383e.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/2249439da521383e.svg", "tolerance": 1e-08, "verified": true}
 {"case": "cirinpen@2", "density": 0.5049856179230741, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.2.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "2.689+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.689, "friedman_reference": {"analytical_or_proved": true, "case": "cirinpen@2", "credit": "Trivial", "date": "", "family_updated": "7/10/12", "metric_expression": "2.689+", "metric_symbol": "s", "metric_value": 2.689, "reference_text": "s = 2tan(36\u00b0) + \u221a5 - 1 | s = 2.689+ | Trivial.", "source_image": "pent.2.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.2.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 2tan(36\u00b0) + \u221a5 - 1 | s = 2.689+ | Trivial.", "friedman_source_image": "pent.2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "042df6c460b769f5", "improvement": -0.00021758992828191381, "max_boundary_excess": -8.904067621218203e-06, "max_pair_overlap_depth": -5.9422400474407056e-05, "metric_expression": "2.68922", "metric_symbol": "s", "metric_value": 2.689217589928282, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.689, "setup": "cirinpen", "side": 2.689217589928282, "solution_path": "data/solutions/generated/cirinpen_002_042df6c460b769f5.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/042df6c460b769f5.svg", "tolerance": 1e-08, "verified": true}
 {"case": "cirinpen@3", "density": 0.6022625992350803, "friedman_analytical_or_proved": false, "friedman_credit": "George Sicherman", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.3.png", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "3.015+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.015, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@3", "credit": "George Sicherman", "date": "July 2012", "family_updated": "7/10/12", "metric_expression": "3.015+", "metric_symbol": "s", "metric_value": 3.015, "reference_text": "s = 3.015+ | Found by George Sicherman | in July 2012.", "source_image": "pent.3.png", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.3.png", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 3.015+ | Found by George Sicherman | in July 2012.", "friedman_source_image": "pent.3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "7afe63c4f78d1c3c", "improvement": -0.0009082861357154748, "max_boundary_excess": -2.348511423333477e-06, "max_pair_overlap_depth": -3.760319804513301e-05, "metric_expression": "3.01591", "metric_symbol": "s", "metric_value": 3.0159082861357156, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.015, "setup": "cirinpen", "side": 3.0159082861357156, "solution_path": "data/solutions/generated/cirinpen_003_7afe63c4f78d1c3c.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7afe63c4f78d1c3c.svg", "tolerance": 1e-08, "verified": true}
@@ -58,6 +62,10 @@
 {"case": "cirinpen@18", "density": 0.7574722105185439, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.18.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "6.586+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.586, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@18", "credit": "David W", "date": "July 2012", "family_updated": "7/10/12", "metric_expression": "6.586+", "metric_symbol": "s", "metric_value": 6.586, "reference_text": "s = 6.586+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.18.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.18.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 6.586+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "34fda06736bbaaf7", "improvement": -0.0012379322999080955, "max_boundary_excess": -8.803338162222119e-06, "max_pair_overlap_depth": -4.5158559001112764e-05, "metric_expression": "6.58724", "metric_symbol": "s", "metric_value": 6.587237932299908, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.586, "setup": "cirinpen", "side": 6.587237932299908, "solution_path": "data/solutions/generated/cirinpen_018_34fda06736bbaaf7.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/34fda06736bbaaf7.svg", "tolerance": 1e-08, "verified": true}
 {"case": "cirinpen@19", "density": 0.7551620068495595, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.19.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "6.777+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.777, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@19", "credit": "David W", "date": "July 2012", "family_updated": "7/10/12", "metric_expression": "6.777+", "metric_symbol": "s", "metric_value": 6.777, "reference_text": "s = 6.777+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.19.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.19.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 6.777+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "dfaba7cef14e53f5", "improvement": -0.0010877146457399789, "max_boundary_excess": -3.911905938958071e-06, "max_pair_overlap_depth": -5.528697090007029e-05, "metric_expression": "6.77809", "metric_symbol": "s", "metric_value": 6.77808771464574, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.777, "setup": "cirinpen", "side": 6.77808771464574, "solution_path": "data/solutions/generated/cirinpen_019_dfaba7cef14e53f5.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/dfaba7cef14e53f5.svg", "tolerance": 1e-08, "verified": true}
 {"case": "cirinpen@20", "density": 0.7572204985441312, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.20.gif", "friedman_family_updated": "7/10/12", "friedman_metric_expression": "6.944+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.944, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@20", "credit": "David W", "date": "July 2012", "family_updated": "7/10/12", "metric_expression": "6.944+", "metric_symbol": "s", "metric_value": 6.944, "reference_text": "s = 6.944+ | Found by David W. Cantrell | in July 2012.", "source_image": "pent.20.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.20.gif", "source_page": "https://erich-friedman.github.io/packing/cirinpen/", "title": "Circles in Pentagons"}, "friedman_reference_text": "s = 6.944+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "d513055d785b23f7", "improvement": -0.0007124298362715109, "max_boundary_excess": -3.4085836122521584e-06, "max_pair_overlap_depth": -2.3984136221066876e-05, "metric_expression": "6.94471", "metric_symbol": "s", "metric_value": 6.9447124298362715, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.944, "setup": "cirinpen", "side": 6.9447124298362715, "solution_path": "data/solutions/generated/cirinpen_020_d513055d785b23f7.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d513055d785b23f7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@21", "density": 0.7549642211430954, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.21.gif", "friedman_metric_expression": "7.107+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.107, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@21", "credit": "David W", "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"}, "friedman_reference_text": "s = 7.107+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "6869ffb03b036ff3", "improvement": -0.01983841780610529, "max_boundary_excess": -5.581345224214829e-06, "max_pair_overlap_depth": -4.1181747931773316e-05, "metric_expression": "7.12684", "metric_symbol": "s", "metric_value": 7.1268384178061055, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.107, "setup": "cirinpen", "side": 7.1268384178061055, "solution_path": "data/solutions/generated/cirinpen_021_6869ffb03b036ff3.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6869ffb03b036ff3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@22", "density": 0.7595290345154431, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.22.gif", "friedman_metric_expression": "7.271+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.271, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@22", "credit": "David W", "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"}, "friedman_reference_text": "s = 7.271+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "ebdb05232e56526e", "improvement": -0.0015983061562394596, "max_boundary_excess": -9.413438632810411e-06, "max_pair_overlap_depth": -6.856237147889743e-05, "metric_expression": "7.27260", "metric_symbol": "s", "metric_value": 7.272598306156239, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.271, "setup": "cirinpen", "side": 7.272598306156239, "solution_path": "data/solutions/generated/cirinpen_022_ebdb05232e56526e.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ebdb05232e56526e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@23", "density": 0.7675010590620791, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.23.gif", "friedman_metric_expression": "7.397+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.397, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@23", "credit": "David W", "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"}, "friedman_reference_text": "s = 7.397+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "0115bd21477c01e6", "improvement": -0.0003280102549396702, "max_boundary_excess": -7.583943801847681e-07, "max_pair_overlap_depth": -3.4243400256706025e-05, "metric_expression": "7.39733", "metric_symbol": "s", "metric_value": 7.39732801025494, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.397, "setup": "cirinpen", "side": 7.39732801025494, "solution_path": "data/solutions/generated/cirinpen_023_0115bd21477c01e6.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0115bd21477c01e6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinpen@24", "density": 0.7719374015643087, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinpen/pent.24.gif", "friedman_metric_expression": "7.534+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.534, "friedman_reference": {"analytical_or_proved": false, "case": "cirinpen@24", "credit": "David W", "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"}, "friedman_reference_text": "s = 7.534+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "pent.24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinpen/", "friedman_title": "Circles in Pentagons", "frontend_seed": true, "id": "9eb26a95274f1d1d", "improvement": -0.0006837609794780874, "max_boundary_excess": -2.468927518428643e-06, "max_pair_overlap_depth": -2.3713548386705696e-05, "metric_expression": "7.53468", "metric_symbol": "s", "metric_value": 7.534683760979478, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.534, "setup": "cirinpen", "side": 7.534683760979478, "solution_path": "data/solutions/generated/cirinpen_024_9eb26a95274f1d1d.json", "source_url": "https://erich-friedman.github.io/packing/cirinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9eb26a95274f1d1d.svg", "tolerance": 1e-08, "verified": true}
 {"case": "cirinsqu@1", "density": 0.7853971453379307, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs1.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@1", "credit": "Trivial", "date": "", "family_updated": "10/9/10", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "cs1.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs1.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "cs1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "329c377d412c468f", "improvement": -1.2962348967526793e-06, "max_boundary_excess": -1.0795596527835016e-07, "max_pair_overlap_depth": 0.0, "metric_expression": "2.00000", "metric_symbol": "s", "metric_value": 2.0000012962348968, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "cirinsqu", "side": 2.0000012962348968, "solution_path": "data/solutions/generated/cirinsqu_001_329c377d412c468f.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/329c377d412c468f.svg", "tolerance": 1e-08, "verified": true}
 {"case": "cirinsqu@2", "density": 0.5390070210000131, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs2.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + \u221a2 = 3.414+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.414, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@2", "credit": "Trivial", "date": "", "family_updated": "10/9/10", "metric_expression": "2 + \u221a2 = 3.414+", "metric_symbol": "s", "metric_value": 3.414, "reference_text": "s = 2 + \u221a2 = 3.414+ | Trivial.", "source_image": "cs2.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs2.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + \u221a2 = 3.414+ | Trivial.", "friedman_source_image": "cs2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "e3bab8445b304ebe", "improvement": -0.00022959896202801033, "max_boundary_excess": -2.1788679802625666e-06, "max_pair_overlap_depth": -1.6252235923275293e-05, "metric_expression": "3.41423", "metric_symbol": "s", "metric_value": 3.414229598962028, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.414, "setup": "cirinsqu", "side": 3.414229598962028, "solution_path": "data/solutions/generated/cirinsqu_002_e3bab8445b304ebe.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e3bab8445b304ebe.svg", "tolerance": 1e-08, "verified": true}
 {"case": "cirinsqu@3", "density": 0.6096071430698954, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs3.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + 1/\u221a2 + \u221a6/2 = 3.931+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.931, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@3", "credit": "Trivial", "date": "", "family_updated": "10/9/10", "metric_expression": "2 + 1/\u221a2 + \u221a6/2 = 3.931+", "metric_symbol": "s", "metric_value": 3.931, "reference_text": "s = 2 + 1/\u221a2 + \u221a6/2 = 3.931+ | Trivial.", "source_image": "cs3.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs3.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + 1/\u221a2 + \u221a6/2 = 3.931+ | Trivial.", "friedman_source_image": "cs3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "63c314af1da3741c", "improvement": -0.0009731189575252763, "max_boundary_excess": -9.540614135605807e-06, "max_pair_overlap_depth": -7.777950709542125e-05, "metric_expression": "3.93197", "metric_symbol": "s", "metric_value": 3.9319731189575253, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.931, "setup": "cirinsqu", "side": 3.9319731189575253, "solution_path": "data/solutions/generated/cirinsqu_003_63c314af1da3741c.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/63c314af1da3741c.svg", "tolerance": 1e-08, "verified": true}
@@ -78,6 +86,10 @@
 {"case": "cirinsqu@18", "density": 0.7546080214690231, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs18.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "2 + 24/\u221a13 = 8.656+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.656, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@18", "credit": "Peikert", "date": "1991", "family_updated": "10/9/10", "metric_expression": "2 + 24/\u221a13 = 8.656+", "metric_symbol": "s", "metric_value": 8.656, "reference_text": "s = 2 + 24/\u221a13 = 8.656+ | Proved by Peikert in 1991.", "source_image": "cs18.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs18.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 2 + 24/\u221a13 = 8.656+ | Proved by Peikert in 1991.", "friedman_source_image": "cs18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "4872462eca76de82", "improvement": -0.0006623865813519814, "max_boundary_excess": -5.585640835636951e-06, "max_pair_overlap_depth": -5.7251545610981225e-05, "metric_expression": "8.65666", "metric_symbol": "s", "metric_value": 8.656662386581353, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.656, "setup": "cirinsqu", "side": 8.656662386581353, "solution_path": "data/solutions/generated/cirinsqu_018_4872462eca76de82.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4872462eca76de82.svg", "tolerance": 1e-08, "verified": true}
 {"case": "cirinsqu@19", "density": 0.752224113091453, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs19.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "8.907+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.907, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@19", "credit": "Peikert", "date": "1991", "family_updated": "10/9/10", "metric_expression": "8.907+", "metric_symbol": "s", "metric_value": 8.907, "reference_text": "s = 8.907+ | Proved by Peikert in 1991.", "source_image": "cs19.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs19.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 8.907+ | Proved by Peikert in 1991.", "friedman_source_image": "cs19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "72fa8cf8e074fd32", "improvement": -0.0009569875134012307, "max_boundary_excess": -9.019564082723974e-06, "max_pair_overlap_depth": -6.564483433546542e-05, "metric_expression": "8.90796", "metric_symbol": "s", "metric_value": 8.907956987513401, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.907, "setup": "cirinsqu", "side": 8.907956987513401, "solution_path": "data/solutions/generated/cirinsqu_019_72fa8cf8e074fd32.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/72fa8cf8e074fd32.svg", "tolerance": 1e-08, "verified": true}
 {"case": "cirinsqu@20", "density": 0.7794478091956536, "friedman_analytical_or_proved": true, "friedman_credit": "Peikert", "friedman_date": "1991", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs20.gif", "friedman_family_updated": "10/9/10", "friedman_metric_expression": "130/17 + 16/17\u221a2 = 8.978+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.978, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@20", "credit": "Peikert", "date": "1991", "family_updated": "10/9/10", "metric_expression": "130/17 + 16/17\u221a2 = 8.978+", "metric_symbol": "s", "metric_value": 8.978, "reference_text": "s = 130/17 + 16/17\u221a2 = 8.978+ | Proved by Peikert in 1991.", "source_image": "cs20.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs20.gif", "source_page": "https://erich-friedman.github.io/packing/cirinsqu/", "title": "Circles in Squares"}, "friedman_reference_text": "s = 130/17 + 16/17\u221a2 = 8.978+ | Proved by Peikert in 1991.", "friedman_source_image": "cs20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "ed16784370181dab", "improvement": -0.0003475703211961445, "max_boundary_excess": -1.3975782322539487e-06, "max_pair_overlap_depth": -5.140241392753708e-05, "metric_expression": "8.97835", "metric_symbol": "s", "metric_value": 8.978347570321196, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.978, "setup": "cirinsqu", "side": 8.978347570321196, "solution_path": "data/solutions/generated/cirinsqu_020_ed16784370181dab.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ed16784370181dab.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@21", "density": 0.7531827030031223, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman Packing Center", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs21.gif", "friedman_metric_expression": "9.358+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.358, "friedman_reference": {"analytical_or_proved": false, "case": "cirinsqu@21", "credit": "Erich Friedman Packing Center", "date": "", "family_updated": "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"}, "friedman_reference_text": "s = 9.358+", "friedman_source_image": "cs21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "65afc927a4d3cb10", "improvement": -0.0011070505635846217, "max_boundary_excess": -6.857662265602471e-06, "max_pair_overlap_depth": -3.291297220409106e-05, "metric_expression": "9.35911", "metric_symbol": "s", "metric_value": 9.359107050563585, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.358, "setup": "cirinsqu", "side": 9.359107050563585, "solution_path": "data/solutions/generated/cirinsqu_021_65afc927a4d3cb10.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/65afc927a4d3cb10.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@22", "density": 0.7716499915329439, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman Packing Center", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs22.gif", "friedman_metric_expression": "9.463+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.463, "friedman_reference": {"analytical_or_proved": false, "case": "cirinsqu@22", "credit": "Erich Friedman Packing Center", "date": "", "family_updated": "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"}, "friedman_reference_text": "s = 9.463+", "friedman_source_image": "cs22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "27d48d864449f174", "improvement": -0.0010297949122062278, "max_boundary_excess": -1.1647620365984324e-06, "max_pair_overlap_depth": -2.796224374757017e-05, "metric_expression": "9.46403", "metric_symbol": "s", "metric_value": 9.464029794912205, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.463, "setup": "cirinsqu", "side": 9.464029794912205, "solution_path": "data/solutions/generated/cirinsqu_022_27d48d864449f174.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/27d48d864449f174.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@23", "density": 0.7628623175184639, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman Packing Center", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs23.gif", "friedman_metric_expression": "2 + 2\u221a2 + 2\u221a6 = 9.727+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.727, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@23", "credit": "Erich Friedman Packing Center", "date": "", "family_updated": "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"}, "friedman_reference_text": "s = 2 + 2\u221a2 + 2\u221a6 = 9.727+", "friedman_source_image": "cs23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "cfa99060ee2203a1", "improvement": -0.005306391434194424, "max_boundary_excess": -1.8298221013957061e-06, "max_pair_overlap_depth": -2.6081243190478887e-05, "metric_expression": "9.73231", "metric_symbol": "s", "metric_value": 9.732306391434195, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.727, "setup": "cirinsqu", "side": 9.732306391434195, "solution_path": "data/solutions/generated/cirinsqu_023_cfa99060ee2203a1.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/cfa99060ee2203a1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "cirinsqu@24", "density": 0.7749295071503051, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman Packing Center", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirinsqu/cs24.gif", "friedman_metric_expression": "6 + \u221a2 + \u221a6 = 9.863+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.863, "friedman_reference": {"analytical_or_proved": true, "case": "cirinsqu@24", "credit": "Erich Friedman Packing Center", "date": "", "family_updated": "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"}, "friedman_reference_text": "s = 6 + \u221a2 + \u221a6 = 9.863+", "friedman_source_image": "cs24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "friedman_title": "Circles in Squares", "frontend_seed": true, "id": "e2eca298edbdb88c", "improvement": -0.0009181131343805049, "max_boundary_excess": -8.506144878683841e-06, "max_pair_overlap_depth": -4.0021533562306644e-05, "metric_expression": "9.86392", "metric_symbol": "s", "metric_value": 9.86391811313438, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.863, "setup": "cirinsqu", "side": 9.86391811313438, "solution_path": "data/solutions/generated/cirinsqu_024_e2eca298edbdb88c.json", "source_url": "https://erich-friedman.github.io/packing/cirinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e2eca298edbdb88c.svg", "tolerance": 1e-08, "verified": true}
 {"case": "cirintri@1", "density": 0.6045962978262086, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct1.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "2\u221a3 = 3.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.464, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@1", "credit": "Trivial", "date": "", "family_updated": "7/19/02", "metric_expression": "2\u221a3 = 3.464+", "metric_symbol": "s", "metric_value": 3.464, "reference_text": "s = 2\u221a3 = 3.464+ | Trivial.", "source_image": "ct1.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct1.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 2\u221a3 = 3.464+ | Trivial.", "friedman_source_image": "ct1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "10a7a380c7f5376a", "improvement": -0.00011161401610815247, "max_boundary_excess": -1.7091087705090047e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "3.46411", "metric_symbol": "s", "metric_value": 3.464111614016108, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.464, "setup": "cirintri", "side": 3.464111614016108, "solution_path": "data/solutions/generated/cirintri_001_10a7a380c7f5376a.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/10a7a380c7f5376a.svg", "tolerance": 1e-08, "verified": true}
 {"case": "cirintri@2", "density": 0.48598475821399, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct2.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "2 + 2\u221a3 = 5.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.464, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@2", "credit": "Trivial", "date": "", "family_updated": "7/19/02", "metric_expression": "2 + 2\u221a3 = 5.464+", "metric_symbol": "s", "metric_value": 5.464, "reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "source_image": "ct2.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct2.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "friedman_source_image": "ct2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "f5cde1b8295da3ad", "improvement": -0.00022144929157175142, "max_boundary_excess": -3.7587277048611867e-06, "max_pair_overlap_depth": -7.068795172848752e-05, "metric_expression": "5.46422", "metric_symbol": "s", "metric_value": 5.464221449291572, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.464, "setup": "cirintri", "side": 5.464221449291572, "solution_path": "data/solutions/generated/cirintri_002_f5cde1b8295da3ad.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f5cde1b8295da3ad.svg", "tolerance": 1e-08, "verified": true}
 {"case": "cirintri@3", "density": 0.7289907317557431, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/cirintri/ct3.gif", "friedman_family_updated": "7/19/02", "friedman_metric_expression": "2 + 2\u221a3 = 5.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.464, "friedman_reference": {"analytical_or_proved": true, "case": "cirintri@3", "credit": "Trivial", "date": "", "family_updated": "7/19/02", "metric_expression": "2 + 2\u221a3 = 5.464+", "metric_symbol": "s", "metric_value": 5.464, "reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "source_image": "ct3.gif", "source_image_url": "https://erich-friedman.github.io/packing/cirintri/ct3.gif", "source_page": "https://erich-friedman.github.io/packing/cirintri/", "title": "Circles in Triangles"}, "friedman_reference_text": "s = 2 + 2\u221a3 = 5.464+ | Trivial.", "friedman_source_image": "ct3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/cirintri/", "friedman_title": "Circles in Triangles", "frontend_seed": true, "id": "fcee9d6e8b7c5ce0", "improvement": -0.000170499845251193, "max_boundary_excess": -1.0755666179917966e-07, "max_pair_overlap_depth": -5.0474041760395494e-05, "metric_expression": "5.46417", "metric_symbol": "s", "metric_value": 5.464170499845252, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.464, "setup": "cirintri", "side": 5.464170499845252, "solution_path": "data/solutions/generated/cirintri_003_fcee9d6e8b7c5ce0.json", "source_url": "https://erich-friedman.github.io/packing/cirintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/fcee9d6e8b7c5ce0.svg", "tolerance": 1e-08, "verified": true}
@@ -138,6 +150,10 @@
 {"case": "domintri@18", "density": 0.8433917909368376, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/18.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "3+4\u221a3 = 9.92820+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.9282, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/23/26", "metric_expression": "3+4\u221a3 = 9.92820+", "metric_symbol": "s", "metric_value": 9.9282, "reference_text": "s = 3+4\u221a3 = 9.92820+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/18.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 3+4\u221a3 = 9.92820+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "286272298adf99a4", "improvement": -0.00035960973454685075, "max_boundary_excess": -4.814371048432239e-06, "max_pair_overlap_depth": -1.8972863250255045e-05, "metric_expression": "9.92856", "metric_symbol": "s", "metric_value": 9.928559609734547, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.9282, "setup": "domintri", "side": 9.928559609734547, "solution_path": "data/solutions/generated/domintri_018_286272298adf99a4.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/286272298adf99a4.svg", "tolerance": 1e-08, "verified": true}
 {"case": "domintri@19", "density": 0.7735444652506167, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/19.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "8+4/\u221a3 = 10.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.3094, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/23/26", "metric_expression": "8+4/\u221a3 = 10.30940+", "metric_symbol": "s", "metric_value": 10.3094, "reference_text": "s = 8+4/\u221a3 = 10.30940+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/19.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 8+4/\u221a3 = 10.30940+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "549d560736459f75", "improvement": -0.34180733668304164, "max_boundary_excess": -1.8670172809952138e-05, "max_pair_overlap_depth": -1.0311598933832045e-05, "metric_expression": "10.65121", "metric_symbol": "s", "metric_value": 10.651207336683042, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 10.3094, "setup": "domintri", "side": 10.651207336683042, "solution_path": "data/solutions/generated/domintri_019_549d560736459f75.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/549d560736459f75.svg", "tolerance": 1e-08, "verified": true}
 {"case": "domintri@20", "density": 0.7733493858543649, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/20.png", "friedman_family_updated": "4/23/26", "friedman_metric_expression": "7+2\u221a3 = 10.46410+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.4641, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@20", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "4/23/26", "metric_expression": "7+2\u221a3 = 10.46410+", "metric_symbol": "s", "metric_value": 10.4641, "reference_text": "s = 7+2\u221a3 = 10.46410+ | Found by Maurizio Morandi | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/domintri/20.png", "source_page": "https://erich-friedman.github.io/packing/domintri/", "title": "Dominoes in Triangles"}, "friedman_reference_text": "s = 7+2\u221a3 = 10.46410+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "1be96e85f810fe3e", "improvement": -0.4651863607413542, "max_boundary_excess": -3.72350908996398e-06, "max_pair_overlap_depth": -7.249978854950712e-05, "metric_expression": "10.92929", "metric_symbol": "s", "metric_value": 10.929286360741354, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 10.4641, "setup": "domintri", "side": 10.929286360741354, "solution_path": "data/solutions/generated/domintri_020_1be96e85f810fe3e.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1be96e85f810fe3e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@21", "density": 0.7704954542050007, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/21.png", "friedman_metric_expression": "2+5\u221a3 = 10.66025+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.66025, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@21", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "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"}, "friedman_reference_text": "s = 2+5\u221a3 = 10.66025+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "de2eca0c1c28a96d", "improvement": -0.5596577659107993, "max_boundary_excess": -3.3920242839708145e-06, "max_pair_overlap_depth": -3.2351846175115995e-05, "metric_expression": "11.21991", "metric_symbol": "s", "metric_value": 11.219907765910799, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 10.66025, "setup": "domintri", "side": 11.219907765910799, "solution_path": "data/solutions/generated/domintri_021_de2eca0c1c28a96d.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/de2eca0c1c28a96d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@22", "density": 0.8205684661731125, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/22.png", "friedman_metric_expression": "4(1+\u221a3) = 10.92820+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.9282, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@22", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "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"}, "friedman_reference_text": "s = 4(1+\u221a3) = 10.92820+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "6301aae692a9ac9b", "improvement": -0.19983821886336273, "max_boundary_excess": -7.931828549005361e-06, "max_pair_overlap_depth": -1.949750011775997e-05, "metric_expression": "11.12804", "metric_symbol": "s", "metric_value": 11.128038218863363, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 10.9282, "setup": "domintri", "side": 11.128038218863363, "solution_path": "data/solutions/generated/domintri_022_6301aae692a9ac9b.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6301aae692a9ac9b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@23", "density": 0.8238455629873455, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/23.png", "friedman_metric_expression": "10+2/\u221a3 = 11.15470+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.1547, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@23", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "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"}, "friedman_reference_text": "s = 10+2/\u221a3 = 11.15470+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "7b6e8b12db0049b9", "improvement": -0.20078516612478836, "max_boundary_excess": -3.686846371587619e-06, "max_pair_overlap_depth": -4.6822971091264876e-05, "metric_expression": "11.35549", "metric_symbol": "s", "metric_value": 11.355485166124788, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 11.1547, "setup": "domintri", "side": 11.355485166124788, "solution_path": "data/solutions/generated/domintri_023_7b6e8b12db0049b9.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7b6e8b12db0049b9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "domintri@24", "density": 0.7994546814908398, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/domintri/24.png", "friedman_metric_expression": "9+4/\u221a3 = 11.30940+", "friedman_metric_symbol": "s", "friedman_metric_value": 11.3094, "friedman_reference": {"analytical_or_proved": true, "case": "domintri@24", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "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"}, "friedman_reference_text": "s = 9+4/\u221a3 = 11.30940+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/domintri/", "friedman_title": "Dominoes in Triangles", "frontend_seed": true, "id": "af99e7edd2e30109", "improvement": -0.46593782822515983, "max_boundary_excess": -2.650568564648374e-06, "max_pair_overlap_depth": -2.5771491973358707e-05, "metric_expression": "11.77534", "metric_symbol": "s", "metric_value": 11.77533782822516, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 11.3094, "setup": "domintri", "side": 11.77533782822516, "solution_path": "data/solutions/generated/domintri_024_af99e7edd2e30109.json", "source_url": "https://erich-friedman.github.io/packing/domintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/af99e7edd2e30109.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexincir@1", "density": 0.826977987261634, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/1.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "r", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@1", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "1", "metric_symbol": "r", "metric_value": 1.0, "reference_text": "r = 1 | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/1.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 1 | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "48f5aa37c90550c8", "improvement": -9.284285680699611e-06, "max_boundary_excess": -6.547655283739573e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_symbol": "r", "metric_value": 1.0000092842856807, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.0, "setup": "hexincir", "side": 2.0000185685713614, "solution_path": "data/solutions/generated/hexincir_001_48f5aa37c90550c8.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/48f5aa37c90550c8.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexincir@2", "density": 0.508894613048892, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/2.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a13/2 = 1.802+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.802, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@2", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "\u221a13/2 = 1.802+", "metric_symbol": "r", "metric_value": 1.802, "reference_text": "r = \u221a13/2 = 1.802+ | Trivial.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/2.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a13/2 = 1.802+ | Trivial.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "3b6bd2554e997adc", "improvement": -0.0008187982614582534, "max_boundary_excess": -1.4989872811899119e-06, "max_pair_overlap_depth": -3.954921521903687e-05, "metric_expression": "1.80282", "metric_symbol": "r", "metric_value": 1.8028187982614583, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.802, "setup": "hexincir", "side": 3.6056375965229166, "solution_path": "data/solutions/generated/hexincir_002_3b6bd2554e997adc.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3b6bd2554e997adc.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexincir@3", "density": 0.6202101203168955, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/3.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "r", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@3", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "2", "metric_symbol": "r", "metric_value": 2.0, "reference_text": "r = 2 | Trivial.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/3.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 2 | Trivial.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "194e619a74e29452", "improvement": -5.624955299809997e-05, "max_boundary_excess": -9.970405754344824e-06, "max_pair_overlap_depth": -7.230141190991447e-05, "metric_expression": "2.00006", "metric_symbol": "r", "metric_value": 2.000056249552998, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "hexincir", "side": 4.000112499105996, "solution_path": "data/solutions/generated/hexincir_003_194e619a74e29452.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/194e619a74e29452.svg", "tolerance": 1e-08, "verified": true}
@@ -158,6 +174,7 @@
 {"case": "hexincir@18", "density": 0.7834006630179079, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a19 = 4.35889+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.35889, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@18", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "\u221a19 = 4.35889+", "metric_symbol": "r", "metric_value": 4.35889, "reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "12eaac899664a007", "improvement": -0.0001945423028058002, "max_boundary_excess": -4.696366953105269e-06, "max_pair_overlap_depth": -1.0490734119961154e-05, "metric_expression": "4.35908", "metric_symbol": "r", "metric_value": 4.3590845423028055, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.35889, "setup": "hexincir", "side": 8.718169084605611, "solution_path": "data/solutions/generated/hexincir_018_12eaac899664a007.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/12eaac899664a007.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexincir@19", "density": 0.8269599994475847, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "\u221a19 = 4.35889+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.35889, "friedman_reference": {"analytical_or_proved": true, "case": "hexincir@19", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "\u221a19 = 4.35889+", "metric_symbol": "r", "metric_value": 4.35889, "reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/19.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = \u221a19 = 4.35889+ | Trivial.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "b4bf200670caf09c", "improvement": -9.681979153608467e-05, "max_boundary_excess": -5.636539265552187e-06, "max_pair_overlap_depth": -6.973398227638761e-06, "metric_expression": "4.35899", "metric_symbol": "r", "metric_value": 4.358986819791536, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.35889, "setup": "hexincir", "side": 8.717973639583072, "solution_path": "data/solutions/generated/hexincir_019_b4bf200670caf09c.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b4bf200670caf09c.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexincir@20", "density": 0.7723857667872704, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/20.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4.62598+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.62598, "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "4.62598+", "metric_symbol": "r", "metric_value": 4.62598, "reference_text": "r = 4.62598+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/hexincir/20.png", "source_page": "https://erich-friedman.github.io/packing/hexincir/", "title": "Hexagons in Circles"}, "friedman_reference_text": "r = 4.62598+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "30108dc5d1ea9a14", "improvement": -0.0015460646281777457, "max_boundary_excess": -1.8288872105642895e-06, "max_pair_overlap_depth": -4.792351042670617e-06, "metric_expression": "4.62753", "metric_symbol": "r", "metric_value": 4.627526064628178, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.62598, "setup": "hexincir", "side": 9.255052129256356, "solution_path": "data/solutions/generated/hexincir_020_30108dc5d1ea9a14.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/30108dc5d1ea9a14.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexincir@21", "density": 0.7917677222663352, "friedman_analytical_or_proved": false, "friedman_credit": "Enea Victor", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexincir/21.png", "friedman_metric_expression": "4.68339+", "friedman_metric_symbol": "r", "friedman_metric_value": 4.68339, "friedman_reference": {"analytical_or_proved": false, "case": "hexincir@21", "credit": "Enea Victor", "date": "April 2026", "family_updated": "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"}, "friedman_reference_text": "r = 4.68339+ | Found by Enea Victor | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexincir/", "friedman_title": "Hexagons in Circles", "frontend_seed": true, "id": "49a047c29bb184c3", "improvement": -1.5457789629635954e-05, "max_boundary_excess": -4.498160996568856e-06, "max_pair_overlap_depth": -3.8704072840012316e-06, "metric_expression": "4.68341", "metric_symbol": "r", "metric_value": 4.68340545778963, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.68339, "setup": "hexincir", "side": 9.36681091557926, "solution_path": "data/solutions/generated/hexincir_021_49a047c29bb184c3.json", "source_url": "https://erich-friedman.github.io/packing/hexincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/49a047c29bb184c3.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexindom@1", "density": 0.433010701548144, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/1.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "\u221a3 = 1.73205+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.73205, "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@1", "credit": "Trivial", "date": "", "family_updated": "4/6/26", "metric_expression": "\u221a3 = 1.73205+", "metric_symbol": "s", "metric_value": 1.73205, "reference_text": "1. | | s = \u221a3 = 1.73205+ | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/1.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "1. | | s = \u221a3 = 1.73205+ | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "899222ca3c83cd8e", "improvement": -4.8082708896668436e-06, "max_boundary_excess": -1.0003297862271054e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.73205", "metric_symbol": "s", "metric_value": 1.7320548082708898, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.73205, "setup": "hexindom", "side": 3.4641096165417795, "solution_path": "data/solutions/generated/hexindom_001_899222ca3c83cd8e.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/899222ca3c83cd8e.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexindom@2", "density": 0.7237057542591544, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/2.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "1.8946+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.8946, "friedman_reference": {"analytical_or_proved": false, "case": "hexindom@2", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/6/26", "metric_expression": "1.8946+", "metric_symbol": "s", "metric_value": 1.8946, "reference_text": "2. | | s = 1.8946+ | Found by Jonathan Viquerat in April 2026.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/2.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "2. | | s = 1.8946+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "419ae881803808e0", "improvement": -0.00011952413629479075, "max_boundary_excess": -6.154031481298006e-06, "max_pair_overlap_depth": -4.420983116036614e-05, "metric_expression": "1.89472", "metric_symbol": "s", "metric_value": 1.8947195241362949, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.8946, "setup": "hexindom", "side": 3.7894390482725897, "solution_path": "data/solutions/generated/hexindom_002_419ae881803808e0.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/419ae881803808e0.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexindom@3", "density": 0.6059845041872388, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexindom/3.png", "friedman_family_updated": "4/6/26", "friedman_metric_expression": "6\u20132\u221a3 = 2.53589+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.53589, "friedman_reference": {"analytical_or_proved": true, "case": "hexindom@3", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/6/26", "metric_expression": "6\u20132\u221a3 = 2.53589+", "metric_symbol": "s", "metric_value": 2.53589, "reference_text": "3. | | s = 6\u20132\u221a3 = 2.53589+ | Found by Jonathan Viquerat in April 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/hexindom/3.png", "source_page": "https://erich-friedman.github.io/packing/hexindom/", "title": "Hexagons in Dominoes"}, "friedman_reference_text": "3. | | s = 6\u20132\u221a3 = 2.53589+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexindom/", "friedman_title": "Hexagons in Dominoes", "frontend_seed": true, "id": "b8984cccc8c8714d", "improvement": -6.074031198854968e-05, "max_boundary_excess": -1.3815485928603266e-06, "max_pair_overlap_depth": -3.5690372763075295e-05, "metric_expression": "2.53595", "metric_symbol": "s", "metric_value": 2.5359507403119887, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.53589, "setup": "hexindom", "side": 5.0719014806239775, "solution_path": "data/solutions/generated/hexindom_003_b8984cccc8c8714d.json", "source_url": "https://erich-friedman.github.io/packing/hexindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b8984cccc8c8714d.svg", "tolerance": 1e-08, "verified": true}
@@ -198,6 +215,17 @@
 {"case": "hexinhex@18", "density": 0.8437116836701195, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "8/\u221a3 = 4.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.618, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@18", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "4/15/26", "metric_expression": "8/\u221a3 = 4.618+", "metric_symbol": "s", "metric_value": 4.618, "reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "e320d39029a817c1", "improvement": -0.0009070314872570151, "max_boundary_excess": 1.0443685916789865e-09, "max_pair_overlap_depth": -3.080790913889686e-05, "metric_expression": "4.61891", "metric_symbol": "s", "metric_value": 4.618907031487257, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.618, "setup": "hexinhex", "side": 4.618907031487257, "solution_path": "data/solutions/generated/hexinhex_018_e320d39029a817c1.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e320d39029a817c1.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexinhex@19", "density": 0.8905854861904853, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "8/\u221a3 = 4.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.618, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@19", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "4/15/26", "metric_expression": "8/\u221a3 = 4.618+", "metric_symbol": "s", "metric_value": 4.618, "reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexinhex/19.gif", "source_page": "https://erich-friedman.github.io/packing/hexinhex/", "title": "Hexagons in Hexagons"}, "friedman_reference_text": "18-19. | | s = 8/\u221a3 = 4.618+ | Found by Maurizio Morandi | in April 2015. |", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4b11a1a09f2a5b70", "improvement": -0.0009046166982376036, "max_boundary_excess": -8.772589960788204e-06, "max_pair_overlap_depth": -3.612300978728111e-05, "metric_expression": "4.61890", "metric_symbol": "s", "metric_value": 4.618904616698238, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.618, "setup": "hexinhex", "side": 4.618904616698238, "solution_path": "data/solutions/generated/hexinhex_019_4b11a1a09f2a5b70.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4b11a1a09f2a5b70.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexinhex@20", "density": 0.7999496824068819, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "friedman_family_updated": "4/15/26", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@20", "credit": "Trivial", "date": "", "family_updated": "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"}, "friedman_reference_text": "20-21. | | s = 5 | Trivial. | |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "2830e2dec38749ef", "improvement": -0.00015724989644283482, "max_boundary_excess": -5.445035556179186e-06, "max_pair_overlap_depth": -1.6551811964360397e-06, "metric_expression": "5.00016", "metric_symbol": "s", "metric_value": 5.000157249896443, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "hexinhex", "side": 5.000157249896443, "solution_path": "data/solutions/generated/hexinhex_020_2830e2dec38749ef.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/2830e2dec38749ef.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@21", "density": 0.8399773177134815, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/21.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@21", "credit": "Trivial", "date": "", "family_updated": "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"}, "friedman_reference_text": "20-21. | | s = 5 | Trivial. | |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4a431b677be571c9", "improvement": -6.750817229672634e-05, "max_boundary_excess": -1.5389132812752791e-06, "max_pair_overlap_depth": -3.519050301936666e-06, "metric_expression": "5.00007", "metric_symbol": "s", "metric_value": 5.000067508172297, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "hexinhex", "side": 5.000067508172297, "solution_path": "data/solutions/generated/hexinhex_021_4a431b677be571c9.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4a431b677be571c9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@22", "density": 0.7873804951730353, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/22.gif", "friedman_metric_expression": "(39+8\u221a3)/10 = 5.285+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.285, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@22", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "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"}, "friedman_reference_text": "22. | | s = (39+8\u221a3)/10 = 5.285+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "003a713177cb171c", "improvement": -0.0009008698048820207, "max_boundary_excess": -4.575542655386671e-06, "max_pair_overlap_depth": -1.0001604064946434e-05, "metric_expression": "5.28590", "metric_symbol": "s", "metric_value": 5.285900869804882, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.285, "setup": "hexinhex", "side": 5.285900869804882, "solution_path": "data/solutions/generated/hexinhex_022_003a713177cb171c.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/003a713177cb171c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@23", "density": 0.7758097131766583, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/23.gif", "friedman_metric_expression": "5.400+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.4, "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@23", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "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"}, "friedman_reference_text": "23. | | s = 5.400+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4a3a3fd07554d52b", "improvement": -0.04485491175923784, "max_boundary_excess": -2.3299387411464314e-06, "max_pair_overlap_depth": -5.1241164786830495e-05, "metric_expression": "5.44485", "metric_symbol": "s", "metric_value": 5.444854911759238, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.4, "setup": "hexinhex", "side": 5.444854911759238, "solution_path": "data/solutions/generated/hexinhex_023_4a3a3fd07554d52b.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4a3a3fd07554d52b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@24", "density": 0.797738483588153, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2015", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/24.gif", "friedman_metric_expression": "19\u221a3/6 = 5.484+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.484, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@24", "credit": "Maurizio Morandi", "date": "April 2015", "family_updated": "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"}, "friedman_reference_text": "24. | | s = 19\u221a3/6 = 5.484+ | Found by Maurizio Morandi | in April 2015.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "c96649ff013a9455", "improvement": -0.00098379990619879, "max_boundary_excess": -9.588312731744032e-06, "max_pair_overlap_depth": -4.485524381903083e-05, "metric_expression": "5.48498", "metric_symbol": "s", "metric_value": 5.484983799906199, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.484, "setup": "hexinhex", "side": 5.484983799906199, "solution_path": "data/solutions/generated/hexinhex_024_c96649ff013a9455.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c96649ff013a9455.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@25", "density": 0.7898226009433017, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/25.gif", "friedman_metric_expression": "5.62390+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.6239, "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@25", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "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"}, "friedman_reference_text": "25. | | s = 5.62390+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4ac680367830872b", "improvement": -0.002171223468265815, "max_boundary_excess": -1.8833146044517865e-07, "max_pair_overlap_depth": -2.7316686140865798e-05, "metric_expression": "5.62607", "metric_symbol": "s", "metric_value": 5.626071223468266, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.6239, "setup": "hexinhex", "side": 5.626071223468266, "solution_path": "data/solutions/generated/hexinhex_025_4ac680367830872b.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4ac680367830872b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@26", "density": 0.7947867651922452, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/26.gif", "friedman_metric_expression": "5.70972+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.70972, "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@26", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "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"}, "friedman_reference_text": "26. | | s = 5.70972+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "0a420d645748969b", "improvement": -0.009823411865984788, "max_boundary_excess": -9.859507481158646e-07, "max_pair_overlap_depth": -3.367354169281356e-05, "metric_expression": "5.71954", "metric_symbol": "s", "metric_value": 5.719543411865985, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.70972, "setup": "hexinhex", "side": 5.719543411865985, "solution_path": "data/solutions/generated/hexinhex_026_0a420d645748969b.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0a420d645748969b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@27", "density": 0.82621496088318, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/27.gif", "friedman_metric_expression": "5.71415+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.71415, "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@27", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "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"}, "friedman_reference_text": "27. | | s = 5.71415+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "4e9628a9f49def85", "improvement": -0.0024177469948583052, "max_boundary_excess": -4.56387472302006e-06, "max_pair_overlap_depth": -5.6693937127594296e-05, "metric_expression": "5.71657", "metric_symbol": "s", "metric_value": 5.716567746994858, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.71415, "setup": "hexinhex", "side": 5.716567746994858, "solution_path": "data/solutions/generated/hexinhex_027_4e9628a9f49def85.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4e9628a9f49def85.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@28", "density": 0.7877627529922571, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Kravatsky et al", "friedman_date": "February 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/28.gif", "friedman_metric_expression": "5.90893+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.90893, "friedman_reference": {"analytical_or_proved": false, "case": "hexinhex@28", "credit": "Alex Kravatsky et al", "date": "February 2026", "family_updated": "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"}, "friedman_reference_text": "28. | | s = 5.90893+ | Found by Alex Kravatsky et al | in February 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "59dc7d7850663cbb", "improvement": -0.052923423059089814, "max_boundary_excess": -8.181764566584125e-06, "max_pair_overlap_depth": -1.7101544528386192e-05, "metric_expression": "5.96185", "metric_symbol": "s", "metric_value": 5.96185342305909, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.90893, "setup": "hexinhex", "side": 5.96185342305909, "solution_path": "data/solutions/generated/hexinhex_028_59dc7d7850663cbb.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/59dc7d7850663cbb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@29", "density": 0.8055194808067645, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@29", "credit": "Trivial", "date": "", "family_updated": "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"}, "friedman_reference_text": "29-31. | | s = 6 | Trivial. |", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "dba25a591b8992bc", "improvement": -0.00013435185279675466, "max_boundary_excess": -5.231638156342025e-06, "max_pair_overlap_depth": -6.307567709251671e-06, "metric_expression": "6.00013", "metric_symbol": "s", "metric_value": 6.000134351852797, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.0, "setup": "hexinhex", "side": 6.000134351852797, "solution_path": "data/solutions/generated/hexinhex_029_dba25a591b8992bc.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/dba25a591b8992bc.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@30", "density": 0.8333115277207207, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@30", "credit": "Trivial", "date": "", "family_updated": "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"}, "friedman_reference_text": "29-31. | | s = 6 | Trivial. |", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "100db5f9f28894cc", "improvement": -7.850174601031767e-05, "max_boundary_excess": -3.7272811687230685e-07, "max_pair_overlap_depth": -4.232627726974414e-06, "metric_expression": "6.00008", "metric_symbol": "s", "metric_value": 6.00007850174601, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.0, "setup": "hexinhex", "side": 6.00007850174601, "solution_path": "data/solutions/generated/hexinhex_030_100db5f9f28894cc.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/100db5f9f28894cc.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinhex@31", "density": 0.8610814974425702, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinhex/31.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexinhex@31", "credit": "Trivial", "date": "", "family_updated": "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"}, "friedman_reference_text": "29-31. | | s = 6 | Trivial. |", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinhex/", "friedman_title": "Hexagons in Hexagons", "frontend_seed": true, "id": "d503e2b08764a35e", "improvement": -0.0001031728611780025, "max_boundary_excess": -1.0312532034243658e-06, "max_pair_overlap_depth": -8.80446118189937e-06, "metric_expression": "6.00010", "metric_symbol": "s", "metric_value": 6.000103172861178, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.0, "setup": "hexinhex", "side": 6.000103172861178, "solution_path": "data/solutions/generated/hexinhex_031_d503e2b08764a35e.json", "source_url": "https://erich-friedman.github.io/packing/hexinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d503e2b08764a35e.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexinsqu@1", "density": 0.6961402306608654, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/1.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(1+\u221a3)/\u221a2 = 1.931+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.931, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@1", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "(1+\u221a3)/\u221a2 = 1.931+", "metric_symbol": "s", "metric_value": 1.931, "reference_text": "s = (1+\u221a3)/\u221a2 = 1.931+ | Trivial. |", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/1.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = (1+\u221a3)/\u221a2 = 1.931+ | Trivial. |", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "1cfff36edc20de72", "improvement": -0.000868569514983486, "max_boundary_excess": -1.8875760125229138e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.93187", "metric_symbol": "s", "metric_value": 1.9318685695149835, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.931, "setup": "hexinsqu", "side": 1.9318685695149835, "solution_path": "data/solutions/generated/hexinsqu_001_1cfff36edc20de72.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1cfff36edc20de72.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexinsqu@2", "density": 0.5214616218348717, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/2.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(1+2\u221a3)/\u221a2 = 3.156+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.156, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@2", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "(1+2\u221a3)/\u221a2 = 3.156+", "metric_symbol": "s", "metric_value": 3.156, "reference_text": "s = (1+2\u221a3)/\u221a2 = 3.156+ | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/2.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = (1+2\u221a3)/\u221a2 = 3.156+ | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "ff43d04cda84c856", "improvement": -0.0006742348964126066, "max_boundary_excess": -1.2405599436706566e-05, "max_pair_overlap_depth": -1.629836664562411e-05, "metric_expression": "3.15667", "metric_symbol": "s", "metric_value": 3.1566742348964127, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.156, "setup": "hexinsqu", "side": 3.1566742348964127, "solution_path": "data/solutions/generated/hexinsqu_002_ff43d04cda84c856.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ff43d04cda84c856.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexinsqu@3", "density": 0.6391474518535116, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/3.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "9(6\u2013\u221a3)/11 = 3.491+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.491, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@3", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "4/28/26", "metric_expression": "9(6\u2013\u221a3)/11 = 3.491+", "metric_symbol": "s", "metric_value": 3.491, "reference_text": "s = 9(6\u2013\u221a3)/11 = 3.491+ | Found by Maurizio Morandi | in March 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/3.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 9(6\u2013\u221a3)/11 = 3.491+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "9525d376eafe3c9c", "improvement": -0.0010949178753740796, "max_boundary_excess": -2.084317521962771e-06, "max_pair_overlap_depth": -8.912711465047796e-05, "metric_expression": "3.49209", "metric_symbol": "s", "metric_value": 3.492094917875374, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.491, "setup": "hexinsqu", "side": 3.492094917875374, "solution_path": "data/solutions/generated/hexinsqu_003_9525d376eafe3c9c.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9525d376eafe3c9c.svg", "tolerance": 1e-08, "verified": true}
@@ -218,6 +246,11 @@
 {"case": "hexinsqu@18", "density": 0.7508119114984774, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/18.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "32(9\u20132\u221a3)/23 = 7.702+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.702, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@18", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "32(9\u20132\u221a3)/23 = 7.702+", "metric_symbol": "s", "metric_value": 7.702, "reference_text": "s = 32(9\u20132\u221a3)/23 = 7.702+ | Found by Maurizio Morandi | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/18.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 32(9\u20132\u221a3)/23 = 7.702+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "04bf4ecb433a40bc", "improvement": -0.1901734023169297, "max_boundary_excess": -6.471545418890209e-06, "max_pair_overlap_depth": -3.179483178339382e-05, "metric_expression": "7.89217", "metric_symbol": "s", "metric_value": 7.89217340231693, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.702, "setup": "hexinsqu", "side": 7.89217340231693, "solution_path": "data/solutions/generated/hexinsqu_018_04bf4ecb433a40bc.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/04bf4ecb433a40bc.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexinsqu@19", "density": 0.7859807737367643, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/19.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "25(3\u2013\u221a3)/4 = 7.924+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.924, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@19", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "25(3\u2013\u221a3)/4 = 7.924+", "metric_symbol": "s", "metric_value": 7.924, "reference_text": "s = 25(3\u2013\u221a3)/4 = 7.924+ | Found by Maurizio Morandi | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/19.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 25(3\u2013\u221a3)/4 = 7.924+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "10d9f5dde53d25ba", "improvement": -0.0009545892016307178, "max_boundary_excess": -2.893895229540556e-06, "max_pair_overlap_depth": -3.6221248433054853e-05, "metric_expression": "7.92495", "metric_symbol": "s", "metric_value": 7.924954589201631, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.924, "setup": "hexinsqu", "side": 7.924954589201631, "solution_path": "data/solutions/generated/hexinsqu_019_10d9f5dde53d25ba.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/10d9f5dde53d25ba.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexinsqu@20", "density": 0.8222377903171622, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/20.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "74(21\u20134\u221a3)/131 = 7.948+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.948, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@20", "credit": "Maurizio Morandi", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "74(21\u20134\u221a3)/131 = 7.948+", "metric_symbol": "s", "metric_value": 7.948, "reference_text": "s = 74(21\u20134\u221a3)/131 = 7.948+ | Found by Maurizio Morandi | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/hexinsqu/20.png", "source_page": "https://erich-friedman.github.io/packing/hexinsqu/", "title": "Hexagons in Squares"}, "friedman_reference_text": "s = 74(21\u20134\u221a3)/131 = 7.948+ | Found by Maurizio Morandi | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "3d530c0ac6e7e3b1", "improvement": -0.0015441274741458955, "max_boundary_excess": -8.121785608292394e-06, "max_pair_overlap_depth": -4.480534023287852e-05, "metric_expression": "7.94954", "metric_symbol": "s", "metric_value": 7.949544127474146, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.948, "setup": "hexinsqu", "side": 7.949544127474146, "solution_path": "data/solutions/generated/hexinsqu_020_3d530c0ac6e7e3b1.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3d530c0ac6e7e3b1.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@21", "density": 0.7762795555424945, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/21.png", "friedman_metric_expression": "8.381+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.381, "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@21", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "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"}, "friedman_reference_text": "s = 8.381+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "5d369a2740fde606", "improvement": -0.002522153681731254, "max_boundary_excess": -4.85221561134309e-06, "max_pair_overlap_depth": -3.989714052887727e-05, "metric_expression": "8.38352", "metric_symbol": "s", "metric_value": 8.383522153681731, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.381, "setup": "hexinsqu", "side": 8.383522153681731, "solution_path": "data/solutions/generated/hexinsqu_021_5d369a2740fde606.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5d369a2740fde606.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@22", "density": 0.7770815845496467, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/22.png", "friedman_metric_expression": "8.568+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.568, "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@22", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "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"}, "friedman_reference_text": "s = 8.568+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "2f0b0033f0c66708", "improvement": -0.008379204155273712, "max_boundary_excess": -2.913077650512531e-06, "max_pair_overlap_depth": -1.9097490104869053e-05, "metric_expression": "8.57638", "metric_symbol": "s", "metric_value": 8.576379204155273, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.568, "setup": "hexinsqu", "side": 8.576379204155273, "solution_path": "data/solutions/generated/hexinsqu_022_2f0b0033f0c66708.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/2f0b0033f0c66708.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@23", "density": 0.7967168154089415, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/23.png", "friedman_metric_expression": "5\u221a3 = 8.660+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.66, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@23", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "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"}, "friedman_reference_text": "s = 5\u221a3 = 8.660+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "31cc17034bd25d7b", "improvement": -0.0003983679346664104, "max_boundary_excess": -5.345963802137002e-06, "max_pair_overlap_depth": -2.1349502021816846e-07, "metric_expression": "8.66040", "metric_symbol": "s", "metric_value": 8.660398367934667, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.66, "setup": "hexinsqu", "side": 8.660398367934667, "solution_path": "data/solutions/generated/hexinsqu_023_31cc17034bd25d7b.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/31cc17034bd25d7b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@24", "density": 0.8058676683577897, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/24.png", "friedman_metric_expression": "8.795+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.795, "friedman_reference": {"analytical_or_proved": false, "case": "hexinsqu@24", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "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"}, "friedman_reference_text": "s = 8.795+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "941fbce4f50492c6", "improvement": -0.0012932219182459903, "max_boundary_excess": -1.0969884292392119e-07, "max_pair_overlap_depth": -1.611027152126354e-05, "metric_expression": "8.79629", "metric_symbol": "s", "metric_value": 8.796293221918246, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.795, "setup": "hexinsqu", "side": 8.796293221918246, "solution_path": "data/solutions/generated/hexinsqu_024_941fbce4f50492c6.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/941fbce4f50492c6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexinsqu@25", "density": 0.7836571783494045, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexinsqu/25.png", "friedman_metric_expression": "30(4\u221a3\u20133)/13 = 9.065+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.065, "friedman_reference": {"analytical_or_proved": true, "case": "hexinsqu@25", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "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"}, "friedman_reference_text": "s = 30(4\u221a3\u20133)/13 = 9.065+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "25.png", "friedman_source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "friedman_title": "Hexagons in Squares", "frontend_seed": true, "id": "d89d09725d796421", "improvement": -0.03901342531098173, "max_boundary_excess": -8.46381858025372e-06, "max_pair_overlap_depth": -3.4782095370111676e-05, "metric_expression": "9.10401", "metric_symbol": "s", "metric_value": 9.104013425310981, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.065, "setup": "hexinsqu", "side": 9.104013425310981, "solution_path": "data/solutions/generated/hexinsqu_025_d89d09725d796421.json", "source_url": "https://erich-friedman.github.io/packing/hexinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d89d09725d796421.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexintri@1", "density": 0.6666490309389511, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/1.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@1", "credit": "Trivial", "date": "", "family_updated": "4/5/26", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "s = 3 | Trivial.", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/1.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 3 | Trivial.", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "c2fff75544b88239", "improvement": -3.9681174644368156e-05, "max_boundary_excess": -7.67464904574664e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "3.00004", "metric_symbol": "s", "metric_value": 3.0000396811746444, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.0, "setup": "hexintri", "side": 3.0000396811746444, "solution_path": "data/solutions/generated/hexintri_001_c2fff75544b88239.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c2fff75544b88239.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexintri@2", "density": 0.4799802064426444, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@2", "credit": "Trivial", "date": "", "family_updated": "4/5/26", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "b77426ecb97f3ce6", "improvement": -0.00010309463302426991, "max_boundary_excess": -2.3591084715906373e-06, "max_pair_overlap_depth": -4.2178351187804886e-05, "metric_expression": "5.00010", "metric_symbol": "s", "metric_value": 5.000103094633024, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "hexintri", "side": 5.000103094633024, "solution_path": "data/solutions/generated/hexintri_002_b77426ecb97f3ce6.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b77426ecb97f3ce6.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexintri@3", "density": 0.7199659208954582, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@3", "credit": "Trivial", "date": "", "family_updated": "4/5/26", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/3.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "748bfe1ef47ea18c", "improvement": -0.00011833442488207169, "max_boundary_excess": -2.3474135610435156e-06, "max_pair_overlap_depth": -4.4955482604913666e-05, "metric_expression": "5.00012", "metric_symbol": "s", "metric_value": 5.000118334424882, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "hexintri", "side": 5.000118334424882, "solution_path": "data/solutions/generated/hexintri_003_748bfe1ef47ea18c.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/748bfe1ef47ea18c.svg", "tolerance": 1e-08, "verified": true}
@@ -238,6 +271,7 @@
 {"case": "hexintri@18", "density": 0.7507767554452202, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "12", "friedman_metric_symbol": "s", "friedman_metric_value": 12.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@18", "credit": "Trivial", "date": "", "family_updated": "4/5/26", "metric_expression": "12", "metric_symbol": "s", "metric_value": 12.0, "reference_text": "s = 12 | Trivial. |", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 12 | Trivial. |", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "8f10cd5e01be9029", "improvement": 0.0062092209316340075, "max_boundary_excess": -6.734105056962567e-06, "max_pair_overlap_depth": -5.8920104462956147e-05, "metric_expression": "11.99379", "metric_symbol": "s", "metric_value": 11.993790779068366, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 12.0, "setup": "hexintri", "side": 11.993790779068366, "solution_path": "data/solutions/generated/hexintri_018_8f10cd5e01be9029.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8f10cd5e01be9029.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexintri@19", "density": 0.7754553480185566, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "12", "friedman_metric_symbol": "s", "friedman_metric_value": 12.0, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@19", "credit": "Trivial", "date": "", "family_updated": "4/5/26", "metric_expression": "12", "metric_symbol": "s", "metric_value": 12.0, "reference_text": "s = 12 | Trivial. |", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/hexintri/19.gif", "source_page": "https://erich-friedman.github.io/packing/hexintri/", "title": "Hexagons in Triangles"}, "friedman_reference_text": "s = 12 | Trivial. |", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "43012deed1bb1dba", "improvement": -0.12478448660763952, "max_boundary_excess": -5.837329751695746e-06, "max_pair_overlap_depth": -3.825923946865206e-05, "metric_expression": "12.12478", "metric_symbol": "s", "metric_value": 12.12478448660764, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 12.0, "setup": "hexintri", "side": 12.12478448660764, "solution_path": "data/solutions/generated/hexintri_019_43012deed1bb1dba.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/43012deed1bb1dba.svg", "tolerance": 1e-08, "verified": true}
 {"case": "hexintri@20", "density": 0.8162942117377381, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "friedman_family_updated": "4/5/26", "friedman_metric_expression": "7\u221a3 = 12.1243+", "friedman_metric_symbol": "s", "friedman_metric_value": 12.1243, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@20", "credit": "Trivial", "date": "", "family_updated": "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"}, "friedman_reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "f59179c5b6665dc4", "improvement": -0.00029566549525483765, "max_boundary_excess": -6.116403950810266e-06, "max_pair_overlap_depth": -3.364591626842106e-05, "metric_expression": "12.12460", "metric_symbol": "s", "metric_value": 12.124595665495255, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 12.1243, "setup": "hexintri", "side": 12.124595665495255, "solution_path": "data/solutions/generated/hexintri_020_f59179c5b6665dc4.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f59179c5b6665dc4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "hexintri@21", "density": 0.8571035425372456, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/hexintri/21.gif", "friedman_metric_expression": "7\u221a3 = 12.1243+", "friedman_metric_symbol": "s", "friedman_metric_value": 12.1243, "friedman_reference": {"analytical_or_proved": true, "case": "hexintri@21", "credit": "Trivial", "date": "", "family_updated": "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"}, "friedman_reference_text": "s = 7\u221a3 = 12.1243+ | Trivial. |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/hexintri/", "friedman_title": "Hexagons in Triangles", "frontend_seed": true, "id": "6cf726ac83ba7d7f", "improvement": -0.00033371669977810825, "max_boundary_excess": -3.7607980864287318e-06, "max_pair_overlap_depth": -2.977721456209892e-05, "metric_expression": "12.12463", "metric_symbol": "s", "metric_value": 12.124633716699778, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 12.1243, "setup": "hexintri", "side": 12.124633716699778, "solution_path": "data/solutions/generated/hexintri_021_6cf726ac83ba7d7f.json", "source_url": "https://erich-friedman.github.io/packing/hexintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6cf726ac83ba7d7f.svg", "tolerance": 1e-08, "verified": true}
 {"case": "octinoct@1", "density": 0.9999940796878448, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/1.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@1", "credit": "Trivial", "date": "", "family_updated": "3/27/26", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/1.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 1 | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "13c63959e19cfeb5", "improvement": -2.96016922152198e-06, "max_boundary_excess": -2.1903479056983753e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00000", "metric_symbol": "s", "metric_value": 1.0000029601692215, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.0, "setup": "octinoct", "side": 1.0000029601692215, "solution_path": "data/solutions/generated/octinoct_001_13c63959e19cfeb5.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/13c63959e19cfeb5.svg", "tolerance": 1e-08, "verified": true}
 {"case": "octinoct@2", "density": 0.4999889107582135, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/2.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@2", "credit": "Trivial", "date": "", "family_updated": "3/27/26", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/2.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 2 | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "937fb450c622d9b9", "improvement": -2.2178852493670576e-05, "max_boundary_excess": -5.909847599495863e-06, "max_pair_overlap_depth": -3.0343321494846753e-05, "metric_expression": "2.00002", "metric_symbol": "s", "metric_value": 2.0000221788524937, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "octinoct", "side": 2.0000221788524937, "solution_path": "data/solutions/generated/octinoct_002_937fb450c622d9b9.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/937fb450c622d9b9.svg", "tolerance": 1e-08, "verified": true}
 {"case": "octinoct@3", "density": 0.6361550822369931, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/3.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "5\u20132\u221a2 = 2.17157+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.17157, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@3", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "5\u20132\u221a2 = 2.17157+", "metric_symbol": "s", "metric_value": 2.17157, "reference_text": "s = 5\u20132\u221a2 = 2.17157+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/3.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5\u20132\u221a2 = 2.17157+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "4cb37df94277ed6e", "improvement": -2.6468916854760494e-05, "max_boundary_excess": -4.359798521217012e-07, "max_pair_overlap_depth": -2.9093807346031175e-05, "metric_expression": "2.17160", "metric_symbol": "s", "metric_value": 2.1715964689168548, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.17157, "setup": "octinoct", "side": 2.1715964689168548, "solution_path": "data/solutions/generated/octinoct_003_4cb37df94277ed6e.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4cb37df94277ed6e.svg", "tolerance": 1e-08, "verified": true}
@@ -258,6 +292,16 @@
 {"case": "octinoct@18", "density": 0.7629999765077309, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/18.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4.85717+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.85717, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@18", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "4.85717+", "metric_symbol": "s", "metric_value": 4.85717, "reference_text": "s = 4.85717+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/18.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4.85717+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "46f5ac176d150ffa", "improvement": 0.00010416375427002578, "max_boundary_excess": -8.225773906749903e-06, "max_pair_overlap_depth": -2.521618462036912e-05, "metric_expression": "4.85707", "metric_symbol": "s", "metric_value": 4.85706583624573, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.85717, "setup": "octinoct", "side": 4.85706583624573, "solution_path": "data/solutions/generated/octinoct_018_46f5ac176d150ffa.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/46f5ac176d150ffa.svg", "tolerance": 1e-08, "verified": true}
 {"case": "octinoct@19", "density": 0.7795195170060211, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/19.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "4.93586+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.93586, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "4.93586+", "metric_symbol": "s", "metric_value": 4.93586, "reference_text": "s = 4.93586+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/19.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 4.93586+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "4a7169be4bda1825", "improvement": -0.0011420082689239663, "max_boundary_excess": -1.1928573301213418e-05, "max_pair_overlap_depth": -1.491417372267989e-06, "metric_expression": "4.93700", "metric_symbol": "s", "metric_value": 4.937002008268924, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.93586, "setup": "octinoct", "side": 4.937002008268924, "solution_path": "data/solutions/generated/octinoct_019_4a7169be4bda1825.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4a7169be4bda1825.svg", "tolerance": 1e-08, "verified": true}
 {"case": "octinoct@20", "density": 0.778654925537014, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/20.gif", "friedman_family_updated": "3/27/26", "friedman_metric_expression": "5.06781+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.06781, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@20", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/27/26", "metric_expression": "5.06781+", "metric_symbol": "s", "metric_value": 5.06781, "reference_text": "s = 5.06781+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/octinoct/20.gif", "source_page": "https://erich-friedman.github.io/packing/octinoct/", "title": "Octagons in Octagons"}, "friedman_reference_text": "s = 5.06781+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "ef9ffbe57f51321a", "improvement": -0.0002585475900360734, "max_boundary_excess": -5.202696065204785e-06, "max_pair_overlap_depth": -3.692189855719619e-05, "metric_expression": "5.06807", "metric_symbol": "s", "metric_value": 5.068068547590036, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.06781, "setup": "octinoct", "side": 5.068068547590036, "solution_path": "data/solutions/generated/octinoct_020_ef9ffbe57f51321a.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ef9ffbe57f51321a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@21", "density": 0.7774838310416734, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/21.gif", "friedman_metric_expression": "5.19715+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.19715, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@21", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "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"}, "friedman_reference_text": "s = 5.19715+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "92c4bcf9428983c2", "improvement": 1.540400287325383e-05, "max_boundary_excess": -7.1696825424876755e-06, "max_pair_overlap_depth": -2.317393259165801e-05, "metric_expression": "5.19713", "metric_symbol": "s", "metric_value": 5.1971345959971265, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.19715, "setup": "octinoct", "side": 5.1971345959971265, "solution_path": "data/solutions/generated/octinoct_021_92c4bcf9428983c2.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/92c4bcf9428983c2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@22", "density": 0.7663269933124698, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/22.gif", "friedman_metric_expression": "5.35750+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.3575, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@22", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "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"}, "friedman_reference_text": "s = 5.35750+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "b8f2befaa2d4a75e", "improvement": -0.0005193617687213603, "max_boundary_excess": -4.99203724676962e-06, "max_pair_overlap_depth": -1.57400449714018e-05, "metric_expression": "5.35802", "metric_symbol": "s", "metric_value": 5.358019361768721, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.3575, "setup": "octinoct", "side": 5.358019361768721, "solution_path": "data/solutions/generated/octinoct_022_b8f2befaa2d4a75e.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b8f2befaa2d4a75e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@23", "density": 0.7845835529808874, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/23.gif", "friedman_metric_expression": "5.41440+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.4144, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@23", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "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"}, "friedman_reference_text": "s = 5.41440+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "d6528e8801e36ce0", "improvement": 7.503853147827755e-05, "max_boundary_excess": -3.3646686331794102e-06, "max_pair_overlap_depth": -4.536567227386712e-05, "metric_expression": "5.41432", "metric_symbol": "s", "metric_value": 5.414324961468521, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.4144, "setup": "octinoct", "side": 5.414324961468521, "solution_path": "data/solutions/generated/octinoct_023_d6528e8801e36ce0.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d6528e8801e36ce0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@24", "density": 0.777859618157, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/24.gif", "friedman_metric_expression": "5.55464+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.55464, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@24", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "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"}, "friedman_reference_text": "s = 5.55464+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "a34ac6a3c52f70df", "improvement": 1.1631965286973411e-05, "max_boundary_excess": -7.721783559078116e-06, "max_pair_overlap_depth": -2.4974900467711336e-05, "metric_expression": "5.55463", "metric_symbol": "s", "metric_value": 5.554628368034713, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.55464, "setup": "octinoct", "side": 5.554628368034713, "solution_path": "data/solutions/generated/octinoct_024_a34ac6a3c52f70df.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a34ac6a3c52f70df.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@25", "density": 0.7805673327264805, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/25.gif", "friedman_metric_expression": "5.65593+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.65593, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@25", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "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"}, "friedman_reference_text": "s = 5.65593+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "113492960b7e7dce", "improvement": -0.003397389940226425, "max_boundary_excess": -6.281212189125961e-06, "max_pair_overlap_depth": -2.6024797291412938e-05, "metric_expression": "5.65933", "metric_symbol": "s", "metric_value": 5.659327389940226, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.65593, "setup": "octinoct", "side": 5.659327389940226, "solution_path": "data/solutions/generated/octinoct_025_113492960b7e7dce.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/113492960b7e7dce.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@26", "density": 0.7881657239941322, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/26.gif", "friedman_metric_expression": "5.73940+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.7394, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@26", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "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"}, "friedman_reference_text": "s = 5.73940+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "581188c4895e4037", "improvement": -0.004116881359766289, "max_boundary_excess": -6.43705423351296e-06, "max_pair_overlap_depth": -2.686615288460814e-05, "metric_expression": "5.74352", "metric_symbol": "s", "metric_value": 5.743516881359766, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.7394, "setup": "octinoct", "side": 5.743516881359766, "solution_path": "data/solutions/generated/octinoct_026_581188c4895e4037.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/581188c4895e4037.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@27", "density": 0.7989711846148311, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/27.gif", "friedman_metric_expression": "5.81238+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.81238, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@27", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "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"}, "friedman_reference_text": "s = 5.81238+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "25c7f85bc0b15209", "improvement": -0.0008341744667159645, "max_boundary_excess": -3.851030556516347e-06, "max_pair_overlap_depth": -2.4661009629944886e-05, "metric_expression": "5.81321", "metric_symbol": "s", "metric_value": 5.813214174466716, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.81238, "setup": "octinoct", "side": 5.813214174466716, "solution_path": "data/solutions/generated/octinoct_027_25c7f85bc0b15209.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/25c7f85bc0b15209.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@28", "density": 0.8242204012359605, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/28.gif", "friedman_metric_expression": "3+2\u221a2 = 5.82842+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.82842, "friedman_reference": {"analytical_or_proved": true, "case": "octinoct@28", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "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"}, "friedman_reference_text": "s = 3+2\u221a2 = 5.82842+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "f8d9c8a9f9a38d45", "improvement": -8.71778893589692e-05, "max_boundary_excess": -6.739062384519148e-06, "max_pair_overlap_depth": -9.673739088000843e-06, "metric_expression": "5.82851", "metric_symbol": "s", "metric_value": 5.828507177889359, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.82842, "setup": "octinoct", "side": 5.828507177889359, "solution_path": "data/solutions/generated/octinoct_028_f8d9c8a9f9a38d45.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f8d9c8a9f9a38d45.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@29", "density": 0.7902111886471865, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/29.gif", "friedman_metric_expression": "6.05746+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.05746, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@29", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "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"}, "friedman_reference_text": "s = 6.05746+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "30789c6bb8fd99b7", "improvement": -0.0005140918720876186, "max_boundary_excess": -7.805265150873157e-06, "max_pair_overlap_depth": -5.6301265520808386e-05, "metric_expression": "6.05797", "metric_symbol": "s", "metric_value": 6.0579740918720875, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.05746, "setup": "octinoct", "side": 6.0579740918720875, "solution_path": "data/solutions/generated/octinoct_029_30789c6bb8fd99b7.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/30789c6bb8fd99b7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "octinoct@30", "density": 0.7919434557655346, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/octinoct/30.gif", "friedman_metric_expression": "6.15432+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.15432, "friedman_reference": {"analytical_or_proved": false, "case": "octinoct@30", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "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"}, "friedman_reference_text": "s = 6.15432+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/octinoct/", "friedman_title": "Octagons in Octagons", "frontend_seed": true, "id": "1a16dc8a4d741008", "improvement": -0.00047426130353134255, "max_boundary_excess": -1.1243912272535679e-05, "max_pair_overlap_depth": -2.8046648627544357e-05, "metric_expression": "6.15479", "metric_symbol": "s", "metric_value": 6.154794261303532, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.15432, "setup": "octinoct", "side": 6.154794261303532, "solution_path": "data/solutions/generated/octinoct_030_1a16dc8a4d741008.json", "source_url": "https://erich-friedman.github.io/packing/octinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1a16dc8a4d741008.svg", "tolerance": 1e-08, "verified": true}
 {"case": "penincir@1", "density": 0.7568185573097284, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/1.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a((5+\u221a5)/10) = .86065+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.86065, "friedman_reference": {"analytical_or_proved": true, "case": "penincir@1", "credit": "Trivial", "date": "", "family_updated": "4/13/26", "metric_expression": "\u221a((5+\u221a5)/10) = .86065+", "metric_symbol": "r", "metric_value": 0.86065, "reference_text": "r = \u221a((5+\u221a5)/10) = .86065+ | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/1.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = \u221a((5+\u221a5)/10) = .86065+ | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "ca75a5cd7cad481c", "improvement": 0.009994599443903796, "max_boundary_excess": -2.0926430426282394e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.85066", "metric_symbol": "r", "metric_value": 0.8506554005560962, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.86065, "setup": "penincir", "side": 1.7013108011121925, "solution_path": "data/solutions/generated/penincir_001_ca75a5cd7cad481c.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ca75a5cd7cad481c.svg", "tolerance": 1e-08, "verified": true}
 {"case": "penincir@2", "density": 0.462509898701161, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/2.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a(5+2\u221a5)/2 = 1.53884+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.53884, "friedman_reference": {"analytical_or_proved": true, "case": "penincir@2", "credit": "Trivial", "date": "", "family_updated": "4/13/26", "metric_expression": "\u221a(5+2\u221a5)/2 = 1.53884+", "metric_symbol": "r", "metric_value": 1.53884, "reference_text": "r = \u221a(5+2\u221a5)/2 = 1.53884+ | Trivial.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/2.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = \u221a(5+2\u221a5)/2 = 1.53884+ | Trivial.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "44da10d1d5897aae", "improvement": -3.743542237466535e-05, "max_boundary_excess": -8.684702690331392e-08, "max_pair_overlap_depth": -5.994543612077171e-05, "metric_expression": "1.53888", "metric_symbol": "r", "metric_value": 1.5388774354223747, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.53884, "setup": "penincir", "side": 3.0777548708447493, "solution_path": "data/solutions/generated/penincir_002_44da10d1d5897aae.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/44da10d1d5897aae.svg", "tolerance": 1e-08, "verified": true}
 {"case": "penincir@3", "density": 0.6275054691586099, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/3.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "(1+\u221a5)/2 = 1.61803+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.61803, "friedman_reference": {"analytical_or_proved": true, "case": "penincir@3", "credit": "Trivial", "date": "", "family_updated": "4/13/26", "metric_expression": "(1+\u221a5)/2 = 1.61803+", "metric_symbol": "r", "metric_value": 1.61803, "reference_text": "r = (1+\u221a5)/2 = 1.61803+ | Trivial.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/3.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = (1+\u221a5)/2 = 1.61803+ | Trivial.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "350d35e2110a508b", "improvement": -5.532631868709892e-05, "max_boundary_excess": -4.919906156253262e-06, "max_pair_overlap_depth": -5.073652219536114e-05, "metric_expression": "1.61809", "metric_symbol": "r", "metric_value": 1.6180853263186872, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.61803, "setup": "penincir", "side": 3.2361706526373744, "solution_path": "data/solutions/generated/penincir_003_350d35e2110a508b.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/350d35e2110a508b.svg", "tolerance": 1e-08, "verified": true}
@@ -278,6 +322,7 @@
 {"case": "penincir@18", "density": 0.7533573813986445, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/18.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.62080+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.6208, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "3.62080+", "metric_symbol": "r", "metric_value": 3.6208, "reference_text": "r = 3.62080+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/18.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.62080+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "767a627015948f32", "improvement": 0.00349375267338381, "max_boundary_excess": -3.7774333678797234e-06, "max_pair_overlap_depth": -3.109065453799076e-05, "metric_expression": "3.61731", "metric_symbol": "r", "metric_value": 3.617306247326616, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.6208, "setup": "penincir", "side": 7.234612494653232, "solution_path": "data/solutions/generated/penincir_018_767a627015948f32.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/767a627015948f32.svg", "tolerance": 1e-08, "verified": true}
 {"case": "penincir@19", "density": 0.771366675320165, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/19.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.67287+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.67287, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "3.67287+", "metric_symbol": "r", "metric_value": 3.67287, "reference_text": "r = 3.67287+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/19.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.67287+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "9d482c8012998879", "improvement": 8.154982387598153e-05, "max_boundary_excess": -3.817340790579493e-06, "max_pair_overlap_depth": -1.6517110137281854e-05, "metric_expression": "3.67279", "metric_symbol": "r", "metric_value": 3.672788450176124, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.67287, "setup": "penincir", "side": 7.345576900352248, "solution_path": "data/solutions/generated/penincir_019_9d482c8012998879.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9d482c8012998879.svg", "tolerance": 1e-08, "verified": true}
 {"case": "penincir@20", "density": 0.7575056542556782, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/20.png", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "3.80415+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.80415, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "3.80415+", "metric_symbol": "r", "metric_value": 3.80415, "reference_text": "r = 3.80415+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/penincir/20.png", "source_page": "https://erich-friedman.github.io/packing/penincir/", "title": "Pentagons in Circles"}, "friedman_reference_text": "r = 3.80415+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "5271226652403829", "improvement": 0.0016291138375779113, "max_boundary_excess": -7.231424091092009e-06, "max_pair_overlap_depth": -3.071782635011289e-05, "metric_expression": "3.80252", "metric_symbol": "r", "metric_value": 3.802520886162422, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.80415, "setup": "penincir", "side": 7.605041772324844, "solution_path": "data/solutions/generated/penincir_020_5271226652403829.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5271226652403829.svg", "tolerance": 1e-08, "verified": true}
+{"case": "penincir@21", "density": 0.7444892702855748, "friedman_analytical_or_proved": false, "friedman_credit": "Cyril Summerfield", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/penincir/21.png", "friedman_metric_expression": "3.90735+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.90735, "friedman_reference": {"analytical_or_proved": false, "case": "penincir@21", "credit": "Cyril Summerfield", "date": "April 2026", "family_updated": "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"}, "friedman_reference_text": "r = 3.90735+ | Found by Cyril Summerfield | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/penincir/", "friedman_title": "Pentagons in Circles", "frontend_seed": true, "id": "b713bb4909b828e8", "improvement": -0.02298868203306892, "max_boundary_excess": -1.870622546595868e-05, "max_pair_overlap_depth": -5.364219534342851e-06, "metric_expression": "3.93034", "metric_symbol": "r", "metric_value": 3.930338682033069, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.90735, "setup": "penincir", "side": 7.860677364066138, "solution_path": "data/solutions/generated/penincir_021_b713bb4909b828e8.json", "source_url": "https://erich-friedman.github.io/packing/penincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b713bb4909b828e8.svg", "tolerance": 1e-08, "verified": true}
 {"case": "peninpen@1", "density": 0.9999780359352667, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/1.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@1", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial.", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/1.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 1 | Trivial.", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "b3173648630fcdeb", "improvement": -1.0982213277443975e-05, "max_boundary_excess": -6.256503348572871e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_symbol": "s", "metric_value": 1.0000109822132774, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.0, "setup": "peninpen", "side": 1.0000109822132774, "solution_path": "data/solutions/generated/peninpen_001_b3173648630fcdeb.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b3173648630fcdeb.svg", "tolerance": 1e-08, "verified": true}
 {"case": "peninpen@2", "density": 0.4999891232484648, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/2.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@2", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/2.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "edac094186a54129", "improvement": -2.175385798786067e-05, "max_boundary_excess": -3.0537211348702708e-06, "max_pair_overlap_depth": -1.9731507571563167e-05, "metric_expression": "2.00002", "metric_symbol": "s", "metric_value": 2.000021753857988, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "peninpen", "side": 2.000021753857988, "solution_path": "data/solutions/generated/peninpen_002_edac094186a54129.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/edac094186a54129.svg", "tolerance": 1e-08, "verified": true}
 {"case": "peninpen@3", "density": 0.599978840427638, "friedman_analytical_or_proved": true, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/3.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a5 = 2.23606+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.23606, "friedman_reference": {"analytical_or_proved": true, "case": "peninpen@3", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "\u221a5 = 2.23606+", "metric_symbol": "s", "metric_value": 2.23606, "reference_text": "s = \u221a5 = 2.23606+ | Found by Jonathan Viquerat in April 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/3.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = \u221a5 = 2.23606+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "bf261a4dce178a90", "improvement": -4.7407077830463606e-05, "max_boundary_excess": -2.7662857614262655e-06, "max_pair_overlap_depth": -2.7755970794667603e-05, "metric_expression": "2.23611", "metric_symbol": "s", "metric_value": 2.2361074070778306, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.23606, "setup": "peninpen", "side": 2.2361074070778306, "solution_path": "data/solutions/generated/peninpen_003_bf261a4dce178a90.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/bf261a4dce178a90.svg", "tolerance": 1e-08, "verified": true}
@@ -298,6 +343,11 @@
 {"case": "peninpen@18", "density": 0.7892194761771266, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/18.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.77541+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.77541, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@18", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.77541+", "metric_symbol": "s", "metric_value": 4.77541, "reference_text": "s = 4.77541+ | Found by Jonathan Viquerat in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/18.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 4.77541+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "9c442356ca78c3de", "improvement": -0.0002934971525236918, "max_boundary_excess": -3.1318004154280254e-06, "max_pair_overlap_depth": -1.258487199295999e-05, "metric_expression": "4.77570", "metric_symbol": "s", "metric_value": 4.775703497152524, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.77541, "setup": "peninpen", "side": 4.775703497152524, "solution_path": "data/solutions/generated/peninpen_018_9c442356ca78c3de.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9c442356ca78c3de.svg", "tolerance": 1e-08, "verified": true}
 {"case": "peninpen@19", "density": 0.7735353200149236, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/19.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.95269+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.95269, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@19", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.95269+", "metric_symbol": "s", "metric_value": 4.95269, "reference_text": "s = 4.95269+ | Found by Ian Watson in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/19.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 4.95269+ | Found by Ian Watson in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "b5440311f7b9b10b", "improvement": -0.0033719480383975764, "max_boundary_excess": -3.8067945532274755e-06, "max_pair_overlap_depth": -5.844604614307913e-06, "metric_expression": "4.95606", "metric_symbol": "s", "metric_value": 4.956061948038397, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.95269, "setup": "peninpen", "side": 4.956061948038397, "solution_path": "data/solutions/generated/peninpen_019_b5440311f7b9b10b.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b5440311f7b9b10b.svg", "tolerance": 1e-08, "verified": true}
 {"case": "peninpen@20", "density": 0.7890584950748962, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/20.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "5.04154+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.04154, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@20", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "5.04154+", "metric_symbol": "s", "metric_value": 5.04154, "reference_text": "s = 5.04154+ | Found by Jonathan Viquerat in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/20.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.04154+ | Found by Jonathan Viquerat in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "74f61b73dca76fef", "improvement": 0.0069930192193110585, "max_boundary_excess": -6.063547145356236e-06, "max_pair_overlap_depth": -1.8870971417950244e-05, "metric_expression": "5.03455", "metric_symbol": "s", "metric_value": 5.034546980780689, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.04154, "setup": "peninpen", "side": 5.034546980780689, "solution_path": "data/solutions/generated/peninpen_020_74f61b73dca76fef.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/74f61b73dca76fef.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@21", "density": 0.7872654636004235, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/21.png", "friedman_metric_expression": "5.15948+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.15948, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@21", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "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"}, "friedman_reference_text": "s = 5.15948+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "1c71a8b98efbf1a2", "improvement": -0.005266945011011437, "max_boundary_excess": -8.105180534871506e-06, "max_pair_overlap_depth": -1.0939088816552811e-05, "metric_expression": "5.16475", "metric_symbol": "s", "metric_value": 5.164746945011012, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.15948, "setup": "peninpen", "side": 5.164746945011012, "solution_path": "data/solutions/generated/peninpen_021_1c71a8b98efbf1a2.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1c71a8b98efbf1a2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@22", "density": 0.7927891464448104, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/22.png", "friedman_metric_expression": "5.26740+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.2674, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@22", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "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"}, "friedman_reference_text": "s = 5.26740+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "07e217f200bb677e", "improvement": -0.0004389908125848052, "max_boundary_excess": -8.647717325013132e-07, "max_pair_overlap_depth": -3.201222129578518e-05, "metric_expression": "5.26784", "metric_symbol": "s", "metric_value": 5.267838990812585, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.2674, "setup": "peninpen", "side": 5.267838990812585, "solution_path": "data/solutions/generated/peninpen_022_07e217f200bb677e.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/07e217f200bb677e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@23", "density": 0.7962909120572189, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/23.png", "friedman_metric_expression": "5.34794+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.34794, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@23", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "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"}, "friedman_reference_text": "s = 5.34794+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "1da2b8cbe37457cd", "improvement": -0.026435892305500808, "max_boundary_excess": -6.938040181393094e-06, "max_pair_overlap_depth": -1.5232433659972955e-05, "metric_expression": "5.37438", "metric_symbol": "s", "metric_value": 5.374375892305501, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.34794, "setup": "peninpen", "side": 5.374375892305501, "solution_path": "data/solutions/generated/peninpen_023_1da2b8cbe37457cd.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1da2b8cbe37457cd.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@24", "density": 0.7831964047098741, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/24.png", "friedman_metric_expression": "5.49241+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.49241, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@24", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "5.49241+", "metric_symbol": "s", "metric_value": 5.49241, "reference_text": "s = 5.49241+ | Found by Ignacio Vallejo in April 2026.", "source_image": "24.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/24.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.49241+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "a420bfbc7a7f6c1e", "improvement": -0.04326109388634514, "max_boundary_excess": -4.519166548492215e-06, "max_pair_overlap_depth": -1.1805376856077743e-06, "metric_expression": "5.53567", "metric_symbol": "s", "metric_value": 5.535671093886345, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.49241, "setup": "peninpen", "side": 5.535671093886345, "solution_path": "data/solutions/generated/peninpen_024_a420bfbc7a7f6c1e.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a420bfbc7a7f6c1e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "peninpen@25", "density": 0.7948227562651979, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninpen/25.png", "friedman_metric_expression": "5.58370+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.5837, "friedman_reference": {"analytical_or_proved": false, "case": "peninpen@25", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "5.58370+", "metric_symbol": "s", "metric_value": 5.5837, "reference_text": "s = 5.58370+ | Found by Ignacio Vallejo in April 2026.", "source_image": "25.png", "source_image_url": "https://erich-friedman.github.io/packing/peninpen/25.png", "source_page": "https://erich-friedman.github.io/packing/peninpen/", "title": "Pentagons in Pentagons"}, "friedman_reference_text": "s = 5.58370+ | Found by Ignacio Vallejo in April 2026.", "friedman_source_image": "25.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninpen/", "friedman_title": "Pentagons in Pentagons", "frontend_seed": true, "id": "4e4dc42ba0fc7882", "improvement": -0.024646760880952634, "max_boundary_excess": -6.4042950585932436e-06, "max_pair_overlap_depth": -2.0039969058138762e-05, "metric_expression": "5.60835", "metric_symbol": "s", "metric_value": 5.608346760880953, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.5837, "setup": "peninpen", "side": 5.608346760880953, "solution_path": "data/solutions/generated/peninpen_025_4e4dc42ba0fc7882.json", "source_url": "https://erich-friedman.github.io/packing/peninpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4e4dc42ba0fc7882.svg", "tolerance": 1e-08, "verified": true}
 {"case": "peninsqu@1", "density": 0.6736263863631768, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/1.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "(3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.59811, "friedman_reference": {"analytical_or_proved": true, "case": "peninsqu@1", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "(3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+", "metric_symbol": "s", "metric_value": 1.59811, "reference_text": "s = (3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+ | Trivial. |", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/1.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = (3\u221a2+\u221a10+2\u221a(5+\u221a5))/8 = 1.59811+ | Trivial. |", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "ec216f3e37e16785", "improvement": -3.043902908794749e-05, "max_boundary_excess": -6.733207856432108e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.59814", "metric_symbol": "s", "metric_value": 1.5981404390290879, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.59811, "setup": "peninsqu", "side": 1.5981404390290879, "solution_path": "data/solutions/generated/peninsqu_001_ec216f3e37e16785.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ec216f3e37e16785.svg", "tolerance": 1e-08, "verified": true}
 {"case": "peninsqu@2", "density": 0.5669967061443146, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/2.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2.46345+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.46345, "friedman_reference": {"analytical_or_proved": true, "case": "peninsqu@2", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "2.46345+", "metric_symbol": "s", "metric_value": 2.46345, "reference_text": "s = 2.46345+ | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/2.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 2.46345+ | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "bb5e10eb4917963f", "improvement": -3.0994037563569776e-05, "max_boundary_excess": -6.416866607183818e-07, "max_pair_overlap_depth": -1.473425980974552e-05, "metric_expression": "2.46348", "metric_symbol": "s", "metric_value": 2.4634809940375635, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.46345, "setup": "peninsqu", "side": 2.4634809940375635, "solution_path": "data/solutions/generated/peninsqu_002_bb5e10eb4917963f.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/bb5e10eb4917963f.svg", "tolerance": 1e-08, "verified": true}
 {"case": "peninsqu@3", "density": 0.6102674136126431, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/peninsqu/3.png", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2.90812+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.90812, "friedman_reference": {"analytical_or_proved": false, "case": "peninsqu@3", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "2.90812+", "metric_symbol": "s", "metric_value": 2.90812, "reference_text": "s = 2.90812+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/peninsqu/3.png", "source_page": "https://erich-friedman.github.io/packing/peninsqu/", "title": "Pentagons in Squares"}, "friedman_reference_text": "s = 2.90812+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/peninsqu/", "friedman_title": "Pentagons in Squares", "frontend_seed": true, "id": "52b96ec8c7f6b741", "improvement": -8.50430757179943e-05, "max_boundary_excess": -3.362613813108376e-06, "max_pair_overlap_depth": -5.5799797820554886e-05, "metric_expression": "2.90821", "metric_symbol": "s", "metric_value": 2.908205043075718, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.90812, "setup": "peninsqu", "side": 2.908205043075718, "solution_path": "data/solutions/generated/peninsqu_003_52b96ec8c7f6b741.json", "source_url": "https://erich-friedman.github.io/packing/peninsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/52b96ec8c7f6b741.svg", "tolerance": 1e-08, "verified": true}
@@ -338,6 +388,21 @@
 {"case": "squincir@18", "density": 0.7617085472368383, "friedman_analytical_or_proved": true, "friedman_credit": "David W", "friedman_date": "March 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/18.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "\u221a481 / 8 = 2.741+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.741, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@18", "credit": "David W", "date": "March 2002", "family_updated": "4/13/26", "metric_expression": "\u221a481 / 8 = 2.741+", "metric_symbol": "r", "metric_value": 2.741, "reference_text": "r = \u221a481 / 8 = 2.741+ | Found by David W. Cantrell | in March 2002.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/18.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a481 / 8 = 2.741+ | Found by David W. Cantrell | in March 2002.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "d726e310dc0e9eaa", "improvement": -0.001627976420446764, "max_boundary_excess": -3.727763966399067e-06, "max_pair_overlap_depth": -2.573974201414142e-05, "metric_expression": "2.74263", "metric_symbol": "r", "metric_value": 2.742627976420447, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.741, "setup": "squincir", "side": 5.485255952840894, "solution_path": "data/solutions/generated/squincir_018_d726e310dc0e9eaa.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d726e310dc0e9eaa.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squincir@19", "density": 0.7678123162790478, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/19.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.802+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.802, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@19", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "2.802+", "metric_symbol": "r", "metric_value": 2.802, "reference_text": "r = 2.802+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/19.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.802+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "b664afe5246d24cb", "improvement": -0.004559972826113423, "max_boundary_excess": -4.8887554640053565e-06, "max_pair_overlap_depth": -1.4158229616034745e-05, "metric_expression": "2.80656", "metric_symbol": "r", "metric_value": 2.8065599728261135, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.802, "setup": "squincir", "side": 5.613119945652227, "solution_path": "data/solutions/generated/squincir_019_b664afe5246d24cb.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b664afe5246d24cb.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squincir@20", "density": 0.7585142435795145, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "June 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/20.gif", "friedman_family_updated": "4/13/26", "friedman_metric_expression": "2.893+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.893, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@20", "credit": "David W", "date": "June 2002", "family_updated": "4/13/26", "metric_expression": "2.893+", "metric_symbol": "r", "metric_value": 2.893, "reference_text": "r = 2.893+ | Found by David W. Cantrell | in June 2002.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/20.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 2.893+ | Found by David W. Cantrell | in June 2002.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "a6ab1017d9a75152", "improvement": -0.004064678977403258, "max_boundary_excess": -5.676979049074049e-06, "max_pair_overlap_depth": -2.975744684063919e-05, "metric_expression": "2.89706", "metric_symbol": "r", "metric_value": 2.897064678977403, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.893, "setup": "squincir", "side": 5.794129357954806, "solution_path": "data/solutions/generated/squincir_020_a6ab1017d9a75152.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a6ab1017d9a75152.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@21", "density": 0.7344962951045566, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/21.gif", "friedman_metric_expression": "\u221a34 / 2 = 2.915+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.915, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@21", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/13/26", "metric_expression": "\u221a34 / 2 = 2.915+", "metric_symbol": "r", "metric_value": 2.915, "reference_text": "r = \u221a34 / 2 = 2.915+ | Found by Erich Friedman | in 1997.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/21.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a34 / 2 = 2.915+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "545b9a64270c81e8", "improvement": -0.10175406268596543, "max_boundary_excess": -5.706230332691575e-06, "max_pair_overlap_depth": -2.743227626145206e-05, "metric_expression": "3.01675", "metric_symbol": "r", "metric_value": 3.0167540626859655, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.915, "setup": "squincir", "side": 6.033508125371931, "solution_path": "data/solutions/generated/squincir_021_545b9a64270c81e8.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/545b9a64270c81e8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@22", "density": 0.7567436824354071, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/22.gif", "friedman_metric_expression": "3.033+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.033, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@22", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "3.033+", "metric_symbol": "r", "metric_value": 3.033, "reference_text": "r = 3.033+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/22.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.033+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "280731f79ac45512", "improvement": -0.00901955895895279, "max_boundary_excess": -6.181418489958901e-06, "max_pair_overlap_depth": -7.085094812397941e-06, "metric_expression": "3.04202", "metric_symbol": "r", "metric_value": 3.0420195589589527, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.033, "setup": "squincir", "side": 6.084039117917905, "solution_path": "data/solutions/generated/squincir_022_280731f79ac45512.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/280731f79ac45512.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@23", "density": 0.7723110310463353, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "June 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/23.gif", "friedman_metric_expression": "3.073+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.073, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@23", "credit": "David W", "date": "June 2002", "family_updated": "4/13/26", "metric_expression": "3.073+", "metric_symbol": "r", "metric_value": 3.073, "reference_text": "r = 3.073+ | Found by David W. Cantrell | in June 2002.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/23.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.073+ | Found by David W. Cantrell | in June 2002.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "1db15c5f1a5b8485", "improvement": -0.005880710049632754, "max_boundary_excess": -7.5142459188271005e-06, "max_pair_overlap_depth": -5.75031423715594e-06, "metric_expression": "3.07888", "metric_symbol": "r", "metric_value": 3.0788807100496327, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.073, "setup": "squincir", "side": 6.157761420099265, "solution_path": "data/solutions/generated/squincir_023_1db15c5f1a5b8485.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1db15c5f1a5b8485.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@24", "density": 0.7887737589513796, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "October 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/24.gif", "friedman_metric_expression": "3.110+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.11, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@24", "credit": "Maurizio Morandi", "date": "October 2010", "family_updated": "4/13/26", "metric_expression": "3.110+", "metric_symbol": "r", "metric_value": 3.11, "reference_text": "r = 3.110+ | Found by Maurizio Morandi | in October 2010.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/24.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.110+ | Found by Maurizio Morandi | in October 2010.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "35e22c7b35c718bd", "improvement": -0.0021065491772924716, "max_boundary_excess": -5.225275177878075e-06, "max_pair_overlap_depth": -2.5024692080766187e-05, "metric_expression": "3.11211", "metric_symbol": "r", "metric_value": 3.1121065491772923, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.11, "setup": "squincir", "side": 6.224213098354585, "solution_path": "data/solutions/generated/squincir_024_35e22c7b35c718bd.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/35e22c7b35c718bd.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@25", "density": 0.7754734182393866, "friedman_analytical_or_proved": true, "friedman_credit": "David W", "friedman_date": "April 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/25.gif", "friedman_metric_expression": "\u221a5809 / 24 = 3.175+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.175, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@25", "credit": "David W", "date": "April 2002", "family_updated": "4/13/26", "metric_expression": "\u221a5809 / 24 = 3.175+", "metric_symbol": "r", "metric_value": 3.175, "reference_text": "r = \u221a5809 / 24 = 3.175+ | Found by David W. Cantrell | in April 2002.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/25.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a5809 / 24 = 3.175+ | Found by David W. Cantrell | in April 2002.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "3b37ffd86fe6327a", "improvement": -0.028403237677212534, "max_boundary_excess": -6.0588717007981074e-06, "max_pair_overlap_depth": -2.0645276876063434e-05, "metric_expression": "3.20340", "metric_symbol": "r", "metric_value": 3.2034032376772124, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.175, "setup": "squincir", "side": 6.406806475354425, "solution_path": "data/solutions/generated/squincir_025_3b37ffd86fe6327a.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3b37ffd86fe6327a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@26", "density": 0.7893607526867172, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/26.gif", "friedman_metric_expression": "\u221a41 / 2 = 3.201+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.201, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@26", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/13/26", "metric_expression": "\u221a41 / 2 = 3.201+", "metric_symbol": "r", "metric_value": 3.201, "reference_text": "r = \u221a41 / 2 = 3.201+ | Found by Erich Friedman | in 1997.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/26.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a41 / 2 = 3.201+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "b818374b7af77c7b", "improvement": -0.03697859131233283, "max_boundary_excess": -1.6484463780663816e-06, "max_pair_overlap_depth": -8.144639675689014e-06, "metric_expression": "3.23798", "metric_symbol": "r", "metric_value": 3.237978591312333, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.201, "setup": "squincir", "side": 6.475957182624666, "solution_path": "data/solutions/generated/squincir_026_b818374b7af77c7b.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b818374b7af77c7b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@27", "density": 0.8061217783571584, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "September 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/27.gif", "friedman_metric_expression": "13\u221a145/48 = 3.261+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.261, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@27", "credit": "Maurizio Morandi", "date": "September 2010", "family_updated": "4/13/26", "metric_expression": "13\u221a145/48 = 3.261+", "metric_symbol": "r", "metric_value": 3.261, "reference_text": "r = 13\u221a145/48 = 3.261+ | Found by Maurizio Morandi | in September 2010.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/27.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 13\u221a145/48 = 3.261+ | Found by Maurizio Morandi | in September 2010.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "f9fe04884031db8c", "improvement": -0.004176172420664148, "max_boundary_excess": -6.5880385129446495e-06, "max_pair_overlap_depth": -3.0313768759615556e-05, "metric_expression": "3.26518", "metric_symbol": "r", "metric_value": 3.2651761724206643, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.261, "setup": "squincir", "side": 6.5303523448413285, "solution_path": "data/solutions/generated/squincir_027_f9fe04884031db8c.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f9fe04884031db8c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@28", "density": 0.7968013155099472, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/28.gif", "friedman_metric_expression": "3.333+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.333, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@28", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "3.333+", "metric_symbol": "r", "metric_value": 3.333, "reference_text": "r = 3.333+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/28.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.333+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "011f385483141804", "improvement": -0.01148350311862334, "max_boundary_excess": -5.831944030365577e-06, "max_pair_overlap_depth": -2.2494860222238566e-05, "metric_expression": "3.34448", "metric_symbol": "r", "metric_value": 3.3444835031186235, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.333, "setup": "squincir", "side": 6.688967006237247, "solution_path": "data/solutions/generated/squincir_028_011f385483141804.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/011f385483141804.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@29", "density": 0.7843503314030067, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/29.gif", "friedman_metric_expression": "3.401+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.401, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@29", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "3.401+", "metric_symbol": "r", "metric_value": 3.401, "reference_text": "r = 3.401+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/29.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.401+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "cf50b73c19c6c40b", "improvement": -0.029591604149518336, "max_boundary_excess": -4.165886964724308e-06, "max_pair_overlap_depth": -7.4185418389438595e-06, "metric_expression": "3.43059", "metric_symbol": "r", "metric_value": 3.430591604149518, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.401, "setup": "squincir", "side": 6.861183208299036, "solution_path": "data/solutions/generated/squincir_029_cf50b73c19c6c40b.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/cf50b73c19c6c40b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@30", "density": 0.7646048232029935, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/30.gif", "friedman_metric_expression": "3.472+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.472, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@30", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "3.472+", "metric_symbol": "r", "metric_value": 3.472, "reference_text": "r = 3.472+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/30.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.472+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "86c752cf32b3c6a2", "improvement": -0.062005120095738775, "max_boundary_excess": -9.387146362449528e-07, "max_pair_overlap_depth": -6.215341934290297e-06, "metric_expression": "3.53401", "metric_symbol": "r", "metric_value": 3.5340051200957388, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.472, "setup": "squincir", "side": 7.0680102401914775, "solution_path": "data/solutions/generated/squincir_030_86c752cf32b3c6a2.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/86c752cf32b3c6a2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@31", "density": 0.7887915525098625, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/31.gif", "friedman_metric_expression": "5 \u221a2 / 2 = 3.535+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.535, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@31", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/13/26", "metric_expression": "5 \u221a2 / 2 = 3.535+", "metric_symbol": "r", "metric_value": 3.535, "reference_text": "r = 5 \u221a2 / 2 = 3.535+ | Found by Erich Friedman | in 1997.", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/31.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 5 \u221a2 / 2 = 3.535+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "fdf9170d30584f4f", "improvement": -0.0019163212872146396, "max_boundary_excess": -2.62119976746078e-06, "max_pair_overlap_depth": -1.7231292489316985e-05, "metric_expression": "3.53692", "metric_symbol": "r", "metric_value": 3.536916321287215, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.535, "setup": "squincir", "side": 7.07383264257443, "solution_path": "data/solutions/generated/squincir_031_fdf9170d30584f4f.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/fdf9170d30584f4f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@32", "density": 0.7813393021086736, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/32.gif", "friedman_metric_expression": "3.584+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.584, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@32", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/13/26", "metric_expression": "3.584+", "metric_symbol": "r", "metric_value": 3.584, "reference_text": "r = 3.584+ | Found by Jonathan Viquerat | in April 2026.", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/32.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.584+ | Found by Jonathan Viquerat | in April 2026.", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "a2628e58e58416df", "improvement": -0.026606982319385075, "max_boundary_excess": -6.923398601088593e-07, "max_pair_overlap_depth": -1.9980644787809254e-05, "metric_expression": "3.61061", "metric_symbol": "r", "metric_value": 3.610606982319385, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.584, "setup": "squincir", "side": 7.22121396463877, "solution_path": "data/solutions/generated/squincir_032_a2628e58e58416df.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a2628e58e58416df.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@33", "density": 0.7968327205597623, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/33.gif", "friedman_metric_expression": "\u221a13 = 3.605+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.605, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@33", "credit": "Maurizio Morandi", "date": "June 2010", "family_updated": "4/13/26", "metric_expression": "\u221a13 = 3.605+", "metric_symbol": "r", "metric_value": 3.605, "reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in June 2010.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/33.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in June 2010.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "257aa24f77df5436", "improvement": -0.025767622252558464, "max_boundary_excess": -3.25349697405386e-06, "max_pair_overlap_depth": -4.400650181701771e-06, "metric_expression": "3.63077", "metric_symbol": "r", "metric_value": 3.6307676222525584, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.605, "setup": "squincir", "side": 7.261535244505117, "solution_path": "data/solutions/generated/squincir_033_257aa24f77df5436.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/257aa24f77df5436.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@34", "density": 0.8164819215284571, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif", "friedman_metric_expression": "3.629+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.629, "friedman_reference": {"analytical_or_proved": false, "case": "squincir@34", "credit": "Maurizio Morandi", "date": "December 2010", "family_updated": "4/13/26", "metric_expression": "3.629+", "metric_symbol": "r", "metric_value": 3.629, "reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "4ba00f951e2b00e9", "improvement": -0.011753164259091342, "max_boundary_excess": -5.55479493646871e-06, "max_pair_overlap_depth": -3.971930798929435e-06, "metric_expression": "3.64075", "metric_symbol": "r", "metric_value": 3.6407531642590913, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.629, "setup": "squincir", "side": 7.281506328518183, "solution_path": "data/solutions/generated/squincir_034_4ba00f951e2b00e9.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4ba00f951e2b00e9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squincir@35", "density": 0.8023678123683218, "friedman_analytical_or_proved": true, "friedman_credit": "David Eppstein", "friedman_date": "March 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squincir/35.gif", "friedman_metric_expression": "\u221a53 / 2 = 3.640+", "friedman_metric_symbol": "r", "friedman_metric_value": 3.64, "friedman_reference": {"analytical_or_proved": true, "case": "squincir@35", "credit": "David Eppstein", "date": "March 2002", "family_updated": "4/13/26", "metric_expression": "\u221a53 / 2 = 3.640+", "metric_symbol": "r", "metric_value": 3.64, "reference_text": "r = \u221a53 / 2 = 3.640+ | Found by David Eppstein | in March 2002.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/squincir/35.gif", "source_page": "https://erich-friedman.github.io/packing/squincir/", "title": "Squares in Circles"}, "friedman_reference_text": "r = \u221a53 / 2 = 3.640+ | Found by David Eppstein | in March 2002.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squincir/", "friedman_title": "Squares in Circles", "frontend_seed": true, "id": "c87a08826ad4f52f", "improvement": -0.08625298278185545, "max_boundary_excess": -2.6779267927601325e-06, "max_pair_overlap_depth": -2.0288665861567523e-05, "metric_expression": "3.72625", "metric_symbol": "r", "metric_value": 3.7262529827818556, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.64, "setup": "squincir", "side": 7.452505965563711, "solution_path": "data/solutions/generated/squincir_035_c87a08826ad4f52f.json", "source_url": "https://erich-friedman.github.io/packing/squincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c87a08826ad4f52f.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squindom@1", "density": 0.499990679660235, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@1", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "1-2. | | s = 1 | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "1-2. | | s = 1 | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "557f8de873a17a8e", "improvement": -9.320470070184328e-06, "max_boundary_excess": -3.7525252651882113e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_symbol": "s", "metric_value": 1.0000093204700702, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.0, "setup": "squindom", "side": 2.0000186409401404, "solution_path": "data/solutions/generated/squindom_001_557f8de873a17a8e.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/557f8de873a17a8e.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squindom@2", "density": 0.9999882998008334, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@2", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "1-2. | | s = 1 | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/2.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "1-2. | | s = 1 | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "7684110dce2e5290", "improvement": -5.850150919473052e-06, "max_boundary_excess": -3.463373909884382e-07, "max_pair_overlap_depth": -9.41881114351023e-06, "metric_expression": "1.00001", "metric_symbol": "s", "metric_value": 1.0000058501509195, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.0, "setup": "squindom", "side": 2.000011700301839, "solution_path": "data/solutions/generated/squindom_002_7684110dce2e5290.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7684110dce2e5290.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squindom@3", "density": 0.6666417193387711, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/3.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3/2 = 1.5", "friedman_metric_symbol": "s", "friedman_metric_value": 1.5, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@3", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "3/2 = 1.5", "metric_symbol": "s", "metric_value": 1.5, "reference_text": "3. | | s = 3/2 = 1.5 | Trivial. |", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/3.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "3. | | s = 3/2 = 1.5 | Trivial. |", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "3047ca63de76a853", "improvement": -2.8066531593262667e-05, "max_boundary_excess": -2.0617527398680835e-06, "max_pair_overlap_depth": -1.9554412996725112e-05, "metric_expression": "1.50003", "metric_symbol": "s", "metric_value": 1.5000280665315933, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.5, "setup": "squindom", "side": 3.0000561330631865, "solution_path": "data/solutions/generated/squindom_003_3047ca63de76a853.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3047ca63de76a853.svg", "tolerance": 1e-08, "verified": true}
@@ -358,6 +423,36 @@
 {"case": "squindom@18", "density": 0.9999599238999353, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3", "friedman_metric_symbol": "s", "friedman_metric_value": 3.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@18", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "3", "metric_symbol": "s", "metric_value": 3.0, "reference_text": "14-18. | | s = 3 | Trivial. |", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/18.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "14-18. | | s = 3 | Trivial. |", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "a6900e1fd3f925c6", "improvement": -6.011595701327366e-05, "max_boundary_excess": -8.408701424045262e-07, "max_pair_overlap_depth": -1.079909316636929e-06, "metric_expression": "3.00006", "metric_symbol": "s", "metric_value": 3.0000601159570133, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.0, "setup": "squindom", "side": 6.0001202319140265, "solution_path": "data/solutions/generated/squindom_018_a6900e1fd3f925c6.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a6900e1fd3f925c6.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squindom@19", "density": 0.775441947176532, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/19.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "3 + 1/\u221a5 = 3.447+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.447, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@19", "credit": "Maurizio Morandi", "date": "June 2010", "family_updated": "8/11/12", "metric_expression": "3 + 1/\u221a5 = 3.447+", "metric_symbol": "s", "metric_value": 3.447, "reference_text": "19. | | s = 3 + 1/\u221a5 = 3.447+ | Found by Maurizio Morandi | in June 2010.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/19.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "19. | | s = 3 + 1/\u221a5 = 3.447+ | Found by Maurizio Morandi | in June 2010.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "43609c899290294d", "improvement": -0.05315403726338541, "max_boundary_excess": -2.428479410898632e-06, "max_pair_overlap_depth": -7.462157437188033e-06, "metric_expression": "3.50015", "metric_symbol": "s", "metric_value": 3.5001540372633855, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.447, "setup": "squindom", "side": 7.000308074526771, "solution_path": "data/solutions/generated/squindom_019_43609c899290294d.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/43609c899290294d.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squindom@20", "density": 0.8162860196976518, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "friedman_family_updated": "8/11/12", "friedman_metric_expression": "7/2 = 3.5", "friedman_metric_symbol": "s", "friedman_metric_value": 3.5, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@20", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "7/2 = 3.5", "metric_symbol": "s", "metric_value": 3.5, "reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "4a48c58d60a1f36b", "improvement": -8.6848505622239e-05, "max_boundary_excess": -4.863306484192975e-06, "max_pair_overlap_depth": -2.3696014737728532e-05, "metric_expression": "3.50009", "metric_symbol": "s", "metric_value": 3.5000868485056222, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.5, "setup": "squindom", "side": 7.0001736970112445, "solution_path": "data/solutions/generated/squindom_020_4a48c58d60a1f36b.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4a48c58d60a1f36b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@21", "density": 0.8571139620178546, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "friedman_metric_expression": "7/2 = 3.5", "friedman_metric_symbol": "s", "friedman_metric_value": 3.5, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@21", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "7/2 = 3.5", "metric_symbol": "s", "metric_value": 3.5, "reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "f91a28177536f6d3", "improvement": -5.899570515355279e-05, "max_boundary_excess": -1.8534056853702905e-06, "max_pair_overlap_depth": -1.3464050134803784e-06, "metric_expression": "3.50006", "metric_symbol": "s", "metric_value": 3.5000589957051536, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.5, "setup": "squindom", "side": 7.000117991410307, "solution_path": "data/solutions/generated/squindom_021_f91a28177536f6d3.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f91a28177536f6d3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@22", "density": 0.7632294028003276, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/22.gif", "friedman_metric_expression": "3.745+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.745, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@22", "credit": "David W", "date": "July 2012", "family_updated": "8/11/12", "metric_expression": "3.745+", "metric_symbol": "s", "metric_value": 3.745, "reference_text": "22. | | s = 3.745+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/22.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "22. | | s = 3.745+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "989a2d320ac47881", "improvement": -0.05137230186723096, "max_boundary_excess": -4.945995979444007e-07, "max_pair_overlap_depth": -2.0302838942054535e-05, "metric_expression": "3.79637", "metric_symbol": "s", "metric_value": 3.796372301867231, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.745, "setup": "squindom", "side": 7.592744603734462, "solution_path": "data/solutions/generated/squindom_022_989a2d320ac47881.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/989a2d320ac47881.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@23", "density": 0.7323860287330793, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2010", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/23.gif", "friedman_metric_expression": "3.849+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.849, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@23", "credit": "Maurizio Morandi", "date": "June 2010", "family_updated": "8/11/12", "metric_expression": "3.849+", "metric_symbol": "s", "metric_value": 3.849, "reference_text": "23. | | s = 3.849+ | Found by Maurizio Morandi | in June 2010. |", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/23.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "23. | | s = 3.849+ | Found by Maurizio Morandi | in June 2010. |", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "be71e0d7682bb396", "improvement": -0.11358776902416201, "max_boundary_excess": -2.7793613528448446e-06, "max_pair_overlap_depth": -3.2193829610394076e-05, "metric_expression": "3.96259", "metric_symbol": "s", "metric_value": 3.962587769024162, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.849, "setup": "squindom", "side": 7.925175538048324, "solution_path": "data/solutions/generated/squindom_023_be71e0d7682bb396.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/be71e0d7682bb396.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@24", "density": 0.749951952861505, "friedman_analytical_or_proved": false, "friedman_credit": "DC after MM", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/24.gif", "friedman_metric_expression": "3.882+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.882, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@24", "credit": "DC after MM", "date": "August 2012", "family_updated": "8/11/12", "metric_expression": "3.882+", "metric_symbol": "s", "metric_value": 3.882, "reference_text": "24. | | s = 3.882+ | Found by DC after MM | in August 2012. |", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/24.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "24. | | s = 3.882+ | Found by DC after MM | in August 2012. |", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "8434a88a5e3ff85b", "improvement": -0.11812813185905613, "max_boundary_excess": -1.6922520051920742e-07, "max_pair_overlap_depth": -6.00535206030095e-06, "metric_expression": "4.00013", "metric_symbol": "s", "metric_value": 4.000128131859056, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.882, "setup": "squindom", "side": 8.000256263718112, "solution_path": "data/solutions/generated/squindom_024_8434a88a5e3ff85b.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8434a88a5e3ff85b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@25", "density": 0.7811918228636051, "friedman_analytical_or_proved": false, "friedman_credit": "DC after MM", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/25.gif", "friedman_metric_expression": "3.939+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.939, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@25", "credit": "DC after MM", "date": "August 2012", "family_updated": "8/11/12", "metric_expression": "3.939+", "metric_symbol": "s", "metric_value": 3.939, "reference_text": "25. | | s = 3.939+ | Found by DC after MM | in August 2012. |", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/25.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "25. | | s = 3.939+ | Found by DC after MM | in August 2012. |", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "a12363b635eb64f9", "improvement": -0.06114894178762942, "max_boundary_excess": -4.4993947669880185e-06, "max_pair_overlap_depth": -4.185053060101751e-06, "metric_expression": "4.00015", "metric_symbol": "s", "metric_value": 4.0001489417876295, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.939, "setup": "squindom", "side": 8.000297883575259, "solution_path": "data/solutions/generated/squindom_025_a12363b635eb64f9.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a12363b635eb64f9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@26", "density": 0.8124517452057956, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/26.gif", "friedman_metric_expression": "3.981+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.981, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@26", "credit": "David W", "date": "July 2012", "family_updated": "8/11/12", "metric_expression": "3.981+", "metric_symbol": "s", "metric_value": 3.981, "reference_text": "26. | | s = 3.981+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in July 2012.)", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/26.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "26. | | s = 3.981+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in July 2012.)", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "e7ee6dac796acc73", "improvement": -0.019118786323000236, "max_boundary_excess": -1.3997631964635104e-06, "max_pair_overlap_depth": -1.7317256868931707e-05, "metric_expression": "4.00012", "metric_symbol": "s", "metric_value": 4.000118786323, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.981, "setup": "squindom", "side": 8.000237572646, "solution_path": "data/solutions/generated/squindom_026_e7ee6dac796acc73.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e7ee6dac796acc73.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@27", "density": 0.8436994977206457, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@27", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "c68e03cc8f5005db", "improvement": -0.00011971448073744284, "max_boundary_excess": -5.175631390130775e-07, "max_pair_overlap_depth": -1.4466911184563003e-06, "metric_expression": "4.00012", "metric_symbol": "s", "metric_value": 4.000119714480737, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.000239428961475, "solution_path": "data/solutions/generated/squindom_027_c68e03cc8f5005db.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c68e03cc8f5005db.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@28", "density": 0.8749068629130922, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@28", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "2c8c79126d60cdac", "improvement": -0.00021290176655508475, "max_boundary_excess": -4.243746303256302e-06, "max_pair_overlap_depth": -1.6386799395987463e-05, "metric_expression": "4.00021", "metric_symbol": "s", "metric_value": 4.000212901766555, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.00042580353311, "solution_path": "data/solutions/generated/squindom_028_2c8c79126d60cdac.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/2c8c79126d60cdac.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@29", "density": 0.9062096331295707, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@29", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d2548471aff7d9f5", "improvement": -8.908848335043018e-05, "max_boundary_excess": -2.8156140130519702e-06, "max_pair_overlap_depth": -2.026030487822794e-06, "metric_expression": "4.00009", "metric_symbol": "s", "metric_value": 4.00008908848335, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.0001781769667, "solution_path": "data/solutions/generated/squindom_029_d2548471aff7d9f5.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d2548471aff7d9f5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@30", "density": 0.9374597146255952, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@30", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d67a491f7b4498c0", "improvement": -8.594490193214455e-05, "max_boundary_excess": -4.188605266186585e-06, "max_pair_overlap_depth": -1.644068809536492e-06, "metric_expression": "4.00009", "metric_symbol": "s", "metric_value": 4.000085944901932, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.000171889803864, "solution_path": "data/solutions/generated/squindom_030_d67a491f7b4498c0.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d67a491f7b4498c0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@31", "density": 0.7739764441627971, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@31", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "0cd7148786dfe563", "improvement": -0.475092096951764, "max_boundary_excess": -3.4161928574860667e-07, "max_pair_overlap_depth": -6.1565491136228445e-06, "metric_expression": "4.47509", "metric_symbol": "s", "metric_value": 4.475092096951764, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 8.950184193903528, "solution_path": "data/solutions/generated/squindom_031_0cd7148786dfe563.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0cd7148786dfe563.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@32", "density": 0.7578873061721337, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "friedman_metric_expression": "4", "friedman_metric_symbol": "s", "friedman_metric_value": 4.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@32", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "4", "metric_symbol": "s", "metric_value": 4.0, "reference_text": "27-32. | | s = 4 | Trivial. | |", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "27-32. | | s = 4 | Trivial. | |", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "bdb0d7e9df92fbf4", "improvement": -0.5947054414830362, "max_boundary_excess": -3.94234973111196e-06, "max_pair_overlap_depth": -1.3360178682031432e-05, "metric_expression": "4.59471", "metric_symbol": "s", "metric_value": 4.594705441483036, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.0, "setup": "squindom", "side": 9.189410882966072, "solution_path": "data/solutions/generated/squindom_032_bdb0d7e9df92fbf4.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/bdb0d7e9df92fbf4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@33", "density": 0.7924875037083852, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/33.gif", "friedman_metric_expression": "3 + \u221a2 = 4.414+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.414, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@33", "credit": "Maurizio Morandi", "date": "July 2012", "family_updated": "8/11/12", "metric_expression": "3 + \u221a2 = 4.414+", "metric_symbol": "s", "metric_value": 4.414, "reference_text": "33. | | s = 3 + \u221a2 = 4.414+ | Found by Maurizio Morandi | in July 2012.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/33.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "33. | | s = 3 + \u221a2 = 4.414+ | Found by Maurizio Morandi | in July 2012.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "a19cffb18f99454d", "improvement": -0.14895053406809566, "max_boundary_excess": -2.1560594953839993e-07, "max_pair_overlap_depth": -1.1686296140012153e-05, "metric_expression": "4.56295", "metric_symbol": "s", "metric_value": 4.562950534068095, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.414, "setup": "squindom", "side": 9.12590106813619, "solution_path": "data/solutions/generated/squindom_033_a19cffb18f99454d.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a19cffb18f99454d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@34", "density": 0.7871273867322012, "friedman_analytical_or_proved": true, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/34.gif", "friedman_metric_expression": "4 + \u221a2/3 = 4.471+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.471, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@34", "credit": "David W", "date": "July 2012", "family_updated": "8/11/12", "metric_expression": "4 + \u221a2/3 = 4.471+", "metric_symbol": "s", "metric_value": 4.471, "reference_text": "34. | | s = 4 + \u221a2/3 = 4.471+ | Found by David W. Cantrell | in July 2012.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/34.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "34. | | s = 4 + \u221a2/3 = 4.471+ | Found by David W. Cantrell | in July 2012.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "754eaf0840f066aa", "improvement": -0.17631327368950522, "max_boundary_excess": -4.1606841634234115e-06, "max_pair_overlap_depth": -1.4162263952677279e-06, "metric_expression": "4.64731", "metric_symbol": "s", "metric_value": 4.647313273689505, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.471, "setup": "squindom", "side": 9.29462654737901, "solution_path": "data/solutions/generated/squindom_034_754eaf0840f066aa.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/754eaf0840f066aa.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@35", "density": 0.8090793490091304, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "friedman_metric_expression": "9/2 = 4.5", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@35", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "9/2 = 4.5", "metric_symbol": "s", "metric_value": 4.5, "reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "ad3aed979d0e55b8", "improvement": -0.15075504839516718, "max_boundary_excess": -5.213118390301474e-07, "max_pair_overlap_depth": -5.817535690066933e-06, "metric_expression": "4.65076", "metric_symbol": "s", "metric_value": 4.650755048395167, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.5, "setup": "squindom", "side": 9.301510096790334, "solution_path": "data/solutions/generated/squindom_035_ad3aed979d0e55b8.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ad3aed979d0e55b8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@36", "density": 0.7686586705061, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "friedman_metric_expression": "9/2 = 4.5", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@36", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "9/2 = 4.5", "metric_symbol": "s", "metric_value": 4.5, "reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "24e6d7b793012d54", "improvement": -0.3391544918635434, "max_boundary_excess": -1.8108160975138787e-06, "max_pair_overlap_depth": -1.3015245498015915e-05, "metric_expression": "4.83915", "metric_symbol": "s", "metric_value": 4.839154491863543, "n": 36, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.5, "setup": "squindom", "side": 9.678308983727087, "solution_path": "data/solutions/generated/squindom_036_24e6d7b793012d54.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/24e6d7b793012d54.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@37", "density": 0.8006073518667697, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/37.gif", "friedman_metric_expression": "10 / 3 + \u221a2 = 4.747+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.747, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@37", "credit": "Maurizio Morandi", "date": "August 2012", "family_updated": "8/11/12", "metric_expression": "10 / 3 + \u221a2 = 4.747+", "metric_symbol": "s", "metric_value": 4.747, "reference_text": "37. | | s = 10 / 3 + \u221a2 = 4.747+ | Found by Maurizio Morandi | in August 2012.", "source_image": "37.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/37.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "37. | | s = 10 / 3 + \u221a2 = 4.747+ | Found by Maurizio Morandi | in August 2012.", "friedman_source_image": "37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "4eb7698c43b9de17", "improvement": -0.06002164063443782, "max_boundary_excess": -4.250322036547516e-06, "max_pair_overlap_depth": -2.0290028124314574e-05, "metric_expression": "4.80702", "metric_symbol": "s", "metric_value": 4.807021640634438, "n": 37, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.747, "setup": "squindom", "side": 9.614043281268875, "solution_path": "data/solutions/generated/squindom_037_4eb7698c43b9de17.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4eb7698c43b9de17.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@38", "density": 0.7599740954685258, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/38.gif", "friedman_metric_expression": "(13 + \u221a2) / 3 = 4.804+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.804, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@38", "credit": "Maurizio Morandi", "date": "August 2012", "family_updated": "8/11/12", "metric_expression": "(13 + \u221a2) / 3 = 4.804+", "metric_symbol": "s", "metric_value": 4.804, "reference_text": "38. | | s = (13 + \u221a2) / 3 = 4.804+ | Found by Maurizio Morandi | in August 2012.", "source_image": "38.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/38.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "38. | | s = (13 + \u221a2) / 3 = 4.804+ | Found by Maurizio Morandi | in August 2012.", "friedman_source_image": "38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "605d8eeb30140800", "improvement": -0.19608521445298788, "max_boundary_excess": -7.686459193578797e-07, "max_pair_overlap_depth": -7.347636921672951e-06, "metric_expression": "5.00009", "metric_symbol": "s", "metric_value": 5.000085214452988, "n": 38, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.804, "setup": "squindom", "side": 10.000170428905976, "solution_path": "data/solutions/generated/squindom_038_605d8eeb30140800.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/605d8eeb30140800.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@39", "density": 0.8096978209200016, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/39.gif", "friedman_metric_expression": "4.839+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.839, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@39", "credit": "David W", "date": "August 2012", "family_updated": "8/11/12", "metric_expression": "4.839+", "metric_symbol": "s", "metric_value": 4.839, "reference_text": "39. | | s = 4.839+ | Found by David W. Cantrell | in August 2012.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/39.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "39. | | s = 4.839+ | Found by David W. Cantrell | in August 2012.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "1909884844694062", "improvement": -0.06844928798604677, "max_boundary_excess": -1.909331257099467e-06, "max_pair_overlap_depth": -1.5029850171544012e-05, "metric_expression": "4.90745", "metric_symbol": "s", "metric_value": 4.907449287986047, "n": 39, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.839, "setup": "squindom", "side": 9.814898575972094, "solution_path": "data/solutions/generated/squindom_039_1909884844694062.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1909884844694062.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@40", "density": 0.812314131386038, "friedman_analytical_or_proved": false, "friedman_credit": "Sigvart Brendberg", "friedman_date": "June 2023", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/40.gif", "friedman_metric_expression": "4.895+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.895, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@40", "credit": "Sigvart Brendberg", "date": "June 2023", "family_updated": "8/11/12", "metric_expression": "4.895+", "metric_symbol": "s", "metric_value": 4.895, "reference_text": "40. | | s = 4.895+ | Found by Sigvart Brendberg | in June 2023.", "source_image": "40.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/40.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "40. | | s = 4.895+ | Found by Sigvart Brendberg | in June 2023.", "friedman_source_image": "40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "c766413f09b40b68", "improvement": -0.06695696807005191, "max_boundary_excess": -4.842672254312674e-07, "max_pair_overlap_depth": -3.709534701634709e-07, "metric_expression": "4.96196", "metric_symbol": "s", "metric_value": 4.9619569680700515, "n": 40, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.895, "setup": "squindom", "side": 9.923913936140103, "solution_path": "data/solutions/generated/squindom_040_c766413f09b40b68.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c766413f09b40b68.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@41", "density": 0.8199463395063403, "friedman_analytical_or_proved": false, "friedman_credit": "Sigvart Brendberg", "friedman_date": "June 2023", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif", "friedman_metric_expression": "4.927+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.927, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@41", "credit": "Sigvart Brendberg", "date": "June 2023", "family_updated": "8/11/12", "metric_expression": "4.927+", "metric_symbol": "s", "metric_value": 4.927, "reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.", "source_image": "41.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.", "friedman_source_image": "41.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "0c31d560a372d60c", "improvement": -0.07316360709587055, "max_boundary_excess": -3.348749109122196e-06, "max_pair_overlap_depth": -8.659590140513984e-06, "metric_expression": "5.00016", "metric_symbol": "s", "metric_value": 5.00016360709587, "n": 41, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.927, "setup": "squindom", "side": 10.00032721419174, "solution_path": "data/solutions/generated/squindom_041_0c31d560a372d60c.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0c31d560a372d60c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@42", "density": 0.8399379995423308, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/42.gif", "friedman_metric_expression": "4.989+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.989, "friedman_reference": {"analytical_or_proved": false, "case": "squindom@42", "credit": "David W", "date": "August 2012", "family_updated": "8/11/12", "metric_expression": "4.989+", "metric_symbol": "s", "metric_value": 4.989, "reference_text": "42. | | s = 4.989+ | Found by David W. Cantrell | in August 2012.", "source_image": "42.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/42.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "42. | | s = 4.989+ | Found by David W. Cantrell | in August 2012.", "friedman_source_image": "42.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "487471a1c6b8324e", "improvement": -0.011184535387124939, "max_boundary_excess": -1.9513369720058904e-06, "max_pair_overlap_depth": -9.964808349360865e-06, "metric_expression": "5.00018", "metric_symbol": "s", "metric_value": 5.000184535387125, "n": 42, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.989, "setup": "squindom", "side": 10.00036907077425, "solution_path": "data/solutions/generated/squindom_042_487471a1c6b8324e.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/487471a1c6b8324e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@43", "density": 0.859888117316887, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@43", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "7f9527ccddc9d648", "improvement": -0.00032527209571497906, "max_boundary_excess": -5.1461540806485566e-08, "max_pair_overlap_depth": -2.005039219099558e-06, "metric_expression": "5.00033", "metric_symbol": "s", "metric_value": 5.000325272095715, "n": 43, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.00065054419143, "solution_path": "data/solutions/generated/squindom_043_7f9527ccddc9d648.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7f9527ccddc9d648.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@44", "density": 0.8799631966546829, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@44", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "1ffd758f1f058de5", "improvement": -0.00010455823792376862, "max_boundary_excess": -4.245467354557775e-06, "max_pair_overlap_depth": -3.962242465904708e-06, "metric_expression": "5.00010", "metric_symbol": "s", "metric_value": 5.000104558237924, "n": 44, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000209116475848, "solution_path": "data/solutions/generated/squindom_044_1ffd758f1f058de5.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1ffd758f1f058de5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@45", "density": 0.8999501217119913, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@45", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "d085ed9682ca2968", "improvement": -0.00013855655918781906, "max_boundary_excess": -1.0485935568738114e-06, "max_pair_overlap_depth": -1.361329106774889e-06, "metric_expression": "5.00014", "metric_symbol": "s", "metric_value": 5.000138556559188, "n": 45, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000277113118376, "solution_path": "data/solutions/generated/squindom_045_d085ed9682ca2968.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d085ed9682ca2968.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@46", "density": 0.9198953665582859, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@46", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "3b408e84cd206068", "improvement": -0.00028435426002282327, "max_boundary_excess": -1.1757865436834436e-06, "max_pair_overlap_depth": -7.423155479191479e-07, "metric_expression": "5.00028", "metric_symbol": "s", "metric_value": 5.000284354260023, "n": 46, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000568708520046, "solution_path": "data/solutions/generated/squindom_046_3b408e84cd206068.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3b408e84cd206068.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@47", "density": 0.8112850662286475, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@47", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "1d33d4d710718c8f", "improvement": -0.3820433347024714, "max_boundary_excess": -3.5226864758541865e-07, "max_pair_overlap_depth": -1.2150556394807666e-05, "metric_expression": "5.38204", "metric_symbol": "s", "metric_value": 5.382043334702471, "n": 47, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.764086669404943, "solution_path": "data/solutions/generated/squindom_047_1d33d4d710718c8f.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1d33d4d710718c8f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@48", "density": 0.9599518570950978, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@48", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "0433c6294c4f3fe7", "improvement": -0.00012537686383318203, "max_boundary_excess": -1.0555756748686917e-06, "max_pair_overlap_depth": -4.3576353303542703e-07, "metric_expression": "5.00013", "metric_symbol": "s", "metric_value": 5.000125376863833, "n": 48, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.000250753727666, "solution_path": "data/solutions/generated/squindom_048_0433c6294c4f3fe7.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0433c6294c4f3fe7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@49", "density": 0.8116252692377275, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@49", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "7b7595adf7fbed15", "improvement": -0.49421009081703016, "max_boundary_excess": -1.0264156866668372e-06, "max_pair_overlap_depth": -6.939509280323719e-06, "metric_expression": "5.49421", "metric_symbol": "s", "metric_value": 5.49421009081703, "n": 49, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 10.98842018163406, "solution_path": "data/solutions/generated/squindom_049_7b7595adf7fbed15.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7b7595adf7fbed15.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squindom@50", "density": 0.8001461788909812, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "squindom@50", "credit": "Trivial", "date": "", "family_updated": "8/11/12", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "43-50. | | s = 5 | Trivial. |", "source_image": "50.gif", "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif", "source_page": "https://erich-friedman.github.io/packing/squindom/", "title": "Squares in Dominoes"}, "friedman_reference_text": "43-50. | | s = 5 | Trivial. |", "friedman_source_image": "50.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squindom/", "friedman_title": "Squares in Dominoes", "frontend_seed": true, "id": "1dc2963cf23fe9ee", "improvement": -0.5896592857036387, "max_boundary_excess": -3.2315115903180924e-06, "max_pair_overlap_depth": -1.8572326916821424e-05, "metric_expression": "5.58966", "metric_symbol": "s", "metric_value": 5.589659285703639, "n": 50, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "squindom", "side": 11.179318571407277, "solution_path": "data/solutions/generated/squindom_050_1dc2963cf23fe9ee.json", "source_url": "https://erich-friedman.github.io/packing/squindom/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1dc2963cf23fe9ee.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squinhex@1", "density": 0.6187916671304767, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/1.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(3+\u221a3)/6 = 0.778+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.778, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@1", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "(3+\u221a3)/6 = 0.778+", "metric_symbol": "s", "metric_value": 0.778, "reference_text": "s = (3+\u221a3)/6 = 0.778+ | Trivial. |", "source_image": "1.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/1.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = (3+\u221a3)/6 = 0.778+ | Trivial. |", "friedman_source_image": "1.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "47260f1f9015c23d", "improvement": -0.010681817229460822, "max_boundary_excess": -3.3038085342535935e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.78868", "metric_symbol": "s", "metric_value": 0.7886818172294608, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.778, "setup": "squinhex", "side": 0.7886818172294608, "solution_path": "data/solutions/generated/squinhex_001_47260f1f9015c23d.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/47260f1f9015c23d.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squinhex@2", "density": 0.5773349997096187, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/2.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2/\u221a3 = 1.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.154, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@2", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "2/\u221a3 = 1.154+", "metric_symbol": "s", "metric_value": 1.154, "reference_text": "s = 2/\u221a3 = 1.154+ | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/2.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2/\u221a3 = 1.154+ | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "21fb35b9b51e59c5", "improvement": -0.0007158081621452261, "max_boundary_excess": -8.964730208767781e-07, "max_pair_overlap_depth": -4.154668371614267e-06, "metric_expression": "1.15472", "metric_symbol": "s", "metric_value": 1.1547158081621451, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.154, "setup": "squinhex", "side": 1.1547158081621451, "solution_path": "data/solutions/generated/squinhex_002_21fb35b9b51e59c5.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/21fb35b9b51e59c5.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squinhex@3", "density": 0.6187647598988664, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/3.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(1+\u221a3)/2 = 1.366+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.366, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@3", "credit": "Maurizio Morandi", "date": "March 2026", "family_updated": "4/29/26", "metric_expression": "(1+\u221a3)/2 = 1.366+", "metric_symbol": "s", "metric_value": 1.366, "reference_text": "s = (1+\u221a3)/2 = 1.366+ | Found by Maurizio Morandi | in March 2026.", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/3.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = (1+\u221a3)/2 = 1.366+ | Found by Maurizio Morandi | in March 2026.", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "a5c3dc7083e49634", "improvement": -6.667945486871218e-05, "max_boundary_excess": -1.5592677317674368e-06, "max_pair_overlap_depth": -3.548280330942233e-05, "metric_expression": "1.36607", "metric_symbol": "s", "metric_value": 1.3660666794548688, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.366, "setup": "squinhex", "side": 1.3660666794548688, "solution_path": "data/solutions/generated/squinhex_003_a5c3dc7083e49634.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a5c3dc7083e49634.svg", "tolerance": 1e-08, "verified": true}
@@ -378,6 +473,26 @@
 {"case": "squinhex@18", "density": 0.8107158050212577, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/18.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.92111+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.92111, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@18", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.92111+", "metric_symbol": "s", "metric_value": 2.92111, "reference_text": "s = 2.92111+ | Found by Ian Watson | in April 2026.", "source_image": "18.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/18.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.92111+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "18.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "e136eeec3de765c3", "improvement": -0.0022075205933282938, "max_boundary_excess": -4.264526989622803e-06, "max_pair_overlap_depth": -7.64695502597501e-06, "metric_expression": "2.92332", "metric_symbol": "s", "metric_value": 2.9233175205933284, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.92111, "setup": "squinhex", "side": 2.9233175205933284, "solution_path": "data/solutions/generated/squinhex_018_e136eeec3de765c3.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e136eeec3de765c3.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squinhex@19", "density": 0.8472470384096148, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/19.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.93511+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.93511, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@19", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.93511+", "metric_symbol": "s", "metric_value": 2.93511, "reference_text": "s = 2.93511+ | Found by Ian Watson | in April 2026.", "source_image": "19.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/19.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2.93511+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "19.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "ae3850bdb0ac1880", "improvement": -0.0028496545666087947, "max_boundary_excess": -6.965076151420116e-06, "max_pair_overlap_depth": -7.201359447650546e-06, "metric_expression": "2.93796", "metric_symbol": "s", "metric_value": 2.9379596545666087, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.93511, "setup": "squinhex", "side": 2.9379596545666087, "solution_path": "data/solutions/generated/squinhex_019_ae3850bdb0ac1880.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ae3850bdb0ac1880.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squinhex@20", "density": 0.7671837266988989, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/20.png", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.16123+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.16123, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@20", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.16123+", "metric_symbol": "s", "metric_value": 3.16123, "reference_text": "s = 3.16123+ | Found by Ian Watson | in April 2026.", "source_image": "20.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/20.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.16123+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "20.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "6b12994046713635", "improvement": -0.0064358571960680955, "max_boundary_excess": -2.567971421646714e-06, "max_pair_overlap_depth": -2.07090961877876e-05, "metric_expression": "3.16767", "metric_symbol": "s", "metric_value": 3.1676658571960683, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.16123, "setup": "squinhex", "side": 3.1676658571960683, "solution_path": "data/solutions/generated/squinhex_020_6b12994046713635.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6b12994046713635.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@21", "density": 0.7670273555344158, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png", "friedman_metric_expression": "3.23496+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.23496, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@21", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.23496+", "metric_symbol": "s", "metric_value": 3.23496, "reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.", "source_image": "21.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "21.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "3a812c823f86feb7", "improvement": -0.011262455551525274, "max_boundary_excess": -1.638368640602293e-06, "max_pair_overlap_depth": -6.590999670152975e-06, "metric_expression": "3.24622", "metric_symbol": "s", "metric_value": 3.2462224555515253, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.23496, "setup": "squinhex", "side": 3.2462224555515253, "solution_path": "data/solutions/generated/squinhex_021_3a812c823f86feb7.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3a812c823f86feb7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@22", "density": 0.770525380181529, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/22.png", "friedman_metric_expression": "3.31573+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.31573, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@22", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.31573+", "metric_symbol": "s", "metric_value": 3.31573, "reference_text": "s = 3.31573+ | Found by Ian Watson | in April 2026.", "source_image": "22.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/22.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.31573+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "22.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "a1e7eaf12003fa2e", "improvement": 0.0006659560348909466, "max_boundary_excess": -2.169977234601665e-06, "max_pair_overlap_depth": -1.9814540655582746e-05, "metric_expression": "3.31506", "metric_symbol": "s", "metric_value": 3.315064043965109, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.31573, "setup": "squinhex", "side": 3.315064043965109, "solution_path": "data/solutions/generated/squinhex_022_a1e7eaf12003fa2e.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a1e7eaf12003fa2e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@23", "density": 0.7678817589014695, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/23.png", "friedman_metric_expression": "3.36437+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.36437, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@23", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.36437+", "metric_symbol": "s", "metric_value": 3.36437, "reference_text": "s = 3.36437+ | Found by Ian Watson | in April 2026.", "source_image": "23.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/23.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.36437+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "23.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "c418f25bcf52655a", "improvement": -0.031028866190116577, "max_boundary_excess": -3.0072288037779673e-06, "max_pair_overlap_depth": -3.3623152545181334e-05, "metric_expression": "3.39540", "metric_symbol": "s", "metric_value": 3.3953988661901167, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.36437, "setup": "squinhex", "side": 3.3953988661901167, "solution_path": "data/solutions/generated/squinhex_023_c418f25bcf52655a.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c418f25bcf52655a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@24", "density": 0.7853118981105532, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/24.png", "friedman_metric_expression": "3.41524+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.41524, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@24", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.41524+", "metric_symbol": "s", "metric_value": 3.41524, "reference_text": "s = 3.41524+ | Found by Ian Watson | in April 2026.", "source_image": "24.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/24.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.41524+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "24.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "94da47c0085910e3", "improvement": -0.014479391564234945, "max_boundary_excess": -2.620667464817998e-06, "max_pair_overlap_depth": -1.0754243918387196e-05, "metric_expression": "3.42972", "metric_symbol": "s", "metric_value": 3.4297193915642348, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.41524, "setup": "squinhex", "side": 3.4297193915642348, "solution_path": "data/solutions/generated/squinhex_024_94da47c0085910e3.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/94da47c0085910e3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@25", "density": 0.7979870877832509, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/25.png", "friedman_metric_expression": "2\u221a3 = 3.46410+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.4641, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@25", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "2\u221a3 = 3.46410+", "metric_symbol": "s", "metric_value": 3.4641, "reference_text": "s = 2\u221a3 = 3.46410+ | Trivial. |", "source_image": "25.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/25.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 2\u221a3 = 3.46410+ | Trivial. |", "friedman_source_image": "25.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "e42cc21b7cb42f7c", "improvement": -0.008430980948480382, "max_boundary_excess": -4.683096739436409e-06, "max_pair_overlap_depth": -1.8538188668593136e-06, "metric_expression": "3.47253", "metric_symbol": "s", "metric_value": 3.4725309809484806, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.4641, "setup": "squinhex", "side": 3.4725309809484806, "solution_path": "data/solutions/generated/squinhex_025_e42cc21b7cb42f7c.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e42cc21b7cb42f7c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@26", "density": 0.8081929307719398, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/26.png", "friedman_metric_expression": "3.4939927+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.4939927, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@26", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.4939927+", "metric_symbol": "s", "metric_value": 3.4939927, "reference_text": "s = 3.4939927+ | Found by Ian Watson | in April 2026.", "source_image": "26.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/26.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.4939927+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "26.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "ffb43ba6e2cd5818", "improvement": -0.02487717357936603, "max_boundary_excess": -9.15748884603073e-07, "max_pair_overlap_depth": -3.1303960409623244e-05, "metric_expression": "3.51887", "metric_symbol": "s", "metric_value": 3.518869873579366, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.4939927, "setup": "squinhex", "side": 3.518869873579366, "solution_path": "data/solutions/generated/squinhex_026_ffb43ba6e2cd5818.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ffb43ba6e2cd5818.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@27", "density": 0.8212390180142829, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/27.png", "friedman_metric_expression": "(9+7\u221a3)/6 = 3.52072+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.52072, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@27", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "(9+7\u221a3)/6 = 3.52072+", "metric_symbol": "s", "metric_value": 3.52072, "reference_text": "s = (9+7\u221a3)/6 = 3.52072+ | Found by Erich Friedman | in April 2026.", "source_image": "27.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/27.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = (9+7\u221a3)/6 = 3.52072+ | Found by Erich Friedman | in April 2026.", "friedman_source_image": "27.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "1daf4383b04cfd35", "improvement": -0.03658539789192261, "max_boundary_excess": -5.73679317656282e-06, "max_pair_overlap_depth": -8.244431831005983e-06, "metric_expression": "3.55731", "metric_symbol": "s", "metric_value": 3.5573053978919225, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.52072, "setup": "squinhex", "side": 3.5573053978919225, "solution_path": "data/solutions/generated/squinhex_027_1daf4383b04cfd35.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1daf4383b04cfd35.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@28", "density": 0.8148431181294798, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/28.png", "friedman_metric_expression": "3.62565+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.62565, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@28", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.62565+", "metric_symbol": "s", "metric_value": 3.62565, "reference_text": "s = 3.62565+ | Found by Ian Watson | in April 2026.", "source_image": "28.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/28.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.62565+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "28.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "a261c762e391859b", "improvement": -0.011121972861151797, "max_boundary_excess": -1.2588144775567533e-07, "max_pair_overlap_depth": -1.6737569052738266e-05, "metric_expression": "3.63677", "metric_symbol": "s", "metric_value": 3.6367719728611516, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.62565, "setup": "squinhex", "side": 3.6367719728611516, "solution_path": "data/solutions/generated/squinhex_028_a261c762e391859b.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a261c762e391859b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@29", "density": 0.8153965094821096, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/29.png", "friedman_metric_expression": "3.66437+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.66437, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@29", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.66437+", "metric_symbol": "s", "metric_value": 3.66437, "reference_text": "s = 3.66437+ | Found by Ian Watson | in April 2026.", "source_image": "29.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/29.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.66437+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "29.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "b4f34cc71652a9b5", "improvement": -0.03551846072849152, "max_boundary_excess": -4.2642198528972326e-06, "max_pair_overlap_depth": -2.258360826079553e-05, "metric_expression": "3.69989", "metric_symbol": "s", "metric_value": 3.6998884607284914, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.66437, "setup": "squinhex", "side": 3.6998884607284914, "solution_path": "data/solutions/generated/squinhex_029_b4f34cc71652a9b5.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b4f34cc71652a9b5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@30", "density": 0.837162051280775, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/30.png", "friedman_metric_expression": "3.69554+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.69554, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@30", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.69554+", "metric_symbol": "s", "metric_value": 3.69554, "reference_text": "s = 3.69554+ | Found by Ian Watson | in April 2026.", "source_image": "30.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/30.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.69554+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "30.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "622f4b213176ff50", "improvement": -0.01835753389360395, "max_boundary_excess": -4.942525026869045e-06, "max_pair_overlap_depth": -2.8250288841569215e-05, "metric_expression": "3.71390", "metric_symbol": "s", "metric_value": 3.7138975338936038, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.69554, "setup": "squinhex", "side": 3.7138975338936038, "solution_path": "data/solutions/generated/squinhex_030_622f4b213176ff50.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/622f4b213176ff50.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@31", "density": 0.8285110718813824, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/31.png", "friedman_metric_expression": "3.78410+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.7841, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.78410+", "metric_symbol": "s", "metric_value": 3.7841, "reference_text": "s = 3.78410+ | Found by Emerson Connelly | in April 2026.", "source_image": "31.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/31.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.78410+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "31.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "5ef6ed65925f4bf8", "improvement": -0.010847266536003097, "max_boundary_excess": -1.2328982304959355e-06, "max_pair_overlap_depth": -1.5474800372561326e-05, "metric_expression": "3.79495", "metric_symbol": "s", "metric_value": 3.794947266536003, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.7841, "setup": "squinhex", "side": 3.794947266536003, "solution_path": "data/solutions/generated/squinhex_031_5ef6ed65925f4bf8.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5ef6ed65925f4bf8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@32", "density": 0.8139313062277866, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/32.png", "friedman_metric_expression": "3.84795+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.84795, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.84795+", "metric_symbol": "s", "metric_value": 3.84795, "reference_text": "s = 3.84795+ | Found by Emerson Connelly | in April 2026.", "source_image": "32.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/32.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.84795+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "32.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "3fefe3c7860a7042", "improvement": -0.04209987405059623, "max_boundary_excess": -9.31294317671141e-06, "max_pair_overlap_depth": -5.122637159571397e-06, "metric_expression": "3.89005", "metric_symbol": "s", "metric_value": 3.890049874050596, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.84795, "setup": "squinhex", "side": 3.890049874050596, "solution_path": "data/solutions/generated/squinhex_032_3fefe3c7860a7042.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3fefe3c7860a7042.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@33", "density": 0.8232428856624427, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/33.png", "friedman_metric_expression": "3.88897+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.88897, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.88897+", "metric_symbol": "s", "metric_value": 3.88897, "reference_text": "s = 3.88897+ | Found by Emerson Connelly | in April 2026.", "source_image": "33.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/33.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.88897+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "33.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "75f6c6042636af47", "improvement": -0.038989792359782616, "max_boundary_excess": -8.523200217199587e-07, "max_pair_overlap_depth": -1.020864303750979e-05, "metric_expression": "3.92796", "metric_symbol": "s", "metric_value": 3.9279597923597827, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.88897, "setup": "squinhex", "side": 3.9279597923597827, "solution_path": "data/solutions/generated/squinhex_033_75f6c6042636af47.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/75f6c6042636af47.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@34", "density": 0.8011598710060369, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/34.png", "friedman_metric_expression": "3.92704+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.92704, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.92704+", "metric_symbol": "s", "metric_value": 3.92704, "reference_text": "s = 3.92704+ | Found by Emerson Connelly | in April 2026.", "source_image": "34.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/34.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.92704+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "34.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "9936488a40de24d9", "improvement": -0.11456551352210997, "max_boundary_excess": -4.6100121240738093e-07, "max_pair_overlap_depth": -4.74894416568894e-06, "metric_expression": "4.04161", "metric_symbol": "s", "metric_value": 4.04160551352211, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.92704, "setup": "squinhex", "side": 4.04160551352211, "solution_path": "data/solutions/generated/squinhex_034_9936488a40de24d9.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9936488a40de24d9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@35", "density": 0.8247475431755152, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/35.png", "friedman_metric_expression": "3.99833+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.99833, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@35", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.99833+", "metric_symbol": "s", "metric_value": 3.99833, "reference_text": "s = 3.99833+ | Found by Emerson Connelly | in April 2026.", "source_image": "35.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/35.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 3.99833+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "af16853a8ef97483", "improvement": -0.04321634902297422, "max_boundary_excess": -2.7980290841403613e-07, "max_pair_overlap_depth": -1.2096346981849138e-06, "metric_expression": "4.04155", "metric_symbol": "s", "metric_value": 4.041546349022974, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.99833, "setup": "squinhex", "side": 4.041546349022974, "solution_path": "data/solutions/generated/squinhex_035_af16853a8ef97483.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/af16853a8ef97483.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@36", "density": 0.8483249224466834, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png", "friedman_metric_expression": "4.03258+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.03258, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@36", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.03258+", "metric_symbol": "s", "metric_value": 4.03258, "reference_text": "s = 4.03258+ | Found by Emerson Connelly | in April 2026.", "source_image": "36.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 4.03258+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "36.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "a763846075248773", "improvement": -0.008934991863539743, "max_boundary_excess": -2.1813389232689927e-06, "max_pair_overlap_depth": -6.121205389897355e-06, "metric_expression": "4.04151", "metric_symbol": "s", "metric_value": 4.04151499186354, "n": 36, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.03258, "setup": "squinhex", "side": 4.04151499186354, "solution_path": "data/solutions/generated/squinhex_036_a763846075248773.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a763846075248773.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@37", "density": 0.8718839158050435, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/37.png", "friedman_metric_expression": "7/\u221a3 = 4.04145+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.04145, "friedman_reference": {"analytical_or_proved": true, "case": "squinhex@37", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "7/\u221a3 = 4.04145+", "metric_symbol": "s", "metric_value": 4.04145, "reference_text": "s = 7/\u221a3 = 4.04145+ | Trivial. |", "source_image": "37.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/37.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 7/\u221a3 = 4.04145+ | Trivial. |", "friedman_source_image": "37.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "a455ecb05be301ad", "improvement": -7.79426845127773e-05, "max_boundary_excess": -1.1637259667017477e-06, "max_pair_overlap_depth": -1.0162747484221413e-05, "metric_expression": "4.04153", "metric_symbol": "s", "metric_value": 4.041527942684513, "n": 37, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.04145, "setup": "squinhex", "side": 4.041527942684513, "solution_path": "data/solutions/generated/squinhex_037_a455ecb05be301ad.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a455ecb05be301ad.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@38", "density": 0.8350388271501855, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/38.png", "friedman_metric_expression": "4.18476+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.18476, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.18476+", "metric_symbol": "s", "metric_value": 4.18476, "reference_text": "s = 4.18476+ | Found by Emerson Connelly | in April 2026.", "source_image": "38.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/38.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 4.18476+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "38.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "bcbfc88586b3e923", "improvement": -0.00040437963386885656, "max_boundary_excess": -1.1747860476968907e-06, "max_pair_overlap_depth": -1.7875980621084864e-05, "metric_expression": "4.18516", "metric_symbol": "s", "metric_value": 4.185164379633869, "n": 38, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.18476, "setup": "squinhex", "side": 4.185164379633869, "solution_path": "data/solutions/generated/squinhex_038_bcbfc88586b3e923.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/bcbfc88586b3e923.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@39", "density": 0.8275155837189719, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/39.png", "friedman_metric_expression": "4.25744+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.25744, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.25744+", "metric_symbol": "s", "metric_value": 4.25744, "reference_text": "s = 4.25744+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/39.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 4.25744+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "85e7e9eb3b3b7f5f", "improvement": -0.001664243334674076, "max_boundary_excess": -3.204496689819836e-06, "max_pair_overlap_depth": -1.602842749781619e-05, "metric_expression": "4.25910", "metric_symbol": "s", "metric_value": 4.259104243334674, "n": 39, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.25744, "setup": "squinhex", "side": 4.259104243334674, "solution_path": "data/solutions/generated/squinhex_039_85e7e9eb3b3b7f5f.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/85e7e9eb3b3b7f5f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinhex@40", "density": 0.8287778526415311, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinhex/40.png", "friedman_metric_expression": "4.31157+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.31157, "friedman_reference": {"analytical_or_proved": false, "case": "squinhex@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.31157+", "metric_symbol": "s", "metric_value": 4.31157, "reference_text": "s = 4.31157+ | Found by Emerson Connelly | in April 2026.", "source_image": "40.png", "source_image_url": "https://erich-friedman.github.io/packing/squinhex/40.png", "source_page": "https://erich-friedman.github.io/packing/squinhex/", "title": "Squares in Hexagons"}, "friedman_reference_text": "s = 4.31157+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "40.png", "friedman_source_url": "https://erich-friedman.github.io/packing/squinhex/", "friedman_title": "Squares in Hexagons", "frontend_seed": true, "id": "f7dadd815b6542ca", "improvement": 0.00149344623519454, "max_boundary_excess": -3.946410988960316e-06, "max_pair_overlap_depth": -1.2739218361978999e-05, "metric_expression": "4.31008", "metric_symbol": "s", "metric_value": 4.310076553764805, "n": 40, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.31157, "setup": "squinhex", "side": 4.310076553764805, "solution_path": "data/solutions/generated/squinhex_040_f7dadd815b6542ca.json", "source_url": "https://erich-friedman.github.io/packing/squinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f7dadd815b6542ca.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squinoct@1", "density": 0.7071036297921394, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/1.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "1/\u221a(2+\u221a2) = .54119+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.54119, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@1", "credit": "Trivial", "date": "", "family_updated": "3/17/26", "metric_expression": "1/\u221a(2+\u221a2) = .54119+", "metric_symbol": "s", "metric_value": 0.54119, "reference_text": "s = 1/\u221a(2+\u221a2) = .54119+ | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/1.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 1/\u221a(2+\u221a2) = .54119+ | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "b63c90f60717ba08", "improvement": -7.30613665711477e-06, "max_boundary_excess": -1.1705346114441018e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.54120", "metric_symbol": "s", "metric_value": 0.5411973061366571, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.54119, "setup": "squinoct", "side": 0.5411973061366571, "solution_path": "data/solutions/generated/squinoct_001_b63c90f60717ba08.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b63c90f60717ba08.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squinoct@2", "density": 0.5389047922692529, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "December 2013", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/2.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": ".87667+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.87667, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@2", "credit": "Maurizio Morandi", "date": "December 2013", "family_updated": "3/17/26", "metric_expression": ".87667+", "metric_symbol": "s", "metric_value": 0.87667, "reference_text": "s = .87667+ | Found by Maurizio Morandi | in December 2013.", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/2.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = .87667+ | Found by Maurizio Morandi | in December 2013.", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "7194ac58cba12fa7", "improvement": -4.0351762315649076e-05, "max_boundary_excess": -8.607981571160174e-06, "max_pair_overlap_depth": -1.1896285956325414e-06, "metric_expression": "0.87671", "metric_symbol": "s", "metric_value": 0.8767103517623156, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.87667, "setup": "squinoct", "side": 0.8767103517623156, "solution_path": "data/solutions/generated/squinoct_002_7194ac58cba12fa7.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7194ac58cba12fa7.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squinoct@3", "density": 0.5862650280603752, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "December 2013", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/3.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "18 \u2013 12\u221a2 = 1.02940+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0294, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@3", "credit": "Erich Friedman", "date": "December 2013", "family_updated": "3/17/26", "metric_expression": "18 \u2013 12\u221a2 = 1.02940+", "metric_symbol": "s", "metric_value": 1.0294, "reference_text": "s = 18 \u2013 12\u221a2 = 1.02940+ | Found by Erich Friedman | in December 2013.", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/3.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 18 \u2013 12\u221a2 = 1.02940+ | Found by Erich Friedman | in December 2013.", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "3d85991afac60053", "improvement": -6.311956912941064e-05, "max_boundary_excess": -1.835100684478856e-06, "max_pair_overlap_depth": -3.4409461626638826e-05, "metric_expression": "1.02946", "metric_symbol": "s", "metric_value": 1.0294631195691295, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.0294, "setup": "squinoct", "side": 1.0294631195691295, "solution_path": "data/solutions/generated/squinoct_003_3d85991afac60053.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3d85991afac60053.svg", "tolerance": 1e-08, "verified": true}
@@ -398,6 +513,16 @@
 {"case": "squinoct@18", "density": 0.7934296897658486, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/18.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.16778+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.16778, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@18", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.16778+", "metric_symbol": "s", "metric_value": 2.16778, "reference_text": "s = 2.16778+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/18.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.16778+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "a7275e2ab7024187", "improvement": 0.00017977070139485463, "max_boundary_excess": -2.9711774532196686e-06, "max_pair_overlap_depth": -1.4522556675777842e-05, "metric_expression": "2.16760", "metric_symbol": "s", "metric_value": 2.167600229298605, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.16778, "setup": "squinoct", "side": 2.167600229298605, "solution_path": "data/solutions/generated/squinoct_018_a7275e2ab7024187.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a7275e2ab7024187.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squinoct@19", "density": 0.793469906795261, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/19.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.22823+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.22823, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.22823+", "metric_symbol": "s", "metric_value": 2.22823, "reference_text": "s = 2.22823+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/19.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.22823+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "330906f1db929cdb", "improvement": 0.0012889040224068893, "max_boundary_excess": -1.0543459428412958e-06, "max_pair_overlap_depth": -1.4850274468458657e-05, "metric_expression": "2.22694", "metric_symbol": "s", "metric_value": 2.226941095977593, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.22823, "setup": "squinoct", "side": 2.226941095977593, "solution_path": "data/solutions/generated/squinoct_019_330906f1db929cdb.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/330906f1db929cdb.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squinoct@20", "density": 0.7898975362386181, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/20.gif", "friedman_family_updated": "3/17/26", "friedman_metric_expression": "2.28730+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.2873, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@20", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.28730+", "metric_symbol": "s", "metric_value": 2.2873, "reference_text": "s = 2.28730+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/20.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.28730+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "a51f6ff7158a3148", "improvement": -0.0026541016910699433, "max_boundary_excess": -1.638361599013347e-06, "max_pair_overlap_depth": -2.1188903268742898e-05, "metric_expression": "2.28995", "metric_symbol": "s", "metric_value": 2.28995410169107, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.2873, "setup": "squinoct", "side": 2.28995410169107, "solution_path": "data/solutions/generated/squinoct_020_a51f6ff7158a3148.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a51f6ff7158a3148.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@21", "density": 0.8091484006744551, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/21.gif", "friedman_metric_expression": "2.32167+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.32167, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@21", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.32167+", "metric_symbol": "s", "metric_value": 2.32167, "reference_text": "s = 2.32167+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/21.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.32167+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "a3759fa0325bb184", "improvement": 0.0032467851108277657, "max_boundary_excess": -2.288437924896875e-06, "max_pair_overlap_depth": -7.589979277911052e-06, "metric_expression": "2.31842", "metric_symbol": "s", "metric_value": 2.3184232148891724, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.32167, "setup": "squinoct", "side": 2.3184232148891724, "solution_path": "data/solutions/generated/squinoct_021_a3759fa0325bb184.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a3759fa0325bb184.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@22", "density": 0.7774325610742356, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/22.gif", "friedman_metric_expression": "2.41811+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.41811, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@22", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.41811+", "metric_symbol": "s", "metric_value": 2.41811, "reference_text": "s = 2.41811+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/22.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.41811+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "bebb10254b247f18", "improvement": -0.0027915964915901093, "max_boundary_excess": -1.6967368563790073e-06, "max_pair_overlap_depth": -1.7892080061754356e-05, "metric_expression": "2.42090", "metric_symbol": "s", "metric_value": 2.42090159649159, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.41811, "setup": "squinoct", "side": 2.42090159649159, "solution_path": "data/solutions/generated/squinoct_022_bebb10254b247f18.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/bebb10254b247f18.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@23", "density": 0.7777209980912639, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/23.gif", "friedman_metric_expression": "2.47329+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.47329, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@23", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.47329+", "metric_symbol": "s", "metric_value": 2.47329, "reference_text": "s = 2.47329+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/23.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.47329+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "004d1c5d4d7bca47", "improvement": -0.0015616154620987643, "max_boundary_excess": -4.985478608046375e-06, "max_pair_overlap_depth": -1.4996046389881279e-05, "metric_expression": "2.47485", "metric_symbol": "s", "metric_value": 2.4748516154620988, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.47329, "setup": "squinoct", "side": 2.4748516154620988, "solution_path": "data/solutions/generated/squinoct_023_004d1c5d4d7bca47.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/004d1c5d4d7bca47.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@24", "density": 0.804709078453695, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/24.gif", "friedman_metric_expression": "6\u221a2 \u2013 6 = 2.48528+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.48528, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@24", "credit": "Trivial", "date": "", "family_updated": "3/17/26", "metric_expression": "6\u221a2 \u2013 6 = 2.48528+", "metric_symbol": "s", "metric_value": 2.48528, "reference_text": "s = 6\u221a2 \u2013 6 = 2.48528+ | Trivial.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/24.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 6\u221a2 \u2013 6 = 2.48528+ | Trivial.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "4f255616aca5e547", "improvement": -4.580955124477981e-05, "max_boundary_excess": -4.67146332394231e-06, "max_pair_overlap_depth": -9.95881463161652e-06, "metric_expression": "2.48533", "metric_symbol": "s", "metric_value": 2.4853258095512447, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.48528, "setup": "squinoct", "side": 2.4853258095512447, "solution_path": "data/solutions/generated/squinoct_024_4f255616aca5e547.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4f255616aca5e547.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@25", "density": 0.8181498541161091, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/25.gif", "friedman_metric_expression": "11/(3+\u221a2) = 2.49195+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.49195, "friedman_reference": {"analytical_or_proved": true, "case": "squinoct@25", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "11/(3+\u221a2) = 2.49195+", "metric_symbol": "s", "metric_value": 2.49195, "reference_text": "s = 11/(3+\u221a2) = 2.49195+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/25.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 11/(3+\u221a2) = 2.49195+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "cf47f0214a5dc773", "improvement": -0.023702995861961007, "max_boundary_excess": -3.2684625650520232e-06, "max_pair_overlap_depth": -1.853051245270798e-05, "metric_expression": "2.51565", "metric_symbol": "s", "metric_value": 2.515652995861961, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.49195, "setup": "squinoct", "side": 2.515652995861961, "solution_path": "data/solutions/generated/squinoct_025_cf47f0214a5dc773.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/cf47f0214a5dc773.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@26", "density": 0.8074475115340339, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/26.gif", "friedman_metric_expression": "2.52841+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.52841, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@26", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.52841+", "metric_symbol": "s", "metric_value": 2.52841, "reference_text": "s = 2.52841+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/26.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.52841+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "5b23f9a6c0d60139", "improvement": -0.054008850877670156, "max_boundary_excess": -2.200162939176049e-06, "max_pair_overlap_depth": -3.6095353424636656e-05, "metric_expression": "2.58242", "metric_symbol": "s", "metric_value": 2.58241885087767, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.52841, "setup": "squinoct", "side": 2.58241885087767, "solution_path": "data/solutions/generated/squinoct_026_5b23f9a6c0d60139.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5b23f9a6c0d60139.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@27", "density": 0.8082183491889691, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/27.gif", "friedman_metric_expression": "2.58695+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.58695, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@27", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.58695+", "metric_symbol": "s", "metric_value": 2.58695, "reference_text": "s = 2.58695+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/27.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.58695+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "7199a9fabf8295f3", "improvement": -0.0434069531833039, "max_boundary_excess": -5.468946855752342e-06, "max_pair_overlap_depth": -2.0325723741110302e-05, "metric_expression": "2.63036", "metric_symbol": "s", "metric_value": 2.6303569531833038, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.58695, "setup": "squinoct", "side": 2.6303569531833038, "solution_path": "data/solutions/generated/squinoct_027_7199a9fabf8295f3.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7199a9fabf8295f3.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@28", "density": 0.8358880435909333, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/28.gif", "friedman_metric_expression": "2.63116+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.63116, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@28", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.63116+", "metric_symbol": "s", "metric_value": 2.63116, "reference_text": "s = 2.63116+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/28.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.63116+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "ad6175b5666f3771", "improvement": -0.002757201469966386, "max_boundary_excess": -5.321806274664218e-06, "max_pair_overlap_depth": -2.3625714268504794e-05, "metric_expression": "2.63392", "metric_symbol": "s", "metric_value": 2.6339172014699663, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.63116, "setup": "squinoct", "side": 2.6339172014699663, "solution_path": "data/solutions/generated/squinoct_028_ad6175b5666f3771.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ad6175b5666f3771.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@29", "density": 0.8053277894510656, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/29.gif", "friedman_metric_expression": "2.70811+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.70811, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@29", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.70811+", "metric_symbol": "s", "metric_value": 2.70811, "reference_text": "s = 2.70811+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/29.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.70811+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "a7c60552360644b6", "improvement": -0.02281526721143523, "max_boundary_excess": -3.928573599716161e-06, "max_pair_overlap_depth": -2.4601383313171965e-05, "metric_expression": "2.73093", "metric_symbol": "s", "metric_value": 2.7309252672114352, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.70811, "setup": "squinoct", "side": 2.7309252672114352, "solution_path": "data/solutions/generated/squinoct_029_a7c60552360644b6.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a7c60552360644b6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinoct@30", "density": 0.8050487180673215, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinoct/30.gif", "friedman_metric_expression": "2.74220+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.7422, "friedman_reference": {"analytical_or_proved": false, "case": "squinoct@30", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/17/26", "metric_expression": "2.74220+", "metric_symbol": "s", "metric_value": 2.7422, "reference_text": "s = 2.74220+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinoct/30.gif", "source_page": "https://erich-friedman.github.io/packing/squinoct/", "title": "Squares in Octagons"}, "friedman_reference_text": "s = 2.74220+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinoct/", "friedman_title": "Squares in Octagons", "frontend_seed": true, "id": "8d25a2ea5990135c", "improvement": -0.03589252210129912, "max_boundary_excess": -4.415473577555007e-06, "max_pair_overlap_depth": -7.985805165922066e-06, "metric_expression": "2.77809", "metric_symbol": "s", "metric_value": 2.778092522101299, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.7422, "setup": "squinoct", "side": 2.778092522101299, "solution_path": "data/solutions/generated/squinoct_030_8d25a2ea5990135c.json", "source_url": "https://erich-friedman.github.io/packing/squinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8d25a2ea5990135c.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squinpen@1", "density": 0.6621920830904189, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/1.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": ".936+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.936, "friedman_reference": {"analytical_or_proved": true, "case": "squinpen@1", "credit": "Trivial", "date": "", "family_updated": "4/8/26", "metric_expression": ".936+", "metric_symbol": "s", "metric_value": 0.936, "reference_text": "s = cos(27\u00b0) / cos(18\u00b0) | s = .936+ | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/1.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = cos(27\u00b0) / cos(18\u00b0) | s = .936+ | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "7c4deaf46828e45f", "improvement": -0.0008790374068264883, "max_boundary_excess": -1.1116494686738636e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.93688", "metric_symbol": "s", "metric_value": 0.9368790374068265, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.936, "setup": "squinpen", "side": 0.9368790374068265, "solution_path": "data/solutions/generated/squinpen_001_7c4deaf46828e45f.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7c4deaf46828e45f.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squinpen@2", "density": 0.49287502021209156, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "March 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/2.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "1.535+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.535, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@2", "credit": "Erich Friedman", "date": "March 2012", "family_updated": "4/8/26", "metric_expression": "1.535+", "metric_symbol": "s", "metric_value": 1.535, "reference_text": "s = 4\u221a(1\u20132/\u221a5)+\u221a5\u20132 | s = 1.535+ | Found by Erich Friedman | in March 2012.", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/2.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4\u221a(1\u20132/\u221a5)+\u221a5\u20132 | s = 1.535+ | Found by Erich Friedman | in March 2012.", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "e0d70422bfa035f2", "improvement": -0.0007556004426736429, "max_boundary_excess": -5.603512178169518e-07, "max_pair_overlap_depth": -4.1992473865937185e-06, "metric_expression": "1.53576", "metric_symbol": "s", "metric_value": 1.5357556004426736, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.535, "setup": "squinpen", "side": 1.5357556004426736, "solution_path": "data/solutions/generated/squinpen_002_e0d70422bfa035f2.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e0d70422bfa035f2.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squinpen@3", "density": 0.6064545372240481, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/3.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "1.695+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.695, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@3", "credit": "David W", "date": "July 2012", "family_updated": "4/8/26", "metric_expression": "1.695+", "metric_symbol": "s", "metric_value": 1.695, "reference_text": "s = 1.695+ | Found by David W. Cantrell | in July 2012. |", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/3.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 1.695+ | Found by David W. Cantrell | in July 2012. |", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "20345bd1acea07ee", "improvement": -0.0006531320538840646, "max_boundary_excess": -5.096669049020619e-07, "max_pair_overlap_depth": -2.3507012493845236e-05, "metric_expression": "1.69565", "metric_symbol": "s", "metric_value": 1.6956531320538841, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.695, "setup": "squinpen", "side": 1.6956531320538841, "solution_path": "data/solutions/generated/squinpen_003_20345bd1acea07ee.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/20345bd1acea07ee.svg", "tolerance": 1e-08, "verified": true}
@@ -418,7 +543,26 @@
 {"case": "squinpen@18", "density": 0.7949963635829483, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/18.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.626+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.626, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@18", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "4/8/26", "metric_expression": "3.626+", "metric_symbol": "s", "metric_value": 3.626, "reference_text": "s = 3.626+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/18.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.626+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "521e6ed1020d53e6", "improvement": -0.001681876520355896, "max_boundary_excess": -2.132718950610418e-06, "max_pair_overlap_depth": -5.952134619235938e-06, "metric_expression": "3.62768", "metric_symbol": "s", "metric_value": 3.627681876520356, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.626, "setup": "squinpen", "side": 3.627681876520356, "solution_path": "data/solutions/generated/squinpen_018_521e6ed1020d53e6.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/521e6ed1020d53e6.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squinpen@19", "density": 0.8016091392666894, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/19.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.710+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.71, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "4/8/26", "metric_expression": "3.710+", "metric_symbol": "s", "metric_value": 3.71, "reference_text": "s = 3.710+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/19.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.710+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "66aeca1af6b9bf65", "improvement": -0.001683910599032501, "max_boundary_excess": -5.240508232322902e-06, "max_pair_overlap_depth": -2.033383687716217e-05, "metric_expression": "3.71168", "metric_symbol": "s", "metric_value": 3.7116839105990325, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.71, "setup": "squinpen", "side": 3.7116839105990325, "solution_path": "data/solutions/generated/squinpen_019_66aeca1af6b9bf65.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/66aeca1af6b9bf65.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squinpen@20", "density": 0.8030009751844291, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/20.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "3.802+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.802, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@20", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "4/8/26", "metric_expression": "3.802+", "metric_symbol": "s", "metric_value": 3.802, "reference_text": "s = 3.802+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/20.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.802+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "8424f972564f51a8", "improvement": -0.00280562795003636, "max_boundary_excess": -2.488842199203112e-06, "max_pair_overlap_depth": -3.2279665458823104e-05, "metric_expression": "3.80481", "metric_symbol": "s", "metric_value": 3.8048056279500364, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.802, "setup": "squinpen", "side": 3.8048056279500364, "solution_path": "data/solutions/generated/squinpen_020_8424f972564f51a8.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8424f972564f51a8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@21", "density": 0.8135799833496993, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/21.gif", "friedman_metric_expression": "3.864+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.864, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@21", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "3.864+", "metric_symbol": "s", "metric_value": 3.864, "reference_text": "s = 3.864+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/21.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.864+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "3fc16f4ddfd45967", "improvement": -0.009334763632923071, "max_boundary_excess": -5.959133691049833e-07, "max_pair_overlap_depth": -1.419469897068204e-05, "metric_expression": "3.87333", "metric_symbol": "s", "metric_value": 3.873334763632923, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.864, "setup": "squinpen", "side": 3.873334763632923, "solution_path": "data/solutions/generated/squinpen_021_3fc16f4ddfd45967.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3fc16f4ddfd45967.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@22", "density": 0.8236901899623935, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/22.gif", "friedman_metric_expression": "3.937+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.937, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@22", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "3.937+", "metric_symbol": "s", "metric_value": 3.937, "reference_text": "s = 3.937+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/22.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 3.937+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "33b95c59890c6cd7", "improvement": -0.0030787983666398233, "max_boundary_excess": -3.1912141987053604e-06, "max_pair_overlap_depth": -2.2837560550437175e-06, "metric_expression": "3.94008", "metric_symbol": "s", "metric_value": 3.9400787983666397, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.937, "setup": "squinpen", "side": 3.9400787983666397, "solution_path": "data/solutions/generated/squinpen_022_33b95c59890c6cd7.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/33b95c59890c6cd7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@23", "density": 0.8342850114016098, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/23.gif", "friedman_metric_expression": "4.002+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.002, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@23", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.002+", "metric_symbol": "s", "metric_value": 4.002, "reference_text": "s = 4.002+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/23.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.002+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "125d15e1f42d4cc7", "improvement": -0.000968856434470311, "max_boundary_excess": -3.142206802972531e-06, "max_pair_overlap_depth": -1.3381668518996914e-05, "metric_expression": "4.00297", "metric_symbol": "s", "metric_value": 4.00296885643447, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.002, "setup": "squinpen", "side": 4.00296885643447, "solution_path": "data/solutions/generated/squinpen_023_125d15e1f42d4cc7.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/125d15e1f42d4cc7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@24", "density": 0.8138659237502952, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/24.gif", "friedman_metric_expression": "4.107+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.107, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@24", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.107+", "metric_symbol": "s", "metric_value": 4.107, "reference_text": "s = 4.107+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/24.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.107+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "5483079483431bd6", "improvement": -0.03304157256133866, "max_boundary_excess": -1.9102638477275247e-07, "max_pair_overlap_depth": -2.2611945261152844e-05, "metric_expression": "4.14004", "metric_symbol": "s", "metric_value": 4.140041572561339, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.107, "setup": "squinpen", "side": 4.140041572561339, "solution_path": "data/solutions/generated/squinpen_024_5483079483431bd6.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5483079483431bd6.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@25", "density": 0.8346264431391957, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/25.gif", "friedman_metric_expression": "4.169+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.169, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@25", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.169+", "metric_symbol": "s", "metric_value": 4.169, "reference_text": "s = 4.169+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/25.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.169+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "965f543dd3a1a5b2", "improvement": -0.003529809873594303, "max_boundary_excess": -4.8760801669609005e-06, "max_pair_overlap_depth": -9.22783607931743e-06, "metric_expression": "4.17253", "metric_symbol": "s", "metric_value": 4.172529809873594, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.169, "setup": "squinpen", "side": 4.172529809873594, "solution_path": "data/solutions/generated/squinpen_025_965f543dd3a1a5b2.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/965f543dd3a1a5b2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@26", "density": 0.846720772454187, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/26.gif", "friedman_metric_expression": "4.223+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.223, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@26", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.223+", "metric_symbol": "s", "metric_value": 4.223, "reference_text": "s = 4.223+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/26.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.223+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "12ea954c92ca25d9", "improvement": -0.0016630925283189768, "max_boundary_excess": -5.329734777233707e-07, "max_pair_overlap_depth": -5.080948892621784e-06, "metric_expression": "4.22466", "metric_symbol": "s", "metric_value": 4.224663092528319, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.223, "setup": "squinpen", "side": 4.224663092528319, "solution_path": "data/solutions/generated/squinpen_026_12ea954c92ca25d9.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/12ea954c92ca25d9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@27", "density": 0.8216861987406389, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/27.gif", "friedman_metric_expression": "4.350+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.35, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@27", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.350+", "metric_symbol": "s", "metric_value": 4.35, "reference_text": "s = 4.350+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/27.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.350+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "c69ed1bfb373f6cd", "improvement": -0.020231063660665072, "max_boundary_excess": -1.6360588600815792e-06, "max_pair_overlap_depth": -1.2793416169033789e-05, "metric_expression": "4.37023", "metric_symbol": "s", "metric_value": 4.370231063660665, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.35, "setup": "squinpen", "side": 4.370231063660665, "solution_path": "data/solutions/generated/squinpen_027_c69ed1bfb373f6cd.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c69ed1bfb373f6cd.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@28", "density": 0.8217452867794004, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/28.gif", "friedman_metric_expression": "4.421+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.421, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@28", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.421+", "metric_symbol": "s", "metric_value": 4.421, "reference_text": "s = 4.421+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/28.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.421+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "117dfd2e5e6c3a3f", "improvement": -0.02926547059333995, "max_boundary_excess": -1.5377994807666766e-06, "max_pair_overlap_depth": -1.4777589123937673e-05, "metric_expression": "4.45027", "metric_symbol": "s", "metric_value": 4.45026547059334, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.421, "setup": "squinpen", "side": 4.45026547059334, "solution_path": "data/solutions/generated/squinpen_028_117dfd2e5e6c3a3f.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/117dfd2e5e6c3a3f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@29", "density": 0.8184635083200854, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/29.gif", "friedman_metric_expression": "4.499+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.499, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@29", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.499+", "metric_symbol": "s", "metric_value": 4.499, "reference_text": "s = 4.499+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/29.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.499+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "c1c4dc57f8cd7d32", "improvement": -0.03910826264420031, "max_boundary_excess": -4.357708770048677e-06, "max_pair_overlap_depth": -3.1603738400165504e-05, "metric_expression": "4.53811", "metric_symbol": "s", "metric_value": 4.5381082626442, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.499, "setup": "squinpen", "side": 4.5381082626442, "solution_path": "data/solutions/generated/squinpen_029_c1c4dc57f8cd7d32.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c1c4dc57f8cd7d32.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@30", "density": 0.8127570507531306, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif", "friedman_metric_expression": "4.550+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.55, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@30", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.550+", "metric_symbol": "s", "metric_value": 4.55, "reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "3b632d53270924b9", "improvement": -0.08186367062158872, "max_boundary_excess": -1.4951723410279072e-06, "max_pair_overlap_depth": -2.2172095294203942e-05, "metric_expression": "4.63186", "metric_symbol": "s", "metric_value": 4.6318636706215885, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.55, "setup": "squinpen", "side": 4.6318636706215885, "solution_path": "data/solutions/generated/squinpen_030_3b632d53270924b9.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3b632d53270924b9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@31", "density": 0.8332446635234546, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/31.gif", "friedman_metric_expression": "4.63041+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.63041, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.63041+", "metric_symbol": "s", "metric_value": 4.63041, "reference_text": "s = 4.63041+ | Found by Emerson Connelly | in April 2026.", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/31.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.63041+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "4553b8253edc54ee", "improvement": -0.01977349429114028, "max_boundary_excess": -4.6392809673557884e-07, "max_pair_overlap_depth": -4.8013099460675335e-06, "metric_expression": "4.65018", "metric_symbol": "s", "metric_value": 4.650183494291141, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.63041, "setup": "squinpen", "side": 4.650183494291141, "solution_path": "data/solutions/generated/squinpen_031_4553b8253edc54ee.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4553b8253edc54ee.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@32", "density": 0.8340860169571754, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/32.gif", "friedman_metric_expression": "4.70774+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.70774, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.70774+", "metric_symbol": "s", "metric_value": 4.70774, "reference_text": "s = 4.70774+ | Found by Emerson Connelly | in April 2026.", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/32.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.70774+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "b157990acac8fece", "improvement": -0.014467675249534295, "max_boundary_excess": -1.5954744867147025e-06, "max_pair_overlap_depth": -3.644093463414655e-06, "metric_expression": "4.72221", "metric_symbol": "s", "metric_value": 4.7222076752495346, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.70774, "setup": "squinpen", "side": 4.7222076752495346, "solution_path": "data/solutions/generated/squinpen_032_b157990acac8fece.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b157990acac8fece.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@33", "density": 0.8323772382762802, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/33.gif", "friedman_metric_expression": "4.75774+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.75774, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.75774+", "metric_symbol": "s", "metric_value": 4.75774, "reference_text": "s = 4.75774+ | Found by Emerson Connelly | in April 2026.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/33.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.75774+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "84c8eef1219afe3a", "improvement": -0.042604278845473686, "max_boundary_excess": -4.034170035268611e-06, "max_pair_overlap_depth": -3.3231050606596924e-05, "metric_expression": "4.80034", "metric_symbol": "s", "metric_value": 4.800344278845474, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.75774, "setup": "squinpen", "side": 4.800344278845474, "solution_path": "data/solutions/generated/squinpen_033_84c8eef1219afe3a.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/84c8eef1219afe3a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@34", "density": 0.8367968433764427, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif", "friedman_metric_expression": "4.81817+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.81817, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.81817+", "metric_symbol": "s", "metric_value": 4.81817, "reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "01337f10c6d18cd5", "improvement": -0.04147959674377155, "max_boundary_excess": -1.1724733779714692e-06, "max_pair_overlap_depth": -1.9583851482152248e-05, "metric_expression": "4.85965", "metric_symbol": "s", "metric_value": 4.859649596743772, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.81817, "setup": "squinpen", "side": 4.859649596743772, "solution_path": "data/solutions/generated/squinpen_034_01337f10c6d18cd5.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/01337f10c6d18cd5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@35", "density": 0.8341954934487554, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/35.gif", "friedman_metric_expression": "4.86994+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.86994, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@35", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.86994+", "metric_symbol": "s", "metric_value": 4.86994, "reference_text": "s = 4.86994+ | Found by Emerson Connelly | in April 2026.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/35.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.86994+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "18582601dada9f12", "improvement": -0.06833892667279251, "max_boundary_excess": -4.548819982417703e-06, "max_pair_overlap_depth": -2.0484902510720104e-05, "metric_expression": "4.93828", "metric_symbol": "s", "metric_value": 4.938278926672792, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.86994, "setup": "squinpen", "side": 4.938278926672792, "solution_path": "data/solutions/generated/squinpen_035_18582601dada9f12.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/18582601dada9f12.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@36", "density": 0.8532713011557852, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/36.gif", "friedman_metric_expression": "4.93902+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.93902, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@36", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.93902+", "metric_symbol": "s", "metric_value": 4.93902, "reference_text": "s = 4.93902+ | Found by Emerson Connelly | in April 2026.", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/36.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.93902+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "106a35f9dda2ef3a", "improvement": -0.013009176461455496, "max_boundary_excess": -3.488354007671054e-06, "max_pair_overlap_depth": -9.039025279156121e-06, "metric_expression": "4.95203", "metric_symbol": "s", "metric_value": 4.952029176461456, "n": 36, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.93902, "setup": "squinpen", "side": 4.952029176461456, "solution_path": "data/solutions/generated/squinpen_036_106a35f9dda2ef3a.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/106a35f9dda2ef3a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@37", "density": 0.8519657791917798, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/37.gif", "friedman_metric_expression": "4.98234+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.98234, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@37", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "4.98234+", "metric_symbol": "s", "metric_value": 4.98234, "reference_text": "s = 4.98234+ | Found by Emerson Connelly | in April 2026.", "source_image": "37.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/37.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 4.98234+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "118ed6265867ee6d", "improvement": -0.041841273572848614, "max_boundary_excess": -2.432358437563004e-06, "max_pair_overlap_depth": -1.088207923216622e-05, "metric_expression": "5.02418", "metric_symbol": "s", "metric_value": 5.024181273572848, "n": 37, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.98234, "setup": "squinpen", "side": 5.024181273572848, "solution_path": "data/solutions/generated/squinpen_037_118ed6265867ee6d.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/118ed6265867ee6d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@38", "density": 0.8517757106785014, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/38.gif", "friedman_metric_expression": "5.05233+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.05233, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "5.05233+", "metric_symbol": "s", "metric_value": 5.05233, "reference_text": "s = 5.05233+ | Found by Emerson Connelly | in April 2026.", "source_image": "38.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/38.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 5.05233+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "05c73c36e688b1e7", "improvement": -0.03986101653920304, "max_boundary_excess": -4.23968996781929e-06, "max_pair_overlap_depth": -2.3209189968509403e-05, "metric_expression": "5.09219", "metric_symbol": "s", "metric_value": 5.0921910165392035, "n": 38, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.05233, "setup": "squinpen", "side": 5.0921910165392035, "solution_path": "data/solutions/generated/squinpen_038_05c73c36e688b1e7.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/05c73c36e688b1e7.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squinpen@39", "density": 0.8585173524687216, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/39.gif", "friedman_family_updated": "4/8/26", "friedman_metric_expression": "5.14034+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.14034, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "5.14034+", "metric_symbol": "s", "metric_value": 5.14034, "reference_text": "s = 5.14034+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/39.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 5.14034+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "id": "d71c022b51de33ef", "improvement": 0.001876469157010341, "max_boundary_excess": -5.100716047053306e-07, "max_pair_overlap_depth": -1.0441692915863499e-06, "n": 39, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 5.14034, "setup": "squinpen", "side": 5.13846353084299, "solution_path": "data/solutions/squinpen_39.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/d71c022b51de33ef.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squinpen@40", "density": 0.8631839411542434, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squinpen/40.gif", "friedman_metric_expression": "5.17250+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.1725, "friedman_reference": {"analytical_or_proved": false, "case": "squinpen@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/8/26", "metric_expression": "5.17250+", "metric_symbol": "s", "metric_value": 5.1725, "reference_text": "s = 5.17250+ | Found by Emerson Connelly | in April 2026.", "source_image": "40.gif", "source_image_url": "https://erich-friedman.github.io/packing/squinpen/40.gif", "source_page": "https://erich-friedman.github.io/packing/squinpen/", "title": "Squares in Pentagons"}, "friedman_reference_text": "s = 5.17250+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squinpen/", "friedman_title": "Squares in Pentagons", "frontend_seed": true, "id": "9fbb25ae252614ca", "improvement": -0.017338380797453645, "max_boundary_excess": -2.5898488984122457e-06, "max_pair_overlap_depth": -1.526607516622036e-05, "metric_expression": "5.18984", "metric_symbol": "s", "metric_value": 5.189838380797454, "n": 40, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.1725, "setup": "squinpen", "side": 5.189838380797454, "solution_path": "data/solutions/generated/squinpen_040_9fbb25ae252614ca.json", "source_url": "https://erich-friedman.github.io/packing/squinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9fbb25ae252614ca.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squintri@1", "density": 0.49741240626661626, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts1.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "1 + 2 / \u221a3 = 2.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.154, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@1", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "1 + 2 / \u221a3 = 2.154+", "metric_symbol": "s", "metric_value": 2.154, "reference_text": "s = 1 + 2 / \u221a3 = 2.154+ | Trivial.", "source_image": "ts1.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts1.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 1 + 2 / \u221a3 = 2.154+ | Trivial.", "friedman_source_image": "ts1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "bc8215883b0d29fa", "improvement": -0.0007226428063047408, "max_boundary_excess": -4.189638991319711e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "2.15472", "metric_symbol": "s", "metric_value": 2.1547226428063047, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.154, "setup": "squintri", "side": 2.1547226428063047, "solution_path": "data/solutions/generated/squintri_001_bc8215883b0d29fa.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/bc8215883b0d29fa.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squintri@2", "density": 0.4640775964340414, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts2.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "2 + 2 / \u221a3 = 3.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.154, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@2", "credit": "Trivial", "date": "", "family_updated": "4/28/26", "metric_expression": "2 + 2 / \u221a3 = 3.154+", "metric_symbol": "s", "metric_value": 3.154, "reference_text": "s = 2 + 2 / \u221a3 = 3.154+ | Trivial.", "source_image": "ts2.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts2.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 2 + 2 / \u221a3 = 3.154+ | Trivial.", "friedman_source_image": "ts2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "9fcb7fc91bdb6f8d", "improvement": -0.000782174335970165, "max_boundary_excess": -6.2952441585539525e-06, "max_pair_overlap_depth": -3.4919698730116744e-05, "metric_expression": "3.15478", "metric_symbol": "s", "metric_value": 3.15478217433597, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.154, "setup": "squintri", "side": 3.15478217433597, "solution_path": "data/solutions/generated/squintri_002_9fcb7fc91bdb6f8d.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9fcb7fc91bdb6f8d.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squintri@3", "density": 0.6632023535454387, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts3.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3 / 2 + \u221a3 = 3.232+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.232, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@3", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "3 / 2 + \u221a3 = 3.232+", "metric_symbol": "s", "metric_value": 3.232, "reference_text": "s = 3 / 2 + \u221a3 = 3.232+ | Found by Erich Friedman | in 1997.", "source_image": "ts3.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts3.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 / 2 + \u221a3 = 3.232+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "6a0fd09e2fb037d5", "improvement": -0.00011853663309757678, "max_boundary_excess": -2.0862631378148764e-06, "max_pair_overlap_depth": -4.0896047962125925e-05, "metric_expression": "3.23212", "metric_symbol": "s", "metric_value": 3.232118536633098, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.232, "setup": "squintri", "side": 3.232118536633098, "solution_path": "data/solutions/generated/squintri_003_6a0fd09e2fb037d5.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6a0fd09e2fb037d5.svg", "tolerance": 1e-08, "verified": true}
@@ -439,6 +583,25 @@
 {"case": "squintri@18", "density": 0.7460471945171483, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts18.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "5 + 4 / \u221a3 = 7.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.309, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@18", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "5 + 4 / \u221a3 = 7.309+", "metric_symbol": "s", "metric_value": 7.309, "reference_text": "s = 5 + 4 / \u221a3 = 7.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts18.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts18.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 4 / \u221a3 = 7.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "7712455ac085d150", "improvement": -0.15553543037287731, "max_boundary_excess": -2.6126528078951194e-06, "max_pair_overlap_depth": -5.242839132613142e-06, "metric_expression": "7.46454", "metric_symbol": "s", "metric_value": 7.4645354303728775, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.309, "setup": "squintri", "side": 7.4645354303728775, "solution_path": "data/solutions/generated/squintri_018_7712455ac085d150.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7712455ac085d150.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squintri@19", "density": 0.787537700321716, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts19.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "4 + 2 \u221a3 = 7.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.464, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@19", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "4 + 2 \u221a3 = 7.464+", "metric_symbol": "s", "metric_value": 7.464, "reference_text": "s = 4 + 2 \u221a3 = 7.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts19.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts19.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 2 \u221a3 = 7.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "805d1e50c1db2842", "improvement": -0.0003295610354463463, "max_boundary_excess": -3.0609380559736765e-06, "max_pair_overlap_depth": -1.836020690809681e-05, "metric_expression": "7.46433", "metric_symbol": "s", "metric_value": 7.464329561035447, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.464, "setup": "squintri", "side": 7.464329561035447, "solution_path": "data/solutions/generated/squintri_019_805d1e50c1db2842.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/805d1e50c1db2842.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squintri@20", "density": 0.795657127614163, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "3 + 8 / \u221a3 = 7.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@20", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "3 + 8 / \u221a3 = 7.618+", "metric_symbol": "s", "metric_value": 7.618, "reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "f4d21a73470ce742", "improvement": -0.0010653922379448844, "max_boundary_excess": -1.382631857088383e-07, "max_pair_overlap_depth": -1.1470843414018717e-05, "metric_expression": "7.61907", "metric_symbol": "s", "metric_value": 7.619065392237945, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.618, "setup": "squintri", "side": 7.619065392237945, "solution_path": "data/solutions/generated/squintri_020_f4d21a73470ce742.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f4d21a73470ce742.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@21", "density": 0.8354483980307021, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "friedman_metric_expression": "3 + 8 / \u221a3 = 7.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 7.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@21", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "3 + 8 / \u221a3 = 7.618+", "metric_symbol": "s", "metric_value": 7.618, "reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts21.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "a2e24601c2557198", "improvement": -0.0010270252659259071, "max_boundary_excess": -2.8035391721895233e-06, "max_pair_overlap_depth": -9.7266150509423e-06, "metric_expression": "7.61903", "metric_symbol": "s", "metric_value": 7.619027025265926, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 7.618, "setup": "squintri", "side": 7.619027025265926, "solution_path": "data/solutions/generated/squintri_021_a2e24601c2557198.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a2e24601c2557198.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@22", "density": 0.7639711289147475, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts22.gif", "friedman_metric_expression": "7 + 2 / \u221a3 = 8.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.154, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@22", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "7 + 2 / \u221a3 = 8.154+", "metric_symbol": "s", "metric_value": 8.154, "reference_text": "s = 7 + 2 / \u221a3 = 8.154+ | Found by Erich Friedman | in 1997.", "source_image": "ts22.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts22.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 7 + 2 / \u221a3 = 8.154+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "bbb028380d997350", "improvement": -0.00097340620692421, "max_boundary_excess": -2.4334644744109685e-07, "max_pair_overlap_depth": -2.16343036094635e-05, "metric_expression": "8.15497", "metric_symbol": "s", "metric_value": 8.154973406206924, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.154, "setup": "squintri", "side": 8.154973406206924, "solution_path": "data/solutions/generated/squintri_022_bbb028380d997350.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/bbb028380d997350.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@23", "density": 0.7550101019412538, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts23.gif", "friedman_metric_expression": "8.301+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.301, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@23", "credit": "David W", "date": "July 2002", "family_updated": "4/28/26", "metric_expression": "8.301+", "metric_symbol": "s", "metric_value": 8.301, "reference_text": "s = 8.301+ | Found by David W. Cantrell | in July 2002.", "source_image": "ts23.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts23.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 8.301+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "ts23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "23ac4c9fa2eea010", "improvement": -0.08659049275331299, "max_boundary_excess": -4.153049577120555e-06, "max_pair_overlap_depth": -3.895329260372726e-05, "metric_expression": "8.38759", "metric_symbol": "s", "metric_value": 8.387590492753313, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.301, "setup": "squintri", "side": 8.387590492753313, "solution_path": "data/solutions/generated/squintri_023_23ac4c9fa2eea010.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/23ac4c9fa2eea010.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@24", "density": 0.7730739404637164, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts24.gif", "friedman_metric_expression": "6 + 4 / \u221a3 = 8.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.309, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@24", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "6 + 4 / \u221a3 = 8.309+", "metric_symbol": "s", "metric_value": 8.309, "reference_text": "s = 6 + 4 / \u221a3 = 8.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts24.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts24.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 6 + 4 / \u221a3 = 8.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "841c613875887f20", "improvement": -0.15829685349927658, "max_boundary_excess": -3.146275899064303e-06, "max_pair_overlap_depth": -4.677275111941714e-06, "metric_expression": "8.46730", "metric_symbol": "s", "metric_value": 8.467296853499276, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.309, "setup": "squintri", "side": 8.467296853499276, "solution_path": "data/solutions/generated/squintri_024_841c613875887f20.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/841c613875887f20.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@25", "density": 0.7913339513148233, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts25.gif", "friedman_metric_expression": "5 + 2 \u221a3 = 8.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.464, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@25", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "5 + 2 \u221a3 = 8.464+", "metric_symbol": "s", "metric_value": 8.464, "reference_text": "s = 5 + 2 \u221a3 = 8.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts25.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts25.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 2 \u221a3 = 8.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "b4f5fafd19e47950", "improvement": -0.0776109564627685, "max_boundary_excess": -3.693763855098152e-06, "max_pair_overlap_depth": -1.4039362742357397e-05, "metric_expression": "8.54161", "metric_symbol": "s", "metric_value": 8.541610956462769, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.464, "setup": "squintri", "side": 8.541610956462769, "solution_path": "data/solutions/generated/squintri_025_b4f5fafd19e47950.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b4f5fafd19e47950.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@26", "density": 0.790058442487887, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "friedman_metric_expression": "4 + 8 / \u221a3 = 8.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@26", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "4 + 8 / \u221a3 = 8.618+", "metric_symbol": "s", "metric_value": 8.618, "reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "029d10bebacbb7a8", "improvement": -0.09979689737383879, "max_boundary_excess": -6.192886858462666e-06, "max_pair_overlap_depth": -1.592089192270496e-05, "metric_expression": "8.71780", "metric_symbol": "s", "metric_value": 8.71779689737384, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.618, "setup": "squintri", "side": 8.71779689737384, "solution_path": "data/solutions/generated/squintri_026_029d10bebacbb7a8.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/029d10bebacbb7a8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@27", "density": 0.8229909021232206, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "friedman_metric_expression": "4 + 8 / \u221a3 = 8.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@27", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "4 + 8 / \u221a3 = 8.618+", "metric_symbol": "s", "metric_value": 8.618, "reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts27.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "d80877f3b5e3e559", "improvement": -0.08630392921703489, "max_boundary_excess": -2.6087107652930556e-07, "max_pair_overlap_depth": -1.4123632457341273e-05, "metric_expression": "8.70430", "metric_symbol": "s", "metric_value": 8.704303929217035, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.618, "setup": "squintri", "side": 8.704303929217035, "solution_path": "data/solutions/generated/squintri_027_d80877f3b5e3e559.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d80877f3b5e3e559.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@28", "density": 0.8400113660191094, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts28.gif", "friedman_metric_expression": "3 + 10 / \u221a3 = 8.773+", "friedman_metric_symbol": "s", "friedman_metric_value": 8.773, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@28", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "3 + 10 / \u221a3 = 8.773+", "metric_symbol": "s", "metric_value": 8.773, "reference_text": "s = 3 + 10 / \u221a3 = 8.773+ | Found by Erich Friedman | in 1997.", "source_image": "ts28.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts28.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 3 + 10 / \u221a3 = 8.773+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "0d20b359435ed501", "improvement": -0.0007673944032049462, "max_boundary_excess": -3.0145694937175628e-06, "max_pair_overlap_depth": -1.3941973455278145e-05, "metric_expression": "8.77377", "metric_symbol": "s", "metric_value": 8.773767394403205, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 8.773, "setup": "squintri", "side": 8.773767394403205, "solution_path": "data/solutions/generated/squintri_028_0d20b359435ed501.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0d20b359435ed501.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@29", "density": 0.7990846545133872, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts29.gif", "friedman_metric_expression": "8 + 2 / \u221a3 = 9.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.154, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@29", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "8 + 2 / \u221a3 = 9.154+", "metric_symbol": "s", "metric_value": 9.154, "reference_text": "s = 8 + 2 / \u221a3 = 9.154+ | Found by Erich Friedman | in 1997.", "source_image": "ts29.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts29.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 8 + 2 / \u221a3 = 9.154+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "3947aab39c0a1a92", "improvement": -0.000872191450978832, "max_boundary_excess": -2.2628787428294703e-06, "max_pair_overlap_depth": -1.875431036468811e-05, "metric_expression": "9.15487", "metric_symbol": "s", "metric_value": 9.154872191450979, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.154, "setup": "squintri", "side": 9.154872191450979, "solution_path": "data/solutions/generated/squintri_029_3947aab39c0a1a92.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3947aab39c0a1a92.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@30", "density": 0.7992784153759376, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2002", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts30.gif", "friedman_metric_expression": "9.301+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.301, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@30", "credit": "David W", "date": "July 2002", "family_updated": "4/28/26", "metric_expression": "9.301+", "metric_symbol": "s", "metric_value": 9.301, "reference_text": "s = 9.301+ | Found by David W. Cantrell | in July 2002.", "source_image": "ts30.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts30.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 9.301+ | Found by David W. Cantrell | in July 2002.", "friedman_source_image": "ts30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "e0b7505d8b6b1d46", "improvement": -0.009248370808917272, "max_boundary_excess": -2.5690858985090003e-06, "max_pair_overlap_depth": -2.654303096472077e-05, "metric_expression": "9.31025", "metric_symbol": "s", "metric_value": 9.310248370808917, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.301, "setup": "squintri", "side": 9.310248370808917, "solution_path": "data/solutions/generated/squintri_030_e0b7505d8b6b1d46.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e0b7505d8b6b1d46.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@31", "density": 0.7864596295366862, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts31.gif", "friedman_metric_expression": "7 + 4 / \u221a3 = 9.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.309, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@31", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "7 + 4 / \u221a3 = 9.309+", "metric_symbol": "s", "metric_value": 9.309, "reference_text": "s = 7 + 4 / \u221a3 = 9.309+ | Found by Erich Friedman | in 1997.", "source_image": "ts31.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts31.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 7 + 4 / \u221a3 = 9.309+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "2fc342f23897d355", "improvement": -0.2319651982792994, "max_boundary_excess": -3.1752928337368137e-06, "max_pair_overlap_depth": -3.6389675686088196e-06, "metric_expression": "9.54097", "metric_symbol": "s", "metric_value": 9.540965198279299, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.309, "setup": "squintri", "side": 9.540965198279299, "solution_path": "data/solutions/generated/squintri_031_2fc342f23897d355.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/2fc342f23897d355.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@32", "density": 0.8113508933844216, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts32.gif", "friedman_metric_expression": "6 + 2 \u221a3 = 9.464+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.464, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@32", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "6 + 2 \u221a3 = 9.464+", "metric_symbol": "s", "metric_value": 9.464, "reference_text": "s = 6 + 2 \u221a3 = 9.464+ | Found by Erich Friedman | in 1997.", "source_image": "ts32.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts32.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 6 + 2 \u221a3 = 9.464+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "5dfb790e771f9b5e", "improvement": -0.07977763160413431, "max_boundary_excess": -1.7955058891584607e-06, "max_pair_overlap_depth": -1.9308988421506967e-06, "metric_expression": "9.54378", "metric_symbol": "s", "metric_value": 9.543777631604135, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.464, "setup": "squintri", "side": 9.543777631604135, "solution_path": "data/solutions/generated/squintri_032_5dfb790e771f9b5e.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5dfb790e771f9b5e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@33", "density": 0.8101986344458209, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "friedman_metric_expression": "5 + 8 / \u221a3 = 9.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@33", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "5 + 8 / \u221a3 = 9.618+", "metric_symbol": "s", "metric_value": 9.618, "reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "3a2374dab53b1d0d", "improvement": -0.08064132353736753, "max_boundary_excess": -4.4569871095880175e-06, "max_pair_overlap_depth": -8.479699437735633e-06, "metric_expression": "9.69864", "metric_symbol": "s", "metric_value": 9.698641323537368, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.618, "setup": "squintri", "side": 9.698641323537368, "solution_path": "data/solutions/generated/squintri_033_3a2374dab53b1d0d.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3a2374dab53b1d0d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@34", "density": 0.8485900582279403, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "friedman_metric_expression": "5 + 8 / \u221a3 = 9.618+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.618, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@34", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "5 + 8 / \u221a3 = 9.618+", "metric_symbol": "s", "metric_value": 9.618, "reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "source_image": "ts34.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "3661302cdd9d0eb0", "improvement": -0.0012269381751668362, "max_boundary_excess": -4.159334309452278e-06, "max_pair_overlap_depth": -1.741303470170763e-05, "metric_expression": "9.61923", "metric_symbol": "s", "metric_value": 9.619226938175167, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.618, "setup": "squintri", "side": 9.619226938175167, "solution_path": "data/solutions/generated/squintri_034_3661302cdd9d0eb0.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3661302cdd9d0eb0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@35", "density": 0.819924784927634, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "friedman_metric_expression": "4 + 10 / \u221a3 = 9.773+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.773, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@35", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "4 + 10 / \u221a3 = 9.773+", "metric_symbol": "s", "metric_value": 9.773, "reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "source_image": "ts36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "767d03b8ae8b30a8", "improvement": -0.15579849696747594, "max_boundary_excess": -4.344704196265019e-07, "max_pair_overlap_depth": -6.54668349642229e-06, "metric_expression": "9.92880", "metric_symbol": "s", "metric_value": 9.928798496967476, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.773, "setup": "squintri", "side": 9.928798496967476, "solution_path": "data/solutions/generated/squintri_035_767d03b8ae8b30a8.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/767d03b8ae8b30a8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@36", "density": 0.8626567214562272, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "friedman_metric_expression": "4 + 10 / \u221a3 = 9.773+", "friedman_metric_symbol": "s", "friedman_metric_value": 9.773, "friedman_reference": {"analytical_or_proved": true, "case": "squintri@36", "credit": "Erich Friedman", "date": "1997", "family_updated": "4/28/26", "metric_expression": "4 + 10 / \u221a3 = 9.773+", "metric_symbol": "s", "metric_value": 9.773, "reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "source_image": "ts36.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "ts36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "8dffe8c81eb0e47e", "improvement": -0.044070890619954284, "max_boundary_excess": -4.088894889268143e-06, "max_pair_overlap_depth": -7.423378060700259e-06, "metric_expression": "9.81707", "metric_symbol": "s", "metric_value": 9.817070890619954, "n": 36, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 9.773, "setup": "squintri", "side": 9.817070890619954, "solution_path": "data/solutions/generated/squintri_036_8dffe8c81eb0e47e.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8dffe8c81eb0e47e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@37", "density": 0.8285699034870297, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts37.gif", "friedman_metric_expression": "10.154+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.154, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@37", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "10.154+", "metric_symbol": "s", "metric_value": 10.154, "reference_text": "s = 10.154+ | Found by Emerson Connelly | in April 2026.", "source_image": "ts37.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts37.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 10.154+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "ts37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "8530be000ac2e9ed", "improvement": -0.0011412138177444575, "max_boundary_excess": -3.3566887422690367e-06, "max_pair_overlap_depth": -1.2239987045248313e-05, "metric_expression": "10.15514", "metric_symbol": "s", "metric_value": 10.155141213817744, "n": 37, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 10.154, "setup": "squintri", "side": 10.155141213817744, "solution_path": "data/solutions/generated/squintri_037_8530be000ac2e9ed.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8530be000ac2e9ed.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@38", "density": 0.8256293316995508, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts38.gif", "friedman_metric_expression": "10.309+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.309, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "10.309+", "metric_symbol": "s", "metric_value": 10.309, "reference_text": "s = 10.309+ | Found by Emerson Connelly | in April 2026.", "source_image": "ts38.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts38.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 10.309+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "ts38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "896b636f9d899bf5", "improvement": -0.0007687369401132571, "max_boundary_excess": -6.231911901047403e-06, "max_pair_overlap_depth": -1.6045122417374102e-05, "metric_expression": "10.30977", "metric_symbol": "s", "metric_value": 10.309768736940113, "n": 38, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 10.309, "setup": "squintri", "side": 10.309768736940113, "solution_path": "data/solutions/generated/squintri_038_896b636f9d899bf5.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/896b636f9d899bf5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "squintri@39", "density": 0.8473139665564875, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts39.gif", "friedman_metric_expression": "10.310+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.31, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "10.310+", "metric_symbol": "s", "metric_value": 10.31, "reference_text": "s = 10.310+ | Found by Emerson Connelly | in April 2026.", "source_image": "ts39.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts39.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 10.310+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "ts39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "frontend_seed": true, "id": "306f80d621673198", "improvement": -2.7007950082591492e-05, "max_boundary_excess": -5.045618537449805e-06, "max_pair_overlap_depth": -1.8490228973488954e-05, "metric_expression": "10.31003", "metric_symbol": "s", "metric_value": 10.310027007950083, "n": 39, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 10.31, "setup": "squintri", "side": 10.310027007950083, "solution_path": "data/solutions/generated/squintri_039_306f80d621673198.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/306f80d621673198.svg", "tolerance": 1e-08, "verified": true}
 {"case": "squintri@40", "density": 0.8436107953893915, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/squintri/ts40.gif", "friedman_family_updated": "4/28/26", "friedman_metric_expression": "10.465+", "friedman_metric_symbol": "s", "friedman_metric_value": 10.465, "friedman_reference": {"analytical_or_proved": false, "case": "squintri@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/28/26", "metric_expression": "10.465+", "metric_symbol": "s", "metric_value": 10.465, "reference_text": "s = 10.465+ | Found by Emerson Connelly | in April 2026.", "source_image": "ts40.gif", "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts40.gif", "source_page": "https://erich-friedman.github.io/packing/squintri/", "title": "Squares in Triangles"}, "friedman_reference_text": "s = 10.465+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "ts40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/squintri/", "friedman_title": "Squares in Triangles", "id": "ca1c4f98d45d3360", "improvement": 0.0007377944127142655, "max_boundary_excess": -6.518279549438242e-07, "max_pair_overlap_depth": -1.3221145032105142e-06, "n": 40, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 10.465, "setup": "squintri", "side": 10.464262205587286, "solution_path": "data/solutions/squintri_40.json", "source_url": "https://erich-friedman.github.io/packing/squintri/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/ca1c4f98d45d3360.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triincir@1", "density": 0.41349293224745, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc1.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1/\u221a3 = .577+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.577, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@1", "credit": "Trivial", "date": "", "family_updated": "8/31/19", "metric_expression": "1/\u221a3 = .577+", "metric_symbol": "r", "metric_value": 0.577, "reference_text": "r = 1/\u221a3 = .577+ | Trivial.", "source_image": "tc1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc1.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1/\u221a3 = .577+ | Trivial.", "friedman_source_image": "tc1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "49954bfbb560620d", "improvement": -0.00035287974439102143, "max_boundary_excess": -6.775275519510515e-07, "max_pair_overlap_depth": 0.0, "metric_expression": "0.57735", "metric_symbol": "r", "metric_value": 0.577352879744391, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.577, "setup": "triincir", "side": 1.154705759488782, "solution_path": "data/solutions/generated/triincir_001_49954bfbb560620d.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/49954bfbb560620d.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triincir@2", "density": 0.3675414068402789, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc2.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "\u221a3/2 = .866+", "friedman_metric_symbol": "r", "friedman_metric_value": 0.866, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@2", "credit": "Trivial", "date": "", "family_updated": "8/31/19", "metric_expression": "\u221a3/2 = .866+", "metric_symbol": "r", "metric_value": 0.866, "reference_text": "r = \u221a3/2 = .866+ | Trivial.", "source_image": "tc2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc2.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = \u221a3/2 = .866+ | Trivial.", "friedman_source_image": "tc2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "92f5511b689fe041", "improvement": -3.858712037896339e-05, "max_boundary_excess": -3.072458078845486e-06, "max_pair_overlap_depth": -1.0890566688626091e-05, "metric_expression": "0.86604", "metric_symbol": "r", "metric_value": 0.866038587120379, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.866, "setup": "triincir", "side": 1.732077174240758, "solution_path": "data/solutions/generated/triincir_002_92f5511b689fe041.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/92f5511b689fe041.svg", "tolerance": 1e-08, "verified": true}
@@ -460,6 +623,17 @@
 {"case": "triincir@18", "density": 0.763334042584198, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc18.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "\u221a13/2 = 1.802+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.802, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@18", "credit": "Erich Friedman", "date": "1997", "family_updated": "8/31/19", "metric_expression": "\u221a13/2 = 1.802+", "metric_symbol": "r", "metric_value": 1.802, "reference_text": "r = \u221a13/2 = 1.802+ | Found by Erich Friedman | in 1997.", "source_image": "tc18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc18.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = \u221a13/2 = 1.802+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tc18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "8d495d33c78cce38", "improvement": -0.000828100052461922, "max_boundary_excess": -1.0688499290090192e-06, "max_pair_overlap_depth": -2.7547144944017887e-06, "metric_expression": "1.80283", "metric_symbol": "r", "metric_value": 1.802828100052462, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.802, "setup": "triincir", "side": 3.605656200104924, "solution_path": "data/solutions/generated/triincir_018_8d495d33c78cce38.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8d495d33c78cce38.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triincir@19", "density": 0.7677097187833641, "friedman_analytical_or_proved": true, "friedman_credit": "Haym Hirsh", "friedman_date": "August 2019", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc19.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "\u221a(10/3) = 1.825+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.825, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@19", "credit": "Haym Hirsh", "date": "August 2019", "family_updated": "8/31/19", "metric_expression": "\u221a(10/3) = 1.825+", "metric_symbol": "r", "metric_value": 1.825, "reference_text": "r = \u221a(10/3) = 1.825+ | Found by Haym Hirsh | in August 2019.", "source_image": "tc19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc19.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = \u221a(10/3) = 1.825+ | Found by Haym Hirsh | in August 2019.", "friedman_source_image": "tc19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "25e61803121deba5", "improvement": -0.021943724350603322, "max_boundary_excess": -6.158152259239102e-07, "max_pair_overlap_depth": -1.4118207399826943e-06, "metric_expression": "1.84694", "metric_symbol": "r", "metric_value": 1.8469437243506033, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.825, "setup": "triincir", "side": 3.6938874487012066, "solution_path": "data/solutions/generated/triincir_019_25e61803121deba5.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/25e61803121deba5.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triincir@20", "density": 0.7838286390350678, "friedman_analytical_or_proved": false, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc20.gif", "friedman_family_updated": "8/31/19", "friedman_metric_expression": "1.874+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.874, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@20", "credit": "Erich Friedman", "date": "1997", "family_updated": "8/31/19", "metric_expression": "1.874+", "metric_symbol": "r", "metric_value": 1.874, "reference_text": "r = 1.874+ | Found by Erich Friedman | in 1997.", "source_image": "tc20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc20.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.874+ | Found by Erich Friedman | in 1997.", "friedman_source_image": "tc20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "1217493f9010e655", "improvement": -0.0013391312177313264, "max_boundary_excess": -1.256942872007727e-07, "max_pair_overlap_depth": -1.3401476308239069e-05, "metric_expression": "1.87534", "metric_symbol": "r", "metric_value": 1.8753391312177314, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.874, "setup": "triincir", "side": 3.750678262435463, "solution_path": "data/solutions/generated/triincir_020_1217493f9010e655.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1217493f9010e655.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@21", "density": 0.7807486191939167, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc21.gif", "friedman_metric_expression": "1.910+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.91, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@21", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "8/31/19", "metric_expression": "1.910+", "metric_symbol": "r", "metric_value": 1.91, "reference_text": "r = 1.910+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tc21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc21.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.910+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tc21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "26dd3deb629b6129", "improvement": -0.015437458779652191, "max_boundary_excess": -9.498317063982853e-07, "max_pair_overlap_depth": -2.835010137536287e-06, "metric_expression": "1.92544", "metric_symbol": "r", "metric_value": 1.9254374587796521, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.91, "setup": "triincir", "side": 3.8508749175593042, "solution_path": "data/solutions/generated/triincir_021_26dd3deb629b6129.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/26dd3deb629b6129.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@22", "density": 0.7874465082238514, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc22.gif", "friedman_metric_expression": "1.943+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.943, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@22", "credit": "Maurizio Morandi", "date": "June 2008", "family_updated": "8/31/19", "metric_expression": "1.943+", "metric_symbol": "r", "metric_value": 1.943, "reference_text": "r = 1.943+ | Found by Maurizio Morandi | in June 2008.", "source_image": "tc22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc22.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.943+ | Found by Maurizio Morandi | in June 2008.", "friedman_source_image": "tc22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "0907be89df20a3ff", "improvement": -0.019348742244891026, "max_boundary_excess": -4.030552757772199e-06, "max_pair_overlap_depth": -1.5844548821419835e-05, "metric_expression": "1.96235", "metric_symbol": "r", "metric_value": 1.962348742244891, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.943, "setup": "triincir", "side": 3.924697484489782, "solution_path": "data/solutions/generated/triincir_022_0907be89df20a3ff.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0907be89df20a3ff.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@23", "density": 0.7918747649774476, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc23.gif", "friedman_metric_expression": "1.988+", "friedman_metric_symbol": "r", "friedman_metric_value": 1.988, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@23", "credit": "Maurizio Morandi", "date": "June 2008", "family_updated": "8/31/19", "metric_expression": "1.988+", "metric_symbol": "r", "metric_value": 1.988, "reference_text": "r = 1.988+ | Found by Maurizio Morandi | in June 2008.", "source_image": "tc23.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc23.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 1.988+ | Found by Maurizio Morandi | in June 2008.", "friedman_source_image": "tc23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "973cadfcac9f0399", "improvement": -0.012833950693412532, "max_boundary_excess": -2.3604816288269603e-06, "max_pair_overlap_depth": -6.566732802859576e-06, "metric_expression": "2.00083", "metric_symbol": "r", "metric_value": 2.0008339506934125, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.988, "setup": "triincir", "side": 4.001667901386825, "solution_path": "data/solutions/generated/triincir_023_973cadfcac9f0399.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/973cadfcac9f0399.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@24", "density": 0.77037708306075, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc24.gif", "friedman_metric_expression": "2", "friedman_metric_symbol": "r", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triincir@24", "credit": "Trivial", "date": "", "family_updated": "8/31/19", "metric_expression": "2", "metric_symbol": "r", "metric_value": 2.0, "reference_text": "r = 2 | Trivial.", "source_image": "tc24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc24.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2 | Trivial.", "friedman_source_image": "tc24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "9ebf7fbae73f62a7", "improvement": -0.07218881407517408, "max_boundary_excess": -1.2456668625482337e-06, "max_pair_overlap_depth": -4.316070905119318e-07, "metric_expression": "2.07219", "metric_symbol": "r", "metric_value": 2.072188814075174, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "triincir", "side": 4.144377628150348, "solution_path": "data/solutions/generated/triincir_024_9ebf7fbae73f62a7.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9ebf7fbae73f62a7.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@25", "density": 0.814798554480224, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2005", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc25.gif", "friedman_metric_expression": "2.055+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.055, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@25", "credit": "David W", "date": "July 2005", "family_updated": "8/31/19", "metric_expression": "2.055+", "metric_symbol": "r", "metric_value": 2.055, "reference_text": "r = 2.055+ | Found by David W. Cantrell | in July 2005.", "source_image": "tc25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc25.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.055+ | Found by David W. Cantrell | in July 2005.", "friedman_source_image": "tc25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "460bfc63493e0a99", "improvement": -0.0014599742843675045, "max_boundary_excess": -5.499842621325968e-07, "max_pair_overlap_depth": -5.533591762807433e-06, "metric_expression": "2.05646", "metric_symbol": "r", "metric_value": 2.0564599742843677, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.055, "setup": "triincir", "side": 4.112919948568735, "solution_path": "data/solutions/generated/triincir_025_460bfc63493e0a99.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/460bfc63493e0a99.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@26", "density": 0.763639473601239, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc26.gif", "friedman_metric_expression": "2.109+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.109, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@26", "credit": "Maurizio Morandi", "date": "April 2008", "family_updated": "8/31/19", "metric_expression": "2.109+", "metric_symbol": "r", "metric_value": 2.109, "reference_text": "r = 2.109+ | Found by Maurizio Morandi | in April 2008.", "source_image": "tc26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc26.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.109+ | Found by Maurizio Morandi | in April 2008.", "friedman_source_image": "tc26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "297d48c1e4300be9", "improvement": -0.057296364393150334, "max_boundary_excess": -2.064436773085987e-06, "max_pair_overlap_depth": -1.3195031345336616e-07, "metric_expression": "2.16630", "metric_symbol": "r", "metric_value": 2.1662963643931503, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.109, "setup": "triincir", "side": 4.332592728786301, "solution_path": "data/solutions/generated/triincir_026_297d48c1e4300be9.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/297d48c1e4300be9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@27", "density": 0.791482135514487, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2005", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc27.gif", "friedman_metric_expression": "2.138+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.138, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@27", "credit": "David W", "date": "July 2005", "family_updated": "8/31/19", "metric_expression": "2.138+", "metric_symbol": "r", "metric_value": 2.138, "reference_text": "r = 2.138+ | Found by David W. Cantrell | in July 2005.", "source_image": "tc27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc27.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.138+ | Found by David W. Cantrell | in July 2005.", "friedman_source_image": "tc27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "0b682f2ff7f493f4", "improvement": -0.03038655259456835, "max_boundary_excess": -8.100188688686671e-07, "max_pair_overlap_depth": -1.2480037501427788e-05, "metric_expression": "2.16839", "metric_symbol": "r", "metric_value": 2.1683865525945683, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.138, "setup": "triincir", "side": 4.3367731051891365, "solution_path": "data/solutions/generated/triincir_027_0b682f2ff7f493f4.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0b682f2ff7f493f4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@28", "density": 0.7833608666700476, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "July 2005", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc28.gif", "friedman_metric_expression": "2.191+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.191, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@28", "credit": "David W", "date": "July 2005", "family_updated": "8/31/19", "metric_expression": "2.191+", "metric_symbol": "r", "metric_value": 2.191, "reference_text": "r = 2.191+ | Found by David W. Cantrell | in July 2005.", "source_image": "tc28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc28.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.191+ | Found by David W. Cantrell | in July 2005.", "friedman_source_image": "tc28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "f7e451634cc50a5c", "improvement": -0.028593586242025903, "max_boundary_excess": -3.334899561835414e-06, "max_pair_overlap_depth": -1.391899336167235e-05, "metric_expression": "2.21959", "metric_symbol": "r", "metric_value": 2.2195935862420257, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.191, "setup": "triincir", "side": 4.4391871724840515, "solution_path": "data/solutions/generated/triincir_028_f7e451634cc50a5c.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f7e451634cc50a5c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@29", "density": 0.8182348688742829, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "June 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc29.gif", "friedman_metric_expression": "2.215+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.215, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@29", "credit": "Maurizio Morandi", "date": "June 2008", "family_updated": "8/31/19", "metric_expression": "2.215+", "metric_symbol": "r", "metric_value": 2.215, "reference_text": "r = 2.215+ | Found by Maurizio Morandi | in June 2008.", "source_image": "tc29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc29.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.215+ | Found by Maurizio Morandi | in June 2008.", "friedman_source_image": "tc29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "73bcaf90b9fd2226", "improvement": 0.004780586805306797, "max_boundary_excess": -3.1271053040349273e-06, "max_pair_overlap_depth": -1.2019034158372577e-05, "metric_expression": "2.21022", "metric_symbol": "r", "metric_value": 2.210219413194693, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.215, "setup": "triincir", "side": 4.420438826389386, "solution_path": "data/solutions/generated/triincir_029_73bcaf90b9fd2226.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/73bcaf90b9fd2226.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@30", "density": 0.7948627844239105, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc30.gif", "friedman_metric_expression": "2.258+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.258, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@30", "credit": "Maurizio Morandi", "date": "July 2008", "family_updated": "8/31/19", "metric_expression": "2.258+", "metric_symbol": "r", "metric_value": 2.258, "reference_text": "r = 2.258+ | Found by Maurizio Morandi | in July 2008.", "source_image": "tc30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc30.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.258+ | Found by Maurizio Morandi | in July 2008.", "friedman_source_image": "tc30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "05c2ceb22d6802af", "improvement": -0.022814299780184122, "max_boundary_excess": -3.282499053458565e-06, "max_pair_overlap_depth": -7.525015305542837e-06, "metric_expression": "2.28081", "metric_symbol": "r", "metric_value": 2.280814299780184, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.258, "setup": "triincir", "side": 4.561628599560368, "solution_path": "data/solutions/generated/triincir_030_05c2ceb22d6802af.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/05c2ceb22d6802af.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triincir@31", "density": 0.8077135574878077, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triincir/tc31.gif", "friedman_metric_expression": "2.272+", "friedman_metric_symbol": "r", "friedman_metric_value": 2.272, "friedman_reference": {"analytical_or_proved": false, "case": "triincir@31", "credit": "Maurizio Morandi", "date": "July 2008", "family_updated": "8/31/19", "metric_expression": "2.272+", "metric_symbol": "r", "metric_value": 2.272, "reference_text": "r = 2.272+ | Found by Maurizio Morandi | in July 2008.", "source_image": "tc31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc31.gif", "source_page": "https://erich-friedman.github.io/packing/triincir/", "title": "Triangles in Circles"}, "friedman_reference_text": "r = 2.272+ | Found by Maurizio Morandi | in July 2008.", "friedman_source_image": "tc31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triincir/", "friedman_title": "Triangles in Circles", "frontend_seed": true, "id": "d099d25f47dd541c", "improvement": -0.027998444456735605, "max_boundary_excess": -5.317100407520314e-06, "max_pair_overlap_depth": -1.0941201894709707e-05, "metric_expression": "2.30000", "metric_symbol": "r", "metric_value": 2.2999984444567354, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.272, "setup": "triincir", "side": 4.599996888913471, "solution_path": "data/solutions/generated/triincir_031_d099d25f47dd541c.json", "source_url": "https://erich-friedman.github.io/packing/triincir/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d099d25f47dd541c.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triindom@1", "density": 0.2886702903701934, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "\u221a3/2", "friedman_metric_symbol": "s", "friedman_metric_value": 0.8660254037844386, "friedman_reference": {"analytical_or_proved": true, "case": "triindom@1", "credit": "Trivial", "date": "", "family_updated": "4/4/26", "metric_expression": "\u221a3/2", "metric_symbol": "s", "metric_value": 0.8660254037844386, "reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "37b1dca676a779e3", "improvement": -7.266428382335377e-06, "max_boundary_excess": -2.4019537994690587e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.86603", "metric_symbol": "s", "metric_value": 0.8660326702128209, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.8660254037844386, "setup": "triindom", "side": 1.7320653404256419, "solution_path": "data/solutions/generated/triindom_001_37b1dca676a779e3.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/37b1dca676a779e3.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triindom@2", "density": 0.5773351362696808, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": "\u221a3/2", "friedman_metric_symbol": "s", "friedman_metric_value": 0.8660254037844386, "friedman_reference": {"analytical_or_proved": true, "case": "triindom@2", "credit": "Trivial", "date": "", "family_updated": "4/4/26", "metric_expression": "\u221a3/2", "metric_symbol": "s", "metric_value": 0.8660254037844386, "reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "source_image": "2.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/2.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "1-2. | | s = \u221a3/2 | Trivial. |", "friedman_source_image": "2.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "31518429031d2b51", "improvement": -1.1349913078717577e-05, "max_boundary_excess": -6.727531273176268e-07, "max_pair_overlap_depth": -0.13184728443338464, "metric_expression": "0.86604", "metric_symbol": "s", "metric_value": 0.8660367536975173, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.8660254037844386, "setup": "triindom", "side": 1.7320735073950346, "solution_path": "data/solutions/generated/triindom_002_31518429031d2b51.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/31518429031d2b51.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triindom@3", "density": 0.6931800833949334, "friedman_analytical_or_proved": false, "friedman_credit": "Jonathan Viquerat", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triindom/3.png", "friedman_family_updated": "4/4/26", "friedman_metric_expression": ".96796+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.96796, "friedman_reference": {"analytical_or_proved": false, "case": "triindom@3", "credit": "Jonathan Viquerat", "date": "April 2026", "family_updated": "4/4/26", "metric_expression": ".96796+", "metric_symbol": "s", "metric_value": 0.96796, "reference_text": "3. | | s = .96796+ | Found by Jonathan Viquerat | in April 2026", "source_image": "3.png", "source_image_url": "https://erich-friedman.github.io/packing/triindom/3.png", "source_page": "https://erich-friedman.github.io/packing/triindom/", "title": "Triangles in Dominoes"}, "friedman_reference_text": "3. | | s = .96796+ | Found by Jonathan Viquerat | in April 2026", "friedman_source_image": "3.png", "friedman_source_url": "https://erich-friedman.github.io/packing/triindom/", "friedman_title": "Triangles in Dominoes", "frontend_seed": true, "id": "b10402bd10926cd1", "improvement": -3.454421484250236e-05, "max_boundary_excess": -1.601436348197538e-06, "max_pair_overlap_depth": -2.0206571078401625e-05, "metric_expression": "0.96799", "metric_symbol": "s", "metric_value": 0.9679945442148425, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.96796, "setup": "triindom", "side": 1.935989088429685, "solution_path": "data/solutions/generated/triindom_003_b10402bd10926cd1.json", "source_url": "https://erich-friedman.github.io/packing/triindom/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b10402bd10926cd1.svg", "tolerance": 1e-08, "verified": true}
@@ -500,8 +674,25 @@
 {"case": "triinhex@18", "density": 0.8297080120836304, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "April 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/18.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "17/9 = 1.888+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.888, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@18", "credit": "Maurizio Morandi", "date": "April 2008", "family_updated": "4/29/26", "metric_expression": "17/9 = 1.888+", "metric_symbol": "s", "metric_value": 1.888, "reference_text": "s = 17/9 = 1.888+ | Found by Maurizio Morandi | in April 2008.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/18.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 17/9 = 1.888+ | Found by Maurizio Morandi | in April 2008.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "6c5f13d522480054", "improvement": -0.013507249150880973, "max_boundary_excess": -1.7176270484116662e-06, "max_pair_overlap_depth": -2.0474118108848582e-05, "metric_expression": "1.90151", "metric_symbol": "s", "metric_value": 1.9015072491508809, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.888, "setup": "triinhex", "side": 1.9015072491508809, "solution_path": "data/solutions/generated/triinhex_018_6c5f13d522480054.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6c5f13d522480054.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinhex@19", "density": 0.8252355857972508, "friedman_analytical_or_proved": false, "friedman_credit": "Alex Adri\u00e1n Nieto", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/19.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.953+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.953, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@19", "credit": "Alex Adri\u00e1n Nieto", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "1.953+", "metric_symbol": "s", "metric_value": 1.953, "reference_text": "s = 1.953+ | Found by Alex Adri\u00e1n Nieto | in April 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/19.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.953+ | Found by Alex Adri\u00e1n Nieto | in April 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "dca0a965c4496e80", "improvement": -0.005899708509202517, "max_boundary_excess": -1.4140126041781837e-06, "max_pair_overlap_depth": -4.097714423223486e-06, "metric_expression": "1.95890", "metric_symbol": "s", "metric_value": 1.9588997085092026, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.953, "setup": "triinhex", "side": 1.9588997085092026, "solution_path": "data/solutions/generated/triinhex_019_dca0a965c4496e80.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/dca0a965c4496e80.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinhex@20", "density": 0.84905335156007, "friedman_analytical_or_proved": false, "friedman_credit": "Aaden Abraham", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/20.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.97591+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.97591, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@20", "credit": "Aaden Abraham", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "1.97591+", "metric_symbol": "s", "metric_value": 1.97591, "reference_text": "s = 1.97591+ | Found by Aaden Abraham | in April 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/20.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.97591+ | Found by Aaden Abraham | in April 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "8af6938cdb16e6d8", "improvement": -0.005488739222003547, "max_boundary_excess": -2.9749927869818494e-07, "max_pair_overlap_depth": -5.967603292744705e-06, "metric_expression": "1.98140", "metric_symbol": "s", "metric_value": 1.9813987392220036, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.97591, "setup": "triinhex", "side": 1.9813987392220036, "solution_path": "data/solutions/generated/triinhex_020_8af6938cdb16e6d8.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8af6938cdb16e6d8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@21", "density": 0.8749527320468723, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/21.gif", "friedman_metric_expression": "1.99878+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.99878, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@21", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "1.99878+", "metric_symbol": "s", "metric_value": 1.99878, "reference_text": "s = 1.99878+ | Found by Ian Watson | in April 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/21.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 1.99878+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "96f74df50573bb81", "improvement": -0.0012740227066210252, "max_boundary_excess": -8.545179480294009e-07, "max_pair_overlap_depth": -6.765642482919887e-06, "metric_expression": "2.00005", "metric_symbol": "s", "metric_value": 2.000054022706621, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.99878, "setup": "triinhex", "side": 2.000054022706621, "solution_path": "data/solutions/generated/triinhex_021_96f74df50573bb81.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/96f74df50573bb81.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@22", "density": 0.9166150664792877, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@22", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial. |", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2 | Trivial. |", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "38182a59461da74e", "improvement": -5.629349013291929e-05, "max_boundary_excess": -4.91184500961419e-07, "max_pair_overlap_depth": -9.942352799940934e-07, "metric_expression": "2.00006", "metric_symbol": "s", "metric_value": 2.000056293490133, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "triinhex", "side": 2.000056293490133, "solution_path": "data/solutions/generated/triinhex_022_38182a59461da74e.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/38182a59461da74e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@23", "density": 0.958278890368788, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@23", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial. |", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2 | Trivial. |", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "dcd331994270a997", "improvement": -5.681247061106731e-05, "max_boundary_excess": -1.0734329507489061e-06, "max_pair_overlap_depth": -9.41664729126046e-06, "metric_expression": "2.00006", "metric_symbol": "s", "metric_value": 2.000056812470611, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "triinhex", "side": 2.000056812470611, "solution_path": "data/solutions/generated/triinhex_023_dcd331994270a997.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/dcd331994270a997.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@24", "density": 0.9999420291406096, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@24", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial. |", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2 | Trivial. |", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "13936a08bfd4d152", "improvement": -5.7973379977482864e-05, "max_boundary_excess": -1.3635152509087512e-06, "max_pair_overlap_depth": -3.8859579855957235e-06, "metric_expression": "2.00006", "metric_symbol": "s", "metric_value": 2.0000579733799775, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "triinhex", "side": 2.0000579733799775, "solution_path": "data/solutions/generated/triinhex_024_13936a08bfd4d152.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/13936a08bfd4d152.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@25", "density": 0.8871759236838516, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/25.gif", "friedman_metric_expression": "13/6 = 2.166+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.166, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@25", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "13/6 = 2.166+", "metric_symbol": "s", "metric_value": 2.166, "reference_text": "s = 13/6 = 2.166+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/25.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 13/6 = 2.166+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "71a7801cfb4a8d31", "improvement": -0.0011526610601886311, "max_boundary_excess": -6.780494307380179e-07, "max_pair_overlap_depth": -1.3308976067882838e-06, "metric_expression": "2.16715", "metric_symbol": "s", "metric_value": 2.1671526610601886, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.166, "setup": "triinhex", "side": 2.1671526610601886, "solution_path": "data/solutions/generated/triinhex_025_71a7801cfb4a8d31.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/71a7801cfb4a8d31.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@26", "density": 0.878430458154361, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/26.gif", "friedman_metric_expression": "2.21991+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.21991, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@26", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.21991+", "metric_symbol": "s", "metric_value": 2.21991, "reference_text": "s = 2.21991+ | Found by Ian Watson | in April 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/26.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.21991+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "658d7f93b604b663", "improvement": -0.0011349903788469007, "max_boundary_excess": -6.149641376243232e-07, "max_pair_overlap_depth": -5.41804289733161e-06, "metric_expression": "2.22104", "metric_symbol": "s", "metric_value": 2.221044990378847, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.21991, "setup": "triinhex", "side": 2.221044990378847, "solution_path": "data/solutions/generated/triinhex_026_658d7f93b604b663.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/658d7f93b604b663.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@27", "density": 0.8328322571122685, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/27.gif", "friedman_metric_expression": "2.29541+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.29541, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@27", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.29541+", "metric_symbol": "s", "metric_value": 2.29541, "reference_text": "s = 2.29541+ | Found by Ian Watson | in April 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/27.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.29541+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "11ad91d5c6b8788e", "improvement": -0.029078960495372286, "max_boundary_excess": -8.325360180907825e-06, "max_pair_overlap_depth": -2.435631066832755e-06, "metric_expression": "2.32449", "metric_symbol": "s", "metric_value": 2.3244889604953722, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.29541, "setup": "triinhex", "side": 2.3244889604953722, "solution_path": "data/solutions/generated/triinhex_027_11ad91d5c6b8788e.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/11ad91d5c6b8788e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@28", "density": 0.8335778928127813, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/28.gif", "friedman_metric_expression": "2.32289+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.32289, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@28", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.32289+", "metric_symbol": "s", "metric_value": 2.32289, "reference_text": "s = 2.32289+ | Found by Ian Watson | in April 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/28.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.32289+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "2b319174d63885b4", "improvement": -0.0431947496358025, "max_boundary_excess": -3.599330529801011e-06, "max_pair_overlap_depth": -6.859690785454564e-06, "metric_expression": "2.36608", "metric_symbol": "s", "metric_value": 2.3660847496358026, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.32289, "setup": "triinhex", "side": 2.3660847496358026, "solution_path": "data/solutions/generated/triinhex_028_2b319174d63885b4.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/2b319174d63885b4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@29", "density": 0.837502602292776, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/29.gif", "friedman_metric_expression": "7/3 = 2.333+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.333, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@29", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "7/3 = 2.333+", "metric_symbol": "s", "metric_value": 2.333, "reference_text": "s = 7/3 = 2.333+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/29.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 7/3 = 2.333+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "64c6a497fdd4bc1d", "improvement": -0.06931687053876034, "max_boundary_excess": -5.555832025645621e-06, "max_pair_overlap_depth": -3.7939764052641323e-06, "metric_expression": "2.40232", "metric_symbol": "s", "metric_value": 2.4023168705387605, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.333, "setup": "triinhex", "side": 2.4023168705387605, "solution_path": "data/solutions/generated/triinhex_029_64c6a497fdd4bc1d.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/64c6a497fdd4bc1d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@30", "density": 0.8237939342513431, "friedman_analytical_or_proved": true, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/30.gif", "friedman_metric_expression": "19/8 = 2.375", "friedman_metric_symbol": "s", "friedman_metric_value": 2.375, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@30", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "19/8 = 2.375", "metric_symbol": "s", "metric_value": 2.375, "reference_text": "s = 19/8 = 2.375 | Found by Ignacio Vallejo | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/30.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 19/8 = 2.375 | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "11d17f9e12268b02", "improvement": -0.08863126687001355, "max_boundary_excess": -2.046588857940021e-06, "max_pair_overlap_depth": -2.8430880139040937e-06, "metric_expression": "2.46363", "metric_symbol": "s", "metric_value": 2.4636312668700135, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.375, "setup": "triinhex", "side": 2.4636312668700135, "solution_path": "data/solutions/generated/triinhex_030_11d17f9e12268b02.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/11d17f9e12268b02.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@31", "density": 0.8505895807478101, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/31.gif", "friedman_metric_expression": "12/5 = 2.400", "friedman_metric_symbol": "s", "friedman_metric_value": 2.4, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "12/5 = 2.400", "metric_symbol": "s", "metric_value": 2.4, "reference_text": "s = 12/5 = 2.400 | Found by Emerson Connelly | in April 2026.", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/31.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 12/5 = 2.400 | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "1ce8108c850d5941", "improvement": -0.06459289672266566, "max_boundary_excess": -7.67227682312255e-06, "max_pair_overlap_depth": -3.638067419098334e-06, "metric_expression": "2.46459", "metric_symbol": "s", "metric_value": 2.4645928967226656, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.4, "setup": "triinhex", "side": 2.4645928967226656, "solution_path": "data/solutions/generated/triinhex_031_1ce8108c850d5941.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1ce8108c850d5941.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@32", "density": 0.8767870241121234, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/32.gif", "friedman_metric_expression": "2.465+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.465, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.465+", "metric_symbol": "s", "metric_value": 2.465, "reference_text": "s = 2.465+ | Found by Emerson Connelly | in April 2026.", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/32.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.465+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "8674581436e5e74d", "improvement": -0.0013363682337788063, "max_boundary_excess": -6.925122041572899e-07, "max_pair_overlap_depth": -1.2807310418028184e-06, "metric_expression": "2.46634", "metric_symbol": "s", "metric_value": 2.4663363682337787, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.465, "setup": "triinhex", "side": 2.4663363682337787, "solution_path": "data/solutions/generated/triinhex_032_8674581436e5e74d.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8674581436e5e74d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@33", "density": 0.8799443949567897, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/33.gif", "friedman_metric_expression": "2.498+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.498, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.498+", "metric_symbol": "s", "metric_value": 2.498, "reference_text": "s = 2.498+ | Found by Emerson Connelly | in April 2026.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/33.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.498+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "5b836a27d2bb958c", "improvement": -0.00207898817969987, "max_boundary_excess": -2.8634496562140136e-06, "max_pair_overlap_depth": -5.829272115620565e-06, "metric_expression": "2.50008", "metric_symbol": "s", "metric_value": 2.5000789881797, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.498, "setup": "triinhex", "side": 2.5000789881797, "solution_path": "data/solutions/generated/triinhex_033_5b836a27d2bb958c.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5b836a27d2bb958c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@34", "density": 0.9066102013779274, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "friedman_metric_expression": "5/2 = 2.500", "friedman_metric_symbol": "s", "friedman_metric_value": 2.5, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "5/2 = 2.500", "metric_symbol": "s", "metric_value": 2.5, "reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "a712744ff3b5bcc9", "improvement": -7.7851001305973e-05, "max_boundary_excess": -1.2753913921730298e-06, "max_pair_overlap_depth": -7.960301433351802e-06, "metric_expression": "2.50008", "metric_symbol": "s", "metric_value": 2.500077851001306, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.5, "setup": "triinhex", "side": 2.500077851001306, "solution_path": "data/solutions/generated/triinhex_034_a712744ff3b5bcc9.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a712744ff3b5bcc9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@35", "density": 0.8784557475555014, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "friedman_metric_expression": "5/2 = 2.500", "friedman_metric_symbol": "s", "friedman_metric_value": 2.5, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@35", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "5/2 = 2.500", "metric_symbol": "s", "metric_value": 2.5, "reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "6c433acba2e3b71c", "improvement": -0.07690526384601659, "max_boundary_excess": -2.8573318260367013e-06, "max_pair_overlap_depth": -2.7042986540104508e-06, "metric_expression": "2.57691", "metric_symbol": "s", "metric_value": 2.5769052638460166, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.5, "setup": "triinhex", "side": 2.5769052638460166, "solution_path": "data/solutions/generated/triinhex_035_6c433acba2e3b71c.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6c433acba2e3b71c.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinhex@36", "density": 0.893589353430048, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/36.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.592+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.592, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@36", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.592+", "metric_symbol": "s", "metric_value": 2.592, "reference_text": "s = 2.592+ | Found by Emerson Connelly | in April 2026.", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/36.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.592+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "id": "e4e0e01451d6ca30", "improvement": 0.0007660070914519146, "max_boundary_excess": -3.7601717225028787e-07, "max_pair_overlap_depth": -3.324194429499272e-06, "n": 36, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 2.592, "setup": "triinhex", "side": 2.591233992908548, "solution_path": "data/solutions/triinhex_36.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/e4e0e01451d6ca30.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinhex@37", "density": 0.8987469977236169, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/37.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.655+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.655, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@37", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.655+", "metric_symbol": "s", "metric_value": 2.655, "reference_text": "s = 2.655+ | Found by Emerson Connelly | in April 2026.", "source_image": "37.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/37.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.655+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "id": "c1697d9445319eaa", "improvement": 0.035571728604908426, "max_boundary_excess": -1.2650118661675414e-07, "max_pair_overlap_depth": -4.4643045216119503e-07, "n": 37, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 2.655, "setup": "triinhex", "side": 2.6194282713950914, "solution_path": "data/solutions/triinhex_37.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/c1697d9445319eaa.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@38", "density": 0.8907392561961515, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "friedman_metric_expression": "8/3 = 2.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.666, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "8/3 = 2.666+", "metric_symbol": "s", "metric_value": 2.666, "reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "76fd196e8c79a5c9", "improvement": -0.0004956329108489754, "max_boundary_excess": -3.7850003642140776e-06, "max_pair_overlap_depth": -3.863933217385096e-06, "metric_expression": "2.66650", "metric_symbol": "s", "metric_value": 2.666495632910849, "n": 38, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.666, "setup": "triinhex", "side": 2.666495632910849, "solution_path": "data/solutions/generated/triinhex_038_76fd196e8c79a5c9.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/76fd196e8c79a5c9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinhex@39", "density": 0.8833522738592235, "friedman_analytical_or_proved": true, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "friedman_metric_expression": "8/3 = 2.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.666, "friedman_reference": {"analytical_or_proved": true, "case": "triinhex@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "8/3 = 2.666+", "metric_symbol": "s", "metric_value": 2.666, "reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "frontend_seed": true, "id": "cf1c7ccbe8f975b2", "improvement": -0.04662470457951118, "max_boundary_excess": -2.2386896785242527e-06, "max_pair_overlap_depth": -9.826603503571008e-06, "metric_expression": "2.71262", "metric_symbol": "s", "metric_value": 2.712624704579511, "n": 39, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.666, "setup": "triinhex", "side": 2.712624704579511, "solution_path": "data/solutions/generated/triinhex_039_cf1c7ccbe8f975b2.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/cf1c7ccbe8f975b2.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinhex@40", "density": 0.9036048260198691, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinhex/40.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.719+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.719, "friedman_reference": {"analytical_or_proved": false, "case": "triinhex@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.719+", "metric_symbol": "s", "metric_value": 2.719, "reference_text": "s = 2.719+ | Found by Emerson Connelly | in April 2026.", "source_image": "40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinhex/40.gif", "source_page": "https://erich-friedman.github.io/packing/triinhex/", "title": "Triangles in Hexagons"}, "friedman_reference_text": "s = 2.719+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinhex/", "friedman_title": "Triangles in Hexagons", "id": "0ebde2f6b4b26d2b", "improvement": 0.002779018588611848, "max_boundary_excess": -5.817255795307e-07, "max_pair_overlap_depth": -1.0085947836913078e-06, "n": 40, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 2.719, "setup": "triinhex", "side": 2.716220981411388, "solution_path": "data/solutions/triinhex_40.json", "source_url": "https://erich-friedman.github.io/packing/triinhex/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/0ebde2f6b4b26d2b.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinoct@1", "density": 0.4152122478191623, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/1.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": ".46470+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.4647, "friedman_reference": {"analytical_or_proved": true, "case": "triinoct@1", "credit": "Trivial", "date": "", "family_updated": "3/22/26", "metric_expression": ".46470+", "metric_symbol": "s", "metric_value": 0.4647, "reference_text": "s = .46470+ | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/1.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = .46470+ | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "92c66f395ff03ab9", "improvement": -4.251046545072912e-05, "max_boundary_excess": -2.3282842257895898e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.46474", "metric_symbol": "s", "metric_value": 0.46474251046545073, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.4647, "setup": "triinoct", "side": 0.46474251046545073, "solution_path": "data/solutions/generated/triinoct_001_92c66f395ff03ab9.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/92c66f395ff03ab9.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinoct@2", "density": 0.40823825072318354, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/2.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "\u221a3/\u221a(4+2\u221a2) = .66282+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.66282, "friedman_reference": {"analytical_or_proved": true, "case": "triinoct@2", "credit": "Trivial", "date": "", "family_updated": "3/22/26", "metric_expression": "\u221a3/\u221a(4+2\u221a2) = .66282+", "metric_symbol": "s", "metric_value": 0.66282, "reference_text": "s = \u221a3/\u221a(4+2\u221a2) = .66282+ | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/2.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = \u221a3/\u221a(4+2\u221a2) = .66282+ | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "5706480ca6648c20", "improvement": -1.5298424264065247e-05, "max_boundary_excess": -4.197393779037103e-06, "max_pair_overlap_depth": -5.033792755404498e-07, "metric_expression": "0.66284", "metric_symbol": "s", "metric_value": 0.662835298424264, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.66282, "setup": "triinoct", "side": 0.662835298424264, "solution_path": "data/solutions/generated/triinoct_002_5706480ca6648c20.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5706480ca6648c20.svg", "tolerance": 1e-08, "verified": true}
@@ -523,6 +714,16 @@
 {"case": "triinoct@18", "density": 0.7984879014669996, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/18.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.41836+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.41836, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@18", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.41836+", "metric_symbol": "s", "metric_value": 1.41836, "reference_text": "s = 1.41836+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/18.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.41836+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "8e956085d3bcc5e4", "improvement": -0.00347617639937825, "max_boundary_excess": -2.3654127749911342e-06, "max_pair_overlap_depth": -6.1952459529668324e-06, "metric_expression": "1.42184", "metric_symbol": "s", "metric_value": 1.4218361763993783, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.41836, "setup": "triinoct", "side": 1.4218361763993783, "solution_path": "data/solutions/generated/triinoct_018_8e956085d3bcc5e4.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8e956085d3bcc5e4.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinoct@19", "density": 0.785495925696758, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/19.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.46749+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.46749, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.46749+", "metric_symbol": "s", "metric_value": 1.46749, "reference_text": "s = 1.46749+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/19.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.46749+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "b85e7f72b874a80d", "improvement": -0.005338941628411087, "max_boundary_excess": -1.1956920861702103e-06, "max_pair_overlap_depth": -5.584055034923985e-06, "metric_expression": "1.47283", "metric_symbol": "s", "metric_value": 1.472828941628411, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.46749, "setup": "triinoct", "side": 1.472828941628411, "solution_path": "data/solutions/generated/triinoct_019_b85e7f72b874a80d.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b85e7f72b874a80d.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinoct@20", "density": 0.7943876162475321, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/20.gif", "friedman_family_updated": "3/22/26", "friedman_metric_expression": "1.49832+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.49832, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@20", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.49832+", "metric_symbol": "s", "metric_value": 1.49832, "reference_text": "s = 1.49832+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/20.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.49832+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "5dc5edf6bbc42f57", "improvement": -0.004289888994578384, "max_boundary_excess": -1.8456961687288941e-06, "max_pair_overlap_depth": -7.334356214305782e-06, "metric_expression": "1.50261", "metric_symbol": "s", "metric_value": 1.5026098889945785, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.49832, "setup": "triinoct", "side": 1.5026098889945785, "solution_path": "data/solutions/generated/triinoct_020_5dc5edf6bbc42f57.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5dc5edf6bbc42f57.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@21", "density": 0.8006209623113996, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/21.gif", "friedman_metric_expression": "1.52615+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.52615, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@21", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.52615+", "metric_symbol": "s", "metric_value": 1.52615, "reference_text": "s = 1.52615+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/21.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.52615+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "550235b8e64c906b", "improvement": -0.007561402736510292, "max_boundary_excess": -3.854617439163859e-07, "max_pair_overlap_depth": -1.236860211395463e-05, "metric_expression": "1.53371", "metric_symbol": "s", "metric_value": 1.5337114027365102, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.52615, "setup": "triinoct", "side": 1.5337114027365102, "solution_path": "data/solutions/generated/triinoct_021_550235b8e64c906b.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/550235b8e64c906b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@22", "density": 0.8117485196689109, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/22.gif", "friedman_metric_expression": "1.55545+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.55545, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@22", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.55545+", "metric_symbol": "s", "metric_value": 1.55545, "reference_text": "s = 1.55545+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/22.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.55545+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "a1924650c6f006ea", "improvement": -0.0035570002935343403, "max_boundary_excess": -4.3062927716738536e-06, "max_pair_overlap_depth": -1.800963083109508e-06, "metric_expression": "1.55901", "metric_symbol": "s", "metric_value": 1.5590070002935343, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.55545, "setup": "triinoct", "side": 1.5590070002935343, "solution_path": "data/solutions/generated/triinoct_022_a1924650c6f006ea.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a1924650c6f006ea.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@23", "density": 0.8210902170609379, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/23.gif", "friedman_metric_expression": "1.58458+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.58458, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@23", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.58458+", "metric_symbol": "s", "metric_value": 1.58458, "reference_text": "s = 1.58458+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/23.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.58458+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "4ca1a825a22b1f04", "improvement": -0.0003714249913302492, "max_boundary_excess": -8.321393677649287e-06, "max_pair_overlap_depth": -1.5960535921788477e-06, "metric_expression": "1.58495", "metric_symbol": "s", "metric_value": 1.5849514249913303, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.58458, "setup": "triinoct", "side": 1.5849514249913303, "solution_path": "data/solutions/generated/triinoct_023_4ca1a825a22b1f04.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4ca1a825a22b1f04.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@24", "density": 0.8373304168984339, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/24.gif", "friedman_metric_expression": "1.60261+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.60261, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@24", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.60261+", "metric_symbol": "s", "metric_value": 1.60261, "reference_text": "s = 1.60261+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.60261+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "e197b92ecac28558", "improvement": -0.0006526103809141315, "max_boundary_excess": -2.085338835265612e-06, "max_pair_overlap_depth": -9.98840296584369e-06, "metric_expression": "1.60326", "metric_symbol": "s", "metric_value": 1.6032626103809142, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.60261, "setup": "triinoct", "side": 1.6032626103809142, "solution_path": "data/solutions/generated/triinoct_024_e197b92ecac28558.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e197b92ecac28558.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@25", "density": 0.8206390570044901, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/25.gif", "friedman_metric_expression": "1.63797+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.63797, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@25", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.63797+", "metric_symbol": "s", "metric_value": 1.63797, "reference_text": "s = 1.63797+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/25.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.63797+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "4e1b861b138850ae", "improvement": -0.014910250491960486, "max_boundary_excess": -2.6877619511415554e-06, "max_pair_overlap_depth": -7.2555966788498405e-06, "metric_expression": "1.65288", "metric_symbol": "s", "metric_value": 1.6528802504919604, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.63797, "setup": "triinoct", "side": 1.6528802504919604, "solution_path": "data/solutions/generated/triinoct_025_4e1b861b138850ae.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/4e1b861b138850ae.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@26", "density": 0.8149644565721081, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/26.gif", "friedman_metric_expression": "1.67666+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.67666, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@26", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.67666+", "metric_symbol": "s", "metric_value": 1.67666, "reference_text": "s = 1.67666+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/26.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.67666+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "cbcb6c755dc046de", "improvement": -0.014812017272631595, "max_boundary_excess": -3.687228372083238e-07, "max_pair_overlap_depth": -1.2896587116006941e-06, "metric_expression": "1.69147", "metric_symbol": "s", "metric_value": 1.6914720172726316, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.67666, "setup": "triinoct", "side": 1.6914720172726316, "solution_path": "data/solutions/generated/triinoct_026_cbcb6c755dc046de.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/cbcb6c755dc046de.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@27", "density": 0.8010680431479879, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/27.gif", "friedman_metric_expression": "1.70882+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.70882, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@27", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.70882+", "metric_symbol": "s", "metric_value": 1.70882, "reference_text": "s = 1.70882+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/27.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.70882+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "836b5a3b2c412e9b", "improvement": -0.029759907189525592, "max_boundary_excess": -9.248042691084391e-07, "max_pair_overlap_depth": -7.87865755902395e-06, "metric_expression": "1.73858", "metric_symbol": "s", "metric_value": 1.7385799071895256, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.70882, "setup": "triinoct", "side": 1.7385799071895256, "solution_path": "data/solutions/generated/triinoct_027_836b5a3b2c412e9b.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/836b5a3b2c412e9b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@28", "density": 0.8165576484730356, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/28.gif", "friedman_metric_expression": "1.73954+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.73954, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@28", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.73954+", "metric_symbol": "s", "metric_value": 1.73954, "reference_text": "s = 1.73954+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/28.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.73954+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "728bf65e8a483e5e", "improvement": -0.014070219094066916, "max_boundary_excess": -4.0057635728717315e-07, "max_pair_overlap_depth": -1.0036991463513445e-05, "metric_expression": "1.75361", "metric_symbol": "s", "metric_value": 1.753610219094067, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.73954, "setup": "triinoct", "side": 1.753610219094067, "solution_path": "data/solutions/generated/triinoct_028_728bf65e8a483e5e.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/728bf65e8a483e5e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@29", "density": 0.8071992437047276, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/29.gif", "friedman_metric_expression": "1.75576+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.75576, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@29", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.75576+", "metric_symbol": "s", "metric_value": 1.75576, "reference_text": "s = 1.75576+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/29.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.75576+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "f6d5bdc33f1fd083", "improvement": -0.03920549021863984, "max_boundary_excess": -2.872640643928272e-06, "max_pair_overlap_depth": -2.128542299273395e-05, "metric_expression": "1.79497", "metric_symbol": "s", "metric_value": 1.7949654902186398, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.75576, "setup": "triinoct", "side": 1.7949654902186398, "solution_path": "data/solutions/generated/triinoct_029_f6d5bdc33f1fd083.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f6d5bdc33f1fd083.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinoct@30", "density": 0.8241852827166171, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinoct/30.gif", "friedman_metric_expression": "1.78101+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.78101, "friedman_reference": {"analytical_or_proved": false, "case": "triinoct@30", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "3/22/26", "metric_expression": "1.78101+", "metric_symbol": "s", "metric_value": 1.78101, "reference_text": "s = 1.78101+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinoct/30.gif", "source_page": "https://erich-friedman.github.io/packing/triinoct/", "title": "Triangles in Octagons"}, "friedman_reference_text": "s = 1.78101+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinoct/", "friedman_title": "Triangles in Octagons", "frontend_seed": true, "id": "55871e661d418192", "improvement": -0.02573007339812161, "max_boundary_excess": -9.550198166939913e-07, "max_pair_overlap_depth": -3.435684308383813e-06, "metric_expression": "1.80674", "metric_symbol": "s", "metric_value": 1.8067400733981216, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.78101, "setup": "triinoct", "side": 1.8067400733981216, "solution_path": "data/solutions/generated/triinoct_030_55871e661d418192.json", "source_url": "https://erich-friedman.github.io/packing/triinoct/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/55871e661d418192.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinpen@1", "density": 0.4121951299103008, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/1.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": ".781+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.781, "friedman_reference": {"analytical_or_proved": true, "case": "triinpen@1", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": ".781+", "metric_symbol": "s", "metric_value": 0.781, "reference_text": "s = cos(42\u00b0) / cos(18\u00b0) | s = .781+ | Trivial. |", "source_image": "1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/1.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = cos(42\u00b0) / cos(18\u00b0) | s = .781+ | Trivial. |", "friedman_source_image": "1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "6d3af7533c544064", "improvement": -0.0004017935524769367, "max_boundary_excess": -5.010333690326338e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "0.78140", "metric_symbol": "s", "metric_value": 0.781401793552477, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.781, "setup": "triinpen", "side": 0.781401793552477, "solution_path": "data/solutions/generated/triinpen_001_6d3af7533c544064.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6d3af7533c544064.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinpen@2", "density": 0.4392461428307515, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/2.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.070+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.07, "friedman_reference": {"analytical_or_proved": true, "case": "triinpen@2", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "1.070+", "metric_symbol": "s", "metric_value": 1.07, "reference_text": "s = \u221a(6/(3+\u221a5)) | s = 1.070+ | Trivial. |", "source_image": "2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/2.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = \u221a(6/(3+\u221a5)) | s = 1.070+ | Trivial. |", "friedman_source_image": "2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "eebb278fed1959e5", "improvement": -0.0005004432401414238, "max_boundary_excess": -7.540244142797655e-06, "max_pair_overlap_depth": -4.677606255020384e-06, "metric_expression": "1.07050", "metric_symbol": "s", "metric_value": 1.0705004432401415, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.07, "setup": "triinpen", "side": 1.0705004432401415, "solution_path": "data/solutions/generated/triinpen_002_eebb278fed1959e5.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/eebb278fed1959e5.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinpen@3", "density": 0.5773621092377123, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/3.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "1.143+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.143, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@3", "credit": "Maurizio Morandi", "date": "August 2012", "family_updated": "4/29/26", "metric_expression": "1.143+", "metric_symbol": "s", "metric_value": 1.143, "reference_text": "s = 1.143+ | Found by Maurizio Morandi | in August 2012. |", "source_image": "3.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/3.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 1.143+ | Found by Maurizio Morandi | in August 2012. |", "friedman_source_image": "3.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "6ec3c588fb678646", "improvement": -0.0005688574140261249, "max_boundary_excess": -1.4403665141977852e-06, "max_pair_overlap_depth": -4.738354987265936e-06, "metric_expression": "1.14357", "metric_symbol": "s", "metric_value": 1.1435688574140261, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.143, "setup": "triinpen", "side": 1.1435688574140261, "solution_path": "data/solutions/generated/triinpen_003_6ec3c588fb678646.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6ec3c588fb678646.svg", "tolerance": 1e-08, "verified": true}
@@ -543,8 +744,25 @@
 {"case": "triinpen@18", "density": 0.8386266626517904, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/18.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.29382+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.29382, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@18", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.29382+", "metric_symbol": "s", "metric_value": 2.29382, "reference_text": "s = 2.29382+ | Found by Ian Watson | in April 2026.", "source_image": "18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/18.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.29382+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "286d64d1342c9a9f", "improvement": -0.0304027693812583, "max_boundary_excess": -2.3683231734867957e-06, "max_pair_overlap_depth": -9.23929068963325e-06, "metric_expression": "2.32422", "metric_symbol": "s", "metric_value": 2.3242227693812585, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.29382, "setup": "triinpen", "side": 2.3242227693812585, "solution_path": "data/solutions/generated/triinpen_018_286d64d1342c9a9f.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/286d64d1342c9a9f.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinpen@19", "density": 0.831205150275822, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.344+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.344, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@19", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "4/29/26", "metric_expression": "2.344+", "metric_symbol": "s", "metric_value": 2.344, "reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/19.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.344+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "5f0b9905f54e5f87", "improvement": -0.05454858293536624, "max_boundary_excess": -1.8779608876987526e-06, "max_pair_overlap_depth": -1.5527720347900675e-05, "metric_expression": "2.39855", "metric_symbol": "s", "metric_value": 2.398548582935366, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.344, "setup": "triinpen", "side": 2.398548582935366, "solution_path": "data/solutions/generated/triinpen_019_5f0b9905f54e5f87.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5f0b9905f54e5f87.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinpen@20", "density": 0.8487102106795418, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/20.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "2.43350+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.4335, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@20", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.43350+", "metric_symbol": "s", "metric_value": 2.4335, "reference_text": "s = 2.43350+ | Found by Ian Watson | in April 2026.", "source_image": "20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/20.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.43350+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "760faebc4d0b131b", "improvement": -0.001848490502489586, "max_boundary_excess": -7.176183787084704e-07, "max_pair_overlap_depth": -8.807499014995557e-06, "metric_expression": "2.43535", "metric_symbol": "s", "metric_value": 2.4353484905024896, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.4335, "setup": "triinpen", "side": 2.4353484905024896, "solution_path": "data/solutions/generated/triinpen_020_760faebc4d0b131b.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/760faebc4d0b131b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@21", "density": 0.8589998748063701, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/21.gif", "friedman_metric_expression": "2.479+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.479, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@21", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "4/29/26", "metric_expression": "2.479+", "metric_symbol": "s", "metric_value": 2.479, "reference_text": "s = 2.479+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/21.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.479+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "115c20fad199fe9d", "improvement": -0.0014982727861765355, "max_boundary_excess": -2.811024693767028e-06, "max_pair_overlap_depth": -2.8209410938284663e-06, "metric_expression": "2.48050", "metric_symbol": "s", "metric_value": 2.4804982727861766, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.479, "setup": "triinpen", "side": 2.4804982727861766, "solution_path": "data/solutions/generated/triinpen_021_115c20fad199fe9d.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/115c20fad199fe9d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@22", "density": 0.8367105270898347, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/22.gif", "friedman_metric_expression": "2.56740+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.5674, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@22", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.56740+", "metric_symbol": "s", "metric_value": 2.5674, "reference_text": "s = 2.56740+ | Found by Ian Watson | in April 2026.", "source_image": "22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/22.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.56740+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "b3ecf4aa9beda411", "improvement": -0.0050654803778220625, "max_boundary_excess": -3.63122781255133e-06, "max_pair_overlap_depth": -1.9313990747837906e-06, "metric_expression": "2.57247", "metric_symbol": "s", "metric_value": 2.572465480377822, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.5674, "setup": "triinpen", "side": 2.572465480377822, "solution_path": "data/solutions/generated/triinpen_022_b3ecf4aa9beda411.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b3ecf4aa9beda411.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@23", "density": 0.8358219621726138, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/23.gif", "friedman_metric_expression": "2.61831+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.61831, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@23", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.61831+", "metric_symbol": "s", "metric_value": 2.61831, "reference_text": "s = 2.61831+ | Found by Ian Watson | in April 2026.", "source_image": "23.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/23.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.61831+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "b2f9cfacd50b72e9", "improvement": -0.013368670719241305, "max_boundary_excess": -5.909725797067009e-06, "max_pair_overlap_depth": -5.3149326107448935e-06, "metric_expression": "2.63168", "metric_symbol": "s", "metric_value": 2.6316786707192414, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.61831, "setup": "triinpen", "side": 2.6316786707192414, "solution_path": "data/solutions/generated/triinpen_023_b2f9cfacd50b72e9.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b2f9cfacd50b72e9.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@24", "density": 0.8203286521496933, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/24.gif", "friedman_metric_expression": "2.66641+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.66641, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@24", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.66641+", "metric_symbol": "s", "metric_value": 2.66641, "reference_text": "s = 2.66641+ | Found by Ian Watson | in April 2026.", "source_image": "24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/24.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.66641+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "76211a17aba30b36", "improvement": -0.04713802590265814, "max_boundary_excess": -7.766120852076588e-07, "max_pair_overlap_depth": -5.665654174702439e-07, "metric_expression": "2.71355", "metric_symbol": "s", "metric_value": 2.713548025902658, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.66641, "setup": "triinpen", "side": 2.713548025902658, "solution_path": "data/solutions/generated/triinpen_024_76211a17aba30b36.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/76211a17aba30b36.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@25", "density": 0.8170666213083482, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/25.gif", "friedman_metric_expression": "2.720+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.72, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@25", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "4/29/26", "metric_expression": "2.720+", "metric_symbol": "s", "metric_value": 2.72, "reference_text": "s = 2.720+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/25.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.720+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "cc904cb82492c4b0", "improvement": -0.055026288404456114, "max_boundary_excess": -3.831253149892822e-06, "max_pair_overlap_depth": -1.0171981972284527e-05, "metric_expression": "2.77503", "metric_symbol": "s", "metric_value": 2.7750262884044563, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.72, "setup": "triinpen", "side": 2.7750262884044563, "solution_path": "data/solutions/generated/triinpen_025_cc904cb82492c4b0.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/cc904cb82492c4b0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@26", "density": 0.8287869991439658, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/26.gif", "friedman_metric_expression": "2.771+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.771, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@26", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "4/29/26", "metric_expression": "2.771+", "metric_symbol": "s", "metric_value": 2.771, "reference_text": "s = 2.771+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/26.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.771+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "810173856676a6fb", "improvement": -0.03890114272185885, "max_boundary_excess": -2.899135639086088e-06, "max_pair_overlap_depth": -1.3139310877985366e-05, "metric_expression": "2.80990", "metric_symbol": "s", "metric_value": 2.8099011427218588, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.771, "setup": "triinpen", "side": 2.8099011427218588, "solution_path": "data/solutions/generated/triinpen_026_810173856676a6fb.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/810173856676a6fb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@27", "density": 0.8321868307827671, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/27.gif", "friedman_metric_expression": "2.81761+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.81761, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@27", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.81761+", "metric_symbol": "s", "metric_value": 2.81761, "reference_text": "s = 2.81761+ | Found by Ian Watson | in April 2026.", "source_image": "27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/27.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.81761+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "8b8ba91284e47068", "improvement": -0.03996274171783831, "max_boundary_excess": -3.050950539540987e-07, "max_pair_overlap_depth": -5.479231620197922e-06, "metric_expression": "2.85757", "metric_symbol": "s", "metric_value": 2.8575727417178385, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.81761, "setup": "triinpen", "side": 2.8575727417178385, "solution_path": "data/solutions/generated/triinpen_027_8b8ba91284e47068.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8b8ba91284e47068.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@28", "density": 0.8534363238461394, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "March 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/28.gif", "friedman_metric_expression": "2.868+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.868, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@28", "credit": "Ignacio Vallejo", "date": "March 2026", "family_updated": "4/29/26", "metric_expression": "2.868+", "metric_symbol": "s", "metric_value": 2.868, "reference_text": "s = 2.868+ | Found by Ignacio Vallejo | in March 2026.", "source_image": "28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/28.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.868+ | Found by Ignacio Vallejo | in March 2026.", "friedman_source_image": "28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "6ad421ad9865e8bf", "improvement": -0.005553490865734201, "max_boundary_excess": -2.0498365378060392e-06, "max_pair_overlap_depth": -1.2746651528505737e-05, "metric_expression": "2.87355", "metric_symbol": "s", "metric_value": 2.873553490865734, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.868, "setup": "triinpen", "side": 2.873553490865734, "solution_path": "data/solutions/generated/triinpen_028_6ad421ad9865e8bf.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/6ad421ad9865e8bf.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@29", "density": 0.8464177208582354, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/29.gif", "friedman_metric_expression": "2.903+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.903, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@29", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.903+", "metric_symbol": "s", "metric_value": 2.903, "reference_text": "s = 2.903+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/29.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.903+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "0d9d40fe56c0f6d4", "improvement": -0.03351657923241014, "max_boundary_excess": -2.7025059194940577e-06, "max_pair_overlap_depth": -2.3448291092131868e-06, "metric_expression": "2.93652", "metric_symbol": "s", "metric_value": 2.93651657923241, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.903, "setup": "triinpen", "side": 2.93651657923241, "solution_path": "data/solutions/generated/triinpen_029_0d9d40fe56c0f6d4.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0d9d40fe56c0f6d4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@30", "density": 0.8397676649377761, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/30.gif", "friedman_metric_expression": "2.952+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.952, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@30", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.952+", "metric_symbol": "s", "metric_value": 2.952, "reference_text": "s = 2.952+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/30.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.952+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "2b832e7a9fa0a7c5", "improvement": -0.04651955266880892, "max_boundary_excess": -7.656844312442343e-06, "max_pair_overlap_depth": -3.4133589315032964e-06, "metric_expression": "2.99852", "metric_symbol": "s", "metric_value": 2.998519552668809, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.952, "setup": "triinpen", "side": 2.998519552668809, "solution_path": "data/solutions/generated/triinpen_030_2b832e7a9fa0a7c5.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/2b832e7a9fa0a7c5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@31", "density": 0.8566123952654375, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/31.gif", "friedman_metric_expression": "2.992+", "friedman_metric_symbol": "s", "friedman_metric_value": 2.992, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "2.992+", "metric_symbol": "s", "metric_value": 2.992, "reference_text": "s = 2.992+ | Found by Emerson Connelly | in April 2026.", "source_image": "31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/31.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 2.992+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "579de3c893a5a64c", "improvement": -0.025967103693977922, "max_boundary_excess": -1.099100289551188e-06, "max_pair_overlap_depth": -2.29204214511336e-05, "metric_expression": "3.01797", "metric_symbol": "s", "metric_value": 3.017967103693978, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.992, "setup": "triinpen", "side": 3.017967103693978, "solution_path": "data/solutions/generated/triinpen_031_579de3c893a5a64c.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/579de3c893a5a64c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@32", "density": 0.8514556204542924, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/32.gif", "friedman_metric_expression": "3.029+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.029, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.029+", "metric_symbol": "s", "metric_value": 3.029, "reference_text": "s = 3.029+ | Found by Emerson Connelly | in April 2026.", "source_image": "32.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/32.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.029+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "70ed9a5e30a88f24", "improvement": -0.04652890272981658, "max_boundary_excess": -2.6611165642007356e-06, "max_pair_overlap_depth": -3.1395889643626163e-06, "metric_expression": "3.07553", "metric_symbol": "s", "metric_value": 3.0755289027298165, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.029, "setup": "triinpen", "side": 3.0755289027298165, "solution_path": "data/solutions/generated/triinpen_032_70ed9a5e30a88f24.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/70ed9a5e30a88f24.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@33", "density": 0.872718269558225, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/33.gif", "friedman_metric_expression": "3.078+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.078, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.078+", "metric_symbol": "s", "metric_value": 3.078, "reference_text": "s = 3.078+ | Found by Emerson Connelly | in April 2026.", "source_image": "33.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/33.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.078+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "13357e078d1002ad", "improvement": -0.006933225403836563, "max_boundary_excess": -1.6488057343371516e-06, "max_pair_overlap_depth": -2.3777449531969808e-05, "metric_expression": "3.08493", "metric_symbol": "s", "metric_value": 3.0849332254038364, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.078, "setup": "triinpen", "side": 3.0849332254038364, "solution_path": "data/solutions/generated/triinpen_033_13357e078d1002ad.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/13357e078d1002ad.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@34", "density": 0.8697735245280512, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/34.gif", "friedman_metric_expression": "3.114+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.114, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.114+", "metric_symbol": "s", "metric_value": 3.114, "reference_text": "s = 3.114+ | Found by Emerson Connelly | in April 2026.", "source_image": "34.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/34.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.114+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "9cac5218ebb67cb5", "improvement": -0.022622102843430802, "max_boundary_excess": -7.423271733968168e-08, "max_pair_overlap_depth": -2.357396563512637e-06, "metric_expression": "3.13662", "metric_symbol": "s", "metric_value": 3.1366221028434307, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.114, "setup": "triinpen", "side": 3.1366221028434307, "solution_path": "data/solutions/generated/triinpen_034_9cac5218ebb67cb5.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9cac5218ebb67cb5.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@35", "density": 0.8649966542185312, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/35.gif", "friedman_metric_expression": "3.150+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.15, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@35", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.150+", "metric_symbol": "s", "metric_value": 3.15, "reference_text": "s = 3.150+ | Found by Emerson Connelly | in April 2026.", "source_image": "35.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/35.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.150+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "e568d5830b049327", "improvement": -0.0411898371667867, "max_boundary_excess": -1.753518123765835e-06, "max_pair_overlap_depth": -1.5568053413739236e-05, "metric_expression": "3.19119", "metric_symbol": "s", "metric_value": 3.1911898371667866, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.15, "setup": "triinpen", "side": 3.1911898371667866, "solution_path": "data/solutions/generated/triinpen_035_e568d5830b049327.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e568d5830b049327.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@36", "density": 0.8954701086953395, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/36.gif", "friedman_metric_expression": "3.177+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.177, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@36", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.177+", "metric_symbol": "s", "metric_value": 3.177, "reference_text": "s = 3.177+ | Found by Emerson Connelly | in April 2026.", "source_image": "36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/36.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.177+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "94f98697d38e8534", "improvement": -0.003911128614793036, "max_boundary_excess": -2.377739372786898e-06, "max_pair_overlap_depth": -3.2778702236946344e-06, "metric_expression": "3.18091", "metric_symbol": "s", "metric_value": 3.180911128614793, "n": 36, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.177, "setup": "triinpen", "side": 3.180911128614793, "solution_path": "data/solutions/generated/triinpen_036_94f98697d38e8534.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/94f98697d38e8534.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinpen@37", "density": 0.9007684327912503, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/37.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.217+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.217, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@37", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.217+", "metric_symbol": "s", "metric_value": 3.217, "reference_text": "s = 3.217+ | Found by Emerson Connelly | in April 2026.", "source_image": "37.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/37.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.217+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "id": "f44599d4a9e5e733", "improvement": 0.0017102585047612529, "max_boundary_excess": -3.6104708733830643e-07, "max_pair_overlap_depth": -4.178008898181318e-06, "n": 37, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 3.217, "setup": "triinpen", "side": 3.215289741495239, "solution_path": "data/solutions/triinpen_37.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/f44599d4a9e5e733.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinpen@38", "density": 0.9005911187149712, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/38.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.261+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.261, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.261+", "metric_symbol": "s", "metric_value": 3.261, "reference_text": "s = 3.261+ | Found by Emerson Connelly | in April 2026.", "source_image": "38.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/38.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.261+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "id": "05bcab1d7902fa55", "improvement": 0.0022293194217613, "max_boundary_excess": -4.649651923094469e-07, "max_pair_overlap_depth": -2.076724902710936e-06, "n": 38, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 3.261, "setup": "triinpen", "side": 3.258770680578239, "solution_path": "data/solutions/triinpen_38.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/05bcab1d7902fa55.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinpen@39", "density": 0.9025101556269666, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/39.gif", "friedman_metric_expression": "3.295+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.295, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.295+", "metric_symbol": "s", "metric_value": 3.295, "reference_text": "s = 3.295+ | Found by Emerson Connelly | in April 2026.", "source_image": "39.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/39.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.295+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "frontend_seed": true, "id": "67a6bbf24108966a", "improvement": -0.002859023967915597, "max_boundary_excess": -1.9740347935670834e-06, "max_pair_overlap_depth": -1.0007850107629501e-05, "metric_expression": "3.29786", "metric_symbol": "s", "metric_value": 3.2978590239679155, "n": 39, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.295, "setup": "triinpen", "side": 3.2978590239679155, "solution_path": "data/solutions/generated/triinpen_039_67a6bbf24108966a.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/67a6bbf24108966a.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinpen@40", "density": 0.9090379593265822, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinpen/40.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.337+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.337, "friedman_reference": {"analytical_or_proved": false, "case": "triinpen@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.337+", "metric_symbol": "s", "metric_value": 3.337, "reference_text": "s = 3.337+ | Found by Emerson Connelly | in April 2026.", "source_image": "40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinpen/40.gif", "source_page": "https://erich-friedman.github.io/packing/triinpen/", "title": "Triangles in Pentagons"}, "friedman_reference_text": "s = 3.337+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinpen/", "friedman_title": "Triangles in Pentagons", "id": "d177c371d1e3f387", "improvement": 0.009141758371615794, "max_boundary_excess": -2.9487074289032124e-07, "max_pair_overlap_depth": -6.944746260284518e-07, "n": 40, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 3.337, "setup": "triinpen", "side": 3.3278582416283844, "solution_path": "data/solutions/triinpen_40.json", "source_url": "https://erich-friedman.github.io/packing/triinpen/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/d177c371d1e3f387.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinsqu@1", "density": 0.4640965865243202, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t1.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "(\u221a2+\u221a6)/4 = .965+", "friedman_metric_symbol": "s", "friedman_metric_value": 0.965, "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@1", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "(\u221a2+\u221a6)/4 = .965+", "metric_symbol": "s", "metric_value": 0.965, "reference_text": "s = (\u221a2+\u221a6)/4 = .965+ | Trivial.", "source_image": "t1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t1.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = (\u221a2+\u221a6)/4 = .965+ | Trivial.", "friedman_source_image": "t1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "d0da9c9aae58c37e", "improvement": -0.0009310593101359288, "max_boundary_excess": -7.031269735994051e-07, "max_pair_overlap_depth": 0.0, "metric_expression": "0.96593", "metric_symbol": "s", "metric_value": 0.9659310593101359, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 0.965, "setup": "triinsqu", "side": 0.9659310593101359, "solution_path": "data/solutions/generated/triinsqu_001_d0da9c9aae58c37e.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d0da9c9aae58c37e.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinsqu@2", "density": 0.5773345801938596, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t2.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "\u221a6/2 = 1.224+", "friedman_metric_symbol": "s", "friedman_metric_value": 1.224, "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@2", "credit": "Trivial", "date": "", "family_updated": "4/29/26", "metric_expression": "\u221a6/2 = 1.224+", "metric_symbol": "s", "metric_value": 1.224, "reference_text": "s = \u221a6/2 = 1.224+ | Trivial.", "source_image": "t2.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t2.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = \u221a6/2 = 1.224+ | Trivial.", "friedman_source_image": "t2.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "536a8bec14614050", "improvement": -0.0007615124236886039, "max_boundary_excess": -3.5296142902332335e-06, "max_pair_overlap_depth": -8.602274652714007e-06, "metric_expression": "1.22476", "metric_symbol": "s", "metric_value": 1.2247615124236886, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.224, "setup": "triinsqu", "side": 1.2247615124236886, "solution_path": "data/solutions/generated/triinsqu_002_536a8bec14614050.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/536a8bec14614050.svg", "tolerance": 1e-08, "verified": true}
@@ -566,7 +784,26 @@
 {"case": "triinsqu@18", "density": 0.8124930238229202, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "July 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t18.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.051+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.051, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@18", "credit": "Maurizio Morandi", "date": "July 2008", "family_updated": "4/29/26", "metric_expression": "3.051+", "metric_symbol": "s", "metric_value": 3.051, "reference_text": "s = 3.051+ | Found by Maurizio Morandi | in July 2008.", "source_image": "t18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t18.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3.051+ | Found by Maurizio Morandi | in July 2008.", "friedman_source_image": "t18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "e37e7e8bffa4ff54", "improvement": -0.04625348434953214, "max_boundary_excess": -2.7140695543143397e-06, "max_pair_overlap_depth": -2.8845175708891446e-05, "metric_expression": "3.09725", "metric_symbol": "s", "metric_value": 3.0972534843495323, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.051, "setup": "triinsqu", "side": 3.0972534843495323, "solution_path": "data/solutions/generated/triinsqu_018_e37e7e8bffa4ff54.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e37e7e8bffa4ff54.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinsqu@19", "density": 0.8324573792569255, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t19.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.12930+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.1293, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@19", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.12930+", "metric_symbol": "s", "metric_value": 3.1293, "reference_text": "s = 3.12930+ | Found by Ian Watson | in April 2026.", "source_image": "t19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t19.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3.12930+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "b548b946ae0b4ba7", "improvement": -0.01443633599486338, "max_boundary_excess": -4.91075951885532e-06, "max_pair_overlap_depth": -2.901764488139058e-06, "metric_expression": "3.14374", "metric_symbol": "s", "metric_value": 3.1437363359948636, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.1293, "setup": "triinsqu", "side": 3.1437363359948636, "solution_path": "data/solutions/generated/triinsqu_019_b548b946ae0b4ba7.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b548b946ae0b4ba7.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinsqu@20", "density": 0.8188093166106081, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t20.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "3.2305+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.2305, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@20", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.2305+", "metric_symbol": "s", "metric_value": 3.2305, "reference_text": "s = 3.2305+ | Found by Ian Watson | in April 2026.", "source_image": "t20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t20.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3.2305+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "3081d28a13591fef", "improvement": -0.02167515790076191, "max_boundary_excess": -4.133822536981461e-06, "max_pair_overlap_depth": -2.11952039982366e-05, "metric_expression": "3.25218", "metric_symbol": "s", "metric_value": 3.252175157900762, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.2305, "setup": "triinsqu", "side": 3.252175157900762, "solution_path": "data/solutions/generated/triinsqu_020_3081d28a13591fef.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3081d28a13591fef.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@21", "density": 0.8197746048663628, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t21.gif", "friedman_metric_expression": "3.3111+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.3111, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@21", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.3111+", "metric_symbol": "s", "metric_value": 3.3111, "reference_text": "s = 3.3111+ | Found by Ian Watson | in April 2026.", "source_image": "t21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t21.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "s = 3.3111+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "3debb201d272befe", "improvement": -0.01942528494838358, "max_boundary_excess": -3.1059976134608187e-06, "max_pair_overlap_depth": -1.7605367639283998e-06, "metric_expression": "3.33053", "metric_symbol": "s", "metric_value": 3.3305252849483837, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.3111, "setup": "triinsqu", "side": 3.3305252849483837, "solution_path": "data/solutions/generated/triinsqu_021_3debb201d272befe.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/3debb201d272befe.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@22", "density": 0.8320198700821632, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t22.gif", "friedman_metric_expression": "3.3757+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.3757, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@22", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.3757+", "metric_symbol": "s", "metric_value": 3.3757, "reference_text": "22. | | s = 3.3757+ | Found by Ian Watson | in April 2026.", "source_image": "t22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t22.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "22. | | s = 3.3757+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "470a866027c799dc", "improvement": -0.008023046534652689, "max_boundary_excess": -1.549110939521453e-06, "max_pair_overlap_depth": -9.024431791848642e-07, "metric_expression": "3.38372", "metric_symbol": "s", "metric_value": 3.383723046534653, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.3757, "setup": "triinsqu", "side": 3.383723046534653, "solution_path": "data/solutions/generated/triinsqu_022_470a866027c799dc.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/470a866027c799dc.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@23", "density": 0.825135735506605, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t23.gif", "friedman_metric_expression": "3.4311+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.4311, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@23", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.4311+", "metric_symbol": "s", "metric_value": 3.4311, "reference_text": "23. | | s = 3.4311+ | Found by Ian Watson | in April 2026.", "source_image": "t23.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t23.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "23. | | s = 3.4311+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t23.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "23d97af9efc6a19d", "improvement": -0.04307377695172354, "max_boundary_excess": -3.0575531387249386e-07, "max_pair_overlap_depth": -1.3951600157491306e-05, "metric_expression": "3.47417", "metric_symbol": "s", "metric_value": 3.4741737769517234, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.4311, "setup": "triinsqu", "side": 3.4741737769517234, "solution_path": "data/solutions/generated/triinsqu_023_23d97af9efc6a19d.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/23d97af9efc6a19d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@24", "density": 0.857512475445178, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "August 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t24.gif", "friedman_metric_expression": "3.468+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.468, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@24", "credit": "Maurizio Morandi", "date": "August 2008", "family_updated": "4/29/26", "metric_expression": "3.468+", "metric_symbol": "s", "metric_value": 3.468, "reference_text": "24. | | s = 3.468+ | Found by Maurizio Morandi | in August 2008.", "source_image": "t24.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t24.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "24. | | s = 3.468+ | Found by Maurizio Morandi | in August 2008.", "friedman_source_image": "t24.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "aa931802df351f6b", "improvement": -0.013254030591762334, "max_boundary_excess": -2.7516785866311762e-06, "max_pair_overlap_depth": -1.795583897323816e-05, "metric_expression": "3.48125", "metric_symbol": "s", "metric_value": 3.4812540305917623, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.468, "setup": "triinsqu", "side": 3.4812540305917623, "solution_path": "data/solutions/generated/triinsqu_024_aa931802df351f6b.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/aa931802df351f6b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@25", "density": 0.8572641065590827, "friedman_analytical_or_proved": false, "friedman_credit": "David W", "friedman_date": "August 2012", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t25.gif", "friedman_metric_expression": "3.537+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.537, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@25", "credit": "David W", "date": "August 2012", "family_updated": "4/29/26", "metric_expression": "3.537+", "metric_symbol": "s", "metric_value": 3.537, "reference_text": "25. | | s = 3.537+ | Found by David W. Cantrell | in August 2012.", "source_image": "t25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t25.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "25. | | s = 3.537+ | Found by David W. Cantrell | in August 2012.", "friedman_source_image": "t25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "16117b2f4cd0a5a0", "improvement": -0.016554677577784283, "max_boundary_excess": -2.280886997301251e-06, "max_pair_overlap_depth": -1.0363527685852691e-05, "metric_expression": "3.55355", "metric_symbol": "s", "metric_value": 3.553554677577784, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.537, "setup": "triinsqu", "side": 3.553554677577784, "solution_path": "data/solutions/generated/triinsqu_025_16117b2f4cd0a5a0.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/16117b2f4cd0a5a0.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@26", "density": 0.8564901139309976, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "September 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t26.gif", "friedman_metric_expression": "3.575+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.575, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@26", "credit": "Maurizio Morandi", "date": "September 2008", "family_updated": "4/29/26", "metric_expression": "3.575+", "metric_symbol": "s", "metric_value": 3.575, "reference_text": "26. | | s = 3.575+ | Found by Maurizio Morandi | in September 2008.", "source_image": "t26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t26.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "26. | | s = 3.575+ | Found by Maurizio Morandi | in September 2008.", "friedman_source_image": "t26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "ebfed25c219baa0e", "improvement": -0.050565994245078016, "max_boundary_excess": -2.7124557589233795e-06, "max_pair_overlap_depth": -1.7247237756201628e-05, "metric_expression": "3.62557", "metric_symbol": "s", "metric_value": 3.625565994245078, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.575, "setup": "triinsqu", "side": 3.625565994245078, "solution_path": "data/solutions/generated/triinsqu_026_ebfed25c219baa0e.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ebfed25c219baa0e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@27", "density": 0.8498602034176942, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t27.gif", "friedman_metric_expression": "3.6726+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.6726, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@27", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.6726+", "metric_symbol": "s", "metric_value": 3.6726, "reference_text": "27. | | s = 3.6726+ | Found by Ian Watson | in April 2026.", "source_image": "t27.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t27.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "27. | | s = 3.6726+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t27.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "dbdb303c3aa850bb", "improvement": -0.03641383792443431, "max_boundary_excess": -5.085430993154038e-06, "max_pair_overlap_depth": -1.0288234183475353e-06, "metric_expression": "3.70901", "metric_symbol": "s", "metric_value": 3.7090138379244344, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.6726, "setup": "triinsqu", "side": 3.7090138379244344, "solution_path": "data/solutions/generated/triinsqu_027_dbdb303c3aa850bb.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/dbdb303c3aa850bb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@28", "density": 0.8409752820125738, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t28.gif", "friedman_metric_expression": "3.7571+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.7571, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@28", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.7571+", "metric_symbol": "s", "metric_value": 3.7571, "reference_text": "28. | | s = 3.7571+ | Found by Ian Watson | in April 2026.", "source_image": "t28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t28.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "28. | | s = 3.7571+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "d660009be45656fb", "improvement": -0.03987482885375426, "max_boundary_excess": -4.926402812612589e-06, "max_pair_overlap_depth": -7.738785352429112e-06, "metric_expression": "3.79697", "metric_symbol": "s", "metric_value": 3.796974828853754, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.7571, "setup": "triinsqu", "side": 3.796974828853754, "solution_path": "data/solutions/generated/triinsqu_028_d660009be45656fb.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/d660009be45656fb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@29", "density": 0.8511488797755807, "friedman_analytical_or_proved": false, "friedman_credit": "Ignacio Vallejo", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t29.gif", "friedman_metric_expression": "3.818+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.818, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@29", "credit": "Ignacio Vallejo", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.818+", "metric_symbol": "s", "metric_value": 3.818, "reference_text": "29. | | s = 3.818+ | Found by Ignacio Vallejo | in April 2026.", "source_image": "t29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t29.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "29. | | s = 3.818+ | Found by Ignacio Vallejo | in April 2026.", "friedman_source_image": "t29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "580739cf26075b25", "improvement": -0.023019845203774647, "max_boundary_excess": -5.02170884848626e-08, "max_pair_overlap_depth": -7.455986605509057e-06, "metric_expression": "3.84102", "metric_symbol": "s", "metric_value": 3.8410198452037747, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.818, "setup": "triinsqu", "side": 3.8410198452037747, "solution_path": "data/solutions/generated/triinsqu_029_580739cf26075b25.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/580739cf26075b25.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@30", "density": 0.8453943070349464, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t30.gif", "friedman_metric_expression": "3.8662+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.8662, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@30", "credit": "Ian Watson", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.8662+", "metric_symbol": "s", "metric_value": 3.8662, "reference_text": "30. | | s = 3.8662+ | Found by Ian Watson | in April 2026.", "source_image": "t30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t30.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "30. | | s = 3.8662+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "t30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "c1d8c0f9af9cd320", "improvement": -0.05375684533529945, "max_boundary_excess": -9.869941090398363e-07, "max_pair_overlap_depth": -3.480593055327219e-06, "metric_expression": "3.91996", "metric_symbol": "s", "metric_value": 3.9199568453352995, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.8662, "setup": "triinsqu", "side": 3.9199568453352995, "solution_path": "data/solutions/generated/triinsqu_030_c1d8c0f9af9cd320.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c1d8c0f9af9cd320.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@31", "density": 0.8400189843781062, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t31.gif", "friedman_metric_expression": "3.936+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.936, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.936+", "metric_symbol": "s", "metric_value": 3.936, "reference_text": "31. | | s = 3.936+ | Found by Emerson Connelly | in April 2026.", "source_image": "t31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t31.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "31. | | s = 3.936+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "272c8c45b9a6dd78", "improvement": -0.06148289712739752, "max_boundary_excess": -1.9869012023909734e-06, "max_pair_overlap_depth": -1.1060967226250717e-05, "metric_expression": "3.99748", "metric_symbol": "s", "metric_value": 3.9974828971273975, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.936, "setup": "triinsqu", "side": 3.9974828971273975, "solution_path": "data/solutions/generated/triinsqu_031_272c8c45b9a6dd78.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/272c8c45b9a6dd78.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@32", "density": 0.833007660060693, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t32.gif", "friedman_metric_expression": "3.997+", "friedman_metric_symbol": "s", "friedman_metric_value": 3.997, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@32", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "3.997+", "metric_symbol": "s", "metric_value": 3.997, "reference_text": "32. | | s = 3.997+ | Found by Emerson Connelly | in April 2026.", "source_image": "t32.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t32.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "32. | | s = 3.997+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "aa2ff1aceeba9dbd", "improvement": -0.0815032212073783, "max_boundary_excess": -5.66081673195531e-06, "max_pair_overlap_depth": -4.793291196181215e-06, "metric_expression": "4.07850", "metric_symbol": "s", "metric_value": 4.078503221207378, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 3.997, "setup": "triinsqu", "side": 4.078503221207378, "solution_path": "data/solutions/generated/triinsqu_032_aa2ff1aceeba9dbd.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/aa2ff1aceeba9dbd.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@33", "density": 0.8366415016689572, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t33.gif", "friedman_metric_expression": "4.058+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.058, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@33", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.058+", "metric_symbol": "s", "metric_value": 4.058, "reference_text": "33. | | s = 4.058+ | Found by Emerson Connelly | in April 2026.", "source_image": "t33.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t33.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "33. | | s = 4.058+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t33.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "652d6c2cf21c385c", "improvement": -0.07473526355298876, "max_boundary_excess": -6.365030008288742e-08, "max_pair_overlap_depth": -1.4601549878645592e-06, "metric_expression": "4.13274", "metric_symbol": "s", "metric_value": 4.132735263552989, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.058, "setup": "triinsqu", "side": 4.132735263552989, "solution_path": "data/solutions/generated/triinsqu_033_652d6c2cf21c385c.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/652d6c2cf21c385c.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@34", "density": 0.8455895674978956, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t34.gif", "friedman_metric_expression": "4.098+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.098, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@34", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.098+", "metric_symbol": "s", "metric_value": 4.098, "reference_text": "34. | | s = 4.098+ | Found by Emerson Connelly | in April 2026.", "source_image": "t34.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t34.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "34. | | s = 4.098+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t34.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "5f00ff525459125e", "improvement": -0.07463088632816373, "max_boundary_excess": -2.422656501976907e-07, "max_pair_overlap_depth": -3.1602008447872976e-06, "metric_expression": "4.17263", "metric_symbol": "s", "metric_value": 4.172630886328164, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.098, "setup": "triinsqu", "side": 4.172630886328164, "solution_path": "data/solutions/generated/triinsqu_034_5f00ff525459125e.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5f00ff525459125e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@35", "density": 0.8584202751980219, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t35.gif", "friedman_metric_expression": "9(2\u221a3\u20133) = 4.176+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.176, "friedman_reference": {"analytical_or_proved": true, "case": "triinsqu@35", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "9(2\u221a3\u20133) = 4.176+", "metric_symbol": "s", "metric_value": 4.176, "reference_text": "35. | | s = 9(2\u221a3\u20133) = 4.176+ | Found by Erich Friedman | in April 2026.", "source_image": "t35.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t35.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "35. | | s = 9(2\u221a3\u20133) = 4.176+ | Found by Erich Friedman | in April 2026.", "friedman_source_image": "t35.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "0fd80a947c5904bb", "improvement": -0.025790132248165953, "max_boundary_excess": -2.0186743648470723e-06, "max_pair_overlap_depth": -1.0972661374369919e-05, "metric_expression": "4.20179", "metric_symbol": "s", "metric_value": 4.201790132248166, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.176, "setup": "triinsqu", "side": 4.201790132248166, "solution_path": "data/solutions/generated/triinsqu_035_0fd80a947c5904bb.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/0fd80a947c5904bb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@36", "density": 0.8656950017914491, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t36.gif", "friedman_metric_expression": "4.214+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.214, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@36", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.214+", "metric_symbol": "s", "metric_value": 4.214, "reference_text": "36. | | s = 4.214+ | Found by Emerson Connelly | in April 2026.", "source_image": "t36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t36.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "36. | | s = 4.214+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "73acd05c27fe131e", "improvement": -0.029450235060704877, "max_boundary_excess": -1.6988749159352698e-06, "max_pair_overlap_depth": -1.0359883173549633e-08, "metric_expression": "4.24345", "metric_symbol": "s", "metric_value": 4.243450235060705, "n": 36, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.214, "setup": "triinsqu", "side": 4.243450235060705, "solution_path": "data/solutions/generated/triinsqu_036_73acd05c27fe131e.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/73acd05c27fe131e.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triinsqu@37", "density": 0.8777550041407036, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t37.gif", "friedman_family_updated": "4/29/26", "friedman_metric_expression": "4.276+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.276, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@37", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.276+", "metric_symbol": "s", "metric_value": 4.276, "reference_text": "37. | | s = 4.276+ | Found by Emerson Connelly | in April 2026.", "source_image": "t37.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t37.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "37. | | s = 4.276+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "id": "8735d9f36ada5e93", "improvement": 0.0036726339396722096, "max_boundary_excess": -2.0547460484616992e-07, "max_pair_overlap_depth": -1.528656046745347e-06, "n": 37, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 4.276, "setup": "triinsqu", "side": 4.272327366060328, "solution_path": "data/solutions/triinsqu_37.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/8735d9f36ada5e93.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@38", "density": 0.8696240777565032, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t38.gif", "friedman_metric_expression": "4.327+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.327, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.327+", "metric_symbol": "s", "metric_value": 4.327, "reference_text": "38. | | s = 4.327+ | Found by Emerson Connelly | in April 2026.", "source_image": "t38.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t38.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "38. | | s = 4.327+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "a013f42c7873094a", "improvement": -0.0228706067926554, "max_boundary_excess": -2.365499665465618e-06, "max_pair_overlap_depth": -2.5247442803078e-06, "metric_expression": "4.34987", "metric_symbol": "s", "metric_value": 4.349870606792655, "n": 38, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.327, "setup": "triinsqu", "side": 4.349870606792655, "solution_path": "data/solutions/generated/triinsqu_038_a013f42c7873094a.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a013f42c7873094a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@39", "density": 0.8718778943291693, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t39.gif", "friedman_metric_expression": "4.383+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.383, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@39", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.383+", "metric_symbol": "s", "metric_value": 4.383, "reference_text": "39. | | s = 4.383+ | Found by Emerson Connelly | in April 2026.", "source_image": "t39.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t39.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "39. | | s = 4.383+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t39.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "5f6780607ec0989b", "improvement": -0.01803465361730261, "max_boundary_excess": -1.974803491340428e-06, "max_pair_overlap_depth": -1.9608803808246478e-05, "metric_expression": "4.40103", "metric_symbol": "s", "metric_value": 4.401034653617303, "n": 39, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.383, "setup": "triinsqu", "side": 4.401034653617303, "solution_path": "data/solutions/generated/triinsqu_039_5f6780607ec0989b.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5f6780607ec0989b.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triinsqu@40", "density": 0.878868813713771, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triinsqu/t40.gif", "friedman_metric_expression": "4.437+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.437, "friedman_reference": {"analytical_or_proved": false, "case": "triinsqu@40", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "4/29/26", "metric_expression": "4.437+", "metric_symbol": "s", "metric_value": 4.437, "reference_text": "40. | | s = 4.437+ | Found by Emerson Connelly | in April 2026.", "source_image": "t40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t40.gif", "source_page": "https://erich-friedman.github.io/packing/triinsqu/", "title": "Triangles in Squares"}, "friedman_reference_text": "40. | | s = 4.437+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "t40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triinsqu/", "friedman_title": "Triangles in Squares", "frontend_seed": true, "id": "ccf2360cc8917adc", "improvement": -0.002338759632142029, "max_boundary_excess": -2.520888573265893e-06, "max_pair_overlap_depth": -1.6780429565876886e-05, "metric_expression": "4.43934", "metric_symbol": "s", "metric_value": 4.439338759632142, "n": 40, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.437, "setup": "triinsqu", "side": 4.439338759632142, "solution_path": "data/solutions/generated/triinsqu_040_ccf2360cc8917adc.json", "source_url": "https://erich-friedman.github.io/packing/triinsqu/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ccf2360cc8917adc.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triintri@1", "density": 0.9999824309457177, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt1.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "1", "friedman_metric_symbol": "s", "friedman_metric_value": 1.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@1", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "1", "metric_symbol": "s", "metric_value": 1.0, "reference_text": "s = 1 | Trivial.", "source_image": "tt1.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt1.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 1 | Trivial.", "friedman_source_image": "tt1.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "cc844f952409d64a", "improvement": -8.784642894887895e-06, "max_boundary_excess": -1.727739205730037e-06, "max_pair_overlap_depth": 0.0, "metric_expression": "1.00001", "metric_symbol": "s", "metric_value": 1.0000087846428949, "n": 1, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 1.0, "setup": "triintri", "side": 1.0000087846428949, "solution_path": "data/solutions/generated/triintri_001_cc844f952409d64a.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/cc844f952409d64a.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triintri@2", "density": 0.49997366021738365, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@2", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "tt4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "tt4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "666ea688ab3bec3c", "improvement": -5.2681646676600025e-05, "max_boundary_excess": -9.520753462741007e-07, "max_pair_overlap_depth": -2.9199608040486602e-05, "metric_expression": "2.00005", "metric_symbol": "s", "metric_value": 2.0000526816466766, "n": 2, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "triintri", "side": 2.0000526816466766, "solution_path": "data/solutions/generated/triintri_002_666ea688ab3bec3c.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/666ea688ab3bec3c.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triintri@3", "density": 0.7499622672788224, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "2", "friedman_metric_symbol": "s", "friedman_metric_value": 2.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@3", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "2", "metric_symbol": "s", "metric_value": 2.0, "reference_text": "s = 2 | Trivial.", "source_image": "tt4.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt4.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 2 | Trivial.", "friedman_source_image": "tt4.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "92df600f3a6e54a1", "improvement": -5.031219332751746e-05, "max_boundary_excess": -1.3199738659319715e-06, "max_pair_overlap_depth": -1.9954872927441247e-05, "metric_expression": "2.00005", "metric_symbol": "s", "metric_value": 2.0000503121933275, "n": 3, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 2.0, "setup": "triintri", "side": 2.0000503121933275, "solution_path": "data/solutions/generated/triintri_003_92df600f3a6e54a1.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/92df600f3a6e54a1.svg", "tolerance": 1e-08, "verified": true}
@@ -587,4 +824,23 @@
 {"case": "triintri@18", "density": 0.8888203671574908, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt18.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "9/2 = 4.500", "friedman_metric_symbol": "s", "friedman_metric_value": 4.5, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@18", "credit": "Erich Friedman", "date": "1997", "family_updated": "2/29/26", "metric_expression": "9/2 = 4.500", "metric_symbol": "s", "metric_value": 4.5, "reference_text": "s = 9/2 = 4.500 | Found by Erich Friedman | in 1997.", "source_image": "tt18.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt18.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 9/2 = 4.500 | Found by Erich Friedman | in 1997.", "friedman_source_image": "tt18.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "b4cfb14015aca75a", "improvement": -0.00017345566104154386, "max_boundary_excess": -2.575746594607548e-06, "max_pair_overlap_depth": -5.0550449839370515e-06, "metric_expression": "4.50017", "metric_symbol": "s", "metric_value": 4.5001734556610415, "n": 18, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.5, "setup": "triintri", "side": 4.5001734556610415, "solution_path": "data/solutions/generated/triintri_018_b4cfb14015aca75a.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/b4cfb14015aca75a.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triintri@19", "density": 0.872322152073677, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt19.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "14/3 = 4.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.666, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@19", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "2/29/26", "metric_expression": "14/3 = 4.666+", "metric_symbol": "s", "metric_value": 4.666, "reference_text": "s = 14/3 = 4.666+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt19.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt19.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 14/3 = 4.666+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt19.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "bf4e89c9b4dd8ae2", "improvement": -0.0010058992763006813, "max_boundary_excess": -5.331642222161759e-07, "max_pair_overlap_depth": -9.690072424628493e-06, "metric_expression": "4.66701", "metric_symbol": "s", "metric_value": 4.667005899276301, "n": 19, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.666, "setup": "triintri", "side": 4.667005899276301, "solution_path": "data/solutions/generated/triintri_019_bf4e89c9b4dd8ae2.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/bf4e89c9b4dd8ae2.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triintri@20", "density": 0.838067095701634, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt20.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "33/8 + 9\u221a21/56 = 4.861+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.861, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@20", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "2/29/26", "metric_expression": "33/8 + 9\u221a21/56 = 4.861+", "metric_symbol": "s", "metric_value": 4.861, "reference_text": "s = 33/8 + 9\u221a21/56 = 4.861+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt20.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt20.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 33/8 + 9\u221a21/56 = 4.861+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt20.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "53a8c84cf6eae28f", "improvement": -0.02412412405335207, "max_boundary_excess": -1.1914189120695684e-06, "max_pair_overlap_depth": -6.957564219201018e-07, "metric_expression": "4.88512", "metric_symbol": "s", "metric_value": 4.885124124053352, "n": 20, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.861, "setup": "triintri", "side": 4.885124124053352, "solution_path": "data/solutions/generated/triintri_020_53a8c84cf6eae28f.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:05:47+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/53a8c84cf6eae28f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@21", "density": 0.8399445306050737, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt21.gif", "friedman_metric_expression": "4.923+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.923, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@21", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "2/29/26", "metric_expression": "4.923+", "metric_symbol": "s", "metric_value": 4.923, "reference_text": "s = 4.923+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt21.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt21.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 4.923+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt21.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "51d32dd1bf4348fb", "improvement": -0.0771650956615133, "max_boundary_excess": -2.830489805416455e-06, "max_pair_overlap_depth": -5.709825519950584e-06, "metric_expression": "5.00017", "metric_symbol": "s", "metric_value": 5.000165095661513, "n": 21, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.923, "setup": "triintri", "side": 5.000165095661513, "solution_path": "data/solutions/generated/triintri_021_51d32dd1bf4348fb.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/51d32dd1bf4348fb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@22", "density": 0.8799245341930954, "friedman_analytical_or_proved": false, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt22.gif", "friedman_metric_expression": "4.996+", "friedman_metric_symbol": "s", "friedman_metric_value": 4.996, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@22", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "2/29/26", "metric_expression": "4.996+", "metric_symbol": "s", "metric_value": 4.996, "reference_text": "s = 4.996+ | Found by Maurizio Morandi | in May 2008.", "source_image": "tt22.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt22.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 4.996+ | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt22.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "2122d833c6fcab70", "improvement": -0.004214405286988132, "max_boundary_excess": -5.380108740330726e-08, "max_pair_overlap_depth": -8.335028905959163e-07, "metric_expression": "5.00021", "metric_symbol": "s", "metric_value": 5.000214405286989, "n": 22, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 4.996, "setup": "triintri", "side": 5.000214405286989, "solution_path": "data/solutions/generated/triintri_022_2122d833c6fcab70.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/2122d833c6fcab70.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@23", "density": 0.9199301650083309, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@23", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "tt25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "tt25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "c27df81200778ffb", "improvement": -0.00018977980346601697, "max_boundary_excess": -6.179779071167411e-07, "max_pair_overlap_depth": -4.1714675197424e-07, "metric_expression": "5.00019", "metric_symbol": "s", "metric_value": 5.000189779803466, "n": 23, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "triintri", "side": 5.000189779803466, "solution_path": "data/solutions/generated/triintri_023_c27df81200778ffb.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c27df81200778ffb.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@24", "density": 0.9599250294051547, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@24", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "tt25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "tt25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "c9e2b321b60a0e78", "improvement": -0.00019524735994114195, "max_boundary_excess": -2.7221451237306384e-06, "max_pair_overlap_depth": -1.3704928858437881e-07, "metric_expression": "5.00020", "metric_symbol": "s", "metric_value": 5.000195247359941, "n": 24, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "triintri", "side": 5.000195247359941, "solution_path": "data/solutions/generated/triintri_024_c9e2b321b60a0e78.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/c9e2b321b60a0e78.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@25", "density": 0.9999421250190796, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "friedman_metric_expression": "5", "friedman_metric_symbol": "s", "friedman_metric_value": 5.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@25", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "5", "metric_symbol": "s", "metric_value": 5.0, "reference_text": "s = 5 | Trivial.", "source_image": "tt25.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5 | Trivial.", "friedman_source_image": "tt25.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "5092959dfa8a0e27", "improvement": -0.0001446937329419029, "max_boundary_excess": -1.7535771332062027e-06, "max_pair_overlap_depth": -7.792197432854309e-07, "metric_expression": "5.00014", "metric_symbol": "s", "metric_value": 5.000144693732942, "n": 25, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.0, "setup": "triintri", "side": 5.000144693732942, "solution_path": "data/solutions/generated/triintri_025_5092959dfa8a0e27.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5092959dfa8a0e27.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@26", "density": 0.8757579251966457, "friedman_analytical_or_proved": false, "friedman_credit": "Joah Frenzley", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt26.gif", "friedman_metric_expression": "5.406+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.406, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@26", "credit": "Joah Frenzley", "date": "April 2026", "family_updated": "2/29/26", "metric_expression": "5.406+", "metric_symbol": "s", "metric_value": 5.406, "reference_text": "s = 5.406+ | Found by Joah Frenzley | in April 2026.", "source_image": "tt26.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt26.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5.406+ | Found by Joah Frenzley | in April 2026.", "friedman_source_image": "tt26.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "8db318b73d49217d", "improvement": -0.04272181972430644, "max_boundary_excess": -1.2897298944239458e-06, "max_pair_overlap_depth": -1.0218222609881256e-05, "metric_expression": "5.44872", "metric_symbol": "s", "metric_value": 5.448721819724306, "n": 26, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.406, "setup": "triintri", "side": 5.448721819724306, "solution_path": "data/solutions/generated/triintri_026_8db318b73d49217d.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8db318b73d49217d.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@27", "density": 0.8924996192164427, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "friedman_metric_expression": "11/2 = 5.500", "friedman_metric_symbol": "s", "friedman_metric_value": 5.5, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@27", "credit": "Erich Friedman", "date": "1997", "family_updated": "2/29/26", "metric_expression": "11/2 = 5.500", "metric_symbol": "s", "metric_value": 5.5, "reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "source_image": "tt28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "friedman_source_image": "tt28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "f1c2be61e829f1e2", "improvement": -0.00019215549305418023, "max_boundary_excess": -1.8365186496628e-06, "max_pair_overlap_depth": -1.8064988390742442e-06, "metric_expression": "5.50019", "metric_symbol": "s", "metric_value": 5.500192155493054, "n": 27, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.5, "setup": "triintri", "side": 5.500192155493054, "solution_path": "data/solutions/generated/triintri_027_f1c2be61e829f1e2.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/f1c2be61e829f1e2.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@28", "density": 0.9255631973649003, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "1997", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "friedman_metric_expression": "11/2 = 5.500", "friedman_metric_symbol": "s", "friedman_metric_value": 5.5, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@28", "credit": "Erich Friedman", "date": "1997", "family_updated": "2/29/26", "metric_expression": "11/2 = 5.500", "metric_symbol": "s", "metric_value": 5.5, "reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "source_image": "tt28.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.", "friedman_source_image": "tt28.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "9562d7d6e075a347", "improvement": -0.00016827626559567932, "max_boundary_excess": -2.296352348617567e-06, "max_pair_overlap_depth": -7.147352432124165e-08, "metric_expression": "5.50017", "metric_symbol": "s", "metric_value": 5.500168276265596, "n": 28, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.5, "setup": "triintri", "side": 5.500168276265596, "solution_path": "data/solutions/generated/triintri_028_9562d7d6e075a347.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/9562d7d6e075a347.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@29", "density": 0.823477123057378, "friedman_analytical_or_proved": true, "friedman_credit": "David W", "friedman_date": "July 2007", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt29.gif", "friedman_metric_expression": "17/3 = 5.666+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.666, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@29", "credit": "David W", "date": "July 2007", "family_updated": "2/29/26", "metric_expression": "17/3 = 5.666+", "metric_symbol": "s", "metric_value": 5.666, "reference_text": "s = 17/3 = 5.666+ | Found by David W. Cantrell | in July 2007.", "source_image": "tt29.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt29.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 17/3 = 5.666+ | Found by David W. Cantrell | in July 2007.", "friedman_source_image": "tt29.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "1e26d810ba567eb4", "improvement": -0.2683509950166121, "max_boundary_excess": -5.6694191623693234e-06, "max_pair_overlap_depth": -2.9353541475263256e-07, "metric_expression": "5.93435", "metric_symbol": "s", "metric_value": 5.9343509950166125, "n": 29, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.666, "setup": "triintri", "side": 5.9343509950166125, "solution_path": "data/solutions/generated/triintri_029_1e26d810ba567eb4.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1e26d810ba567eb4.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@30", "density": 0.8727149559817791, "friedman_analytical_or_proved": true, "friedman_credit": "Maurizio Morandi", "friedman_date": "May 2008", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt30.gif", "friedman_metric_expression": "23/4 = 5.75", "friedman_metric_symbol": "s", "friedman_metric_value": 5.75, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@30", "credit": "Maurizio Morandi", "date": "May 2008", "family_updated": "2/29/26", "metric_expression": "23/4 = 5.75", "metric_symbol": "s", "metric_value": 5.75, "reference_text": "s = 23/4 = 5.75 | Found by Maurizio Morandi | in May 2008.", "source_image": "tt30.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt30.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 23/4 = 5.75 | Found by Maurizio Morandi | in May 2008.", "friedman_source_image": "tt30.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "1ace87e09c5f6fc8", "improvement": -0.11306107243262797, "max_boundary_excess": -1.1340847276256848e-05, "max_pair_overlap_depth": -5.548494655616132e-06, "metric_expression": "5.86306", "metric_symbol": "s", "metric_value": 5.863061072432628, "n": 30, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.75, "setup": "triintri", "side": 5.863061072432628, "solution_path": "data/solutions/generated/triintri_030_1ace87e09c5f6fc8.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/1ace87e09c5f6fc8.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@31", "density": 0.8655205028371107, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt31.gif", "friedman_metric_expression": "5.912+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.912, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@31", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "2/29/26", "metric_expression": "5.912+", "metric_symbol": "s", "metric_value": 5.912, "reference_text": "s = 5.912+ | Found by Emerson Connelly | in April 2026.", "source_image": "tt31.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt31.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5.912+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "tt31.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "e94aa7c2fc600373", "improvement": -0.07269699341354574, "max_boundary_excess": -1.1753168632427688e-06, "max_pair_overlap_depth": -1.577861272879927e-05, "metric_expression": "5.98470", "metric_symbol": "s", "metric_value": 5.984696993413546, "n": 31, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.912, "setup": "triintri", "side": 5.984696993413546, "solution_path": "data/solutions/generated/triintri_031_e94aa7c2fc600373.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e94aa7c2fc600373.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@32", "density": 0.8888356604955802, "friedman_analytical_or_proved": false, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt32.gif", "friedman_metric_expression": "5.951+", "friedman_metric_symbol": "s", "friedman_metric_value": 5.951, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@32", "credit": "Ian Watson", "date": "April 2026", "family_updated": "2/29/26", "metric_expression": "5.951+", "metric_symbol": "s", "metric_value": 5.951, "reference_text": "s = 5.951+ | Found by Ian Watson | in April 2026.", "source_image": "tt32.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt32.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 5.951+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "tt32.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "ea3eb3c434a6db88", "improvement": -0.049179653895976116, "max_boundary_excess": -2.19130606600491e-06, "max_pair_overlap_depth": -2.006545093746759e-06, "metric_expression": "6.00018", "metric_symbol": "s", "metric_value": 6.000179653895976, "n": 32, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 5.951, "setup": "triintri", "side": 6.000179653895976, "solution_path": "data/solutions/generated/triintri_032_ea3eb3c434a6db88.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ea3eb3c434a6db88.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@33", "density": 0.9165918569883487, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@33", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial. |", "source_image": "tt36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6 | Trivial. |", "friedman_source_image": "tt36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "5e7c3bf3ddd6ef7e", "improvement": -0.0002448466611522093, "max_boundary_excess": -4.630617313298577e-07, "max_pair_overlap_depth": -7.583551231427066e-09, "metric_expression": "6.00024", "metric_symbol": "s", "metric_value": 6.000244846661152, "n": 33, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.0, "setup": "triintri", "side": 6.000244846661152, "solution_path": "data/solutions/generated/triintri_033_5e7c3bf3ddd6ef7e.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5e7c3bf3ddd6ef7e.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@34", "density": 0.944346274522294, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@34", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial. |", "source_image": "tt36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6 | Trivial. |", "friedman_source_image": "tt36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "ec0928eb613cde82", "improvement": -0.0003118581825578559, "max_boundary_excess": -1.3696973961467693e-06, "max_pair_overlap_depth": -5.928110144992615e-07, "metric_expression": "6.00031", "metric_symbol": "s", "metric_value": 6.000311858182558, "n": 34, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.0, "setup": "triintri", "side": 6.000311858182558, "solution_path": "data/solutions/generated/triintri_034_ec0928eb613cde82.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/ec0928eb613cde82.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@35", "density": 0.9721621988323501, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@35", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial. |", "source_image": "tt36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6 | Trivial. |", "friedman_source_image": "tt36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "e1b770e700ac967a", "improvement": -0.00018522360819872574, "max_boundary_excess": -2.5752242400016007e-06, "max_pair_overlap_depth": -5.014035051667667e-07, "metric_expression": "6.00019", "metric_symbol": "s", "metric_value": 6.000185223608199, "n": 35, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.0, "setup": "triintri", "side": 6.000185223608199, "solution_path": "data/solutions/generated/triintri_035_e1b770e700ac967a.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/e1b770e700ac967a.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@36", "density": 0.9999547600515969, "friedman_analytical_or_proved": true, "friedman_credit": "Trivial", "friedman_date": "", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "friedman_metric_expression": "6", "friedman_metric_symbol": "s", "friedman_metric_value": 6.0, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@36", "credit": "Trivial", "date": "", "family_updated": "2/29/26", "metric_expression": "6", "metric_symbol": "s", "metric_value": 6.0, "reference_text": "s = 6 | Trivial. |", "source_image": "tt36.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6 | Trivial. |", "friedman_source_image": "tt36.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "8e7fac2536d01e26", "improvement": -0.00013572445035237024, "max_boundary_excess": -1.1037978552332137e-06, "max_pair_overlap_depth": -5.02408139535504e-08, "metric_expression": "6.00014", "metric_symbol": "s", "metric_value": 6.000135724450352, "n": 36, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.0, "setup": "triintri", "side": 6.000135724450352, "solution_path": "data/solutions/generated/triintri_036_8e7fac2536d01e26.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/8e7fac2536d01e26.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@37", "density": 0.9223731676430976, "friedman_analytical_or_proved": true, "friedman_credit": "Ian Watson", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt37.gif", "friedman_metric_expression": "19/3 = 6.333+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.333, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@37", "credit": "Ian Watson", "date": "April 2026", "family_updated": "2/29/26", "metric_expression": "19/3 = 6.333+", "metric_symbol": "s", "metric_value": 6.333, "reference_text": "s = 19/3 = 6.333+ | Found by Ian Watson | in April 2026.", "source_image": "tt37.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt37.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 19/3 = 6.333+ | Found by Ian Watson | in April 2026.", "friedman_source_image": "tt37.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "a824891b660555f5", "improvement": -0.0005547879590457327, "max_boundary_excess": -2.1058084789851627e-06, "max_pair_overlap_depth": -1.0503324543442716e-06, "metric_expression": "6.33355", "metric_symbol": "s", "metric_value": 6.333554787959046, "n": 37, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.333, "setup": "triintri", "side": 6.333554787959046, "solution_path": "data/solutions/generated/triintri_037_a824891b660555f5.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/a824891b660555f5.svg", "tolerance": 1e-08, "verified": true}
 {"case": "triintri@38", "density": 0.917799816589891, "friedman_analytical_or_proved": false, "friedman_credit": "Emerson Connelly", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt38.gif", "friedman_family_updated": "2/29/26", "friedman_metric_expression": "6.436+", "friedman_metric_symbol": "s", "friedman_metric_value": 6.436, "friedman_reference": {"analytical_or_proved": false, "case": "triintri@38", "credit": "Emerson Connelly", "date": "April 2026", "family_updated": "2/29/26", "metric_expression": "6.436+", "metric_symbol": "s", "metric_value": 6.436, "reference_text": "s = 6.436+ | Found by Emerson Connelly | in April 2026.", "source_image": "tt38.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt38.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 6.436+ | Found by Emerson Connelly | in April 2026.", "friedman_source_image": "tt38.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "id": "44f351bb9dc615aa", "improvement": 0.0014554065684695416, "max_boundary_excess": -1.300761040461767e-07, "max_pair_overlap_depth": -1.4944448277348643e-06, "n": 38, "notes": "Seeded from the certified top-10 candidate bundle.", "reference_side": 6.436, "setup": "triintri", "side": 6.43454459343153, "solution_path": "data/solutions/triintri_38.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-04-30T23:19:18+00:00", "submitted_by": "Nathan Roll / polygon-packer-c", "svg_path": "data/svg/44f351bb9dc615aa.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@39", "density": 0.922995893638428, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "friedman_metric_expression": "13/2 = 6.500", "friedman_metric_symbol": "s", "friedman_metric_value": 6.5, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@39", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "2/29/26", "metric_expression": "13/2 = 6.500", "metric_symbol": "s", "metric_value": 6.5, "reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "source_image": "tt40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "friedman_source_image": "tt40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "5ff069bd30790b7f", "improvement": -0.0002853099319573005, "max_boundary_excess": -2.7141701112233934e-06, "max_pair_overlap_depth": -2.524988351737534e-07, "metric_expression": "6.50029", "metric_symbol": "s", "metric_value": 6.500285309931957, "n": 39, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.5, "setup": "triintri", "side": 6.500285309931957, "solution_path": "data/solutions/generated/triintri_039_5ff069bd30790b7f.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/5ff069bd30790b7f.svg", "tolerance": 1e-08, "verified": true}
+{"case": "triintri@40", "density": 0.9466291268019702, "friedman_analytical_or_proved": true, "friedman_credit": "Erich Friedman", "friedman_date": "April 2026", "friedman_external_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "friedman_metric_expression": "13/2 = 6.500", "friedman_metric_symbol": "s", "friedman_metric_value": 6.5, "friedman_reference": {"analytical_or_proved": true, "case": "triintri@40", "credit": "Erich Friedman", "date": "April 2026", "family_updated": "2/29/26", "metric_expression": "13/2 = 6.500", "metric_symbol": "s", "metric_value": 6.5, "reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "source_image": "tt40.gif", "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif", "source_page": "https://erich-friedman.github.io/packing/triintri/", "title": "Triangles in Triangles"}, "friedman_reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.", "friedman_source_image": "tt40.gif", "friedman_source_url": "https://erich-friedman.github.io/packing/triintri/", "friedman_title": "Triangles in Triangles", "frontend_seed": true, "id": "7890a1da940c9143", "improvement": -0.00039973752172350885, "max_boundary_excess": -3.4343626129297504e-07, "max_pair_overlap_depth": -3.1212060811469655e-06, "metric_expression": "6.50040", "metric_symbol": "s", "metric_value": 6.5003997375217235, "n": 40, "notes": "Generated seed layout for frontend figures with polygon-packer-c.", "record_type": "verified", "reference_side": 6.5, "setup": "triintri", "side": 6.5003997375217235, "solution_path": "data/solutions/generated/triintri_040_7890a1da940c9143.json", "source_url": "https://erich-friedman.github.io/packing/triintri/", "submitted_at": "2026-05-01T01:47:21+00:00", "submitted_by": "polygon-packer-c seed", "svg_path": "data/svg/7890a1da940c9143.svg", "tolerance": 1e-08, "verified": true}
diff --git a/data/solutions/generated/cirinhex_021_38040eceeb63c1e3.json b/data/solutions/generated/cirinhex_021_38040eceeb63c1e3.json
new file mode 100644
index 0000000000000000000000000000000000000000..a9b231563191d8bec03b7e5df57064088de27415
--- /dev/null
+++ b/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/"
+}
diff --git a/data/solutions/generated/cirinhex_022_cd7262f9f7d0d279.json b/data/solutions/generated/cirinhex_022_cd7262f9f7d0d279.json
new file mode 100644
index 0000000000000000000000000000000000000000..31f1ca7f92e864001630d43ae8a1219227c23662
--- /dev/null
+++ b/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/"
+}
diff --git a/data/solutions/generated/cirinhex_023_de2d2aabdc650ad2.json b/data/solutions/generated/cirinhex_023_de2d2aabdc650ad2.json
new file mode 100644
index 0000000000000000000000000000000000000000..d49a09be66b647a83e79362ff4ced0b48b0b72bf
--- /dev/null
+++ b/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
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+    {
+      "id": 5,
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+      "x": 3.142975626993475,
+      "y": -2.9692619457033222
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.0706102912732397,
+      "x": -4.428656184153742,
+      "y": -0.7423914146316885
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.194880962719564,
+      "x": -2.4286079474462356,
+      "y": -0.7423829528891153
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.05362310039570196,
+      "x": -1.4285495285772492,
+      "y": -2.4744464378242124
+    },
+    {
+      "id": 9,
+      "rotation_radians": -0.04828619363738929,
+      "x": 2.1429402259937884,
+      "y": -1.2371729423835607
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.017894170040258006,
+      "x": 4.142991184861336,
+      "y": -1.2371598083927178
+    },
+    {
+      "id": 11,
+      "rotation_radians": -0.23786786676194394,
+      "x": -4.143003601974824,
+      "y": 1.2371495608799508
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.3622812222566325,
+      "x": -2.1429503246384707,
+      "y": 1.2371540698147925
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.05883702898002627,
+      "x": 0.14288460691346438,
+      "y": -1.2372044076656052
+    },
+    {
+      "id": 14,
+      "rotation_radians": -0.07059320164637754,
+      "x": 2.4285942378869207,
+      "y": 0.7423708601300019
+    },
+    {
+      "id": 15,
+      "rotation_radians": 0.012581426087907478,
+      "x": 4.428655322968817,
+      "y": 0.7423831250699681
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.23982721363557236,
+      "x": -3.1429848488660874,
+      "y": 2.9692473720807393
+    },
+    {
+      "id": 17,
+      "rotation_radians": -0.09396706273511284,
+      "x": -0.571548281067351,
+      "y": 2.4744377931725365
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.12447529699376898,
+      "x": 0.4284816272783447,
+      "y": 0.7423485356873205
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.11075029989314435,
+      "x": 1.4285187692648917,
+      "y": 2.474433833598133
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.091778809990234,
+      "x": 3.4286305925283314,
+      "y": 2.474476667709342
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.11688101755512745,
+      "x": -1.5715780807919115,
+      "y": 4.206528001283203
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.1740629354558044,
+      "x": 0.4284791762750046,
+      "y": 4.206535118372205
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.24808376284602468,
+      "x": 2.4285379009372052,
+      "y": 4.206534222200379
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/cirinhex_024_61a86ae12328c1ca.json b/data/solutions/generated/cirinhex_024_61a86ae12328c1ca.json
new file mode 100644
index 0000000000000000000000000000000000000000..4d84fe9b8b10636295b564c7c17e2411f15b4518
--- /dev/null
+++ b/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,
+    "sides": 6,
+    "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": [
+    {
+      "id": 1,
+      "rotation_radians": 0.29868867667172333,
+      "x": -2.4827172327226656,
+      "y": -4.300210939855668
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.24268588290445803,
+      "x": -0.4636451903499858,
+      "y": -4.3001821162682115
+    },
+    {
+      "id": 3,
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+      "x": 0.7094364886649773,
+      "y": -2.6801915828945164
+    },
+    {
+      "id": 4,
+      "rotation_radians": -0.4774536142453228,
+      "x": 1.8823578673188928,
+      "y": -4.3002069815220825
+    },
+    {
+      "id": 5,
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+      "x": 3.298267043938587,
+      "y": -2.8876155094113427
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+    {
+      "id": 6,
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+      "x": -3.482550438870808,
+      "y": -2.568002390825985
+    },
+    {
+      "id": 7,
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+      "x": -1.4824938642123424,
+      "y": -2.5682604616141034
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.09093544894997521,
+      "x": -0.3012691827632311,
+      "y": -0.9543160721277714
+    },
+    {
+      "id": 9,
+      "rotation_radians": -0.23616463773800914,
+      "x": 2.0831481636600997,
+      "y": -1.2225498987586527
+    },
+    {
+      "id": 10,
+      "rotation_radians": -0.7558481172542992,
+      "x": 4.298292166442882,
+      "y": -1.1555235379806554
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.23311241931330964,
+      "x": -4.482763151029765,
+      "y": -0.8360125661904245
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.18680876756828377,
+      "x": -2.433006109740818,
+      "y": -0.7864604383319492
+    },
+    {
+      "id": 13,
+      "rotation_radians": -0.03929007335552636,
+      "x": 0.305062577512009,
+      "y": 0.9515830011006554
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.4606149629028032,
+      "x": 2.4212031306852784,
+      "y": 0.7840705301795579
+    },
+    {
+      "id": 15,
+      "rotation_radians": -0.06486466302540819,
+      "x": 4.482765579841461,
+      "y": 0.8360094887455386
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.18418748770154905,
+      "x": -4.298297198249282,
+      "y": 1.1555140060293898
+    },
+    {
+      "id": 17,
+      "rotation_radians": -0.4130475718211696,
+      "x": -2.205545838021324,
+      "y": 1.2030653633059902
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.015028066339343052,
+      "x": -0.7669842611695801,
+      "y": 2.640045293490313
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.14359382592425576,
+      "x": 1.4826766354798526,
+      "y": 2.568155539014148
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.062454278700796416,
+      "x": 3.4827385948723815,
+      "y": 2.5681017396208587
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.09701789144025728,
+      "x": -3.298269764141387,
+      "y": 2.887610133398389
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.36753378024609773,
+      "x": -1.8823644499449348,
+      "y": 4.300202073045761
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.17246626897426362,
+      "x": 0.40620727194605777,
+      "y": 4.28333434889399
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.860472800784408,
+      "x": 2.4827213991085153,
+      "y": 4.300214568152071
+    }
+  ],
+  "problem": "24 equal items for Circles in Hexagons",
+  "setup": "cirinhex",
+  "source_image": "https://erich-friedman.github.io/packing/cirinhex/hc24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/cirinhex/"
+}
diff --git a/data/solutions/generated/cirinpen_021_6869ffb03b036ff3.json b/data/solutions/generated/cirinpen_021_6869ffb03b036ff3.json
new file mode 100644
index 0000000000000000000000000000000000000000..52862d10c97206338a985204838e0ee894476783
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
+      "rotation_radians": 3.6598410754965203,
+      "x": -3.791914864944996,
+      "y": 2.873492806719302
+    },
+    {
+      "id": 2,
+      "rotation_radians": 3.0657055802984927,
+      "x": -0.5025036604155535,
+      "y": 0.5989582411121483
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.9586271994924896,
+      "x": 2.459984300036194,
+      "y": 3.2254344972734414
+    },
+    {
+      "id": 4,
+      "rotation_radians": 4.063291469707737,
+      "x": 2.995561327721157,
+      "y": -0.8052411560860837
+    },
+    {
+      "id": 5,
+      "rotation_radians": 4.490713885977809,
+      "x": -0.8672773862621552,
+      "y": -3.8237425368619213
+    },
+    {
+      "id": 6,
+      "rotation_radians": 5.766333422116452,
+      "x": -3.9000387200451256,
+      "y": -1.5225359699433918
+    },
+    {
+      "id": 7,
+      "rotation_radians": 2.846174714548013,
+      "x": 3.6506887107682435,
+      "y": 1.6181098812605919
+    },
+    {
+      "id": 8,
+      "rotation_radians": 1.131801534800253,
+      "x": -0.9958098723690724,
+      "y": -1.8278031640785375
+    },
+    {
+      "id": 9,
+      "rotation_radians": 4.554133510959788,
+      "x": 4.826360580705366,
+      "y": 1.681528749194627e-05
+    },
+    {
+      "id": 10,
+      "rotation_radians": 5.459745905099429,
+      "x": -2.762588255322658,
+      "y": -3.1720074086688013
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.3428301931023547,
+      "x": 0.2062154313429499,
+      "y": 2.469249664733531
+    },
+    {
+      "id": 12,
+      "rotation_radians": 4.804487564171946,
+      "x": 1.4914208535462765,
+      "y": -4.5901211701013045
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.554815991127502,
+      "x": 1.706882920453977,
+      "y": 1.1470265265959527
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.5258648018939053,
+      "x": 0.997134659804434,
+      "y": -0.7244308013315206
+    },
+    {
+      "id": 15,
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+      "x": 2.7954171674533197,
+      "y": -2.7953184185401607
+    },
+    {
+      "id": 16,
+      "rotation_radians": 3.19744942172433,
+      "x": -2.2883921236032947,
+      "y": -0.30153771074620705
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.662124483753993,
+      "x": -2.118734973636749,
+      "y": 1.7771332497773848
+    },
+    {
+      "id": 18,
+      "rotation_radians": 2.1919608400230377,
+      "x": 0.7969879457534769,
+      "y": -2.7144632623148897
+    },
+    {
+      "id": 19,
+      "rotation_radians": 6.041368698167864,
+      "x": -1.410002962501893,
+      "y": 3.6474223673488635
+    },
+    {
+      "id": 20,
+      "rotation_radians": 4.752171864428064,
+      "x": -3.9046002503233974,
+      "y": 0.8766116939608358
+    },
+    {
+      "id": 21,
+      "rotation_radians": 4.3504420688203425,
+      "x": 0.8213047026883471,
+      "y": 4.37238239963541
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/cirinpen_022_ebdb05232e56526e.json b/data/solutions/generated/cirinpen_022_ebdb05232e56526e.json
new file mode 100644
index 0000000000000000000000000000000000000000..fbba23f6ee4bb38bc34c8dc66d45f04236075766
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
+      "rotation_radians": 5.847475548390671,
+      "x": 0.9838469024426377,
+      "y": -0.8793369785741922
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+      "y": 1.9689004048216454
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+    {
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+    },
+    {
+      "id": 16,
+      "rotation_radians": 4.903614876999143,
+      "x": -4.004913422293476,
+      "y": -1.597876787354115
+    },
+    {
+      "id": 17,
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+      "x": -1.9980275761924906,
+      "y": 3.5618309364048137
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.16139505065608656,
+      "x": 1.5167791187312776,
+      "y": -4.703645521669129
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.7315603974115586,
+      "x": 2.7029040619279256,
+      "y": 0.14303054988656203
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+    {
+      "id": 20,
+      "rotation_radians": 0.46857498517519725,
+      "x": -3.925362811179894,
+      "y": 2.905909804892462
+    },
+    {
+      "id": 21,
+      "rotation_radians": 2.0504942245794413,
+      "x": -2.1760253347659906,
+      "y": 1.5696980439706367
+    },
+    {
+      "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/"
+}
diff --git a/data/solutions/generated/cirinpen_023_0115bd21477c01e6.json b/data/solutions/generated/cirinpen_023_0115bd21477c01e6.json
new file mode 100644
index 0000000000000000000000000000000000000000..351971beb882eadc710e832ab125ad44f7d4bf86
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
+      "rotation_radians": 2.8222736615166593,
+      "x": -4.090773508160569,
+      "y": -2.9721034251773983
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+      "y": -0.25642322905933246
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+    {
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+    {
+      "id": 17,
+      "rotation_radians": 0.6243873634175942,
+      "x": -2.6175571975638956,
+      "y": 1.619398370489704
+    },
+    {
+      "id": 18,
+      "rotation_radians": 3.562757611715143,
+      "x": -0.6282326052087157,
+      "y": 1.8262135576571241
+    },
+    {
+      "id": 19,
+      "rotation_radians": 2.558727740809431,
+      "x": 1.148745446599776,
+      "y": 2.744096428386879
+    },
+    {
+      "id": 20,
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+      "x": 3.145541439734377,
+      "y": 2.630158995905486
+    },
+    {
+      "id": 21,
+      "rotation_radians": 4.2596984430786335,
+      "x": -2.184559458549131,
+      "y": 3.5775023321469903
+    },
+    {
+      "id": 22,
+      "rotation_radians": 4.710151075394056,
+      "x": -0.2865497098197199,
+      "y": 4.208158076687209
+    },
+    {
+      "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/"
+}
diff --git a/data/solutions/generated/cirinpen_024_9eb26a95274f1d1d.json b/data/solutions/generated/cirinpen_024_9eb26a95274f1d1d.json
new file mode 100644
index 0000000000000000000000000000000000000000..dca2e88f8ea23502996053be24a333ed512821f2
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
+      "rotation_radians": -0.3532721745682055,
+      "x": -3.379357969116141,
+      "y": -3.3026568261384885
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+    {
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+      "x": -4.185289950951898,
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+    {
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+    {
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+      "rotation_radians": -0.10991847079557145,
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+      "y": 2.3572448997833977
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+    {
+      "id": 20,
+      "rotation_radians": 0.01810255201149933,
+      "x": 3.607022518560743,
+      "y": 2.155793301662741
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+    {
+      "id": 21,
+      "rotation_radians": 0.2504663815347544,
+      "x": -3.777223692906887,
+      "y": 3.1733764728250495
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+    {
+      "id": 22,
+      "rotation_radians": 0.4085313106253057,
+      "x": -1.8620199438861875,
+      "y": 3.795662172919909
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+    {
+      "id": 23,
+      "rotation_radians": -0.06215533964713401,
+      "x": 0.04125787789502965,
+      "y": 4.4140066535720734
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.2876373325120611,
+      "x": 2.0390419533684594,
+      "y": 4.313118458580701
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/cirinsqu_021_65afc927a4d3cb10.json b/data/solutions/generated/cirinsqu_021_65afc927a4d3cb10.json
new file mode 100644
index 0000000000000000000000000000000000000000..6fe4c6cc2a61ff94447181933967ac3f43133990
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
+      "rotation_radians": 0.031335834800858345,
+      "x": -3.6774811073260305,
+      "y": -1.5261713953792755
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+      "x": -0.8612573420227886,
+      "y": 1.2974271941789646
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+    {
+      "id": 18,
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+      "x": -0.42532892371560177,
+      "y": 3.249374445756573
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+    {
+      "id": 19,
+      "rotation_radians": 0.3149068469111136,
+      "x": 1.528953871093923,
+      "y": 3.674710090728344
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.1906369352992562,
+      "x": 2.943193397409424,
+      "y": 2.2604579446779938
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.20491149943447068,
+      "x": 5.6959787298459636e-06,
+      "y": 5.20365824844967
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/cirinsqu_022_27d48d864449f174.json b/data/solutions/generated/cirinsqu_022_27d48d864449f174.json
new file mode 100644
index 0000000000000000000000000000000000000000..f2504f8df3db9147e5a8be5716b3bd1d7f0fe4e0
--- /dev/null
+++ b/data/solutions/generated/cirinsqu_022_27d48d864449f174.json
@@ -0,0 +1,192 @@
+{
+  "case": "cirinsqu@22",
+  "container": {
+    "circumradius": 6.692079645333952,
+    "orientation_radians": 0.0,
+    "side_length": 9.464029794912205,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "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": [
+    {
+      "id": 1,
+      "rotation_radians": 3.195614645097412,
+      "x": -3.2882116544307144e-06,
+      "y": 5.277833270198971
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+      "x": -7.218302839580598e-06,
+      "y": -5.277850572745698
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+      "x": -2.899064002679962,
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+      "x": 2.4493646443838086,
+      "y": 1.6242747857094724e-05
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+      "y": -4.196026786707226e-05
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+    {
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+    {
+      "id": 18,
+      "rotation_radians": 0.4158339453198946,
+      "x": -1.4147054485460309,
+      "y": -3.863135766291049
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+    {
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+      "rotation_radians": 1.0577387941192682,
+      "x": -0.8972190709774015,
+      "y": 1.931346912172529
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+    {
+      "id": 20,
+      "rotation_radians": 4.5486397065461635,
+      "x": 3.863549915188038,
+      "y": -1.4142944557555825
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+    {
+      "id": 21,
+      "rotation_radians": 4.173976828456406,
+      "x": 1.034727379128662,
+      "y": 1.4138744083726473
+    },
+    {
+      "id": 22,
+      "rotation_radians": 5.736372326506457,
+      "x": 1.0348821487746689,
+      "y": -1.4139789312874715
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/cirinsqu_023_cfa99060ee2203a1.json b/data/solutions/generated/cirinsqu_023_cfa99060ee2203a1.json
new file mode 100644
index 0000000000000000000000000000000000000000..6425646ba296098d91ee94bed7d08128efbf8370
--- /dev/null
+++ b/data/solutions/generated/cirinsqu_023_cfa99060ee2203a1.json
@@ -0,0 +1,198 @@
+{
+  "case": "cirinsqu@23",
+  "container": {
+    "circumradius": 6.881779845968298,
+    "orientation_radians": 0.0,
+    "side_length": 9.732306391434195,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "placements": [
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+      "id": 1,
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+      "x": -5.467457365604396,
+      "y": -8.456804019123251e-05
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+    },
+    {
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+      "y": -4.2428370243061835
+    },
+    {
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+      "x": 1.6037967090877872,
+      "y": -1.4141505713794587
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+    },
+    {
+      "id": 19,
+      "rotation_radians": 3.9777802366695587,
+      "x": -2.638949421454309,
+      "y": -2.8285854308164087
+    },
+    {
+      "id": 20,
+      "rotation_radians": 4.35197073011435,
+      "x": -1.2248022174868705,
+      "y": 1.4142375351836145
+    },
+    {
+      "id": 21,
+      "rotation_radians": 2.0314454901507744,
+      "x": 0.18943795525473975,
+      "y": 2.828494295268786
+    },
+    {
+      "id": 22,
+      "rotation_radians": 3.030460614117156,
+      "x": 2.1214946715631573,
+      "y": -3.346042759481892
+    },
+    {
+      "id": 23,
+      "rotation_radians": 1.6642104761378178,
+      "x": 0.7072500482914589,
+      "y": -4.760294826880028
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/cirinsqu_024_e2eca298edbdb88c.json b/data/solutions/generated/cirinsqu_024_e2eca298edbdb88c.json
new file mode 100644
index 0000000000000000000000000000000000000000..6795e7391a86ac22c4ea2bde3f37f03f5f879d53
--- /dev/null
+++ b/data/solutions/generated/cirinsqu_024_e2eca298edbdb88c.json
@@ -0,0 +1,204 @@
+{
+  "case": "cirinsqu@24",
+  "container": {
+    "circumradius": 6.9748433868661355,
+    "orientation_radians": 0.0,
+    "side_length": 9.86391811313438,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "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"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "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"
+    },
+    "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": [
+    {
+      "id": 1,
+      "rotation_radians": 6.458980337601513,
+      "x": -2.9863185775333847e-06,
+      "y": 5.5606043215398016
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+    {
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+    {
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+    {
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+      "x": -3.8285005882428615,
+      "y": 1.0000033867078308
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+    {
+      "id": 12,
+      "rotation_radians": 1.279032094866606,
+      "x": 8.822483508541562e-07,
+      "y": -5.560614904068849
+    },
+    {
+      "id": 13,
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+      "x": -5.055459888683431e-06,
+      "y": 2.732108269658693
+    },
+    {
+      "id": 14,
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+      "x": 1.0000303675170052,
+      "y": -1.828478318891239
+    },
+    {
+      "id": 15,
+      "rotation_radians": 2.7178646767568786,
+      "x": 5.560610261844937,
+      "y": 2.8976611308494123e-06
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+    {
+      "id": 16,
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+      "x": 1.000033167388488,
+      "y": -3.828530664900395
+    },
+    {
+      "id": 17,
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+      "x": -1.000060620317526,
+      "y": -3.8285511639757286
+    },
+    {
+      "id": 18,
+      "rotation_radians": 3.540869972304411,
+      "x": -2.7321267667729785,
+      "y": -2.8284822136546923
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.8693068505285926,
+      "x": -5.560609607487422,
+      "y": 8.18750016831956e-06
+    },
+    {
+      "id": 20,
+      "rotation_radians": 1.7480243356156557,
+      "x": 3.828520872558982,
+      "y": 1.0000270904595943
+    },
+    {
+      "id": 21,
+      "rotation_radians": 4.876678510948428,
+      "x": -1.0000115111194912,
+      "y": -1.8284999714046837
+    },
+    {
+      "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/"
+}
diff --git a/data/solutions/generated/domintri_021_de2eca0c1c28a96d.json b/data/solutions/generated/domintri_021_de2eca0c1c28a96d.json
new file mode 100644
index 0000000000000000000000000000000000000000..55eebb8a4eadca9ebc2d66b0f5993ce5ceea4633
--- /dev/null
+++ b/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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+      "x": -1.0970558160588972,
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+      "y": -1.2805843435529938
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+    {
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+    },
+    {
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+      "x": 1.3952799367842732,
+      "y": 0.016320113360215
+    },
+    {
+      "id": 11,
+      "rotation_radians": 4.1860873273969315,
+      "x": -2.041118834908269,
+      "y": 1.2224078934666474
+    },
+    {
+      "id": 12,
+      "rotation_radians": 4.186093972059615,
+      "x": -1.0840075511797593,
+      "y": 0.8790733356683307
+    },
+    {
+      "id": 13,
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+      "x": -2.1129962711763177,
+      "y": 4.382312648961315
+    },
+    {
+      "id": 14,
+      "rotation_radians": 1.045560172490332,
+      "x": 0.8199292738156931,
+      "y": 2.110927527547445
+    },
+    {
+      "id": 15,
+      "rotation_radians": 3.1415989187948656,
+      "x": -2.238859521988467,
+      "y": -2.839650950642868
+    },
+    {
+      "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
+    },
+    {
+      "id": 19,
+      "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/"
+}
diff --git a/data/solutions/generated/domintri_022_6301aae692a9ac9b.json b/data/solutions/generated/domintri_022_6301aae692a9ac9b.json
new file mode 100644
index 0000000000000000000000000000000000000000..54730ad2cca2a99e1c9713262d5728559ac7ef3e
--- /dev/null
+++ b/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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+    {
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+      "x": -1.0982499951584226,
+      "y": 0.11019828267086891
+    },
+    {
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+      "x": -2.200834432194795,
+      "y": -0.8992045031364964
+    },
+    {
+      "id": 12,
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+      "x": -1.6907669706066129,
+      "y": -3.3963349850826146
+    },
+    {
+      "id": 13,
+      "rotation_radians": 3.5876760300774526,
+      "x": 3.7098398593218485,
+      "y": 0.28859698377449977
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.005956313778215679,
+      "x": -2.1961787392692256,
+      "y": -1.8992448549743952
+    },
+    {
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+      "rotation_radians": 0.7829858100425973,
+      "x": 0.6935188359199477,
+      "y": 2.0435257460572
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.7717182259200654,
+      "x": 0.8947079480316786,
+      "y": 0.8283228573649937
+    },
+    {
+      "id": 17,
+      "rotation_radians": 4.798983898743175,
+      "x": 1.4318079639678114,
+      "y": -1.5900520756822254
+    },
+    {
+      "id": 18,
+      "rotation_radians": 6.806782417722895,
+      "x": -0.0515307405427594,
+      "y": -3.161732721748257
+    },
+    {
+      "id": 19,
+      "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/"
+}
diff --git a/data/solutions/generated/domintri_023_7b6e8b12db0049b9.json b/data/solutions/generated/domintri_023_7b6e8b12db0049b9.json
new file mode 100644
index 0000000000000000000000000000000000000000..8db3532504b78ad9a0276ff0edda8da3b5051a8a
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
+      "rotation_radians": 5.235988682925896,
+      "x": 2.854715852572897,
+      "y": -0.9822256266578756
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+    {
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+    {
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+      "y": 2.514647184343075
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+      "y": 2.2022361286129195
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+    {
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+      "y": -0.7519915104185423
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+    {
+      "id": 11,
+      "rotation_radians": 4.712342072194746,
+      "x": -2.777995614234273,
+      "y": -2.9455916244172813
+    },
+    {
+      "id": 12,
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+      "y": -0.9454965390192629
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+    {
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+      "x": 1.9372456438189367,
+      "y": 2.089315739810874
+    },
+    {
+      "id": 14,
+      "rotation_radians": 4.768023334773085,
+      "x": 0.30095859897588645,
+      "y": -1.1383151074622373
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+    {
+      "id": 15,
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+      "x": 2.92055815733062,
+      "y": 0.7913663406495277
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.10587347636396144,
+      "x": -1.230718921808486,
+      "y": 1.5098164615980858
+    },
+    {
+      "id": 17,
+      "rotation_radians": 3.6651882116609684,
+      "x": -2.142285090089191,
+      "y": -4.444647686400859
+    },
+    {
+      "id": 18,
+      "rotation_radians": 5.241701089429151,
+      "x": 1.9590439798814532,
+      "y": -1.4924356940194763
+    },
+    {
+      "id": 19,
+      "rotation_radians": 3.1845284625117616,
+      "x": -1.2521489440944509,
+      "y": -2.8820127656683727
+    },
+    {
+      "id": 20,
+      "rotation_radians": 4.712382700736236,
+      "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/"
+}
diff --git a/data/solutions/generated/domintri_024_af99e7edd2e30109.json b/data/solutions/generated/domintri_024_af99e7edd2e30109.json
new file mode 100644
index 0000000000000000000000000000000000000000..ba1c329225227361aeeed4a57c47ad3791baa9c2
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
+      "rotation_radians": 4.712389934733722,
+      "x": -2.899227610821278,
+      "y": -4.304995106041819
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+    {
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+    {
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+      "x": -0.8980094121819339,
+      "y": 3.1415099463730156
+    },
+    {
+      "id": 11,
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+      "x": -2.3850856722422,
+      "y": -1.7974402727667562
+    },
+    {
+      "id": 12,
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+      "x": -2.318578871200283,
+      "y": 0.2182874353625639
+    },
+    {
+      "id": 13,
+      "rotation_radians": 3.665189651104246,
+      "x": 4.860624371439264,
+      "y": -0.5414702129689867
+    },
+    {
+      "id": 14,
+      "rotation_radians": 3.9861362932504463,
+      "x": 1.6084588874034904,
+      "y": -0.9028494543790576
+    },
+    {
+      "id": 15,
+      "rotation_radians": 2.4356863540739853,
+      "x": 1.9772253011575238,
+      "y": 0.7865368650314114
+    },
+    {
+      "id": 16,
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+      "x": 4.182414770372991,
+      "y": 0.9330346291831157
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.5734715250141864,
+      "x": -1.8960407627282814,
+      "y": 1.7237744541041897
+    },
+    {
+      "id": 18,
+      "rotation_radians": 4.712628503474931,
+      "x": -1.8988276756100098,
+      "y": 3.726647680227827
+    },
+    {
+      "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/"
+}
diff --git a/data/solutions/generated/hexincir_021_49a047c29bb184c3.json b/data/solutions/generated/hexincir_021_49a047c29bb184c3.json
new file mode 100644
index 0000000000000000000000000000000000000000..1ca2073d34ac4e9bc62c76e1ead1559d20741653
--- /dev/null
+++ b/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
+    },
+    {
+      "id": 2,
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+      "x": -1.5903858435706528,
+      "y": -3.436742261694003
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+    {
+      "id": 3,
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+      "x": 0.1746101921887048,
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+    {
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+      "x": 1.8831879385912498,
+      "y": -3.255767116324947
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+    {
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+    },
+    {
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+      "x": -3.731597059653315,
+      "y": -0.6661585515623543
+    },
+    {
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+      "y": -1.7082857609996405
+    },
+    {
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+      "x": 1.980821866846759,
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+    },
+    {
+      "id": 10,
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+      "x": 3.679610537074053,
+      "y": -0.17859839116112855
+    },
+    {
+      "id": 11,
+      "rotation_radians": -0.31904806144756886,
+      "x": -3.379876329161349,
+      "y": 1.0561532958196433
+    },
+    {
+      "id": 12,
+      "rotation_radians": -0.3469332273044722,
+      "x": -2.064987149902747,
+      "y": -0.14591191573769463
+    },
+    {
+      "id": 13,
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+      "y": 0.20788746786882886
+    },
+    {
+      "id": 14,
+      "rotation_radians": -0.08964970814351197,
+      "x": 1.768560528614802,
+      "y": 1.0792693139403637
+    },
+    {
+      "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
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.17541427989402222,
+      "x": 0.6614533852778779,
+      "y": 3.7324291832889203
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.1680190681011985,
+      "x": 2.2393293533348455,
+      "y": 2.916365539251016
+    },
+    {
+      "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/"
+}
diff --git a/data/solutions/generated/hexinhex_021_4a431b677be571c9.json b/data/solutions/generated/hexinhex_021_4a431b677be571c9.json
new file mode 100644
index 0000000000000000000000000000000000000000..1fe1ae6d582faf702631eab5f21a90ac9d965de3
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
+      "rotation_radians": 7.901581286981117e-07,
+      "x": -0.5000174463538043,
+      "y": 0.8660408791733488
+    },
+    {
+      "id": 2,
+      "rotation_radians": -8.371924427954672e-07,
+      "x": -0.49998926754271145,
+      "y": -0.8660342103698403
+    },
+    {
+      "id": 3,
+      "rotation_radians": -2.660678494033981e-07,
+      "x": 1.0000192810757436,
+      "y": 1.7876577640023134e-05
+    },
+    {
+      "id": 4,
+      "rotation_radians": -7.438935821621196e-08,
+      "x": -2.000028448902631,
+      "y": -1.3886483582868472e-05
+    },
+    {
+      "id": 5,
+      "rotation_radians": -3.2787528884077454e-07,
+      "x": 1.0000286771626443,
+      "y": -1.7320685106263434
+    },
+    {
+      "id": 6,
+      "rotation_radians": -5.648917492132542e-07,
+      "x": 1.0000042693678135,
+      "y": 1.732087424964717
+    },
+    {
+      "id": 7,
+      "rotation_radians": 7.623293417932666e-07,
+      "x": -1.9999814394233528,
+      "y": -1.7320956192726793
+    },
+    {
+      "id": 8,
+      "rotation_radians": 5.726382936736113e-07,
+      "x": -2.0001063176145357,
+      "y": 1.7320682172424777
+    },
+    {
+      "id": 9,
+      "rotation_radians": -6.540268107444737e-07,
+      "x": -0.49996917052936474,
+      "y": -2.598161234269701
+    },
+    {
+      "id": 10,
+      "rotation_radians": 5.893385085121173e-07,
+      "x": -0.5000298003785586,
+      "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/"
+}
diff --git a/data/solutions/generated/hexinhex_022_003a713177cb171c.json b/data/solutions/generated/hexinhex_022_003a713177cb171c.json
new file mode 100644
index 0000000000000000000000000000000000000000..a784fc1f0fe301f70dd0311fc60a7314f9ade977
--- /dev/null
+++ b/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,
+      "rotation_radians": 1.0471964243690233,
+      "x": -0.8465356906115851,
+      "y": -1.008001384697747
+    },
+    {
+      "id": 2,
+      "rotation_radians": 1.0471925015639367,
+      "x": 0.4286947354500659,
+      "y": 0.24745906523627786
+    },
+    {
+      "id": 3,
+      "rotation_radians": 1.0471921178895922,
+      "x": -0.999963622630636,
+      "y": 1.2371515521504806
+    },
+    {
+      "id": 4,
+      "rotation_radians": 1.0473711363341365,
+      "x": 0.7758044556209438,
+      "y": -1.838585427866387
+    },
+    {
+      "id": 5,
+      "rotation_radians": 1.0471723762321445,
+      "x": -2.2781650026899674,
+      "y": -0.01318902810934708
+    },
+    {
+      "id": 6,
+      "rotation_radians": 1.047185677727647,
+      "x": 0.8921159321085792,
+      "y": 1.9795671934369528
+    },
+    {
+      "id": 7,
+      "rotation_radians": 1.0471934642756702,
+      "x": 2.0001087823245354,
+      "y": -0.4949536465220614
+    },
+    {
+      "id": 8,
+      "rotation_radians": 1.0473701591968814,
+      "x": -0.701296886063352,
+      "y": -2.744353655814245
+    },
+    {
+      "id": 9,
+      "rotation_radians": 1.0469715937771917,
+      "x": 2.5169734501572147,
+      "y": 1.2371406434857135
+    },
+    {
+      "id": 10,
+      "rotation_radians": 1.0471963786561402,
+      "x": -2.2856875527979277,
+      "y": -1.9795445376748466
+    },
+    {
+      "id": 11,
+      "rotation_radians": 1.0471875095671135,
+      "x": -0.5714934761306859,
+      "y": 2.969259004112351
+    },
+    {
+      "id": 12,
+      "rotation_radians": 1.04719219489969,
+      "x": -2.5714067598523314,
+      "y": 1.9795563389686834
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.8332652268188954,
+      "x": 2.4531047160616755,
+      "y": -3.001523655027058
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.9991355688565592,
+      "x": 0.7793511360680909,
+      "y": -3.6878671720994323
+    },
+    {
+      "id": 15,
+      "rotation_radians": 1.0470094102348377,
+      "x": 2.571467616004173,
+      "y": 2.9692528044040043
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.0471960240490028,
+      "x": -3.7143688437562132,
+      "y": -0.9898645330004745
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.047210784800021,
+      "x": -2.142943973523644,
+      "y": -3.7116633490312636
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.9956310829320324,
+      "x": 4.0460012205776,
+      "y": 0.36589452870687333
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.0473861046353776,
+      "x": -3.857179015040217,
+      "y": 0.7423189733842023
+    },
+    {
+      "id": 20,
+      "rotation_radians": 1.04718488413327,
+      "x": 0.9999371354762571,
+      "y": 3.711676177264519
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.0471929177769443,
+      "x": -2.142935018978356,
+      "y": 3.7116676593171736
+    },
+    {
+      "id": 22,
+      "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/"
+}
diff --git a/data/solutions/generated/hexinhex_023_4a3a3fd07554d52b.json b/data/solutions/generated/hexinhex_023_4a3a3fd07554d52b.json
new file mode 100644
index 0000000000000000000000000000000000000000..1891ff153c193b644abd8f19f254182396bfa7fb
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
+      "rotation_radians": 0.006824620830609338,
+      "x": -0.8215524173648067,
+      "y": 0.3833682180057374
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.006887590796000111,
+      "x": 0.6936706663775765,
+      "y": 1.2832588465885684
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.006870225593018362,
+      "x": 0.6977844597861459,
+      "y": -0.44889990182527684
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.006814396948659165,
+      "x": -0.8257158232369509,
+      "y": 2.115490971936615
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.34651449238529747,
+      "x": -0.4351448621892691,
+      "y": -2.1674658732709595
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.005731451096614905,
+      "x": -2.345562932213716,
+      "y": 1.2819965805747553
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.31554696974886914,
+      "x": -1.9848001392956673,
+      "y": -1.0491983368579847
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.008912950088087655,
+      "x": 2.3613595035259056,
+      "y": 0.14049169280427942
+    },
+    {
+      "id": 9,
+      "rotation_radians": 0.3483902208172997,
+      "x": 1.3208908710031535,
+      "y": -2.19037366814471
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.01945067079844383,
+      "x": 0.6128106277181141,
+      "y": 3.0963682810886533
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.00690087172167663,
+      "x": 2.214650037528482,
+      "y": 2.1137766462463046
+    },
+    {
+      "id": 12,
+      "rotation_radians": 1.5368440542013492e-05,
+      "x": -1.5038578437444563,
+      "y": -3.8492620204221404
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.43716582828517564,
+      "x": 3.113096006781232,
+      "y": -2.0460795269340837
+    },
+    {
+      "id": 14,
+      "rotation_radians": -0.013428134888334211,
+      "x": -2.6876590619184264,
+      "y": 3.0225154291664778
+    },
+    {
+      "id": 15,
+      "rotation_radians": 1.0536825029093306,
+      "x": -1.070373462630855,
+      "y": 3.846130696762821
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.0027837382088517154,
+      "x": -3.8608575221997232,
+      "y": -1.0086596087949697
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.388601801481054,
+      "x": 0.3871562789463161,
+      "y": -3.7244345293755545
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.00278120197750176,
+      "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/"
+}
diff --git a/data/solutions/generated/hexinhex_024_c96649ff013a9455.json b/data/solutions/generated/hexinhex_024_c96649ff013a9455.json
new file mode 100644
index 0000000000000000000000000000000000000000..8520479a576a6bfa4d38b0780ad11382caed0967
--- /dev/null
+++ b/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
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.5219383906438466,
+      "x": -1.7839236617020782,
+      "y": 1.031042760699711
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.5219389230113706,
+      "x": -3.0312291824916215,
+      "y": -2.250011245153297
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.5218365132267586,
+      "x": -0.4476103067022221,
+      "y": -0.7415609461474315
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.5218365331876277,
+      "x": 1.2990758104304285,
+      "y": 2.2500661359032113
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.5218365542948107,
+      "x": 0.43641481446158853,
+      "y": 0.7480604969662029
+    },
+    {
+      "id": 7,
+      "rotation_radians": 1.3013690437770573,
+      "x": 1.4398691636475018,
+      "y": -3.786176657836199
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.5218360708863679,
+      "x": 1.475346144585559,
+      "y": -0.8522038341235827
+    },
+    {
+      "id": 9,
+      "rotation_radians": 0.9386272368052709,
+      "x": 4.038648429428672,
+      "y": 0.6746618235339499
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.5218360712586747,
+      "x": 0.43305161567370953,
+      "y": -2.250078827625604
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.4454952035909719,
+      "x": -1.3900697076117499,
+      "y": 3.7526566453179586
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.5218364314140617,
+      "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/"
+}
diff --git a/data/solutions/generated/hexinhex_025_4ac680367830872b.json b/data/solutions/generated/hexinhex_025_4ac680367830872b.json
new file mode 100644
index 0000000000000000000000000000000000000000..a3ea79040194d68b84aabeafc0fde6dbe9d1993f
--- /dev/null
+++ b/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,
+    "side_length": 1.0,
+    "sides": 6,
+    "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": [
+    {
+      "id": 1,
+      "rotation_radians": 0.4404121765384839,
+      "x": 1.019021234597671,
+      "y": 2.3905736879836557
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.3999075408620485,
+      "x": -1.1425408951861156,
+      "y": -0.3336362510333009
+    },
+    {
+      "id": 3,
+      "rotation_radians": -3.565189770830876e-06,
+      "x": -3.9709882598434536,
+      "y": 1.1346010666673292
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.4113703210325995,
+      "x": -2.096108328296395,
+      "y": 1.1463031474509824
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.40108219042967813,
+      "x": 2.12292447271252,
+      "y": 0.9750186069695558
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.3999538634453954,
+      "x": 1.3675403137082716,
+      "y": -2.3678080581856578
+    },
+    {
+      "id": 7,
+      "rotation_radians": 3.815218827437013e-06,
+      "x": 4.162746024611598,
+      "y": -0.8024734756085733
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.3995460824606092,
+      "x": 2.240178937779094,
+      "y": -3.879860409648887
+    },
+    {
+      "id": 9,
+      "rotation_radians": 1.0471923633428646,
+      "x": -4.2811023181540095,
+      "y": -0.5974797865459995
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.39990325948956207,
+      "x": -0.7953764009297908,
+      "y": 2.3593740371946623
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.3999078201716624,
+      "x": 0.5403043391673978,
+      "y": -0.836988419266176
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.44040471255817926,
+      "x": 0.10741346745285342,
+      "y": 3.87575942048007
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.3998925646745878,
+      "x": 3.112956109712789,
+      "y": -2.3680932259951986
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.4578517522342325,
+      "x": 1.9313961504752526,
+      "y": 3.8744663969461857
+    },
+    {
+      "id": 15,
+      "rotation_radians": 0.4027292721148159,
+      "x": 0.4937891835046935,
+      "y": -3.8795956582700364
+    },
+    {
+      "id": 16,
+      "rotation_radians": 3.327305808765827e-06,
+      "x": 4.089326673326304,
+      "y": 0.929620669005078
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.39388723426160094,
+      "x": -2.9337233305545376,
+      "y": 2.6800337975116557
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.0472038713901486,
+      "x": -2.853548471922297,
+      "y": -3.0700700282088156
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.0472035797397783,
+      "x": -2.7085885142217805,
+      "y": -1.3379869225596897
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.39990898203483444,
+      "x": 0.1347966582898977,
+      "y": 0.872079381249544
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.10670324081108794,
+      "x": -0.9975100260872356,
+      "y": -2.2351322519601666
+    },
+    {
+      "id": 22,
+      "rotation_radians": 9.404165937614054e-08,
+      "x": -1.3940294427334645,
+      "y": -4.006272413805417
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.3938885226186919,
+      "x": -1.6526728502152843,
+      "y": 3.8807210014942926
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.4681883289884034,
+      "x": 3.0372325709650285,
+      "y": 2.486971402026309
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.3999090114205805,
+      "x": 2.2856884807216695,
+      "y": -0.8372893887163753
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/hexinhex_026_0a420d645748969b.json b/data/solutions/generated/hexinhex_026_0a420d645748969b.json
new file mode 100644
index 0000000000000000000000000000000000000000..2b0c108a311dc6fe404e5e5e9638931551593103
--- /dev/null
+++ b/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"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.3541024515660062,
+      "x": 0.526694788807339,
+      "y": -0.9291844886285529
+    },
+    {
+      "id": 2,
+      "rotation_radians": -0.353574260238975,
+      "x": -1.0147859725998067,
+      "y": 0.042099623659466394
+    },
+    {
+      "id": 3,
+      "rotation_radians": -0.3597236915995284,
+      "x": 0.7294631402338068,
+      "y": 0.8456713400964821
+    },
+    {
+      "id": 4,
+      "rotation_radians": -0.3541309585775437,
+      "x": -1.9155281148310246,
+      "y": -1.4961370545819486
+    },
+    {
+      "id": 5,
+      "rotation_radians": -0.35411831150756623,
+      "x": 2.2827565532422867,
+      "y": -0.9219194804718274
+    },
+    {
+      "id": 6,
+      "rotation_radians": -0.35417585024586384,
+      "x": -0.31631061862816373,
+      "y": 2.2826634418769554
+    },
+    {
+      "id": 7,
+      "rotation_radians": -0.354128008362101,
+      "x": -2.8239619977128974,
+      "y": 0.0009709427420007558
+    },
+    {
+      "id": 8,
+      "rotation_radians": -0.35411134847320597,
+      "x": 1.4110178861110547,
+      "y": -2.4463204158422114
+    },
+    {
+      "id": 9,
+      "rotation_radians": -0.35417646476141423,
+      "x": 1.4137376063428249,
+      "y": 2.441844023168373
+    },
+    {
+      "id": 10,
+      "rotation_radians": -0.35411350344710935,
+      "x": -0.35355112700732755,
+      "y": -2.450476653529668
+    },
+    {
+      "id": 11,
+      "rotation_radians": -0.3535740721381933,
+      "x": -1.9435639101153799,
+      "y": 1.5224740964282764
+    },
+    {
+      "id": 12,
+      "rotation_radians": -0.3541115832783557,
+      "x": 2.6972337417166123,
+      "y": 0.771535491816866
+    },
+    {
+      "id": 13,
+      "rotation_radians": -0.07960365292203393,
+      "x": -2.8326112306914015,
+      "y": -3.1941538004507035
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.4098614943793958,
+      "x": 4.474046084910885,
+      "y": -0.015820937541490936
+    },
+    {
+      "id": 15,
+      "rotation_radians": -0.3450978479114158,
+      "x": -1.2208481091934769,
+      "y": 3.928767509518961
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.3749104752333129,
+      "x": -3.6949771038664365,
+      "y": -1.5286399283579921
+    },
+    {
+      "id": 17,
+      "rotation_radians": -0.3628619607090081,
+      "x": 3.1726860763864795,
+      "y": -2.4369685646753583
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.3549396112927512,
+      "x": 0.534766653890469,
+      "y": 3.966127331042614
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.354113575917858,
+      "x": 0.5307976534187556,
+      "y": -3.967583838405066
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.35413189398597195,
+      "x": -3.701743348667028,
+      "y": 1.5235243241048018
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.35445266291016725,
+      "x": -4.5812409781094034,
+      "y": -1.4503157448658867e-05
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.3541118739299409,
+      "x": 3.170819327409159,
+      "y": 2.443134067781432
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.3535153244459023,
+      "x": 2.290739581708319,
+      "y": -3.9676650806506344
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.35494504532542276,
+      "x": 2.291982730404979,
+      "y": 3.9650464610423617
+    },
+    {
+      "id": 25,
+      "rotation_radians": -0.07958110726521547,
+      "x": -1.3189864559174005,
+      "y": -4.050201163797114
+    },
+    {
+      "id": 26,
+      "rotation_radians": -0.3450867771124415,
+      "x": -2.822335713849042,
+      "y": 3.0498909615868617
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/hexinhex_027_4e9628a9f49def85.json b/data/solutions/generated/hexinhex_027_4e9628a9f49def85.json
new file mode 100644
index 0000000000000000000000000000000000000000..49cec5b49bc8cb214b00dbeb0d952213a7ead14a
--- /dev/null
+++ b/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": {
+      "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"
+    },
+    "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,
+      "rotation_radians": 3.824060113450139,
+      "x": 0.3476103325076376,
+      "y": -2.429582104061147
+    },
+    {
+      "id": 2,
+      "rotation_radians": 4.86676174384588,
+      "x": 2.8116816078495375,
+      "y": -2.1320758541336838e-05
+    },
+    {
+      "id": 3,
+      "rotation_radians": 1.7296688037616177,
+      "x": -3.1558594094922774,
+      "y": -2.4604552346699706
+    },
+    {
+      "id": 4,
+      "rotation_radians": 4.87045184370137,
+      "x": -0.5041959176500256,
+      "y": -3.9629867282810785
+    },
+    {
+      "id": 5,
+      "rotation_radians": 5.234656996097622,
+      "x": 2.87950836722448,
+      "y": -3.1804338900332496
+    },
+    {
+      "id": 6,
+      "rotation_radians": 1.0453802231629092,
+      "x": -4.223766569975458,
+      "y": 0.8240180095255282
+    },
+    {
+      "id": 7,
+      "rotation_radians": 5.234149066224134,
+      "x": -4.191108951655736,
+      "y": -0.908197918259244
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.6824814339337278,
+      "x": 0.3449148392058114,
+      "y": 2.463658347600896
+    },
+    {
+      "id": 9,
+      "rotation_radians": 5.9292099848515125,
+      "x": -0.5524742502924744,
+      "y": -0.9007546865374491
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.6779736936726078,
+      "x": 1.9608013045007948,
+      "y": -1.5352836623216297
+    },
+    {
+      "id": 11,
+      "rotation_radians": 3.136661436438432,
+      "x": 1.301015713535152,
+      "y": 4.082170582975325
+    },
+    {
+      "id": 12,
+      "rotation_radians": 7.325451530437888,
+      "x": 2.8228125832546125,
+      "y": 3.2532639144392346
+    },
+    {
+      "id": 13,
+      "rotation_radians": 3.824058511955816,
+      "x": -1.4057678745425017,
+      "y": -2.434757444656067
+    },
+    {
+      "id": 14,
+      "rotation_radians": 3.824069591452841,
+      "x": -2.305698315305127,
+      "y": 3.9328902843122946
+    },
+    {
+      "id": 15,
+      "rotation_radians": 0.6824745634118679,
+      "x": -2.31024262523726,
+      "y": -0.9292517993049171
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.7337766145846158,
+      "x": -3.184450814494896,
+      "y": 2.41200452431685
+    },
+    {
+      "id": 17,
+      "rotation_radians": 3.8348152058496305,
+      "x": 1.055747663198931,
+      "y": -0.02999068469952672
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.7296729878214439,
+      "x": -1.4046635594093142,
+      "y": 2.433120846767069
+    },
+    {
+      "id": 19,
+      "rotation_radians": 4.871653222893496,
+      "x": -0.5034700730656557,
+      "y": 0.9332319665455696
+    },
+    {
+      "id": 20,
+      "rotation_radians": 2.796910023758765,
+      "x": 3.681275501940237,
+      "y": 1.5570589989988135
+    },
+    {
+      "id": 21,
+      "rotation_radians": 4.871266421198897,
+      "x": -0.5562939625649187,
+      "y": 3.963273911961122
+    },
+    {
+      "id": 22,
+      "rotation_radians": 3.819564039911621,
+      "x": 4.560640783960255,
+      "y": 0.025828091039544213
+    },
+    {
+      "id": 23,
+      "rotation_radians": 3.137508582944148,
+      "x": 1.3894721423719638,
+      "y": -4.0713867986372545
+    },
+    {
+      "id": 24,
+      "rotation_radians": 4.877739156562641,
+      "x": 1.9250859484807448,
+      "y": 1.5169388154210195
+    },
+    {
+      "id": 25,
+      "rotation_radians": -0.3692255417094895,
+      "x": 3.7085452217057817,
+      "y": -1.5017319587341917
+    },
+    {
+      "id": 26,
+      "rotation_radians": 1.729665506304759,
+      "x": -2.258560158123236,
+      "y": -3.9632477628505542
+    },
+    {
+      "id": 27,
+      "rotation_radians": 3.8240674183610937,
+      "x": -2.2708500456821903,
+      "y": 0.9097712566785343
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/hexinhex_028_59dc7d7850663cbb.json b/data/solutions/generated/hexinhex_028_59dc7d7850663cbb.json
new file mode 100644
index 0000000000000000000000000000000000000000..82c2664ef9fdb991ff9c3a8119496e2eefe16523
--- /dev/null
+++ b/data/solutions/generated/hexinhex_028_59dc7d7850663cbb.json
@@ -0,0 +1,230 @@
+{
+  "case": "hexinhex@28",
+  "container": {
+    "circumradius": 5.9618534230590905,
+    "orientation_radians": 0.0,
+    "side_length": 5.96185342305909,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "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"
+  },
+  "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@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"
+    },
+    "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,
+      "rotation_radians": 0.15126342348636831,
+      "x": -0.8914888487537967,
+      "y": -0.12739671511641137
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.10890959119943425,
+      "x": 0.6168828906758234,
+      "y": 0.7791944812914786
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.21412976395165392,
+      "x": 1.5071415592020259,
+      "y": -0.8486616741106179
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.06485151858693809,
+      "x": -0.9272033365710187,
+      "y": 1.648296066175677
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.21411362767735692,
+      "x": -0.022174196480069866,
+      "y": -1.7413716945997826
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.08059389875945881,
+      "x": -2.4250968534887725,
+      "y": 0.7584266445893665
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.1749648295573365,
+      "x": -1.8474723139340152,
+      "y": -1.7004759906096134
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.18686341930623218,
+      "x": 2.4615525076741003,
+      "y": 0.6963555788199075
+    },
+    {
+      "id": 9,
+      "rotation_radians": 0.2141083464229419,
+      "x": 1.5155603538831837,
+      "y": -2.6195057942467685
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.06484246451724923,
+      "x": 0.564924864158322,
+      "y": 2.5328232172132674
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.08656725508158856,
+      "x": 2.4643515742892337,
+      "y": 2.4811231457056575
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.16544798443053157,
+      "x": -0.9694826897818356,
+      "y": -3.3090475501282732
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.18696724057457387,
+      "x": 3.3219561220647975,
+      "y": -0.9037757619105173
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.07198051257523758,
+      "x": -2.440814004381843,
+      "y": 2.517664566371024
+    },
+    {
+      "id": 15,
+      "rotation_radians": 0.0274267746136424,
+      "x": -0.9500907919967709,
+      "y": 3.441072704276657
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.08058207809547493,
+      "x": -3.4133189042095053,
+      "y": -0.8590137363841174
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.16546333737798724,
+      "x": 0.5514005796498148,
+      "y": -4.186984359217049
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.07690732291097965,
+      "x": -3.935388833932618,
+      "y": 1.63113047236408
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.08071081372452572,
+      "x": -3.4091776449524978,
+      "y": -2.596507208196542
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.18695568907794818,
+      "x": 4.854851730095892,
+      "y": -0.029565444603184415
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.18699466792960237,
+      "x": 2.3864243862381844,
+      "y": -4.219203151888164
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.08655911807226012,
+      "x": 2.4786452780093273,
+      "y": 4.221005909948852
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.05674953241794722,
+      "x": 3.9905280937005148,
+      "y": 1.6283941770837358
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.0058696367720585535,
+      "x": -2.479224259913543,
+      "y": -4.294143814986175
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.1869600281171308,
+      "x": 3.3336511273634404,
+      "y": -2.6644017757835616
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.006006660566126943,
+      "x": -2.4748107523891107,
+      "y": 4.285085651355501
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.027382846218310383,
+      "x": 0.5651509322929736,
+      "y": 4.283717881716352
+    },
+    {
+      "id": 28,
+      "rotation_radians": 0.021598128692634486,
+      "x": -4.949589228504777,
+      "y": 1.5822131732876393e-05
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/hexinhex_029_dba25a591b8992bc.json b/data/solutions/generated/hexinhex_029_dba25a591b8992bc.json
new file mode 100644
index 0000000000000000000000000000000000000000..a56fe65b1fcf10df77bb80a01afc1dc71b6801dd
--- /dev/null
+++ b/data/solutions/generated/hexinhex_029_dba25a591b8992bc.json
@@ -0,0 +1,236 @@
+{
+  "case": "hexinhex@29",
+  "container": {
+    "circumradius": 6.000134351852798,
+    "orientation_radians": 0.0,
+    "side_length": 6.000134351852797,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "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": {
+    "circumradius": 1.0000000000000002,
+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "hexinhex@29",
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+      "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/"
+}
diff --git a/data/solutions/generated/hexinhex_030_100db5f9f28894cc.json b/data/solutions/generated/hexinhex_030_100db5f9f28894cc.json
new file mode 100644
index 0000000000000000000000000000000000000000..6599925fd3c050b01845d502834893b1412d71f6
--- /dev/null
+++ b/data/solutions/generated/hexinhex_030_100db5f9f28894cc.json
@@ -0,0 +1,242 @@
+{
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+  "container": {
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+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "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"
+  },
+  "item": {
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+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
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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",
+    "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"
+  },
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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/"
+}
diff --git a/data/solutions/generated/hexinhex_031_d503e2b08764a35e.json b/data/solutions/generated/hexinhex_031_d503e2b08764a35e.json
new file mode 100644
index 0000000000000000000000000000000000000000..270900d9b341086d8dec873e6e2eb0a8e47315ff
--- /dev/null
+++ b/data/solutions/generated/hexinhex_031_d503e2b08764a35e.json
@@ -0,0 +1,248 @@
+{
+  "case": "hexinhex@31",
+  "container": {
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+    "orientation_radians": 0.0,
+    "side_length": 6.000103172861178,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "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": {
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+    "side_length": 1.0,
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+    "type": "regular_polygon"
+  },
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+    "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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+    {
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+      "rotation_radians": 4.483782094384345e-07,
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+      "y": -1.7320058514154326
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.7033231775487548e-07,
+      "x": -9.746397840182894e-05,
+      "y": -3.4641706513359964
+    },
+    {
+      "id": 20,
+      "rotation_radians": -1.4669612877472878e-07,
+      "x": 2.9999955374802845,
+      "y": -3.464256652713817
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.207755958622689e-07,
+      "x": -1.5001315345465358,
+      "y": -4.3302009850286876
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.1594462056923785e-07,
+      "x": -1.4999098507566224,
+      "y": 4.330213781482313
+    },
+    {
+      "id": 23,
+      "rotation_radians": 1.8933346495570021e-07,
+      "x": 1.4999225281883937,
+      "y": -4.330215243321034
+    },
+    {
+      "id": 24,
+      "rotation_radians": -1.5725238027214725e-07,
+      "x": 1.5001556447630628,
+      "y": 4.330201192159377
+    },
+    {
+      "id": 25,
+      "rotation_radians": 5.851190839552243e-07,
+      "x": -4.500036533545838,
+      "y": 0.8661367545616072
+    },
+    {
+      "id": 26,
+      "rotation_radians": -8.255802123894274e-08,
+      "x": 3.0001231222089593,
+      "y": 3.46406262319174
+    },
+    {
+      "id": 27,
+      "rotation_radians": 1.5163257735508872e-07,
+      "x": 4.500140538833788,
+      "y": 0.8659301673795337
+    },
+    {
+      "id": 28,
+      "rotation_radians": 2.9204572663096774e-07,
+      "x": -3.000112142726159,
+      "y": -3.464083435330626
+    },
+    {
+      "id": 29,
+      "rotation_radians": 1.7873633058504198e-07,
+      "x": 4.500029983242889,
+      "y": -0.8661492840486752
+    },
+    {
+      "id": 30,
+      "rotation_radians": 2.597768331234049e-07,
+      "x": -2.9999891519986814,
+      "y": 3.4642686962984572
+    },
+    {
+      "id": 31,
+      "rotation_radians": 4.009630559569833e-07,
+      "x": -4.5001329150531655,
+      "y": -0.8659432469098659
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/hexinsqu_021_5d369a2740fde606.json b/data/solutions/generated/hexinsqu_021_5d369a2740fde606.json
new file mode 100644
index 0000000000000000000000000000000000000000..a471fd9873bb3743220cca9dbe8af7544b82539f
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
+      "rotation_radians": 2.3751101279227043,
+      "x": -0.16970643692594198,
+      "y": 2.22447398681181
+    },
+    {
+      "id": 2,
+      "rotation_radians": 2.375095668288798,
+      "x": 1.5398107008920296,
+      "y": 1.921573588348337
+    },
+    {
+      "id": 3,
+      "rotation_radians": 1.3279190677744106,
+      "x": -0.6152771770127541,
+      "y": 3.8987113542722494
+    },
+    {
+      "id": 4,
+      "rotation_radians": 5.516422105218625,
+      "x": 0.28194249393639303,
+      "y": 0.5518704983668915
+    },
+    {
+      "id": 5,
+      "rotation_radians": 2.3782796717684316,
+      "x": 0.8713037008886259,
+      "y": -1.0823236922604575
+    },
+    {
+      "id": 6,
+      "rotation_radians": 1.3276837993039377,
+      "x": 1.9914183093669462,
+      "y": 0.2489653186679852
+    },
+    {
+      "id": 7,
+      "rotation_radians": 3.4426452665568976,
+      "x": -4.542825664827087,
+      "y": -0.03636405381888811
+    },
+    {
+      "id": 8,
+      "rotation_radians": 3.927596585612022,
+      "x": -1.2502601833098461,
+      "y": -3.263563754526016
+    },
+    {
+      "id": 9,
+      "rotation_radians": 1.832958105760932,
+      "x": 0.09822484141338368,
+      "y": -4.601222530546293
+    },
+    {
+      "id": 10,
+      "rotation_radians": 4.444613179025525,
+      "x": -2.7979917665753042,
+      "y": -0.2818358353803969
+    },
+    {
+      "id": 11,
+      "rotation_radians": 4.444608402128186,
+      "x": -2.662321375619116,
+      "y": -2.036723311865229
+    },
+    {
+      "id": 12,
+      "rotation_radians": 1.3247573938320223,
+      "x": -1.8458574452791054,
+      "y": 2.6679839302818418
+    },
+    {
+      "id": 13,
+      "rotation_radians": 2.8803961108739036,
+      "x": 2.1467066863296718,
+      "y": -2.5561414256674446
+    },
+    {
+      "id": 14,
+      "rotation_radians": 5.540264090352187,
+      "x": 3.3689129620674496,
+      "y": -1.1461679219909906
+    },
+    {
+      "id": 15,
+      "rotation_radians": 6.02199172479513,
+      "x": 0.4458108231377275,
+      "y": -2.9008721133886057
+    },
+    {
+      "id": 16,
+      "rotation_radians": 5.673346101648995,
+      "x": -1.0495448702268826,
+      "y": -0.97020104704018
+    },
+    {
+      "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
+    },
+    {
+      "id": 20,
+      "rotation_radians": 3.4443460849655927,
+      "x": 4.594158462176817,
+      "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/"
+}
diff --git a/data/solutions/generated/hexinsqu_022_2f0b0033f0c66708.json b/data/solutions/generated/hexinsqu_022_2f0b0033f0c66708.json
new file mode 100644
index 0000000000000000000000000000000000000000..c19116f5812589e5fa7be968b1434d47c059aa71
--- /dev/null
+++ b/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,
+      "rotation_radians": 0.7977010015728918,
+      "x": -2.760500702697093,
+      "y": -1.8897809696803076
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.8019114174642531,
+      "x": -1.5341594848070275,
+      "y": -3.11615456575505
+    },
+    {
+      "id": 3,
+      "rotation_radians": 1.308983373129213,
+      "x": -0.2065246914401924,
+      "y": -4.633125847806705
+    },
+    {
+      "id": 4,
+      "rotation_radians": 1.8325837113524788,
+      "x": 1.3195003643956449,
+      "y": -3.5201512107782444
+    },
+    {
+      "id": 5,
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+      "x": 3.405104303084936,
+      "y": -1.4272608509577445
+    },
+    {
+      "id": 6,
+      "rotation_radians": 6.033690002439361,
+      "x": -3.985371399736603,
+      "y": -0.6649128869000597
+    },
+    {
+      "id": 7,
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+      "x": -1.1743758480028128,
+      "y": -1.1134821303094966
+    },
+    {
+      "id": 8,
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+      "x": 0.05186917788639797,
+      "y": -2.336786034085349
+    },
+    {
+      "id": 9,
+      "rotation_radians": 3.915930434147693,
+      "x": 1.7192722238064366,
+      "y": -1.8284262763074883
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.6315458078148712,
+      "x": 4.706038888687644,
+      "y": -0.03971830478073898
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.7977014689051477,
+      "x": -3.764737144860528,
+      "y": 1.0663007939846807
+    },
+    {
+      "id": 12,
+      "rotation_radians": 2.356132346051416,
+      "x": -1.9541707615023542,
+      "y": 0.6094880901440287
+    },
+    {
+      "id": 13,
+      "rotation_radians": 1.785789454404328,
+      "x": 0.4825043632790665,
+      "y": -0.515227772819107
+    },
+    {
+      "id": 14,
+      "rotation_radians": 4.927379468106776,
+      "x": 2.173230331426509,
+      "y": -0.13886264373359675
+    },
+    {
+      "id": 15,
+      "rotation_radians": 2.66219544476157,
+      "x": 3.455043903611295,
+      "y": 1.2285030759467375
+    },
+    {
+      "id": 16,
+      "rotation_radians": 2.356136348267536,
+      "x": -2.3548537079657006,
+      "y": 2.2953179477700094
+    },
+    {
+      "id": 17,
+      "rotation_radians": 2.3501761576648503,
+      "x": -0.6815180880430817,
+      "y": 1.7948354285893688
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.23767755862958886,
+      "x": 0.9999535717812034,
+      "y": 1.3324183856038594
+    },
+    {
+      "id": 19,
+      "rotation_radians": 5.49772929906356,
+      "x": 0.5353872833247472,
+      "y": 3.043558517056281
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.26174382834459464,
+      "x": 2.216036909919325,
+      "y": 2.6235846136622643
+    },
+    {
+      "id": 21,
+      "rotation_radians": 6.5449207377591465,
+      "x": -1.1300958607014044,
+      "y": 3.520100304752904
+    },
+    {
+      "id": 22,
+      "rotation_radians": 3.403309537170139,
+      "x": 0.10527038026378016,
+      "y": 4.734307604755597
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/hexinsqu_023_31cc17034bd25d7b.json b/data/solutions/generated/hexinsqu_023_31cc17034bd25d7b.json
new file mode 100644
index 0000000000000000000000000000000000000000..1f8db7015008b6923af50277ee4358737aad3bf8
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
+      "rotation_radians": 1.3089958892197966,
+      "x": 2.3324225660155875,
+      "y": -2.3324292470230468
+    },
+    {
+      "id": 2,
+      "rotation_radians": 4.450573503999844,
+      "x": -1.3541111854930894,
+      "y": -1.0954122458343778
+    },
+    {
+      "id": 3,
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+      "x": 4.804317121722751,
+      "y": 0.0947465349690251
+    },
+    {
+      "id": 4,
+      "rotation_radians": 1.3197591545926493,
+      "x": -1.9034694153889438,
+      "y": 0.5800446690076764
+    },
+    {
+      "id": 5,
+      "rotation_radians": 0.28638043078872377,
+      "x": 0.8158392910723246,
+      "y": 2.8972131900422435
+    },
+    {
+      "id": 6,
+      "rotation_radians": 5.497764719461516,
+      "x": 2.529563165937119,
+      "y": 2.3694938332808433
+    },
+    {
+      "id": 7,
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+      "x": 0.36596446786474357,
+      "y": -1.7829076664879528
+    },
+    {
+      "id": 8,
+      "rotation_radians": 2.266003237764056,
+      "x": 1.822300636954561,
+      "y": -0.6329234922837796
+    },
+    {
+      "id": 9,
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+      "x": -0.8074794578366769,
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+      "x": 3.5794741034677684,
+      "y": -1.1299416227913983
+    },
+    {
+      "id": 11,
+      "rotation_radians": 2.3158234798411947,
+      "x": -3.1430134649087047,
+      "y": -0.6756237879599019
+    },
+    {
+      "id": 12,
+      "rotation_radians": 1.3089938067122178,
+      "x": 1.0577808341541846,
+      "y": -3.507310534549994
+    },
+    {
+      "id": 13,
+      "rotation_radians": 4.480216295352059,
+      "x": -0.6057166627395408,
+      "y": 1.846571775714521
+    },
+    {
+      "id": 14,
+      "rotation_radians": 5.4977667774325045,
+      "x": -2.3340066002845132,
+      "y": 2.3340121843712116
+    },
+    {
+      "id": 15,
+      "rotation_radians": 4.450562802683287,
+      "x": -3.5717846015052914,
+      "y": 1.1222560113083253
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.3406725194813578,
+      "x": 3.078327637555984,
+      "y": 0.6437498853677918
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.308987939532052,
+      "x": -2.514979745057465,
+      "y": -2.3840801021032765
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.26177518746955575,
+      "x": 1.299915124430481,
+      "y": 1.1496209110169906
+    },
+    {
+      "id": 19,
+      "rotation_radians": 4.450561474019668,
+      "x": -0.05279515627685617,
+      "y": 0.05280395901232762
+    },
+    {
+      "id": 20,
+      "rotation_radians": 5.49776525809453,
+      "x": -1.1247940160755785,
+      "y": 3.574334667928198
+    },
+    {
+      "id": 21,
+      "rotation_radians": 3.403380916286967,
+      "x": 0.24192493888512073,
+      "y": 4.657141176573033
+    },
+    {
+      "id": 22,
+      "rotation_radians": 4.4505878021011505,
+      "x": -0.09663726729610306,
+      "y": -4.80242259844813
+    },
+    {
+      "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/"
+}
diff --git a/data/solutions/generated/hexinsqu_024_941fbce4f50492c6.json b/data/solutions/generated/hexinsqu_024_941fbce4f50492c6.json
new file mode 100644
index 0000000000000000000000000000000000000000..571d4518611d7090fe8370f6e2a3845460ed31f6
--- /dev/null
+++ b/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,
+      "x": -0.0629985429975633,
+      "y": 4.8742560475230885
+    },
+    {
+      "id": 2,
+      "rotation_radians": 2.7734857616067785,
+      "x": -3.5308022267417494,
+      "y": 1.396251009472839
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+    {
+      "id": 3,
+      "rotation_radians": 4.868940163160825,
+      "x": 0.2678827411833474,
+      "y": 0.27457309471435026
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.6961635602740237,
+      "x": -2.1917356596280153,
+      "y": 2.7452657254883746
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+    {
+      "id": 5,
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+      "x": 2.403338994053616,
+      "y": 2.40934099311739
+    },
+    {
+      "id": 6,
+      "rotation_radians": 4.883451328404109,
+      "x": 1.1690656629713196,
+      "y": 3.642451408081969
+    },
+    {
+      "id": 7,
+      "rotation_radians": 5.921948788903831,
+      "x": 3.634270998861003,
+      "y": 1.1783822129953256
+    },
+    {
+      "id": 8,
+      "rotation_radians": 3.826047517962225,
+      "x": 2.741468685031521,
+      "y": -2.188314483145284
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+    {
+      "id": 9,
+      "rotation_radians": 2.7745464172650336,
+      "x": 1.5002987690660428,
+      "y": -0.9563545849974936
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+    {
+      "id": 10,
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+      "x": 4.878662139050818,
+      "y": -0.06943697349790708
+    },
+    {
+      "id": 11,
+      "rotation_radians": 1.725637943672936,
+      "x": -2.406591827506523,
+      "y": -2.407177870822691
+    },
+    {
+      "id": 12,
+      "rotation_radians": 5.918862579381371,
+      "x": 0.05807186948085872,
+      "y": -4.871164706561672
+    },
+    {
+      "id": 13,
+      "rotation_radians": -0.3612369292941675,
+      "x": 3.184181509755131,
+      "y": -0.5031718089130688
+    },
+    {
+      "id": 14,
+      "rotation_radians": 1.726283172687747,
+      "x": 1.3976820302852142,
+      "y": -3.5293578717958716
+    },
+    {
+      "id": 15,
+      "rotation_radians": 5.921422955630515,
+      "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/"
+}
diff --git a/data/solutions/generated/hexinsqu_025_d89d09725d796421.json b/data/solutions/generated/hexinsqu_025_d89d09725d796421.json
new file mode 100644
index 0000000000000000000000000000000000000000..bcfb12a791676935c98a1915a05f2e7e518cb8db
--- /dev/null
+++ b/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
+    },
+    {
+      "id": 2,
+      "rotation_radians": 2.356195747317991,
+      "x": 0.09474308243049272,
+      "y": 5.1179851715760405
+    },
+    {
+      "id": 3,
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+      "x": -0.20936437440957217,
+      "y": 2.346122755522066
+    },
+    {
+      "id": 4,
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+      "x": -3.727579475899307,
+      "y": 1.4116075138742592
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+    {
+      "id": 5,
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+      "x": 3.7779094468578007,
+      "y": 1.2385247094279157
+    },
+    {
+      "id": 6,
+      "rotation_radians": 3.291585808941434,
+      "x": 3.730076034909709,
+      "y": -1.3020085106116608
+    },
+    {
+      "id": 7,
+      "rotation_radians": 2.356178998269235,
+      "x": 2.562170310339731,
+      "y": 2.650571523375503
+    },
+    {
+      "id": 8,
+      "rotation_radians": -0.7853966367687021,
+      "x": -2.354519090660921,
+      "y": 2.6681118862085915
+    },
+    {
+      "id": 9,
+      "rotation_radians": 2.356177854833813,
+      "x": -3.8742303889724163,
+      "y": -1.3385032538619157
+    },
+    {
+      "id": 10,
+      "rotation_radians": 4.450573479518846,
+      "x": 0.11572873646049141,
+      "y": 0.1979206358387157
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.2607071230754677,
+      "x": -1.4309396185424443,
+      "y": 1.1181177443412673
+    },
+    {
+      "id": 12,
+      "rotation_radians": 1.3089804016181483,
+      "x": -2.327427965186894,
+      "y": -2.2580297279169677
+    },
+    {
+      "id": 13,
+      "rotation_radians": 1.3089977697492767,
+      "x": -1.1300430100973524,
+      "y": 3.8932067070204317
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.26178370637788245,
+      "x": -1.1030341751415824,
+      "y": -1.0328698985981448
+    },
+    {
+      "id": 15,
+      "rotation_radians": 3.402200373941947,
+      "x": 1.0155388843583855,
+      "y": 3.5708749996276556
+    },
+    {
+      "id": 16,
+      "rotation_radians": 2.350758245764546,
+      "x": -0.17789509616946556,
+      "y": -2.5814533134396087
+    },
+    {
+      "id": 17,
+      "rotation_radians": 3.204679592964309,
+      "x": 1.2395338176412294,
+      "y": -3.811360266472643
+    },
+    {
+      "id": 18,
+      "rotation_radians": 3.854037047684209,
+      "x": -5.095735377399876,
+      "y": 0.06872011991407326
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.0953057348520077,
+      "x": -0.013360919726782314,
+      "y": -5.068793523909988
+    },
+    {
+      "id": 20,
+      "rotation_radians": 5.461157007395922,
+      "x": 2.2913639071748957,
+      "y": -0.13000806385609504
+    },
+    {
+      "id": 21,
+      "rotation_radians": 4.72820445636781,
+      "x": 5.071608730417592,
+      "y": -0.005786589201378384
+    },
+    {
+      "id": 22,
+      "rotation_radians": 5.487854705500991,
+      "x": 1.0448972845602236,
+      "y": -1.3514292782458313
+    },
+    {
+      "id": 23,
+      "rotation_radians": 4.353065408072961,
+      "x": 2.4934455495676695,
+      "y": -2.5364649288629395
+    },
+    {
+      "id": 24,
+      "rotation_radians": 2.3561782330096954,
+      "x": 1.337285461650252,
+      "y": 1.4259169021236733
+    },
+    {
+      "id": 25,
+      "rotation_radians": 6.544968154660768,
+      "x": -1.4078896442279345,
+      "y": -3.8048464160637527
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/hexintri_021_6cf726ac83ba7d7f.json b/data/solutions/generated/hexintri_021_6cf726ac83ba7d7f.json
new file mode 100644
index 0000000000000000000000000000000000000000..9188a7bf2b7115f7f69c190c8bc1d1f913d986f4
--- /dev/null
+++ b/data/solutions/generated/hexintri_021_6cf726ac83ba7d7f.json
@@ -0,0 +1,188 @@
+{
+  "case": "hexintri@21",
+  "container": {
+    "circumradius": 7.00016054016223,
+    "orientation_radians": 0.0,
+    "side_length": 12.124633716699778,
+    "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": {
+    "circumradius": 1.0000000000000002,
+    "side_length": 1.0,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "hexintri@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": [
+    {
+      "id": 1,
+      "rotation_radians": -0.0030398564401798852,
+      "x": 2.0000686853718537,
+      "y": -1.7320926736998798
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.45447806536461716,
+      "x": -2.5910366057857788,
+      "y": 4.493984313802931
+    },
+    {
+      "id": 3,
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+    {
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+      "y": -2.5981814587208234
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.044157583753369,
+      "x": 0.5000214093550591,
+      "y": -0.8660433592915127
+    },
+    {
+      "id": 18,
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+      "x": 0.5000098322870491,
+      "y": -2.5981571048412975
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+    {
+      "id": 19,
+      "rotation_radians": 1.0441922001401638,
+      "x": -1.0000322845635021,
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+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.49051181746238914,
+      "x": -2.6173928570438845,
+      "y": -4.531947867109468
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.0441598911509304,
+      "x": -1.0000254706526575,
+      "y": 7.949627308408943e-06
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/octinoct_021_92c4bcf9428983c2.json b/data/solutions/generated/octinoct_021_92c4bcf9428983c2.json
new file mode 100644
index 0000000000000000000000000000000000000000..46873d2434d3e1f55b52f1ba93327d15da8acd82
--- /dev/null
+++ b/data/solutions/generated/octinoct_021_92c4bcf9428983c2.json
@@ -0,0 +1,188 @@
+{
+  "case": "octinoct@21",
+  "container": {
+    "circumradius": 6.790383586607595,
+    "orientation_radians": 0.0,
+    "side_length": 5.1971345959971265,
+    "sides": 8,
+    "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": {
+    "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@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": [
+    {
+      "id": 1,
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+      "x": 0.0026959501419075702,
+      "y": 5.482681170215482
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+    {
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+      "y": -1.6387940990684917
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.0014952882036121426,
+      "x": -2.7641750739082784,
+      "y": 0.2565345411089217
+    },
+    {
+      "id": 18,
+      "rotation_radians": 7.992742901443847e-06,
+      "x": -5.142131249244154,
+      "y": 0.8248616467825739
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.9157130758664028e-05,
+      "x": 4.558404614219804,
+      "y": 2.2340753608649204
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.13097144841992128,
+      "x": 2.3091562449076544,
+      "y": 1.2118594744507065
+    },
+    {
+      "id": 21,
+      "rotation_radians": 6.978409263442952e-06,
+      "x": -2.228580382872541,
+      "y": 4.560682323177018
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/octinoct_022_b8f2befaa2d4a75e.json b/data/solutions/generated/octinoct_022_b8f2befaa2d4a75e.json
new file mode 100644
index 0000000000000000000000000000000000000000..42fa71379cdc2a78982598463bca522c3ef155f4
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
+      "rotation_radians": 5.4977943867584225,
+      "x": 5.200854348883957,
+      "y": 1.1905293703273452
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+    {
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+      "x": 2.152117723823794,
+      "y": -2.241819258770687
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+      "x": 4.194905174048309,
+      "y": -3.619154859601694
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+      "x": 3.076427596250851,
+      "y": -0.010395834460669063
+    },
+    {
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+      "x": -2.4012505660395362,
+      "y": -1.4281623844355025
+    },
+    {
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+      "x": -2.595683677261443,
+      "y": -4.613829405044768
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.7853940669025994,
+      "x": 5.118794087778671,
+      "y": -1.3886633723226485
+    },
+    {
+      "id": 14,
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+      "x": 0.13347837127295858,
+      "y": -0.818133838139317
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+    {
+      "id": 15,
+      "rotation_radians": 2.3504146666070516,
+      "x": -0.26113347446748075,
+      "y": 1.6268837888037138
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.7828557918264474,
+      "x": -2.6396252338058512,
+      "y": 1.0618517376610774
+    },
+    {
+      "id": 17,
+      "rotation_radians": 4.712394285123516,
+      "x": -1.5432080427103378,
+      "y": 3.712108134778865
+    },
+    {
+      "id": 18,
+      "rotation_radians": 4.71237614251748,
+      "x": -4.95310980551691,
+      "y": 1.7886686419043951
+    },
+    {
+      "id": 19,
+      "rotation_radians": 3.9269952573764697,
+      "x": -0.009564622931623431,
+      "y": 5.6900394842816
+    },
+    {
+      "id": 20,
+      "rotation_radians": 5.492020247759835,
+      "x": 2.1109738309129438,
+      "y": 2.203343066983049
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.03230783452179647,
+      "x": -0.5721805183486408,
+      "y": -3.148800203105373
+    },
+    {
+      "id": 22,
+      "rotation_radians": -1.2890708267210215e-05,
+      "x": -0.20765600112515012,
+      "y": -5.608000386692329
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/octinoct_023_d6528e8801e36ce0.json b/data/solutions/generated/octinoct_023_d6528e8801e36ce0.json
new file mode 100644
index 0000000000000000000000000000000000000000..c9faec6287ac5c307687f5180edc2d2905fcce52
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
+      "rotation_radians": 3.9270181483970337,
+      "x": -4.079363476429201,
+      "y": -4.075703341115646
+    },
+    {
+      "id": 2,
+      "rotation_radians": 1.5708233945626737,
+      "x": -1.8493724329491528,
+      "y": -5.0008110780239
+    },
+    {
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+      "x": 0.5386056659366816,
+      "y": -5.54447594382163
+    },
+    {
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+      "x": 2.7690937103494764,
+      "y": -4.620559636475766
+    },
+    {
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+      "y": 3.1543811501501597
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+    {
+      "id": 21,
+      "rotation_radians": 5.4978041507125495,
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+    {
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+    {
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+      "x": 1.8493028780205083,
+      "y": 5.000626067025402
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/octinoct_024_a34ac6a3c52f70df.json b/data/solutions/generated/octinoct_024_a34ac6a3c52f70df.json
new file mode 100644
index 0000000000000000000000000000000000000000..4c6de10229ec975e194454ef08861ea13e14f56c
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
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+    {
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+    {
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+      "y": 1.1956544456687483
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.7881058458627486,
+      "x": -5.286857681182137,
+      "y": 1.5995536133065837
+    },
+    {
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+      "rotation_radians": 0.7853668954293739,
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+      "y": 3.849869327132821
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.7386088444183039,
+      "x": 0.46648386380864454,
+      "y": 3.5293196358389443
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.7853957059929876,
+      "x": 4.555075737923532,
+      "y": 3.3697662269535447
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/octinoct_025_113492960b7e7dce.json b/data/solutions/generated/octinoct_025_113492960b7e7dce.json
new file mode 100644
index 0000000000000000000000000000000000000000..1b158039788b38bb0ccece5584285e35a40fd68a
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
+      "rotation_radians": 0.5693215399299264,
+      "x": -2.0570783014243563,
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+    {
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+    },
+    {
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+      "x": 3.422073649224173,
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+    {
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+      "y": -6.0842049925837385
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.0014567238837104467,
+      "x": -4.4115857695793,
+      "y": -4.043460118512249
+    },
+    {
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+      "x": 5.629752042885831,
+      "y": -0.9747380362871849
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.7853323216964855,
+      "x": -0.009496795473022629,
+      "y": 6.083718094033468
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.638954685861762e-05,
+      "x": 4.731047832584925,
+      "y": -3.2751755928211477
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.08172653490960273,
+      "x": -4.402638274050974,
+      "y": 3.9717840870423635
+    },
+    {
+      "id": 21,
+      "rotation_radians": -1.839424057805183e-05,
+      "x": 0.4198849394069394,
+      "y": 3.6484184544221208
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.2096433545864106,
+      "x": -1.8912666776527096,
+      "y": -2.688119502905674
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.0688242073084812,
+      "x": -2.268020663642456,
+      "y": 5.114073750277366
+    },
+    {
+      "id": 24,
+      "rotation_radians": 2.3329973843458612e-05,
+      "x": 5.449687591278974,
+      "y": 1.5401658308235053
+    },
+    {
+      "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/"
+}
diff --git a/data/solutions/generated/octinoct_026_581188c4895e4037.json b/data/solutions/generated/octinoct_026_581188c4895e4037.json
new file mode 100644
index 0000000000000000000000000000000000000000..cdca4dedf67a3e0e0d6a812e1fdbd634b2fedbf4
--- /dev/null
+++ b/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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+      "y": 0.7287471525373916
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+    {
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+    {
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+      "x": -1.5780902786558744,
+      "y": -0.375386867720952
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+    {
+      "id": 23,
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+    },
+    {
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+      "rotation_radians": 0.7853947842715419,
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+    },
+    {
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+      "x": -2.189454752619741,
+      "y": -5.290765587537986
+    },
+    {
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+      "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/"
+}
diff --git a/data/solutions/generated/octinoct_027_25c7f85bc0b15209.json b/data/solutions/generated/octinoct_027_25c7f85bc0b15209.json
new file mode 100644
index 0000000000000000000000000000000000000000..3d46d67663fab4bc15614558076f1977d0f6eccd
--- /dev/null
+++ b/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,
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+      "y": -6.249407967499408
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+      "x": -2.163382112402952,
+      "y": -5.392634214861737
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+    {
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+      "x": 2.5378258433761354,
+      "y": 2.7488513132569423
+    },
+    {
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+      "rotation_radians": 4.720929148512929,
+      "x": -2.4542659081461036,
+      "y": -2.8953857484067966
+    },
+    {
+      "id": 19,
+      "rotation_radians": 6.283187276116029,
+      "x": -5.3532674174145845,
+      "y": -2.232770245518803
+    },
+    {
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+      "x": -2.196608111460055,
+      "y": 5.362955613503642
+    },
+    {
+      "id": 21,
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+      "x": 6.192385520359506,
+      "y": -0.23262710822111485
+    },
+    {
+      "id": 22,
+      "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/"
+}
diff --git a/data/solutions/generated/octinoct_028_f8d9c8a9f9a38d45.json b/data/solutions/generated/octinoct_028_f8d9c8a9f9a38d45.json
new file mode 100644
index 0000000000000000000000000000000000000000..721ae7a399b4f521f43878beb319adf3097f615c
--- /dev/null
+++ b/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",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "id": 1,
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+    {
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+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.5707946774360875,
+      "x": -6.308730467243412,
+      "y": 2.569595976860316e-06
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/octinoct_029_30789c6bb8fd99b7.json b/data/solutions/generated/octinoct_029_30789c6bb8fd99b7.json
new file mode 100644
index 0000000000000000000000000000000000000000..f671d257c5c4b707e132abed8bbb84c9a8cf51f6
--- /dev/null
+++ b/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,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "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": {
+    "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@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"
+    },
+    "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": [
+    {
+      "id": 1,
+      "rotation_radians": 0.7839586495971684,
+      "x": -2.5871120064416018,
+      "y": -5.536158591683675
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+    {
+      "id": 2,
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+      "x": 3.155452268601462,
+      "y": 2.68834614881321
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+    {
+      "id": 3,
+      "rotation_radians": -0.0016474603951101175,
+      "x": -2.7040270776523063,
+      "y": 3.1016012493263725
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+    {
+      "id": 4,
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+    {
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+      "x": -5.739626081208593,
+      "y": -2.0976982877937935
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+    {
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+      "x": 5.692462644906289,
+      "y": -2.21156535603614
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+    {
+      "id": 7,
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+    {
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+      "rotation_radians": 6.673349538625338e-06,
+      "x": 4.768536736867518,
+      "y": -4.442088396525415
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+    {
+      "id": 9,
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+      "x": 2.605624941511477,
+      "y": -5.529235729832928
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+    {
+      "id": 10,
+      "rotation_radians": -0.0017031268410607455,
+      "x": -0.4541292888423293,
+      "y": -1.1937002517127346
+    },
+    {
+      "id": 11,
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+      "x": 3.163746247131458,
+      "y": -2.226486011793599
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+    {
+      "id": 12,
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+    },
+    {
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+      "x": -3.268423423551006,
+      "y": -1.7466366215358107
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+    {
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+      "x": -5.594405912567706,
+      "y": 2.4483052827116283
+    },
+    {
+      "id": 16,
+      "rotation_radians": 7.259773801631304e-06,
+      "x": 6.597411195567688,
+      "y": 0.026812147941377738
+    },
+    {
+      "id": 17,
+      "rotation_radians": -8.584782412412758e-06,
+      "x": 5.63228122689041,
+      "y": 2.3568496053714987
+    },
+    {
+      "id": 18,
+      "rotation_radians": 4.807551762723889e-07,
+      "x": 0.03089077330613029,
+      "y": 6.5957191819521706
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.9439213108691074,
+      "x": -0.08086250925463227,
+      "y": -6.021240030378052
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.001703082415839968,
+      "x": 1.7361125717418449,
+      "y": -0.17208461612653775
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.7853953675047748,
+      "x": -2.429723941467776,
+      "y": 5.602091921395527
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.7639094493245863,
+      "x": -4.758346731116102,
+      "y": -4.430563250811375
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.7836901679661165,
+      "x": 4.574209814153218,
+      "y": 4.712903894525254
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.7837010482216619,
+      "x": -1.3946143270687228,
+      "y": -3.417311625359392
+    },
+    {
+      "id": 25,
+      "rotation_radians": -0.0017033604387581532,
+      "x": 0.8049735329434445,
+      "y": 2.0554563982703047
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.5622816904271657,
+      "x": -3.842677708622351,
+      "y": 0.604458342794656
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.7930902521230568,
+      "x": -6.5236555849265985,
+      "y": 0.19490108312809984
+    },
+    {
+      "id": 28,
+      "rotation_radians": -2.983905443773624e-06,
+      "x": -0.4114664340756128,
+      "y": 4.165726686348186
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.8978844187165769,
+      "x": 2.0741034354781682,
+      "y": 4.95850629054105
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/octinoct_030_1a16dc8a4d741008.json b/data/solutions/generated/octinoct_030_1a16dc8a4d741008.json
new file mode 100644
index 0000000000000000000000000000000000000000..28abd55e15e234c8ede85c3a9d442cebe14f806e
--- /dev/null
+++ b/data/solutions/generated/octinoct_030_1a16dc8a4d741008.json
@@ -0,0 +1,242 @@
+{
+  "case": "octinoct@30",
+  "container": {
+    "circumradius": 8.04162623825285,
+    "orientation_radians": 0.0,
+    "side_length": 6.154794261303532,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "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": {
+    "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@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"
+    },
+    "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": [
+    {
+      "id": 1,
+      "rotation_radians": 0.7853985669273894,
+      "x": -4.460853529556884,
+      "y": -4.887285530319528
+    },
+    {
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+    {
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+      "x": 0.00020618510854237274,
+      "y": -6.734945110374791
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+    {
+      "id": 4,
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+      "x": 0.8163691869300846,
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+    {
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+      "x": 3.0022237528214784,
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+    {
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+      "x": 5.037903725476704,
+      "y": -4.097222196205068
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+    {
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+    {
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+      "y": -1.769381117374732
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+    {
+      "id": 9,
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+      "y": -1.9724622772304243
+    },
+    {
+      "id": 11,
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+      "x": 2.8156137476943788,
+      "y": -2.958832667570038
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+    {
+      "id": 12,
+      "rotation_radians": -0.7853817880747395,
+      "x": 5.961748265107965,
+      "y": -1.8666899360110738
+    },
+    {
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+      "x": -6.521888332162401,
+      "y": -0.5145812510916653
+    },
+    {
+      "id": 14,
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+      "y": 0.6687071775351029
+    },
+    {
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+      "x": -1.3898170204765354,
+      "y": -0.28495679762075954
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.013827605036687557,
+      "x": 1.3838630790356377,
+      "y": 0.2836089709276332
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.7741340224768467,
+      "x": 3.804735143361905,
+      "y": -0.7559987412781047
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.7853920758039332,
+      "x": 6.521926000021451,
+      "y": 0.5144650504667468
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.785390939290023,
+      "x": -5.946833135651572,
+      "y": 1.8604090238128743
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.08365649714303072,
+      "x": -2.8210264976902355,
+      "y": 2.8848880437574733
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.8050529313993353,
+      "x": -0.5144365311461893,
+      "y": 1.975301061663274
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.8794636074514369,
+      "x": 1.5062396406342393,
+      "y": 3.462983921029856
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.7854141245152652,
+      "x": 3.4191050294297676,
+      "y": 1.696614781172084
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.7853832283949629,
+      "x": 5.598040121807019,
+      "y": 2.744966519119988
+    },
+    {
+      "id": 25,
+      "rotation_radians": 3.330350278091846e-06,
+      "x": -5.037946228772615,
+      "y": 4.097122598291171
+    },
+    {
+      "id": 26,
+      "rotation_radians": -1.0526171557492808e-05,
+      "x": -3.0023045122063396,
+      "y": 5.491439084918123
+    },
+    {
+      "id": 27,
+      "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/"
+}
diff --git a/data/solutions/generated/penincir_021_b713bb4909b828e8.json b/data/solutions/generated/penincir_021_b713bb4909b828e8.json
new file mode 100644
index 0000000000000000000000000000000000000000..9479ecd0899b3220585fcde1e97fe87ec28d20ac
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
+      "rotation_radians": -0.024134982253120198,
+      "x": -2.5052356478600597,
+      "y": -1.7899875569344428
+    },
+    {
+      "id": 2,
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+      "x": -1.4054616311501196,
+      "y": -2.869011179991396
+    },
+    {
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+      "x": -0.010184043443905824,
+      "y": -2.594226098580287
+    },
+    {
+      "id": 4,
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+      "x": 1.350655422183028,
+      "y": -2.8042623700222182
+    },
+    {
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+      "x": 2.4558447640150503,
+      "y": -1.8795981370133357
+    },
+    {
+      "id": 6,
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+      "x": -3.0737291872185684,
+      "y": -0.38062057366407054
+    },
+    {
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+      "y": -1.2725495314445174
+    },
+    {
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+      "x": 1.6246499029168366,
+      "y": -0.5624593586661817
+    },
+    {
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+      "x": 3.020663468211921,
+      "y": -0.6000063252809855
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+    {
+      "id": 11,
+      "rotation_radians": -0.8977529832935082,
+      "x": -2.9115646675167146,
+      "y": 1.0075756617843024
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+    {
+      "id": 12,
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+      "x": -1.7371970101808605,
+      "y": -0.026610739305269037
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+    {
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+      "y": 0.22167079812226745
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+    {
+      "id": 14,
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+    {
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+      "x": 2.989299090521316,
+      "y": 0.7848181709730626
+    },
+    {
+      "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
+    },
+    {
+      "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/"
+}
diff --git a/data/solutions/generated/peninpen_021_1c71a8b98efbf1a2.json b/data/solutions/generated/peninpen_021_1c71a8b98efbf1a2.json
new file mode 100644
index 0000000000000000000000000000000000000000..037c625a3d1a7ca5f5eded5d6e498135e0d846c9
--- /dev/null
+++ b/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
+    },
+    {
+      "id": 2,
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+      "x": -1.2956626185036004,
+      "y": 2.5895085843890553
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+    {
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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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+    {
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+    {
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+    {
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+      "y": -2.062641297099786
+    },
+    {
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+    {
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+      "rotation_radians": 1.2638088185675576e-05,
+      "x": 1.0947583408442618,
+      "y": -3.36931972943828
+    },
+    {
+      "id": 16,
+      "rotation_radians": -3.0205189876895802e-05,
+      "x": -0.46507522498454335,
+      "y": -2.8613969604951817
+    },
+    {
+      "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,
+      "y": 0.4867050422936623
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.3745288243736087,
+      "x": 1.064695900254714,
+      "y": 0.9017223055855533
+    },
+    {
+      "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/"
+}
diff --git a/data/solutions/generated/peninpen_022_07e217f200bb677e.json b/data/solutions/generated/peninpen_022_07e217f200bb677e.json
new file mode 100644
index 0000000000000000000000000000000000000000..52e7e294da26c3a618be826f217961aabeecd376
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
+      "rotation_radians": 3.5656610694771376e-06,
+      "x": -2.937064016182957,
+      "y": -2.1264074111022766
+    },
+    {
+      "id": 2,
+      "rotation_radians": 6.661855145488751e-07,
+      "x": -1.4025845200932818,
+      "y": -2.6324856117295585
+    },
+    {
+      "id": 3,
+      "rotation_radians": -0.5732000090866805,
+      "x": 0.06814313577472773,
+      "y": -2.940898682985223
+    },
+    {
+      "id": 4,
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+      "x": 1.4476621900551523,
+      "y": -2.959224943246937
+    },
+    {
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+    {
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+      "x": -1.79876078029997,
+      "y": -1.2999281298292646
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+    {
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+      "x": 1.973952177704273,
+      "y": -0.38441170078998294
+    },
+    {
+      "id": 10,
+      "rotation_radians": 3.826856296429339e-07,
+      "x": 3.3508415092577146,
+      "y": -0.38479775143609507
+    },
+    {
+      "id": 11,
+      "rotation_radians": -0.028141450132241178,
+      "x": -2.9232701064214877,
+      "y": -0.5041867041543232
+    },
+    {
+      "id": 12,
+      "rotation_radians": -0.08953018803460663,
+      "x": -1.3096456636714913,
+      "y": 0.018193822649291008
+    },
+    {
+      "id": 13,
+      "rotation_radians": -0.12573762238656258,
+      "x": 0.31702962697481846,
+      "y": 0.11804475408528063
+    },
+    {
+      "id": 14,
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+      "x": 1.4713149852473846,
+      "y": 1.070122741232727
+    },
+    {
+      "id": 15,
+      "rotation_radians": -1.2544664665159269,
+      "x": 2.851033365522404,
+      "y": 1.0708915888273165
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.5626713206987076,
+      "x": -2.7764363311644593,
+      "y": 0.9719633673950818
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.5418635726325061,
+      "x": -1.2603573212771335,
+      "y": 1.4429191807943715
+    },
+    {
+      "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/"
+}
diff --git a/data/solutions/generated/peninpen_023_1da2b8cbe37457cd.json b/data/solutions/generated/peninpen_023_1da2b8cbe37457cd.json
new file mode 100644
index 0000000000000000000000000000000000000000..1b48f662928b7825f7de3fcfd76e1b7f20039c8a
--- /dev/null
+++ b/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": [
+    {
+      "id": 1,
+      "rotation_radians": 0.6050741474158858,
+      "x": -1.768246508466418,
+      "y": 1.4037773966656382
+    },
+    {
+      "id": 2,
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+      "x": -3.0103775498944687,
+      "y": -0.9291130646383552
+    },
+    {
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+      "x": 0.696438705719324,
+      "y": -2.1995987596364266
+    },
+    {
+      "id": 4,
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+      "x": 1.089615824424435,
+      "y": -3.519339950284296
+    },
+    {
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+      "x": 2.075951184457128,
+      "y": -2.2588066574199717
+    },
+    {
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+      "x": 3.447614420418823,
+      "y": 0.37627130233454237
+    },
+    {
+      "id": 7,
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+      "x": -2.9725612486391375,
+      "y": 0.6410689547466103
+    },
+    {
+      "id": 8,
+      "rotation_radians": -1.0558702568020267e-05,
+      "x": -2.8850703622635567,
+      "y": 2.2278663317871215
+    },
+    {
+      "id": 9,
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+      "id": 10,
+      "rotation_radians": 1.226225244817876,
+      "x": -1.3373837910549915,
+      "y": 2.7150991941472085
+    },
+    {
+      "id": 11,
+      "rotation_radians": 1.2368552323787623,
+      "x": 1.4948824722361305,
+      "y": 3.0472016338780366
+    },
+    {
+      "id": 12,
+      "rotation_radians": 1.2510669503710734,
+      "x": -1.257526698530509,
+      "y": 0.08829990355533612
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.8620362257097788,
+      "x": 2.839949292755376,
+      "y": -0.9756509764246234
+    },
+    {
+      "id": 14,
+      "rotation_radians": 1.4110213565331724,
+      "x": 1.3427250560249013,
+      "y": -0.8901579856302211
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+    {
+      "id": 15,
+      "rotation_radians": 0.7736365844869931,
+      "x": 0.5496579103435701,
+      "y": 0.2567401498750461
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.8584377270154175,
+      "x": 1.0591639117186842,
+      "y": 1.737547852578575
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.6306282197395175,
+      "x": -1.5543380896186356,
+      "y": -1.266400366613812
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.6283383185519722,
+      "x": 2.0711018482552412,
+      "y": 0.42674680822471883
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.2333149105012227,
+      "x": -0.39114758859004256,
+      "y": 1.4151840862478318
+    },
+    {
+      "id": 20,
+      "rotation_radians": 1.2566403322878883,
+      "x": 2.4486131598359777,
+      "y": 1.7513404490963358
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.2588480532935649,
+      "x": -0.17834193158644307,
+      "y": -1.0600192740406174
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.5978360104869263,
+      "x": 0.11251949970597934,
+      "y": 3.031445120956196
+    },
+    {
+      "id": 23,
+      "rotation_radians": 1.2566691189502817,
+      "x": -2.456356599256893,
+      "y": -2.367185343167629
+    }
+  ],
+  "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/"
+}
diff --git a/data/solutions/generated/peninpen_024_a420bfbc7a7f6c1e.json b/data/solutions/generated/peninpen_024_a420bfbc7a7f6c1e.json
new file mode 100644
index 0000000000000000000000000000000000000000..1c71a94a5ab5c27b1756e10630e64a6f76faa2eb
--- /dev/null
+++ b/data/solutions/generated/peninpen_024_a420bfbc7a7f6c1e.json
@@ -0,0 +1,206 @@
+{
+  "case": "peninpen@24",
+  "container": {
+    "circumradius": 4.70892309078544,
+    "orientation_radians": 0.0,
+    "side_length": 5.535671093886345,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "peninpen@24",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "5.49241+",
+    "metric_symbol": "s",
+    "metric_value": 5.49241,
+    "reference_text": "s = 5.49241+ | Found by Ignacio Vallejo in April 2026.",
+    "source_image": "24.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/peninpen/24.png",
+    "source_page": "https://erich-friedman.github.io/packing/peninpen/",
+    "title": "Pentagons in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.8506508083520399,
+    "side_length": 1.0,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "peninpen@24",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "5.49241+",
+      "metric_symbol": "s",
+      "metric_value": 5.49241,
+      "reference_text": "s = 5.49241+ | Found by Ignacio Vallejo in April 2026.",
+      "source_image": "24.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/peninpen/24.png",
+      "source_page": "https://erich-friedman.github.io/packing/peninpen/",
+      "title": "Pentagons in Pentagons"
+    },
+    "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": [
+    {
+      "id": 1,
+      "rotation_radians": 4.356591666173748,
+      "x": 1.891684404214394,
+      "y": -2.431629465365306
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+    {
+      "id": 2,
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+      "x": 1.921090074438924,
+      "y": 2.3918937279293058
+    },
+    {
+      "id": 3,
+      "rotation_radians": 1.2330573855474616,
+      "x": 2.7861757587467064,
+      "y": -1.2860620057410506
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+    {
+      "id": 4,
+      "rotation_radians": 5.079283394559978,
+      "x": 0.9589990405221211,
+      "y": 1.3928400801704983
+    },
+    {
+      "id": 5,
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+      "x": -2.9075337608794403,
+      "y": -2.3372959769915695
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+    {
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+      "x": 0.06158977448588036,
+      "y": -2.4624118572961935
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+    {
+      "id": 7,
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+      "x": 0.6747570286493002,
+      "y": 0.04399260819300963
+    },
+    {
+      "id": 8,
+      "rotation_radians": 5.02650338986574,
+      "x": 1.0931695885498316,
+      "y": 3.6371662651161545
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+    {
+      "id": 9,
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+      "x": -1.363408431841968,
+      "y": -2.834852832036906
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+    {
+      "id": 10,
+      "rotation_radians": 2.7903551182448774,
+      "x": 3.7216318201650105,
+      "y": 7.254688238148213e-06
+    },
+    {
+      "id": 11,
+      "rotation_radians": 2.4389608991600196,
+      "x": 2.872513276637967,
+      "y": 1.2209680964941958
+    },
+    {
+      "id": 12,
+      "rotation_radians": 7.363853680329552,
+      "x": -0.5036107915210942,
+      "y": 0.9319917712682565
+    },
+    {
+      "id": 13,
+      "rotation_radians": 2.5133017514282074,
+      "x": 1.0250783632065519,
+      "y": -3.61504043526393
+    },
+    {
+      "id": 14,
+      "rotation_radians": 3.7280700134969607,
+      "x": 1.000521684810539,
+      "y": -1.3398640944619424
+    },
+    {
+      "id": 15,
+      "rotation_radians": 1.81211683242972,
+      "x": 2.21126116900064,
+      "y": 0.00354831019002566
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.258668097150394,
+      "x": -2.944135997419651,
+      "y": 2.3243592941202915
+    },
+    {
+      "id": 17,
+      "rotation_radians": 3.6228620622164045,
+      "x": -3.055551286828431,
+      "y": -0.776959307956299
+    },
+    {
+      "id": 18,
+      "rotation_radians": 2.632744082850765,
+      "x": -1.7451646903682925,
+      "y": -0.026611521089879055
+    },
+    {
+      "id": 19,
+      "rotation_radians": 4.45117292242423,
+      "x": 0.027297571277765078,
+      "y": 2.5093773119077687
+    },
+    {
+      "id": 20,
+      "rotation_radians": 6.913529495429238,
+      "x": -1.8918616826516623,
+      "y": 1.4303768205058625
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.2685600809535555,
+      "x": -3.1154887732280603,
+      "y": 0.7626891768793539
+    },
+    {
+      "id": 22,
+      "rotation_radians": 2.701465210007258,
+      "x": -0.4473353968238972,
+      "y": -0.8548545760318886
+    },
+    {
+      "id": 23,
+      "rotation_radians": 5.6549214352932,
+      "x": -1.8063193864587443,
+      "y": -1.511259656261703
+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.3390704977412737,
+      "x": -1.4398486989181365,
+      "y": 2.7732964512474996
+    }
+  ],
+  "problem": "24 equal items for Pentagons in Pentagons",
+  "setup": "peninpen",
+  "source_image": "https://erich-friedman.github.io/packing/peninpen/24.png",
+  "source_page": "https://erich-friedman.github.io/packing/peninpen/"
+}
diff --git a/data/solutions/generated/peninpen_025_4e4dc42ba0fc7882.json b/data/solutions/generated/peninpen_025_4e4dc42ba0fc7882.json
new file mode 100644
index 0000000000000000000000000000000000000000..239b4041abf5870f06fcea8bde5cfede2efb9da9
--- /dev/null
+++ b/data/solutions/generated/peninpen_025_4e4dc42ba0fc7882.json
@@ -0,0 +1,212 @@
+{
+  "case": "peninpen@25",
+  "container": {
+    "circumradius": 4.770744705661928,
+    "orientation_radians": 0.0,
+    "side_length": 5.608346760880953,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "peninpen@25",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "5.58370+",
+    "metric_symbol": "s",
+    "metric_value": 5.5837,
+    "reference_text": "s = 5.58370+ | Found by Ignacio Vallejo in April 2026.",
+    "source_image": "25.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/peninpen/25.png",
+    "source_page": "https://erich-friedman.github.io/packing/peninpen/",
+    "title": "Pentagons in Pentagons"
+  },
+  "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@25",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "5.58370+",
+      "metric_symbol": "s",
+      "metric_value": 5.5837,
+      "reference_text": "s = 5.58370+ | Found by Ignacio Vallejo in April 2026.",
+      "source_image": "25.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/peninpen/25.png",
+      "source_page": "https://erich-friedman.github.io/packing/peninpen/",
+      "title": "Pentagons in Pentagons"
+    },
+    "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": [
+    {
+      "id": 1,
+      "rotation_radians": 3.769903689670823,
+      "x": 2.3221638417154975,
+      "y": -2.1993250799228177
+    },
+    {
+      "id": 2,
+      "rotation_radians": 1.812085215953143,
+      "x": 1.0631739367002893,
+      "y": 1.9360396133020412
+    },
+    {
+      "id": 3,
+      "rotation_radians": 1.25663756063932,
+      "x": 3.273478094068038,
+      "y": -0.8899535995749163
+    },
+    {
+      "id": 4,
+      "rotation_radians": 3.697027828006428,
+      "x": -0.33787161113685527,
+      "y": 1.5832652918035197
+    },
+    {
+      "id": 5,
+      "rotation_radians": 6.33642570037977,
+      "x": -0.5573305087638676,
+      "y": -1.3177589960076024
+    },
+    {
+      "id": 6,
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+      "x": 3.4273759451190275,
+      "y": 0.6781317563558839
+    },
+    {
+      "id": 7,
+      "rotation_radians": 3.769912024059506,
+      "x": -2.8508717401780688,
+      "y": 2.4083050315685233
+    },
+    {
+      "id": 8,
+      "rotation_radians": 1.2539699879211348,
+      "x": 2.473121066127644,
+      "y": 1.989296097135557
+    },
+    {
+      "id": 9,
+      "rotation_radians": -0.6268020977450363,
+      "x": -1.9502406481652623,
+      "y": -1.513705132063095
+    },
+    {
+      "id": 10,
+      "rotation_radians": 1.2550168356444609,
+      "x": 1.3693233160332623,
+      "y": -3.5074299993362454
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.628316565751241,
+      "x": 1.897045950658772,
+      "y": -0.8901894752202083
+    },
+    {
+      "id": 12,
+      "rotation_radians": 5.5827903974045725,
+      "x": -1.7195788120590005,
+      "y": 1.565441272525172
+    },
+    {
+      "id": 13,
+      "rotation_radians": 6.283190518130932,
+      "x": -3.1714084961059723,
+      "y": 0.8943655715274582
+    },
+    {
+      "id": 14,
+      "rotation_radians": 3.0437941109420112,
+      "x": 0.12357034209847603,
+      "y": 3.208202092545383
+    },
+    {
+      "id": 15,
+      "rotation_radians": 3.1389015981146997,
+      "x": 2.0496114861930335,
+      "y": 0.6796214014395858
+    },
+    {
+      "id": 16,
+      "rotation_radians": 2.5132627710609716,
+      "x": -3.0494015186561927,
+      "y": -2.34379993639658
+    },
+    {
+      "id": 17,
+      "rotation_radians": 3.7699023199721893,
+      "x": -3.1714117460334172,
+      "y": -0.765363561844659
+    },
+    {
+      "id": 18,
+      "rotation_radians": 3.7672323423070253,
+      "x": 0.8418516429340493,
+      "y": 0.0009858357827563617
+    },
+    {
+      "id": 19,
+      "rotation_radians": 3.7621690076326697,
+      "x": -1.5141976591404773,
+      "y": -2.824120238372827
+    },
+    {
+      "id": 20,
+      "rotation_radians": 5.652163218862014,
+      "x": -0.5341310367937605,
+      "y": 0.1639577394644999
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.8731337403924972,
+      "x": -0.04152209510640528,
+      "y": -3.1503440605870554
+    },
+    {
+      "id": 22,
+      "rotation_radians": 5.654868056830739,
+      "x": -2.0729933161930223,
+      "y": 0.06450192527248179
+    },
+    {
+      "id": 23,
+      "rotation_radians": 2.232826860277828,
+      "x": 0.8164950005604785,
+      "y": -1.938548093274357
+    },
+    {
+      "id": 24,
+      "rotation_radians": 4.953753200132949,
+      "x": -1.2928743565097058,
+      "y": 2.8782055631807255
+    },
+    {
+      "id": 25,
+      "rotation_radians": 2.4332483820818145,
+      "x": 1.5190461513316118,
+      "y": 3.2404537294344387
+    }
+  ],
+  "problem": "25 equal items for Pentagons in Pentagons",
+  "setup": "peninpen",
+  "source_image": "https://erich-friedman.github.io/packing/peninpen/25.png",
+  "source_page": "https://erich-friedman.github.io/packing/peninpen/"
+}
diff --git a/data/solutions/generated/squincir_021_545b9a64270c81e8.json b/data/solutions/generated/squincir_021_545b9a64270c81e8.json
new file mode 100644
index 0000000000000000000000000000000000000000..31c6ad226b03d2b2c681cb0d2c855db7e55e12dc
--- /dev/null
+++ b/data/solutions/generated/squincir_021_545b9a64270c81e8.json
@@ -0,0 +1,185 @@
+{
+  "case": "squincir@21",
+  "container": {
+    "radius": 3.0167540626859655,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squincir@21",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "4/13/26",
+    "metric_expression": "\u221a34 / 2 = 2.915+",
+    "metric_symbol": "r",
+    "metric_value": 2.915,
+    "reference_text": "r = \u221a34 / 2 = 2.915+ | Found by Erich Friedman | in 1997.",
+    "source_image": "21.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squincir/21.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squincir/",
+    "title": "Squares in Circles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squincir@21",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "4/13/26",
+      "metric_expression": "\u221a34 / 2 = 2.915+",
+      "metric_symbol": "r",
+      "metric_value": 2.915,
+      "reference_text": "r = \u221a34 / 2 = 2.915+ | Found by Erich Friedman | in 1997.",
+      "source_image": "21.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squincir/21.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squincir/",
+      "title": "Squares in Circles"
+    },
+    "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/squincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.8098533539475898,
+      "x": -2.0841858325129454,
+      "y": -0.9731531925199317
+    },
+    {
+      "id": 2,
+      "rotation_radians": -0.8190271079877968,
+      "x": -1.1972275425660042,
+      "y": -1.9997641643979935
+    },
+    {
+      "id": 3,
+      "rotation_radians": -0.8030811772348383,
+      "x": -0.20223793431201062,
+      "y": -2.402186190653557
+    },
+    {
+      "id": 4,
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+    {
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+      "rotation_radians": -0.814007681572148,
+      "x": -1.1667170828517455,
+      "y": 2.009955098764813
+    }
+  ],
+  "problem": "21 equal items for Squares in Circles",
+  "setup": "squincir",
+  "source_image": "https://erich-friedman.github.io/packing/squincir/21.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squincir/"
+}
diff --git a/data/solutions/generated/squincir_022_280731f79ac45512.json b/data/solutions/generated/squincir_022_280731f79ac45512.json
new file mode 100644
index 0000000000000000000000000000000000000000..269d75df47d6d8820f9b7cf43727925c66048992
--- /dev/null
+++ b/data/solutions/generated/squincir_022_280731f79ac45512.json
@@ -0,0 +1,191 @@
+{
+  "case": "squincir@22",
+  "container": {
+    "radius": 3.0420195589589527,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squincir@22",
+    "credit": "Jonathan Viquerat",
+    "date": "April 2026",
+    "family_updated": "4/13/26",
+    "metric_expression": "3.033+",
+    "metric_symbol": "r",
+    "metric_value": 3.033,
+    "reference_text": "r = 3.033+ | Found by Jonathan Viquerat | in April 2026.",
+    "source_image": "22.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squincir/22.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squincir/",
+    "title": "Squares in Circles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squincir@22",
+      "credit": "Jonathan Viquerat",
+      "date": "April 2026",
+      "family_updated": "4/13/26",
+      "metric_expression": "3.033+",
+      "metric_symbol": "r",
+      "metric_value": 3.033,
+      "reference_text": "r = 3.033+ | Found by Jonathan Viquerat | in April 2026.",
+      "source_image": "22.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squincir/22.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squincir/",
+      "title": "Squares in Circles"
+    },
+    "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/squincir/",
+    "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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+      "y": 0.6630230339551688
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+    {
+      "id": 18,
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+    {
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+    {
+      "id": 20,
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+      "x": 1.8227627994297764,
+      "y": 1.6871079933752304
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.2785327426979096,
+      "x": -1.7046414775989136,
+      "y": 1.6912016824210552
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.5060419526812601,
+      "x": -0.6382976251623611,
+      "y": 2.2589116839888157
+    }
+  ],
+  "problem": "22 equal items for Squares in Circles",
+  "setup": "squincir",
+  "source_image": "https://erich-friedman.github.io/packing/squincir/22.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squincir/"
+}
diff --git a/data/solutions/generated/squincir_023_1db15c5f1a5b8485.json b/data/solutions/generated/squincir_023_1db15c5f1a5b8485.json
new file mode 100644
index 0000000000000000000000000000000000000000..5b9350b2b0cd25feb0e654fe125042fcf2db4f97
--- /dev/null
+++ b/data/solutions/generated/squincir_023_1db15c5f1a5b8485.json
@@ -0,0 +1,197 @@
+{
+  "case": "squincir@23",
+  "container": {
+    "radius": 3.0788807100496327,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squincir@23",
+    "credit": "David W",
+    "date": "June 2002",
+    "family_updated": "4/13/26",
+    "metric_expression": "3.073+",
+    "metric_symbol": "r",
+    "metric_value": 3.073,
+    "reference_text": "r = 3.073+ | Found by David W. Cantrell | in June 2002.",
+    "source_image": "23.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squincir/23.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squincir/",
+    "title": "Squares in Circles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squincir@23",
+      "credit": "David W",
+      "date": "June 2002",
+      "family_updated": "4/13/26",
+      "metric_expression": "3.073+",
+      "metric_symbol": "r",
+      "metric_value": 3.073,
+      "reference_text": "r = 3.073+ | Found by David W. Cantrell | in June 2002.",
+      "source_image": "23.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squincir/23.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squincir/",
+      "title": "Squares in Circles"
+    },
+    "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/squincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.954539788042857,
+      "x": 0.07406850378618582,
+      "y": 2.420401716721138
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+      "x": -0.9170389100372671,
+      "y": 2.2833549800923145
+    },
+    {
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+      "rotation_radians": -0.5754992510714746,
+      "x": -1.452633918116048,
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+    {
+      "id": 15,
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+      "y": -0.958131564537793
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+    {
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+      "x": 2.507061574804799,
+      "y": 0.2711245992534689
+    },
+    {
+      "id": 17,
+      "rotation_radians": 5.676675705064346,
+      "x": -0.48275331597003424,
+      "y": -0.12393409384524108
+    },
+    {
+      "id": 18,
+      "rotation_radians": 5.676922374400414,
+      "x": 2.256007462921527,
+      "y": -0.7929313694400374
+    },
+    {
+      "id": 19,
+      "rotation_radians": 5.742973006344311,
+      "x": 0.4228582610936691,
+      "y": -2.27201761987809
+    },
+    {
+      "id": 20,
+      "rotation_radians": 1.029330904572255,
+      "x": 1.3828868873512146,
+      "y": -1.985831542793041
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.9960109735388312,
+      "x": -2.3892983959254708,
+      "y": 0.37873409678875897
+    },
+    {
+      "id": 22,
+      "rotation_radians": 2.586198229307896,
+      "x": -0.7235367137455647,
+      "y": -1.318331328689908
+    },
+    {
+      "id": 23,
+      "rotation_radians": 1.0052567276578925,
+      "x": 0.263730760153233,
+      "y": -1.1276606724727292
+    }
+  ],
+  "problem": "23 equal items for Squares in Circles",
+  "setup": "squincir",
+  "source_image": "https://erich-friedman.github.io/packing/squincir/23.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squincir/"
+}
diff --git a/data/solutions/generated/squincir_024_35e22c7b35c718bd.json b/data/solutions/generated/squincir_024_35e22c7b35c718bd.json
new file mode 100644
index 0000000000000000000000000000000000000000..cae7501566bded65d1a12a9c17fd092997c31cb0
--- /dev/null
+++ b/data/solutions/generated/squincir_024_35e22c7b35c718bd.json
@@ -0,0 +1,203 @@
+{
+  "case": "squincir@24",
+  "container": {
+    "radius": 3.1121065491772923,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squincir@24",
+    "credit": "Maurizio Morandi",
+    "date": "October 2010",
+    "family_updated": "4/13/26",
+    "metric_expression": "3.110+",
+    "metric_symbol": "r",
+    "metric_value": 3.11,
+    "reference_text": "r = 3.110+ | Found by Maurizio Morandi | in October 2010.",
+    "source_image": "24.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squincir/24.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squincir/",
+    "title": "Squares in Circles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squincir@24",
+      "credit": "Maurizio Morandi",
+      "date": "October 2010",
+      "family_updated": "4/13/26",
+      "metric_expression": "3.110+",
+      "metric_symbol": "r",
+      "metric_value": 3.11,
+      "reference_text": "r = 3.110+ | Found by Maurizio Morandi | in October 2010.",
+      "source_image": "24.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squincir/24.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squincir/",
+      "title": "Squares in Circles"
+    },
+    "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/squincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.7413639432520747,
+      "x": 1.0778007971219459,
+      "y": -0.9544307258935
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+    {
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+      "y": 0.785130562534579
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+    {
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+      "y": -2.3058746175675835
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+    {
+      "id": 20,
+      "rotation_radians": 3.308804346380394,
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+    {
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+    {
+      "id": 22,
+      "rotation_radians": 1.515620957304112,
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+    {
+      "id": 23,
+      "rotation_radians": 3.3104582657177546,
+      "x": -0.20193729160908838,
+      "y": 0.700363656655629
+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.739661009882332,
+      "x": 0.37711631760409975,
+      "y": 1.5156959579364715
+    }
+  ],
+  "problem": "24 equal items for Squares in Circles",
+  "setup": "squincir",
+  "source_image": "https://erich-friedman.github.io/packing/squincir/24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squincir/"
+}
diff --git a/data/solutions/generated/squincir_025_3b37ffd86fe6327a.json b/data/solutions/generated/squincir_025_3b37ffd86fe6327a.json
new file mode 100644
index 0000000000000000000000000000000000000000..3d8857db6a6061a679e1c217bfcb9f92111478bb
--- /dev/null
+++ b/data/solutions/generated/squincir_025_3b37ffd86fe6327a.json
@@ -0,0 +1,209 @@
+{
+  "case": "squincir@25",
+  "container": {
+    "radius": 3.2034032376772124,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squincir@25",
+    "credit": "David W",
+    "date": "April 2002",
+    "family_updated": "4/13/26",
+    "metric_expression": "\u221a5809 / 24 = 3.175+",
+    "metric_symbol": "r",
+    "metric_value": 3.175,
+    "reference_text": "r = \u221a5809 / 24 = 3.175+ | Found by David W. Cantrell | in April 2002.",
+    "source_image": "25.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squincir/25.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squincir/",
+    "title": "Squares in Circles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squincir@25",
+      "credit": "David W",
+      "date": "April 2002",
+      "family_updated": "4/13/26",
+      "metric_expression": "\u221a5809 / 24 = 3.175+",
+      "metric_symbol": "r",
+      "metric_value": 3.175,
+      "reference_text": "r = \u221a5809 / 24 = 3.175+ | Found by David W. Cantrell | in April 2002.",
+      "source_image": "25.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squincir/25.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squincir/",
+      "title": "Squares in Circles"
+    },
+    "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/squincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
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+      "x": 0.8598780426718231,
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+    {
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+      "y": -2.4598465459555428
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+    {
+      "id": 14,
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+      "y": -0.8803783933608468
+    },
+    {
+      "id": 15,
+      "rotation_radians": 4.461080345400606,
+      "x": -0.6216313218173916,
+      "y": -0.011113657388322819
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.2996960564047926,
+      "x": 1.0186616659866172,
+      "y": 1.231877848774689
+    },
+    {
+      "id": 17,
+      "rotation_radians": 4.629123671130316,
+      "x": -0.739308536292065,
+      "y": 1.4462924276153943
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.4760351196382593,
+      "x": -2.1228542122766494,
+      "y": 1.440044219104886
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.4658040273113249,
+      "x": -1.4416657206891916,
+      "y": 2.1935814846484423
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.2585043143152078,
+      "x": -2.4964870051044263,
+      "y": 0.2048858427793573
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.7973958484219004,
+      "x": 2.255914281952782,
+      "y": -1.4135432332344569
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.2585028469710633,
+      "x": -2.4342823273287615,
+      "y": -0.9158620072921978
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.09475015692239813,
+      "x": -1.4435479210167126,
+      "y": 0.7040851762621848
+    },
+    {
+      "id": 24,
+      "rotation_radians": 3.374810682432845,
+      "x": 0.5277325686451007,
+      "y": -0.3877544486603007
+    },
+    {
+      "id": 25,
+      "rotation_radians": 4.71280742787829,
+      "x": -1.8849068261687614,
+      "y": -1.8820272241467741
+    }
+  ],
+  "problem": "25 equal items for Squares in Circles",
+  "setup": "squincir",
+  "source_image": "https://erich-friedman.github.io/packing/squincir/25.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squincir/"
+}
diff --git a/data/solutions/generated/squincir_026_b818374b7af77c7b.json b/data/solutions/generated/squincir_026_b818374b7af77c7b.json
new file mode 100644
index 0000000000000000000000000000000000000000..6aa1ba2e31c04ec3847d8650d182bd4016cc5fc8
--- /dev/null
+++ b/data/solutions/generated/squincir_026_b818374b7af77c7b.json
@@ -0,0 +1,215 @@
+{
+  "case": "squincir@26",
+  "container": {
+    "radius": 3.237978591312333,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squincir@26",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "4/13/26",
+    "metric_expression": "\u221a41 / 2 = 3.201+",
+    "metric_symbol": "r",
+    "metric_value": 3.201,
+    "reference_text": "r = \u221a41 / 2 = 3.201+ | Found by Erich Friedman | in 1997.",
+    "source_image": "26.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squincir/26.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squincir/",
+    "title": "Squares in Circles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squincir@26",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "4/13/26",
+      "metric_expression": "\u221a41 / 2 = 3.201+",
+      "metric_symbol": "r",
+      "metric_value": 3.201,
+      "reference_text": "r = \u221a41 / 2 = 3.201+ | Found by Erich Friedman | in 1997.",
+      "source_image": "26.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squincir/26.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squincir/",
+      "title": "Squares in Circles"
+    },
+    "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/squincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 3.2084149710494256,
+      "x": -2.2217092444989044,
+      "y": -1.3368960275565245
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+    {
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+    },
+    {
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+      "x": 1.558295145333208,
+      "y": -0.6215829882972498
+    },
+    {
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+    {
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+      "x": -2.470160389385848,
+      "y": 1.053286247986866
+    },
+    {
+      "id": 14,
+      "rotation_radians": 1.9197703720813593,
+      "x": -1.5727243782659297,
+      "y": 0.6115758711669071
+    },
+    {
+      "id": 15,
+      "rotation_radians": 4.813293346433685,
+      "x": 0.03384957750568061,
+      "y": -0.7530678178824354
+    },
+    {
+      "id": 16,
+      "rotation_radians": 4.813286538489896,
+      "x": 0.673824817897437,
+      "y": 0.015468559690438716
+    },
+    {
+      "id": 17,
+      "rotation_radians": 3.202096550107757,
+      "x": 1.464673780451137,
+      "y": 0.6773293497744893
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.6312626372164298,
+      "x": 2.2201411394392334,
+      "y": 1.34408159786266
+    },
+    {
+      "id": 19,
+      "rotation_radians": 5.0517963913164445,
+      "x": -1.8037803127344123,
+      "y": 1.848410967630869
+    },
+    {
+      "id": 20,
+      "rotation_radians": 5.051770365749857,
+      "x": -0.906478216298031,
+      "y": 1.4067642256687356
+    },
+    {
+      "id": 21,
+      "rotation_radians": 3.2424951076778052,
+      "x": -0.6608711085940007,
+      "y": -0.022696553431958866
+    },
+    {
+      "id": 22,
+      "rotation_radians": 6.384079100693917,
+      "x": -0.020925683011836747,
+      "y": 0.7458036726573972
+    },
+    {
+      "id": 23,
+      "rotation_radians": 4.813266785297811,
+      "x": 0.749439623743733,
+      "y": 1.407883772551976
+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.6312817513276503,
+      "x": 1.5764802910200466,
+      "y": 2.125614705045973
+    },
+    {
+      "id": 25,
+      "rotation_radians": 2.2796707051005547,
+      "x": -0.5893579106248277,
+      "y": 2.5263442222762613
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.7088796207108242,
+      "x": 0.4217447035283305,
+      "y": 2.632542042275213
+    }
+  ],
+  "problem": "26 equal items for Squares in Circles",
+  "setup": "squincir",
+  "source_image": "https://erich-friedman.github.io/packing/squincir/26.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squincir/"
+}
diff --git a/data/solutions/generated/squincir_027_f9fe04884031db8c.json b/data/solutions/generated/squincir_027_f9fe04884031db8c.json
new file mode 100644
index 0000000000000000000000000000000000000000..dbb1ca1f8f98dcc68c7c47617dbc6e18ab58c311
--- /dev/null
+++ b/data/solutions/generated/squincir_027_f9fe04884031db8c.json
@@ -0,0 +1,221 @@
+{
+  "case": "squincir@27",
+  "container": {
+    "radius": 3.2651761724206643,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squincir@27",
+    "credit": "Maurizio Morandi",
+    "date": "September 2010",
+    "family_updated": "4/13/26",
+    "metric_expression": "13\u221a145/48 = 3.261+",
+    "metric_symbol": "r",
+    "metric_value": 3.261,
+    "reference_text": "r = 13\u221a145/48 = 3.261+ | Found by Maurizio Morandi | in September 2010.",
+    "source_image": "27.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squincir/27.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squincir/",
+    "title": "Squares in Circles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squincir@27",
+      "credit": "Maurizio Morandi",
+      "date": "September 2010",
+      "family_updated": "4/13/26",
+      "metric_expression": "13\u221a145/48 = 3.261+",
+      "metric_symbol": "r",
+      "metric_value": 3.261,
+      "reference_text": "r = 13\u221a145/48 = 3.261+ | Found by Maurizio Morandi | in September 2010.",
+      "source_image": "27.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squincir/27.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squincir/",
+      "title": "Squares in Circles"
+    },
+    "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/squincir/",
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+  "problem": "27 equal items for Squares in Circles",
+  "setup": "squincir",
+  "source_image": "https://erich-friedman.github.io/packing/squincir/27.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squincir/"
+}
diff --git a/data/solutions/generated/squincir_028_011f385483141804.json b/data/solutions/generated/squincir_028_011f385483141804.json
new file mode 100644
index 0000000000000000000000000000000000000000..01a904f3282542044017096648e1db0bb0062b21
--- /dev/null
+++ b/data/solutions/generated/squincir_028_011f385483141804.json
@@ -0,0 +1,227 @@
+{
+  "case": "squincir@28",
+  "container": {
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+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squincir@28",
+    "credit": "Jonathan Viquerat",
+    "date": "April 2026",
+    "family_updated": "4/13/26",
+    "metric_expression": "3.333+",
+    "metric_symbol": "r",
+    "metric_value": 3.333,
+    "reference_text": "r = 3.333+ | Found by Jonathan Viquerat | in April 2026.",
+    "source_image": "28.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squincir/28.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squincir/",
+    "title": "Squares in Circles"
+  },
+  "item": {
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+      "case": "squincir@28",
+      "credit": "Jonathan Viquerat",
+      "date": "April 2026",
+      "family_updated": "4/13/26",
+      "metric_expression": "3.333+",
+      "metric_symbol": "r",
+      "metric_value": 3.333,
+      "reference_text": "r = 3.333+ | Found by Jonathan Viquerat | in April 2026.",
+      "source_image": "28.gif",
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+      "source_page": "https://erich-friedman.github.io/packing/squincir/",
+      "title": "Squares in Circles"
+    },
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+    "source_url": "https://erich-friedman.github.io/packing/squincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
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+  ],
+  "problem": "28 equal items for Squares in Circles",
+  "setup": "squincir",
+  "source_image": "https://erich-friedman.github.io/packing/squincir/28.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squincir/"
+}
diff --git a/data/solutions/generated/squincir_029_cf50b73c19c6c40b.json b/data/solutions/generated/squincir_029_cf50b73c19c6c40b.json
new file mode 100644
index 0000000000000000000000000000000000000000..cea8e98bb4eba6c856048118813f3492f0b4879c
--- /dev/null
+++ b/data/solutions/generated/squincir_029_cf50b73c19c6c40b.json
@@ -0,0 +1,233 @@
+{
+  "case": "squincir@29",
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+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squincir@29",
+    "credit": "Jonathan Viquerat",
+    "date": "April 2026",
+    "family_updated": "4/13/26",
+    "metric_expression": "3.401+",
+    "metric_symbol": "r",
+    "metric_value": 3.401,
+    "reference_text": "r = 3.401+ | Found by Jonathan Viquerat | in April 2026.",
+    "source_image": "29.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squincir/29.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squincir/",
+    "title": "Squares in Circles"
+  },
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+      "case": "squincir@29",
+      "credit": "Jonathan Viquerat",
+      "date": "April 2026",
+      "family_updated": "4/13/26",
+      "metric_expression": "3.401+",
+      "metric_symbol": "r",
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+      "reference_text": "r = 3.401+ | Found by Jonathan Viquerat | in April 2026.",
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+      "source_image_url": "https://erich-friedman.github.io/packing/squincir/29.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squincir/",
+      "title": "Squares in Circles"
+    },
+    "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/squincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
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+      "y": 2.7548211313377764
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.7308569324387444,
+      "x": 0.3914419205757068,
+      "y": 1.6363086562969087
+    },
+    {
+      "id": 29,
+      "rotation_radians": -0.8243077744702784,
+      "x": 1.4197791018013404,
+      "y": 2.3499553186863964
+    }
+  ],
+  "problem": "29 equal items for Squares in Circles",
+  "setup": "squincir",
+  "source_image": "https://erich-friedman.github.io/packing/squincir/29.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squincir/"
+}
diff --git a/data/solutions/generated/squincir_030_86c752cf32b3c6a2.json b/data/solutions/generated/squincir_030_86c752cf32b3c6a2.json
new file mode 100644
index 0000000000000000000000000000000000000000..f9343f46626fcaf24cc18206fa9b6ae3591399da
--- /dev/null
+++ b/data/solutions/generated/squincir_030_86c752cf32b3c6a2.json
@@ -0,0 +1,239 @@
+{
+  "case": "squincir@30",
+  "container": {
+    "radius": 3.5340051200957388,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squincir@30",
+    "credit": "Jonathan Viquerat",
+    "date": "April 2026",
+    "family_updated": "4/13/26",
+    "metric_expression": "3.472+",
+    "metric_symbol": "r",
+    "metric_value": 3.472,
+    "reference_text": "r = 3.472+ | Found by Jonathan Viquerat | in April 2026.",
+    "source_image": "30.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squincir/30.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squincir/",
+    "title": "Squares in Circles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squincir@30",
+      "credit": "Jonathan Viquerat",
+      "date": "April 2026",
+      "family_updated": "4/13/26",
+      "metric_expression": "3.472+",
+      "metric_symbol": "r",
+      "metric_value": 3.472,
+      "reference_text": "r = 3.472+ | Found by Jonathan Viquerat | in April 2026.",
+      "source_image": "30.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squincir/30.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squincir/",
+      "title": "Squares in Circles"
+    },
+    "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/squincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.009882471040625467,
+      "x": -2.465424437551226,
+      "y": -1.5500676449354736
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+    {
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+    {
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+      "y": -0.20476324303832322
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+    {
+      "id": 17,
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+      "x": 1.8359956822556385,
+      "y": 0.23606166522378208
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.3814300213675812,
+      "x": 2.86425971159942,
+      "y": 0.557595093383557
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.30820654530850483,
+      "x": -2.4973578186197893,
+      "y": 1.3230548748171183
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.396494230634461,
+      "x": -1.4016605885132596,
+      "y": 1.397710923549736
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.38285238808648786,
+      "x": -0.3381442424610822,
+      "y": 0.5887604061809639
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.3828725217308665,
+      "x": 0.6503490643022961,
+      "y": 0.8198614133083835
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.38289411509033827,
+      "x": 1.5692420629226917,
+      "y": 1.2144506326792033
+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.1894057224123902,
+      "x": 2.533711020541661,
+      "y": 1.5039113679958498
+    },
+    {
+      "id": 25,
+      "rotation_radians": 1.1743256036669145,
+      "x": -1.7166132751864214,
+      "y": 2.3494292041071385
+    },
+    {
+      "id": 26,
+      "rotation_radians": 1.1819800221549508,
+      "x": -0.8101435170342115,
+      "y": 2.78530530900527
+    },
+    {
+      "id": 27,
+      "rotation_radians": -0.40487043141653356,
+      "x": -0.4528829962204167,
+      "y": 1.7296820099693875
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.4190383415970961,
+      "x": 0.2534874047066095,
+      "y": 2.846363981415381
+    },
+    {
+      "id": 29,
+      "rotation_radians": -0.37890989609152237,
+      "x": 0.5783440134794621,
+      "y": 1.8788186702064933
+    },
+    {
+      "id": 30,
+      "rotation_radians": -0.08077974405760081,
+      "x": 1.5631950025511612,
+      "y": 2.43586735908429
+    }
+  ],
+  "problem": "30 equal items for Squares in Circles",
+  "setup": "squincir",
+  "source_image": "https://erich-friedman.github.io/packing/squincir/30.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squincir/"
+}
diff --git a/data/solutions/generated/squincir_031_fdf9170d30584f4f.json b/data/solutions/generated/squincir_031_fdf9170d30584f4f.json
new file mode 100644
index 0000000000000000000000000000000000000000..1d390056b5eee05afe0b750acf3b605070d89a5e
--- /dev/null
+++ b/data/solutions/generated/squincir_031_fdf9170d30584f4f.json
@@ -0,0 +1,245 @@
+{
+  "case": "squincir@31",
+  "container": {
+    "radius": 3.536916321287215,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squincir@31",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "4/13/26",
+    "metric_expression": "5 \u221a2 / 2 = 3.535+",
+    "metric_symbol": "r",
+    "metric_value": 3.535,
+    "reference_text": "r = 5 \u221a2 / 2 = 3.535+ | Found by Erich Friedman | in 1997.",
+    "source_image": "31.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squincir/31.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squincir/",
+    "title": "Squares in Circles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squincir@31",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "4/13/26",
+      "metric_expression": "5 \u221a2 / 2 = 3.535+",
+      "metric_symbol": "r",
+      "metric_value": 3.535,
+      "reference_text": "r = 5 \u221a2 / 2 = 3.535+ | Found by Erich Friedman | in 1997.",
+      "source_image": "31.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squincir/31.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squincir/",
+      "title": "Squares in Circles"
+    },
+    "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/squincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 3.613091503944107,
+      "x": 2.8547369781762493,
+      "y": -0.9266313969435208
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+    {
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+    {
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+    {
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+    {
+      "id": 11,
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+      "x": -1.355959096988358,
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+      "x": -1.7950342485817266,
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+    },
+    {
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+      "x": 0.031321491764003465,
+      "y": 1.1359972742758404
+    },
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+      "id": 17,
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+      "x": 2.9706471328297033,
+      "y": 0.20957165779320952
+    },
+    {
+      "id": 18,
+      "rotation_radians": 5.967156902733381,
+      "x": 0.0001003930824325047,
+      "y": -0.0011855712481417852
+    },
+    {
+      "id": 19,
+      "rotation_radians": 4.541931564574397,
+      "x": 1.7872267266290311,
+      "y": -0.3263619161519231
+    },
+    {
+      "id": 20,
+      "rotation_radians": 4.396369440281043,
+      "x": 0.9520204502869317,
+      "y": -1.7610058732080773
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.31604613287522415,
+      "x": -0.10639730600478849,
+      "y": -1.1764951659163678
+    },
+    {
+      "id": 22,
+      "rotation_radians": 2.8255665137849557,
+      "x": 2.6697209539891027,
+      "y": 1.3676678038439876
+    },
+    {
+      "id": 23,
+      "rotation_radians": 3.531731685936447,
+      "x": -2.2673452593783523,
+      "y": 1.811197434364086
+    },
+    {
+      "id": 24,
+      "rotation_radians": 6.264289021571575,
+      "x": -1.95461202967836,
+      "y": -2.2317844579548654
+    },
+    {
+      "id": 25,
+      "rotation_radians": 5.9672199290929,
+      "x": 0.06023879391227996,
+      "y": -2.213613233471222
+    },
+    {
+      "id": 26,
+      "rotation_radians": 2.046673713379487,
+      "x": 0.9142092441242312,
+      "y": 2.8587566291095388
+    },
+    {
+      "id": 27,
+      "rotation_radians": 5.967157571432839,
+      "x": 0.8919803728229324,
+      "y": 0.451149128794063
+    },
+    {
+      "id": 28,
+      "rotation_radians": 0.6701735146486443,
+      "x": -2.932213767424269,
+      "y": -0.15640804990004667
+    },
+    {
+      "id": 29,
+      "rotation_radians": 5.967179114447542,
+      "x": -0.9922416829699654,
+      "y": 1.7381452463324156
+    },
+    {
+      "id": 30,
+      "rotation_radians": 2.8257917288234022,
+      "x": 0.9233235182999385,
+      "y": 1.58847501686805
+    },
+    {
+      "id": 31,
+      "rotation_radians": 2.825832895078422,
+      "x": 1.358120896308774,
+      "y": -2.6764924728223938
+    }
+  ],
+  "problem": "31 equal items for Squares in Circles",
+  "setup": "squincir",
+  "source_image": "https://erich-friedman.github.io/packing/squincir/31.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squincir/"
+}
diff --git a/data/solutions/generated/squincir_032_a2628e58e58416df.json b/data/solutions/generated/squincir_032_a2628e58e58416df.json
new file mode 100644
index 0000000000000000000000000000000000000000..600649b78d5f12c10df2714ff7fd078a1fb307b2
--- /dev/null
+++ b/data/solutions/generated/squincir_032_a2628e58e58416df.json
@@ -0,0 +1,251 @@
+{
+  "case": "squincir@32",
+  "container": {
+    "radius": 3.610606982319385,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squincir@32",
+    "credit": "Jonathan Viquerat",
+    "date": "April 2026",
+    "family_updated": "4/13/26",
+    "metric_expression": "3.584+",
+    "metric_symbol": "r",
+    "metric_value": 3.584,
+    "reference_text": "r = 3.584+ | Found by Jonathan Viquerat | in April 2026.",
+    "source_image": "32.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squincir/32.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squincir/",
+    "title": "Squares in Circles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squincir@32",
+      "credit": "Jonathan Viquerat",
+      "date": "April 2026",
+      "family_updated": "4/13/26",
+      "metric_expression": "3.584+",
+      "metric_symbol": "r",
+      "metric_value": 3.584,
+      "reference_text": "r = 3.584+ | Found by Jonathan Viquerat | in April 2026.",
+      "source_image": "32.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squincir/32.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squincir/",
+      "title": "Squares in Circles"
+    },
+    "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/squincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 2.2864915439666627,
+      "x": 0.39987079873902476,
+      "y": -1.854826792309375
+    },
+    {
+      "id": 2,
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+      "x": 2.982296644276978,
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+    {
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+      "y": -0.17857426772123797
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+    {
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+      "x": -0.6922705940955584,
+      "y": -1.965086927123493
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+    {
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+    {
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+    {
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+    {
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+      "y": 0.583151334964437
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+    {
+      "id": 27,
+      "rotation_radians": 3.857288931641837,
+      "x": 2.419876556056628,
+      "y": -1.6389041725536102
+    },
+    {
+      "id": 28,
+      "rotation_radians": 5.428091441675418,
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+      "y": -1.5749467815282987
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+    {
+      "id": 29,
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+      "y": 0.7846981039746788
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+    {
+      "id": 30,
+      "rotation_radians": 2.285242991487999,
+      "x": -0.24788746590136895,
+      "y": 3.0056623265987197
+    },
+    {
+      "id": 31,
+      "rotation_radians": 6.406568929925422,
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+      "y": 1.5648508397911423
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+    {
+      "id": 32,
+      "rotation_radians": 3.6552840099312105,
+      "x": -0.4866402878942031,
+      "y": -0.9746570759776594
+    }
+  ],
+  "problem": "32 equal items for Squares in Circles",
+  "setup": "squincir",
+  "source_image": "https://erich-friedman.github.io/packing/squincir/32.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squincir/"
+}
diff --git a/data/solutions/generated/squincir_033_257aa24f77df5436.json b/data/solutions/generated/squincir_033_257aa24f77df5436.json
new file mode 100644
index 0000000000000000000000000000000000000000..4465a1429059ce9cc4e759c29cc3ccc28956a4ae
--- /dev/null
+++ b/data/solutions/generated/squincir_033_257aa24f77df5436.json
@@ -0,0 +1,257 @@
+{
+  "case": "squincir@33",
+  "container": {
+    "radius": 3.6307676222525584,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squincir@33",
+    "credit": "Maurizio Morandi",
+    "date": "June 2010",
+    "family_updated": "4/13/26",
+    "metric_expression": "\u221a13 = 3.605+",
+    "metric_symbol": "r",
+    "metric_value": 3.605,
+    "reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in June 2010.",
+    "source_image": "33.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squincir/33.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squincir/",
+    "title": "Squares in Circles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squincir@33",
+      "credit": "Maurizio Morandi",
+      "date": "June 2010",
+      "family_updated": "4/13/26",
+      "metric_expression": "\u221a13 = 3.605+",
+      "metric_symbol": "r",
+      "metric_value": 3.605,
+      "reference_text": "r = \u221a13 = 3.605+ | Found by Maurizio Morandi | in June 2010.",
+      "source_image": "33.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squincir/33.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squincir/",
+      "title": "Squares in Circles"
+    },
+    "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/squincir/",
+    "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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+      "y": 0.35262604382584806
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+    {
+      "id": 24,
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+      "x": 0.3332243088745847,
+      "y": -1.5040057978809298
+    },
+    {
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+      "x": -2.0690467599975766,
+      "y": -0.055072998382127966
+    },
+    {
+      "id": 26,
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+      "x": -2.8829329210990378,
+      "y": 1.024306101932159
+    },
+    {
+      "id": 27,
+      "rotation_radians": 4.487631904258664,
+      "x": -1.5929298707396295,
+      "y": 1.211652238859628
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.4499588288417045,
+      "x": -2.247993318583647,
+      "y": 2.031386918759507
+    },
+    {
+      "id": 29,
+      "rotation_radians": 4.439223258233423,
+      "x": -1.4356418255642507,
+      "y": 2.7297575317178535
+    },
+    {
+      "id": 30,
+      "rotation_radians": 3.5323522935604985,
+      "x": -0.16058544159223193,
+      "y": 2.951361396090916
+    },
+    {
+      "id": 31,
+      "rotation_radians": 4.1900101733139214,
+      "x": -2.016448090020737,
+      "y": -2.1383161802428865
+    },
+    {
+      "id": 32,
+      "rotation_radians": 4.083230190657136,
+      "x": -3.054274192661619,
+      "y": -0.2306425051144722
+    },
+    {
+      "id": 33,
+      "rotation_radians": 6.009976750019901,
+      "x": -0.830586313506223,
+      "y": 1.9226425203211472
+    }
+  ],
+  "problem": "33 equal items for Squares in Circles",
+  "setup": "squincir",
+  "source_image": "https://erich-friedman.github.io/packing/squincir/33.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squincir/"
+}
diff --git a/data/solutions/generated/squincir_034_4ba00f951e2b00e9.json b/data/solutions/generated/squincir_034_4ba00f951e2b00e9.json
new file mode 100644
index 0000000000000000000000000000000000000000..6ea45fa92756820dca03d41e22e4a3c9d864ce69
--- /dev/null
+++ b/data/solutions/generated/squincir_034_4ba00f951e2b00e9.json
@@ -0,0 +1,263 @@
+{
+  "case": "squincir@34",
+  "container": {
+    "radius": 3.6407531642590913,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squincir@34",
+    "credit": "Maurizio Morandi",
+    "date": "December 2010",
+    "family_updated": "4/13/26",
+    "metric_expression": "3.629+",
+    "metric_symbol": "r",
+    "metric_value": 3.629,
+    "reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.",
+    "source_image": "34.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squincir/",
+    "title": "Squares in Circles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squincir@34",
+      "credit": "Maurizio Morandi",
+      "date": "December 2010",
+      "family_updated": "4/13/26",
+      "metric_expression": "3.629+",
+      "metric_symbol": "r",
+      "metric_value": 3.629,
+      "reference_text": "r = 3.629+ | Found by Maurizio Morandi | in December 2010.",
+      "source_image": "34.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squincir/34.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squincir/",
+      "title": "Squares in Circles"
+    },
+    "generator": "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/squincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
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+      "x": 0.8129444329329324,
+      "y": -0.7848741902427581
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+    },
+    {
+      "id": 24,
+      "rotation_radians": 2.674785111184572,
+      "x": -0.46401929136439113,
+      "y": 3.0063592978263616
+    },
+    {
+      "id": 25,
+      "rotation_radians": 2.674459344110304,
+      "x": -0.15506974448770042,
+      "y": -1.1049053434341167
+    },
+    {
+      "id": 26,
+      "rotation_radians": 1.0541572690263028,
+      "x": 2.23816908309881,
+      "y": -1.911584213775291
+    },
+    {
+      "id": 27,
+      "rotation_radians": 1.255621913340777,
+      "x": 2.71701196033184,
+      "y": 1.475088445614714
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.109112664138045,
+      "x": -1.4166928316728782,
+      "y": 2.6939173248105286
+    },
+    {
+      "id": 29,
+      "rotation_radians": 5.76566844907294,
+      "x": -0.648645924911652,
+      "y": -2.886559035477173
+    },
+    {
+      "id": 30,
+      "rotation_radians": 4.377628781186769,
+      "x": -2.803341138502257,
+      "y": -1.3291286534846343
+    },
+    {
+      "id": 31,
+      "rotation_radians": -0.39583881596275705,
+      "x": -1.9161332656116066,
+      "y": -2.2568077026353675
+    },
+    {
+      "id": 32,
+      "rotation_radians": 4.285893779000873,
+      "x": -2.2419927048937836,
+      "y": 1.927193457565686
+    },
+    {
+      "id": 33,
+      "rotation_radians": 5.814195601371649,
+      "x": 0.46608056763920436,
+      "y": -3.0070403283766316
+    },
+    {
+      "id": 34,
+      "rotation_radians": 2.6785926209261772,
+      "x": -0.9853027151624411,
+      "y": -0.32572338100665293
+    }
+  ],
+  "problem": "34 equal items for Squares in Circles",
+  "setup": "squincir",
+  "source_image": "https://erich-friedman.github.io/packing/squincir/34.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squincir/"
+}
diff --git a/data/solutions/generated/squincir_035_c87a08826ad4f52f.json b/data/solutions/generated/squincir_035_c87a08826ad4f52f.json
new file mode 100644
index 0000000000000000000000000000000000000000..542eaeb7093bb3262eeb4fda85e85fa7bde30cce
--- /dev/null
+++ b/data/solutions/generated/squincir_035_c87a08826ad4f52f.json
@@ -0,0 +1,269 @@
+{
+  "case": "squincir@35",
+  "container": {
+    "radius": 3.7262529827818556,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squincir@35",
+    "credit": "David Eppstein",
+    "date": "March 2002",
+    "family_updated": "4/13/26",
+    "metric_expression": "\u221a53 / 2 = 3.640+",
+    "metric_symbol": "r",
+    "metric_value": 3.64,
+    "reference_text": "r = \u221a53 / 2 = 3.640+ | Found by David Eppstein | in March 2002.",
+    "source_image": "35.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squincir/35.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squincir/",
+    "title": "Squares in Circles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squincir@35",
+      "credit": "David Eppstein",
+      "date": "March 2002",
+      "family_updated": "4/13/26",
+      "metric_expression": "\u221a53 / 2 = 3.640+",
+      "metric_symbol": "r",
+      "metric_value": 3.64,
+      "reference_text": "r = \u221a53 / 2 = 3.640+ | Found by David Eppstein | in March 2002.",
+      "source_image": "35.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squincir/35.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squincir/",
+      "title": "Squares in Circles"
+    },
+    "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/squincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 3.1177190704392395,
+      "x": 0.6458331594907907,
+      "y": -2.0387686924203643
+    },
+    {
+      "id": 2,
+      "rotation_radians": 1.5445299082978625,
+      "x": -1.128528783157479,
+      "y": 0.41533367003674176
+    },
+    {
+      "id": 3,
+      "rotation_radians": 4.178855476272564,
+      "x": -2.1211490454078556,
+      "y": -0.25291065597058054
+    },
+    {
+      "id": 4,
+      "rotation_radians": 4.05177013973617,
+      "x": -3.0086018182244247,
+      "y": 0.6439080585093573
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+    {
+      "id": 5,
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+      "x": 0.3316040972027136,
+      "y": 2.102175077027387
+    },
+    {
+      "id": 6,
+      "rotation_radians": 1.5874917105606514,
+      "x": 2.0960060507682368,
+      "y": -0.6337100170824315
+    },
+    {
+      "id": 7,
+      "rotation_radians": 2.5733126229331824,
+      "x": -0.6885687662033211,
+      "y": 3.1172665214975948
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.016694357140375458,
+      "x": 0.8783341505963397,
+      "y": -0.45424069696716607
+    },
+    {
+      "id": 9,
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+      "x": -0.025981858295238226,
+      "y": -3.0281866227432195
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+    {
+      "id": 10,
+      "rotation_radians": 6.29997296065109,
+      "x": 0.659408270870456,
+      "y": 0.757958509578761
+    },
+    {
+      "id": 11,
+      "rotation_radians": 6.27841347781387,
+      "x": -1.5826601128881572,
+      "y": -1.3771590015198356
+    },
+    {
+      "id": 12,
+      "rotation_radians": 2.333016921910779,
+      "x": 0.41614306915803706,
+      "y": 3.105894163966718
+    },
+    {
+      "id": 13,
+      "rotation_radians": 1.5873762935543132,
+      "x": 1.4007646428716443,
+      "y": -1.3526317376107766
+    },
+    {
+      "id": 14,
+      "rotation_radians": 4.105591039049294,
+      "x": -3.145311771892693,
+      "y": -0.40750569113994856
+    },
+    {
+      "id": 15,
+      "rotation_radians": 6.236610125376206,
+      "x": -1.1224261477441517,
+      "y": 1.8372542555040503
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.2752980200601138,
+      "x": 1.4993175775004393,
+      "y": 1.5222131010956692
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.016813787448056765,
+      "x": 2.225951916828853,
+      "y": -2.2716362415067684
+    },
+    {
+      "id": 18,
+      "rotation_radians": 4.493084091901665,
+      "x": 3.0305984847435643,
+      "y": -0.04769999712655469
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.544533477484642,
+      "x": -2.5105377499257435,
+      "y": 1.8611320462435181
+    },
+    {
+      "id": 20,
+      "rotation_radians": 6.259310062947521,
+      "x": 1.3091085686166395,
+      "y": -2.7880961621619473
+    },
+    {
+      "id": 21,
+      "rotation_radians": -1.5539692919682524,
+      "x": 1.6060236781053647,
+      "y": 0.2982594114114923
+    },
+    {
+      "id": 22,
+      "rotation_radians": 6.256919906340121,
+      "x": -1.8546140235328632,
+      "y": 1.1049573271534185
+    },
+    {
+      "id": 23,
+      "rotation_radians": 1.564145064133917,
+      "x": -0.6576966712812352,
+      "y": -1.9081268779343117
+    },
+    {
+      "id": 24,
+      "rotation_radians": 2.922802087339346,
+      "x": 2.458531878490361,
+      "y": 1.960108698668887
+    },
+    {
+      "id": 25,
+      "rotation_radians": 6.017925794596394,
+      "x": -2.802926384960205,
+      "y": -1.5028886137442279
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.3305111078591523,
+      "x": -1.1144999139798397,
+      "y": -2.9507603417939126
+    },
+    {
+      "id": 27,
+      "rotation_radians": 3.133347476702202,
+      "x": -0.40052123445432236,
+      "y": 1.1182353560828044
+    },
+    {
+      "id": 28,
+      "rotation_radians": 3.1147133986128024,
+      "x": -0.08018916334365038,
+      "y": 0.031032190618514314
+    },
+    {
+      "id": 29,
+      "rotation_radians": 1.587612406501192,
+      "x": 2.7544075634332796,
+      "y": -1.3915270391222887
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.5449274189209048,
+      "x": 0.08694984872072202,
+      "y": -1.1890222899069394
+    },
+    {
+      "id": 31,
+      "rotation_radians": 4.665798352456974,
+      "x": -1.7961081855833767,
+      "y": 2.5763438459455648
+    },
+    {
+      "id": 32,
+      "rotation_radians": 3.356435939651828,
+      "x": -2.0185735072708964,
+      "y": -2.407254875585765
+    },
+    {
+      "id": 33,
+      "rotation_radians": 0.7621853443721511,
+      "x": 1.4071917362487067,
+      "y": 2.70602733662259
+    },
+    {
+      "id": 34,
+      "rotation_radians": 4.490465086599031,
+      "x": 2.7140179174890715,
+      "y": 0.9367532724770482
+    },
+    {
+      "id": 35,
+      "rotation_radians": 1.543839029613572,
+      "x": -0.8305155469735691,
+      "y": -0.6803922587656265
+    }
+  ],
+  "problem": "35 equal items for Squares in Circles",
+  "setup": "squincir",
+  "source_image": "https://erich-friedman.github.io/packing/squincir/35.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squincir/"
+}
diff --git a/data/solutions/generated/squindom_021_f91a28177536f6d3.json b/data/solutions/generated/squindom_021_f91a28177536f6d3.json
new file mode 100644
index 0000000000000000000000000000000000000000..25ee5cbb2eb4d04f1a724359c0c1a0fc3c78df50
--- /dev/null
+++ b/data/solutions/generated/squindom_021_f91a28177536f6d3.json
@@ -0,0 +1,186 @@
+{
+  "case": "squindom@21",
+  "container": {
+    "height": 3.5000589957051536,
+    "type": "rectangle",
+    "width": 7.000117991410307
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squindom@21",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "8/11/12",
+    "metric_expression": "7/2 = 3.5",
+    "metric_symbol": "s",
+    "metric_value": 3.5,
+    "reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |",
+    "source_image": "21.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squindom@21",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "8/11/12",
+      "metric_expression": "7/2 = 3.5",
+      "metric_symbol": "s",
+      "metric_value": 3.5,
+      "reference_text": "20-21. | | s = 7/2 = 3.5 | Trivial. |",
+      "source_image": "21.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/21.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.7853918991504293,
+      "x": -2.0000369800888413,
+      "y": -1.2150856666054841
+    },
+    {
+      "id": 2,
+      "rotation_radians": -0.7854083777908036,
+      "x": -1.0000168820872473,
+      "y": -1.209670973904345
+    },
+    {
+      "id": 3,
+      "rotation_radians": -0.7854046525638491,
+      "x": 1.0000190128377635,
+      "y": -1.1958518406299787
+    },
+    {
+      "id": 4,
+      "rotation_radians": -0.7854073651036669,
+      "x": 2.0000356387959184,
+      "y": -1.217696389379652
+    },
+    {
+      "id": 5,
+      "rotation_radians": -0.7854048581848055,
+      "x": 3.0000529167856564,
+      "y": -1.0991376873167218
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.785389320835276,
+      "x": -2.0000272039722216,
+      "y": -0.16657054068541133
+    },
+    {
+      "id": 7,
+      "rotation_radians": -0.7854089440847648,
+      "x": -1.0000138509427983,
+      "y": -0.19025492335287947
+    },
+    {
+      "id": 8,
+      "rotation_radians": -0.7854050755247408,
+      "x": 5.868539675178144e-06,
+      "y": -0.9770643408977603
+    },
+    {
+      "id": 9,
+      "rotation_radians": -0.7854132829457822,
+      "x": 2.0000325871604536,
+      "y": -0.1876386920289742
+    },
+    {
+      "id": 10,
+      "rotation_radians": -0.7854072523450751,
+      "x": 3.0000506899716304,
+      "y": 0.014216294333314344
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.7853932142923192,
+      "x": -3.0000546677530266,
+      "y": -0.8970349796311728
+    },
+    {
+      "id": 12,
+      "rotation_radians": -0.7854288438618008,
+      "x": -1.0000182702208522,
+      "y": 0.8415230918348111
+    },
+    {
+      "id": 13,
+      "rotation_radians": -0.7854082274196935,
+      "x": 6.682319462997664e-06,
+      "y": 0.19345716680101502
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.7853843402204125,
+      "x": 1.0000215307008247,
+      "y": 0.031542024391078886
+    },
+    {
+      "id": 15,
+      "rotation_radians": 0.7853871256194819,
+      "x": 2.000037178458823,
+      "y": 1.0455599960690019
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.7853946499871368,
+      "x": -3.000049407378919,
+      "y": 0.13809847655684865
+    },
+    {
+      "id": 17,
+      "rotation_radians": -0.7854291924791497,
+      "x": -2.0000253172242695,
+      "y": 1.140806689880004
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.7854209313565669,
+      "x": 6.871927491170315e-06,
+      "y": 1.2298166696079393
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.7854237099085849,
+      "x": 1.0000224034270964,
+      "y": 1.193470322187966
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.7854072341189983,
+      "x": 3.000051082221715,
+      "y": 1.220058384602865
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.7853872526941186,
+      "x": -3.0000515381196577,
+      "y": 1.1988428423784532
+    }
+  ],
+  "problem": "21 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/21.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_022_989a2d320ac47881.json b/data/solutions/generated/squindom_022_989a2d320ac47881.json
new file mode 100644
index 0000000000000000000000000000000000000000..3472332b3e5c2de930cdb0acf7d582fe1ce1efb5
--- /dev/null
+++ b/data/solutions/generated/squindom_022_989a2d320ac47881.json
@@ -0,0 +1,192 @@
+{
+  "case": "squindom@22",
+  "container": {
+    "height": 3.796372301867231,
+    "type": "rectangle",
+    "width": 7.592744603734462
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squindom@22",
+    "credit": "David W",
+    "date": "July 2012",
+    "family_updated": "8/11/12",
+    "metric_expression": "3.745+",
+    "metric_symbol": "s",
+    "metric_value": 3.745,
+    "reference_text": "22. | | s = 3.745+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)",
+    "source_image": "22.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/22.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squindom@22",
+      "credit": "David W",
+      "date": "July 2012",
+      "family_updated": "8/11/12",
+      "metric_expression": "3.745+",
+      "metric_symbol": "s",
+      "metric_value": 3.745,
+      "reference_text": "22. | | s = 3.745+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in June 2010.)",
+      "source_image": "22.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/22.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 4.484895155362694,
+      "x": 1.7369021228473196,
+      "y": 1.2092835806327404
+    },
+    {
+      "id": 2,
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+      "y": 0.7571390444174052
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+    {
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+    {
+      "id": 11,
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+    {
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+      "y": 0.5121249700235148
+    },
+    {
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+    {
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+      "y": -1.2108245781507316
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+    {
+      "id": 15,
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+    {
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+      "rotation_radians": 2.3561967551776752,
+      "x": 2.2963316253515633,
+      "y": -1.3981762278749263
+    },
+    {
+      "id": 17,
+      "rotation_radians": 6.051429499945408,
+      "x": 1.7261176786731152,
+      "y": -0.35373506767928525
+    },
+    {
+      "id": 18,
+      "rotation_radians": 2.3561966478004246,
+      "x": 3.2963602190658787,
+      "y": -1.3981682055988185
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.7854009419066176,
+      "x": -3.296358967005251,
+      "y": -0.30297979071244163
+    },
+    {
+      "id": 20,
+      "rotation_radians": 3.927583142411791,
+      "x": 3.2960588644219446,
+      "y": -0.3978391675536038
+    },
+    {
+      "id": 21,
+      "rotation_radians": 2.9098321427610436,
+      "x": 1.0558855468057922,
+      "y": 0.40762249300239495
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.3337806174679037,
+      "x": -0.7234478052880953,
+      "y": 1.2108232585309033
+    }
+  ],
+  "problem": "22 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/22.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_023_be71e0d7682bb396.json b/data/solutions/generated/squindom_023_be71e0d7682bb396.json
new file mode 100644
index 0000000000000000000000000000000000000000..27aabb646b4f630776180b0c065dfc8c14f0810c
--- /dev/null
+++ b/data/solutions/generated/squindom_023_be71e0d7682bb396.json
@@ -0,0 +1,198 @@
+{
+  "case": "squindom@23",
+  "container": {
+    "height": 3.962587769024162,
+    "type": "rectangle",
+    "width": 7.925175538048324
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squindom@23",
+    "credit": "Maurizio Morandi",
+    "date": "June 2010",
+    "family_updated": "8/11/12",
+    "metric_expression": "3.849+",
+    "metric_symbol": "s",
+    "metric_value": 3.849,
+    "reference_text": "23. | | s = 3.849+ | Found by Maurizio Morandi | in June 2010. |",
+    "source_image": "23.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/23.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squindom@23",
+      "credit": "Maurizio Morandi",
+      "date": "June 2010",
+      "family_updated": "8/11/12",
+      "metric_expression": "3.849+",
+      "metric_symbol": "s",
+      "metric_value": 3.849,
+      "reference_text": "23. | | s = 3.849+ | Found by Maurizio Morandi | in June 2010. |",
+      "source_image": "23.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/23.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.25957226962716895,
+      "x": -1.1313259245090852,
+      "y": -1.2977970649444168
+    },
+    {
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+    {
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+    {
+      "id": 4,
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+    {
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+      "y": -0.3155860244467636
+    },
+    {
+      "id": 11,
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+      "x": -3.0219622133863395,
+      "y": -0.8561519852556345
+    },
+    {
+      "id": 12,
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+      "x": -1.0423914292853367,
+      "y": 0.37021858207094716
+    },
+    {
+      "id": 13,
+      "rotation_radians": -0.26067787401736797,
+      "x": 0.20497919933108502,
+      "y": 0.3863657586503646
+    },
+    {
+      "id": 14,
+      "rotation_radians": -0.3440776457400964,
+      "x": 2.5950548503801336,
+      "y": 0.45887080125203794
+    },
+    {
+      "id": 15,
+      "rotation_radians": -0.34337798214496523,
+      "x": 3.296524282386571,
+      "y": 1.3153362473920533
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.7840369558147454,
+      "x": -3.4495490634491075,
+      "y": 0.43782082673682654
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.812932590320239,
+      "x": -2.431904739175613,
+      "y": 0.46606157118825686
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.2775033649756536,
+      "x": -0.2744728477705638,
+      "y": 1.274131894162974
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.30274421572058025,
+      "x": 0.8517801547857949,
+      "y": 1.3063097234066465
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.7476912771659449,
+      "x": 2.013271407697623,
+      "y": 1.4627975395879402
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.7860971988060388,
+      "x": -3.4612744703756086,
+      "y": 1.4761595220080532
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.7860812464374592,
+      "x": -2.4607866443418502,
+      "y": 1.4796941436942053
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.7853860060330564,
+      "x": -1.4603664637997624,
+      "y": 1.4812243986499432
+    }
+  ],
+  "problem": "23 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/23.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_024_8434a88a5e3ff85b.json b/data/solutions/generated/squindom_024_8434a88a5e3ff85b.json
new file mode 100644
index 0000000000000000000000000000000000000000..e1d62c12c9946e2ce846e14559294e66f47b95c5
--- /dev/null
+++ b/data/solutions/generated/squindom_024_8434a88a5e3ff85b.json
@@ -0,0 +1,204 @@
+{
+  "case": "squindom@24",
+  "container": {
+    "height": 4.000128131859056,
+    "type": "rectangle",
+    "width": 8.000256263718112
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squindom@24",
+    "credit": "DC after MM",
+    "date": "August 2012",
+    "family_updated": "8/11/12",
+    "metric_expression": "3.882+",
+    "metric_symbol": "s",
+    "metric_value": 3.882,
+    "reference_text": "24. | | s = 3.882+ | Found by DC after MM | in August 2012. |",
+    "source_image": "24.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/24.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squindom@24",
+      "credit": "DC after MM",
+      "date": "August 2012",
+      "family_updated": "8/11/12",
+      "metric_expression": "3.882+",
+      "metric_symbol": "s",
+      "metric_value": 3.882,
+      "reference_text": "24. | | s = 3.882+ | Found by DC after MM | in August 2012. |",
+      "source_image": "24.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/24.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 5.497773245434293,
+      "x": 1.386450075740939,
+      "y": 1.5000533989842615
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.7853944205342598,
+      "x": 0.8374323561087443,
+      "y": 0.5000215454309479
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+    {
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+      "x": 3.421705357490767,
+      "y": -1.3930990933570007
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+    {
+      "id": 4,
+      "rotation_radians": 3.926998877762796,
+      "x": -0.720718913418049,
+      "y": 1.5000598663327946
+    },
+    {
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+      "rotation_radians": 2.3562027485185038,
+      "x": -0.3825195692753249,
+      "y": -1.5000503405319197
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+    {
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+      "x": -3.4992840986299942,
+      "y": -1.4992425098780577
+    },
+    {
+      "id": 7,
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+      "x": -2.4262413708564368,
+      "y": 1.301052591898861
+    },
+    {
+      "id": 8,
+      "rotation_radians": 3.926980687287558,
+      "x": 0.8506418784965332,
+      "y": -1.5000503069860245
+    },
+    {
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+      "rotation_radians": 0.7853506039548388,
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+    {
+      "id": 10,
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+      "x": -2.3330476992779094,
+      "y": -0.34718346939583394
+    },
+    {
+      "id": 11,
+      "rotation_radians": 3.9986316587738715,
+      "x": 3.4637965499626313,
+      "y": 0.8434582052161129
+    },
+    {
+      "id": 12,
+      "rotation_radians": 2.356251561275129,
+      "x": 2.4230445136471777,
+      "y": 1.5000146441094866
+    },
+    {
+      "id": 13,
+      "rotation_radians": 7.0685969661916666,
+      "x": -0.027810057388743148,
+      "y": -0.5000235906107428
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.7553173687940397,
+      "x": -3.4696816719805126,
+      "y": -0.48555438857142946
+    },
+    {
+      "id": 15,
+      "rotation_radians": 4.933837223314598,
+      "x": 2.2648470824960043,
+      "y": -1.2848377153686414
+    },
+    {
+      "id": 16,
+      "rotation_radians": 3.9148757310951647,
+      "x": -2.4375151510016724,
+      "y": -1.483099026143694
+    },
+    {
+      "id": 17,
+      "rotation_radians": 3.0848982717510123,
+      "x": -3.2941151693516275,
+      "y": 0.7166148300372415
+    },
+    {
+      "id": 18,
+      "rotation_radians": 5.4976790551948955,
+      "x": 1.8441006083291107,
+      "y": 0.4999528337466489
+    },
+    {
+      "id": 19,
+      "rotation_radians": 3.964178091540639,
+      "x": -1.1452780437006198,
+      "y": -0.48163495460885797
+    },
+    {
+      "id": 20,
+      "rotation_radians": 3.926950481865273,
+      "x": -1.4249185867674907,
+      "y": -1.4999274793689572
+    },
+    {
+      "id": 21,
+      "rotation_radians": 2.3561769470135214,
+      "x": -0.16275598002589192,
+      "y": 0.5000102845091525
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.084906887365437,
+      "x": 2.7805324597379775,
+      "y": -0.30856561920230485
+    },
+    {
+      "id": 23,
+      "rotation_radians": 1.4193641223379092,
+      "x": -1.6095679377469063,
+      "y": 0.6597667555295477
+    },
+    {
+      "id": 24,
+      "rotation_radians": 3.927000377994096,
+      "x": 0.35858000575185933,
+      "y": 1.500058935989261
+    }
+  ],
+  "problem": "24 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_025_a12363b635eb64f9.json b/data/solutions/generated/squindom_025_a12363b635eb64f9.json
new file mode 100644
index 0000000000000000000000000000000000000000..f921b30af6e15eb1f26a2ba7fe11b9cb10425a71
--- /dev/null
+++ b/data/solutions/generated/squindom_025_a12363b635eb64f9.json
@@ -0,0 +1,210 @@
+{
+  "case": "squindom@25",
+  "container": {
+    "height": 4.0001489417876295,
+    "type": "rectangle",
+    "width": 8.000297883575259
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squindom@25",
+    "credit": "DC after MM",
+    "date": "August 2012",
+    "family_updated": "8/11/12",
+    "metric_expression": "3.939+",
+    "metric_symbol": "s",
+    "metric_value": 3.939,
+    "reference_text": "25. | | s = 3.939+ | Found by DC after MM | in August 2012. |",
+    "source_image": "25.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/25.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squindom@25",
+      "credit": "DC after MM",
+      "date": "August 2012",
+      "family_updated": "8/11/12",
+      "metric_expression": "3.939+",
+      "metric_symbol": "s",
+      "metric_value": 3.939,
+      "reference_text": "25. | | s = 3.939+ | Found by DC after MM | in August 2012. |",
+      "source_image": "25.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/25.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
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+    {
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+    {
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+    {
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+      "x": -3.45494248133919,
+      "y": 0.5000270551974373
+    }
+  ],
+  "problem": "25 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/25.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_026_e7ee6dac796acc73.json b/data/solutions/generated/squindom_026_e7ee6dac796acc73.json
new file mode 100644
index 0000000000000000000000000000000000000000..7aee1ae818429e100ec13dd17eaa84f00d91cded
--- /dev/null
+++ b/data/solutions/generated/squindom_026_e7ee6dac796acc73.json
@@ -0,0 +1,216 @@
+{
+  "case": "squindom@26",
+  "container": {
+    "height": 4.000118786323,
+    "type": "rectangle",
+    "width": 8.000237572646
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squindom@26",
+    "credit": "David W",
+    "date": "July 2012",
+    "family_updated": "8/11/12",
+    "metric_expression": "3.981+",
+    "metric_symbol": "s",
+    "metric_value": 3.981,
+    "reference_text": "26. | | s = 3.981+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in July 2012.)",
+    "source_image": "26.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/26.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squindom@26",
+      "credit": "David W",
+      "date": "July 2012",
+      "family_updated": "8/11/12",
+      "metric_expression": "3.981+",
+      "metric_symbol": "s",
+      "metric_value": 3.981,
+      "reference_text": "26. | | s = 3.981+ | Found by David W. Cantrell | in July 2012 (after Maurizio | Morandi in July 2012.)",
+      "source_image": "26.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/26.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "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": 0.42768067968262213
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+    {
+      "id": 21,
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+      "y": 1.5000465122141513
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+    {
+      "id": 22,
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+    },
+    {
+      "id": 23,
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+      "x": 2.230355958175134,
+      "y": 1.5000461140453596
+    },
+    {
+      "id": 24,
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+      "x": 3.4161246115874038,
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+    },
+    {
+      "id": 25,
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+      "x": -2.5186097080432135,
+      "y": 1.3233049755135076
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.7853979302789923,
+      "x": -1.3116552877251701,
+      "y": 1.5000446388620206
+    }
+  ],
+  "problem": "26 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/26.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_027_c68e03cc8f5005db.json b/data/solutions/generated/squindom_027_c68e03cc8f5005db.json
new file mode 100644
index 0000000000000000000000000000000000000000..fa1316b8c518014550d52cf87ccca826176acea6
--- /dev/null
+++ b/data/solutions/generated/squindom_027_c68e03cc8f5005db.json
@@ -0,0 +1,222 @@
+{
+  "case": "squindom@27",
+  "container": {
+    "height": 4.000119714480737,
+    "type": "rectangle",
+    "width": 8.000239428961475
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squindom@27",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "8/11/12",
+    "metric_expression": "4",
+    "metric_symbol": "s",
+    "metric_value": 4.0,
+    "reference_text": "27-32. | | s = 4 | Trivial. | |",
+    "source_image": "32.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squindom@27",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "8/11/12",
+      "metric_expression": "4",
+      "metric_symbol": "s",
+      "metric_value": 4.0,
+      "reference_text": "27-32. | | s = 4 | Trivial. | |",
+      "source_image": "32.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+    {
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+      "x": 1.4490892105110433,
+      "y": -1.5000475660579056
+    },
+    {
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+    {
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+      "y": 1.4808383814889372
+    },
+    {
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+    },
+    {
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+    {
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+      "y": 0.444291247115255
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+    {
+      "id": 24,
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+      "x": -2.7631381000040354,
+      "y": -1.5000523646755581
+    },
+    {
+      "id": 25,
+      "rotation_radians": 3.9269941658977725,
+      "x": -1.4599714101245986,
+      "y": -0.5000131164676574
+    },
+    {
+      "id": 26,
+      "rotation_radians": 5.497788891784701,
+      "x": 0.3556778456255573,
+      "y": 1.5000472036759553
+    },
+    {
+      "id": 27,
+      "rotation_radians": 5.497791546339028,
+      "x": -1.3992107654592207,
+      "y": 0.5000188939439782
+    }
+  ],
+  "problem": "27 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/32.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_028_2c8c79126d60cdac.json b/data/solutions/generated/squindom_028_2c8c79126d60cdac.json
new file mode 100644
index 0000000000000000000000000000000000000000..4971f5825d7cc16e2a15df5b9118d1fbb47a3e66
--- /dev/null
+++ b/data/solutions/generated/squindom_028_2c8c79126d60cdac.json
@@ -0,0 +1,228 @@
+{
+  "case": "squindom@28",
+  "container": {
+    "height": 4.000212901766555,
+    "type": "rectangle",
+    "width": 8.00042580353311
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squindom@28",
+    "credit": "Trivial",
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+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
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+      "metric_expression": "4",
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+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
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+  "source_image": "https://erich-friedman.github.io/packing/squindom/32.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_029_d2548471aff7d9f5.json b/data/solutions/generated/squindom_029_d2548471aff7d9f5.json
new file mode 100644
index 0000000000000000000000000000000000000000..b46e4775fdac2f9deb88bf649db99ed88350160f
--- /dev/null
+++ b/data/solutions/generated/squindom_029_d2548471aff7d9f5.json
@@ -0,0 +1,234 @@
+{
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+    "family_updated": "8/11/12",
+    "metric_expression": "4",
+    "metric_symbol": "s",
+    "metric_value": 4.0,
+    "reference_text": "27-32. | | s = 4 | Trivial. | |",
+    "source_image": "32.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
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+      "metric_expression": "4",
+      "metric_symbol": "s",
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+      "reference_text": "27-32. | | s = 4 | Trivial. | |",
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+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
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+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/32.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_030_d67a491f7b4498c0.json b/data/solutions/generated/squindom_030_d67a491f7b4498c0.json
new file mode 100644
index 0000000000000000000000000000000000000000..93e91a216958ba0ce96bd4f1c1a244a28f48717c
--- /dev/null
+++ b/data/solutions/generated/squindom_030_d67a491f7b4498c0.json
@@ -0,0 +1,240 @@
+{
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+    "metric_expression": "4",
+    "metric_symbol": "s",
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+    "reference_text": "27-32. | | s = 4 | Trivial. | |",
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+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
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+      "metric_expression": "4",
+      "metric_symbol": "s",
+      "metric_value": 4.0,
+      "reference_text": "27-32. | | s = 4 | Trivial. | |",
+      "source_image": "32.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
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+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/squindom/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
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+    {
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+      "x": -3.500078922454429,
+      "y": -1.5000335563516753
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+  ],
+  "problem": "30 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/32.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_031_0cd7148786dfe563.json b/data/solutions/generated/squindom_031_0cd7148786dfe563.json
new file mode 100644
index 0000000000000000000000000000000000000000..971f5e0bc3b7eaf53b062c40893bb7fd2a7988cf
--- /dev/null
+++ b/data/solutions/generated/squindom_031_0cd7148786dfe563.json
@@ -0,0 +1,246 @@
+{
+  "case": "squindom@31",
+  "container": {
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+    "type": "rectangle",
+    "width": 8.950184193903528
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squindom@31",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "8/11/12",
+    "metric_expression": "4",
+    "metric_symbol": "s",
+    "metric_value": 4.0,
+    "reference_text": "27-32. | | s = 4 | Trivial. | |",
+    "source_image": "32.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
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+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squindom@31",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "8/11/12",
+      "metric_expression": "4",
+      "metric_symbol": "s",
+      "metric_value": 4.0,
+      "reference_text": "27-32. | | s = 4 | Trivial. | |",
+      "source_image": "32.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "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": 1.5313931227361717
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+    {
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+    {
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+    {
+      "id": 30,
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+      "x": 3.9155637022815046,
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+    {
+      "id": 31,
+      "rotation_radians": 0.7852081379169132,
+      "x": -3.9672694970377913,
+      "y": 1.7374093196774574
+    }
+  ],
+  "problem": "31 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/32.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_032_bdb0d7e9df92fbf4.json b/data/solutions/generated/squindom_032_bdb0d7e9df92fbf4.json
new file mode 100644
index 0000000000000000000000000000000000000000..f3382186cc1b269ec16d31d7c339829db9e49fab
--- /dev/null
+++ b/data/solutions/generated/squindom_032_bdb0d7e9df92fbf4.json
@@ -0,0 +1,252 @@
+{
+  "case": "squindom@32",
+  "container": {
+    "height": 4.594705441483036,
+    "type": "rectangle",
+    "width": 9.189410882966072
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squindom@32",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "8/11/12",
+    "metric_expression": "4",
+    "metric_symbol": "s",
+    "metric_value": 4.0,
+    "reference_text": "27-32. | | s = 4 | Trivial. | |",
+    "source_image": "32.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squindom@32",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "8/11/12",
+      "metric_expression": "4",
+      "metric_symbol": "s",
+      "metric_value": 4.0,
+      "reference_text": "27-32. | | s = 4 | Trivial. | |",
+      "source_image": "32.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/32.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "id": 1,
+      "rotation_radians": -0.041753355380678564,
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+    {
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+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.08014363117924467,
+      "x": 0.6185422076046551,
+      "y": 0.814609584825775
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.09252723577132181,
+      "x": 1.9307829804113983,
+      "y": 0.8194616648490621
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.08820346478110364,
+      "x": 3.234003879579424,
+      "y": 0.8186419560446758
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.09016443238987784,
+      "x": -3.2266828809553516,
+      "y": 0.8273451030684739
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.5157651549058311,
+      "x": -1.353836461443158,
+      "y": 1.6779693495308958
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.0013923871120249196,
+      "x": -0.12148075668781007,
+      "y": 1.589733398205229
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.10172159246976563,
+      "x": 1.287152668208149,
+      "y": 1.5935276385280321
+    },
+    {
+      "id": 29,
+      "rotation_radians": -0.09269247036578694,
+      "x": 2.5917251736858575,
+      "y": 1.5890627160486868
+    },
+    {
+      "id": 30,
+      "rotation_radians": -0.08898329182300357,
+      "x": 3.890385985456141,
+      "y": 1.593030407278116
+    },
+    {
+      "id": 31,
+      "rotation_radians": 0.09057343727811841,
+      "x": -3.890469775041153,
+      "y": 1.5931169188986456
+    },
+    {
+      "id": 32,
+      "rotation_radians": 0.09014807598369487,
+      "x": -2.583491953122733,
+      "y": 1.5931132656398357
+    }
+  ],
+  "problem": "32 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/32.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_033_a19cffb18f99454d.json b/data/solutions/generated/squindom_033_a19cffb18f99454d.json
new file mode 100644
index 0000000000000000000000000000000000000000..8f999117aa6cd75fbd1ded0f8f3f6c637a4da41d
--- /dev/null
+++ b/data/solutions/generated/squindom_033_a19cffb18f99454d.json
@@ -0,0 +1,258 @@
+{
+  "case": "squindom@33",
+  "container": {
+    "height": 4.562950534068095,
+    "type": "rectangle",
+    "width": 9.12590106813619
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squindom@33",
+    "credit": "Maurizio Morandi",
+    "date": "July 2012",
+    "family_updated": "8/11/12",
+    "metric_expression": "3 + \u221a2 = 4.414+",
+    "metric_symbol": "s",
+    "metric_value": 4.414,
+    "reference_text": "33. | | s = 3 + \u221a2 = 4.414+ | Found by Maurizio Morandi | in July 2012.",
+    "source_image": "33.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/33.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squindom@33",
+      "credit": "Maurizio Morandi",
+      "date": "July 2012",
+      "family_updated": "8/11/12",
+      "metric_expression": "3 + \u221a2 = 4.414+",
+      "metric_symbol": "s",
+      "metric_value": 4.414,
+      "reference_text": "33. | | s = 3 + \u221a2 = 4.414+ | Found by Maurizio Morandi | in July 2012.",
+      "source_image": "33.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/33.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.7287852012578488,
+      "x": -3.0269671656228003,
+      "y": -1.7537547236281361
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+      "y": -0.012504980592907384
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+    {
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+    },
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+      "y": -0.23847931115360785
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+    {
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+      "y": 0.7931524612756176
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.1421113961546854,
+      "x": 0.24694302988110284,
+      "y": 0.6959964635341146
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.7868464402904133,
+      "x": 1.6824180876822687,
+      "y": 0.7807091107926749
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.7834444481362997,
+      "x": 3.060369528699765,
+      "y": 0.780033972955821
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.785694837573915,
+      "x": 4.061927280449205,
+      "y": 0.7476337901897232
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.785404455144381,
+      "x": -4.062937679675912,
+      "y": 1.5694279941549016
+    },
+    {
+      "id": 26,
+      "rotation_radians": -0.08038048038862919,
+      "x": -2.4020897246654025,
+      "y": 0.7617668892842435
+    },
+    {
+      "id": 27,
+      "rotation_radians": -0.3770238657604943,
+      "x": -0.3554819275602311,
+      "y": 1.6231048895548097
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.7874193484463539,
+      "x": 1.9693004182111327,
+      "y": 1.7804485288731648
+    },
+    {
+      "id": 29,
+      "rotation_radians": -0.7845438797278707,
+      "x": 2.992424615192605,
+      "y": 1.7807068315977364
+    },
+    {
+      "id": 30,
+      "rotation_radians": 0.7833238673294896,
+      "x": 4.010253268805426,
+      "y": 1.7802689819846491
+    },
+    {
+      "id": 31,
+      "rotation_radians": 0.7854015261537193,
+      "x": -3.062911943566802,
+      "y": 1.7814642740457913
+    },
+    {
+      "id": 32,
+      "rotation_radians": -0.1691429311632393,
+      "x": -1.7299630744303238,
+      "y": 1.580854399152367
+    },
+    {
+      "id": 33,
+      "rotation_radians": 0.7854035608025345,
+      "x": 0.9403633643191432,
+      "y": 1.781457173180023
+    }
+  ],
+  "problem": "33 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/33.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_034_754eaf0840f066aa.json b/data/solutions/generated/squindom_034_754eaf0840f066aa.json
new file mode 100644
index 0000000000000000000000000000000000000000..2faadb3ca580083d08447d15476c8c9b3560d304
--- /dev/null
+++ b/data/solutions/generated/squindom_034_754eaf0840f066aa.json
@@ -0,0 +1,264 @@
+{
+  "case": "squindom@34",
+  "container": {
+    "height": 4.647313273689505,
+    "type": "rectangle",
+    "width": 9.29462654737901
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squindom@34",
+    "credit": "David W",
+    "date": "July 2012",
+    "family_updated": "8/11/12",
+    "metric_expression": "4 + \u221a2/3 = 4.471+",
+    "metric_symbol": "s",
+    "metric_value": 4.471,
+    "reference_text": "34. | | s = 4 + \u221a2/3 = 4.471+ | Found by David W. Cantrell | in July 2012.",
+    "source_image": "34.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/34.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squindom@34",
+      "credit": "David W",
+      "date": "July 2012",
+      "family_updated": "8/11/12",
+      "metric_expression": "4 + \u221a2/3 = 4.471+",
+      "metric_symbol": "s",
+      "metric_value": 4.471,
+      "reference_text": "34. | | s = 4 + \u221a2/3 = 4.471+ | Found by David W. Cantrell | in July 2012.",
+      "source_image": "34.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/34.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 5.497297721026898,
+      "x": -4.14698106189298,
+      "y": -0.6172447649450313
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+    {
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+      "y": -1.8183510718704528
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+    },
+    {
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+    },
+    {
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+    },
+    {
+      "id": 14,
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+      "x": 1.168798094434418,
+      "y": -0.6125833449343414
+    },
+    {
+      "id": 15,
+      "rotation_radians": 0.7109447939282832,
+      "x": -3.742151479181572,
+      "y": 1.6120199559790178
+    },
+    {
+      "id": 16,
+      "rotation_radians": 3.1863923326839148,
+      "x": -1.9407936604103297,
+      "y": 0.6567075910948151
+    },
+    {
+      "id": 17,
+      "rotation_radians": 2.356191067673371,
+      "x": -4.1472907250471085,
+      "y": 0.5761128466828043
+    },
+    {
+      "id": 18,
+      "rotation_radians": 4.75720250292157,
+      "x": -1.2181669619447408,
+      "y": -0.034983265048724024
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.0761596798648971,
+      "x": -2.586658958672432,
+      "y": 1.7012743148897858
+    },
+    {
+      "id": 20,
+      "rotation_radians": 3.927040650398648,
+      "x": -1.4285202866130995,
+      "y": 1.8234371386550703
+    },
+    {
+      "id": 21,
+      "rotation_radians": 3.9250491995877876,
+      "x": 4.1463243110923775,
+      "y": -1.8226620804652145
+    },
+    {
+      "id": 22,
+      "rotation_radians": 6.323388567489319,
+      "x": 2.5146897043171994,
+      "y": 0.8720977200860628
+    },
+    {
+      "id": 23,
+      "rotation_radians": 5.4968503429834525,
+      "x": -2.1452185416109955,
+      "y": -0.8220663125654846
+    },
+    {
+      "id": 24,
+      "rotation_radians": 5.497808615422619,
+      "x": -0.42844282950678525,
+      "y": 1.8236224077149088
+    },
+    {
+      "id": 25,
+      "rotation_radians": 2.3562012449931107,
+      "x": -4.147292754304297,
+      "y": -1.7339799124874715
+    },
+    {
+      "id": 26,
+      "rotation_radians": 1.5742382615088912,
+      "x": 1.7787907424119387,
+      "y": 1.5758841007596116
+    },
+    {
+      "id": 27,
+      "rotation_radians": 3.926989061997307,
+      "x": 4.147296472401776,
+      "y": 0.8839113350552618
+    },
+    {
+      "id": 28,
+      "rotation_radians": 3.3513481480127996,
+      "x": 3.955670412423959,
+      "y": -0.6309092327624211
+    },
+    {
+      "id": 29,
+      "rotation_radians": 6.3309232013628005,
+      "x": 1.8418500264171596,
+      "y": 0.12716089056966362
+    },
+    {
+      "id": 30,
+      "rotation_radians": 3.9269852655624056,
+      "x": -3.147246663827052,
+      "y": -1.7516211253776361
+    },
+    {
+      "id": 31,
+      "rotation_radians": 3.916752162388921,
+      "x": 2.142010553727651,
+      "y": -1.8185512455104063
+    },
+    {
+      "id": 32,
+      "rotation_radians": 3.927007775792703,
+      "x": 0.5716187191683285,
+      "y": 1.8236439968297593
+    },
+    {
+      "id": 33,
+      "rotation_radians": 4.760176332742305,
+      "x": 3.1900507063087806,
+      "y": 0.12374398642502124
+    },
+    {
+      "id": 34,
+      "rotation_radians": 2.345958085870376,
+      "x": 0.14180224382309733,
+      "y": -1.8185419735066652
+    }
+  ],
+  "problem": "34 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/34.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_035_ad3aed979d0e55b8.json b/data/solutions/generated/squindom_035_ad3aed979d0e55b8.json
new file mode 100644
index 0000000000000000000000000000000000000000..a2004223decfbd5c7bf5c044fe0fc2eac2403e0c
--- /dev/null
+++ b/data/solutions/generated/squindom_035_ad3aed979d0e55b8.json
@@ -0,0 +1,270 @@
+{
+  "case": "squindom@35",
+  "container": {
+    "height": 4.650755048395167,
+    "type": "rectangle",
+    "width": 9.301510096790334
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squindom@35",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "8/11/12",
+    "metric_expression": "9/2 = 4.5",
+    "metric_symbol": "s",
+    "metric_value": 4.5,
+    "reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |",
+    "source_image": "36.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squindom@35",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "8/11/12",
+      "metric_expression": "9/2 = 4.5",
+      "metric_symbol": "s",
+      "metric_value": 4.5,
+      "reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |",
+      "source_image": "36.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.720758287342919,
+      "x": -4.119297352745927,
+      "y": -1.7939474821803942
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.21138479544060065,
+      "x": -1.3716213629933236,
+      "y": -1.633997788278379
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+    {
+      "id": 3,
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+      "x": -0.10985911695180389,
+      "y": -1.6431827126733614
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.7851264893423023,
+      "x": 1.1502935393966678,
+      "y": -1.8252166689613347
+    },
+    {
+      "id": 5,
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+      "x": 2.150444462722123,
+      "y": -1.8241253041197476
+    },
+    {
+      "id": 6,
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+      "x": 3.1506435155623587,
+      "y": -1.825359128593868
+    },
+    {
+      "id": 7,
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+      "x": -2.5703425214397444,
+      "y": -1.633112197536568
+    },
+    {
+      "id": 8,
+      "rotation_radians": 0.21138681461677963,
+      "x": -0.8062709957891782,
+      "y": -0.8086766900438526
+    },
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+      "x": 2.3641178590889966,
+      "y": 1.6281489268743436
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+  ],
+  "problem": "35 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/36.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_036_24e6d7b793012d54.json b/data/solutions/generated/squindom_036_24e6d7b793012d54.json
new file mode 100644
index 0000000000000000000000000000000000000000..abe1ad56d2b816a1ffec6d7d2fbf1caa722b894a
--- /dev/null
+++ b/data/solutions/generated/squindom_036_24e6d7b793012d54.json
@@ -0,0 +1,276 @@
+{
+  "case": "squindom@36",
+  "container": {
+    "height": 4.839154491863543,
+    "type": "rectangle",
+    "width": 9.678308983727087
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squindom@36",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "8/11/12",
+    "metric_expression": "9/2 = 4.5",
+    "metric_symbol": "s",
+    "metric_value": 4.5,
+    "reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |",
+    "source_image": "36.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squindom@36",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "8/11/12",
+      "metric_expression": "9/2 = 4.5",
+      "metric_symbol": "s",
+      "metric_value": 4.5,
+      "reference_text": "35-36. | | s = 9/2 = 4.5 | Trivial. |",
+      "source_image": "36.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/36.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "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": 32,
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+    {
+      "id": 33,
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+    },
+    {
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+    {
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+    },
+    {
+      "id": 36,
+      "rotation_radians": -0.7852955696826162,
+      "x": 4.299180902746536,
+      "y": 1.9194403770621855
+    }
+  ],
+  "problem": "36 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/36.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_037_4eb7698c43b9de17.json b/data/solutions/generated/squindom_037_4eb7698c43b9de17.json
new file mode 100644
index 0000000000000000000000000000000000000000..8997d838269e99b05d6f020c57c2b1517e9766c2
--- /dev/null
+++ b/data/solutions/generated/squindom_037_4eb7698c43b9de17.json
@@ -0,0 +1,282 @@
+{
+  "case": "squindom@37",
+  "container": {
+    "height": 4.807021640634438,
+    "type": "rectangle",
+    "width": 9.614043281268875
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squindom@37",
+    "credit": "Maurizio Morandi",
+    "date": "August 2012",
+    "family_updated": "8/11/12",
+    "metric_expression": "10 / 3 + \u221a2 = 4.747+",
+    "metric_symbol": "s",
+    "metric_value": 4.747,
+    "reference_text": "37. | | s = 10 / 3 + \u221a2 = 4.747+ | Found by Maurizio Morandi | in August 2012.",
+    "source_image": "37.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/37.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squindom@37",
+      "credit": "Maurizio Morandi",
+      "date": "August 2012",
+      "family_updated": "8/11/12",
+      "metric_expression": "10 / 3 + \u221a2 = 4.747+",
+      "metric_symbol": "s",
+      "metric_value": 4.747,
+      "reference_text": "37. | | s = 10 / 3 + \u221a2 = 4.747+ | Found by Maurizio Morandi | in August 2012.",
+      "source_image": "37.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/37.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "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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+      "rotation_radians": 0.7315201750362337,
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+      "y": -1.8772941021934684
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+    {
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+    },
+    {
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+      "y": -1.894318117436874
+    },
+    {
+      "id": 32,
+      "rotation_radians": 1.2777356844748542,
+      "x": -0.42333462677725403,
+      "y": 0.01760639492932676
+    },
+    {
+      "id": 33,
+      "rotation_radians": 4.797959087847485,
+      "x": -1.781934555548164,
+      "y": 1.6989665488100727
+    },
+    {
+      "id": 34,
+      "rotation_radians": 2.848524594246549,
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+      "y": -0.8648274712942297
+    },
+    {
+      "id": 35,
+      "rotation_radians": -0.7844488520768174,
+      "x": -1.9049688295401774,
+      "y": -1.9030218090620261
+    },
+    {
+      "id": 36,
+      "rotation_radians": 3.9280151453242764,
+      "x": 4.21763826747666,
+      "y": -1.4604926671264302
+    },
+    {
+      "id": 37,
+      "rotation_radians": 0.7917175688394452,
+      "x": -3.2306931526872704,
+      "y": 1.9000175008766431
+    }
+  ],
+  "problem": "37 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/37.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_038_605d8eeb30140800.json b/data/solutions/generated/squindom_038_605d8eeb30140800.json
new file mode 100644
index 0000000000000000000000000000000000000000..4d4e1c35c5bfbcde3ec17b15b0a37a69eeafb767
--- /dev/null
+++ b/data/solutions/generated/squindom_038_605d8eeb30140800.json
@@ -0,0 +1,288 @@
+{
+  "case": "squindom@38",
+  "container": {
+    "height": 5.000085214452988,
+    "type": "rectangle",
+    "width": 10.000170428905976
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squindom@38",
+    "credit": "Maurizio Morandi",
+    "date": "August 2012",
+    "family_updated": "8/11/12",
+    "metric_expression": "(13 + \u221a2) / 3 = 4.804+",
+    "metric_symbol": "s",
+    "metric_value": 4.804,
+    "reference_text": "38. | | s = (13 + \u221a2) / 3 = 4.804+ | Found by Maurizio Morandi | in August 2012.",
+    "source_image": "38.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/38.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squindom@38",
+      "credit": "Maurizio Morandi",
+      "date": "August 2012",
+      "family_updated": "8/11/12",
+      "metric_expression": "(13 + \u221a2) / 3 = 4.804+",
+      "metric_symbol": "s",
+      "metric_value": 4.804,
+      "reference_text": "38. | | s = (13 + \u221a2) / 3 = 4.804+ | Found by Maurizio Morandi | in August 2012.",
+      "source_image": "38.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/38.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "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": 33,
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+      "y": 2.000035947486556
+    },
+    {
+      "id": 34,
+      "rotation_radians": 1.0123067953329479,
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+      "y": 1.8559765888818727
+    },
+    {
+      "id": 35,
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+      "x": 4.38038778196857,
+      "y": 1.856600858612425
+    },
+    {
+      "id": 36,
+      "rotation_radians": -1.8258422114537145,
+      "x": -3.163339767070165,
+      "y": 1.8157929021894212
+    },
+    {
+      "id": 37,
+      "rotation_radians": -1.586144124245357,
+      "x": -1.78252211084705,
+      "y": 1.793002558441866
+    },
+    {
+      "id": 38,
+      "rotation_radians": 0.785395044266692,
+      "x": 0.17334319739840529,
+      "y": 2.0000356129153927
+    }
+  ],
+  "problem": "38 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/38.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_039_1909884844694062.json b/data/solutions/generated/squindom_039_1909884844694062.json
new file mode 100644
index 0000000000000000000000000000000000000000..181441833b5a5d62cc03d7a269af071116472cd2
--- /dev/null
+++ b/data/solutions/generated/squindom_039_1909884844694062.json
@@ -0,0 +1,294 @@
+{
+  "case": "squindom@39",
+  "container": {
+    "height": 4.907449287986047,
+    "type": "rectangle",
+    "width": 9.814898575972094
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squindom@39",
+    "credit": "David W",
+    "date": "August 2012",
+    "family_updated": "8/11/12",
+    "metric_expression": "4.839+",
+    "metric_symbol": "s",
+    "metric_value": 4.839,
+    "reference_text": "39. | | s = 4.839+ | Found by David W. Cantrell | in August 2012.",
+    "source_image": "39.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/39.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squindom@39",
+      "credit": "David W",
+      "date": "August 2012",
+      "family_updated": "8/11/12",
+      "metric_expression": "4.839+",
+      "metric_symbol": "s",
+      "metric_value": 4.839,
+      "reference_text": "39. | | s = 4.839+ | Found by David W. Cantrell | in August 2012.",
+      "source_image": "39.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/39.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "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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+      "y": 1.9406461993472715
+    },
+    {
+      "id": 30,
+      "rotation_radians": -2.7816118719897784,
+      "x": -2.671373432698939,
+      "y": 0.7870140685707837
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+    {
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+      "y": 0.9052391335015707
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+    {
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+      "rotation_radians": 1.9077969199579257,
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+      "y": 0.8856450474189883
+    },
+    {
+      "id": 33,
+      "rotation_radians": 0.3336541784887466,
+      "x": 1.1973259125362625,
+      "y": 1.768250929530082
+    },
+    {
+      "id": 34,
+      "rotation_radians": -0.7913305114260292,
+      "x": 2.404524853316268,
+      "y": 1.9499841549453913
+    },
+    {
+      "id": 35,
+      "rotation_radians": -0.7878902150292628,
+      "x": 3.4071493206233954,
+      "y": 1.9524661097639475
+    },
+    {
+      "id": 36,
+      "rotation_radians": 0.8179831786840591,
+      "x": -3.3426788358275643,
+      "y": 1.9358625229029676
+    },
+    {
+      "id": 37,
+      "rotation_radians": -0.7496520248376032,
+      "x": -2.315201142957877,
+      "y": 1.9321826612686341
+    },
+    {
+      "id": 38,
+      "rotation_radians": -1.2355526402784112,
+      "x": -1.0165644347300842,
+      "y": 1.7859763345404165
+    },
+    {
+      "id": 39,
+      "rotation_radians": -1.2337943989977842,
+      "x": 0.09444947405946705,
+      "y": 1.7863791655329755
+    }
+  ],
+  "problem": "39 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/39.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_040_c766413f09b40b68.json b/data/solutions/generated/squindom_040_c766413f09b40b68.json
new file mode 100644
index 0000000000000000000000000000000000000000..4f60823d3df6a5474496102879fd26dfbdfdb944
--- /dev/null
+++ b/data/solutions/generated/squindom_040_c766413f09b40b68.json
@@ -0,0 +1,300 @@
+{
+  "case": "squindom@40",
+  "container": {
+    "height": 4.9619569680700515,
+    "type": "rectangle",
+    "width": 9.923913936140103
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squindom@40",
+    "credit": "Sigvart Brendberg",
+    "date": "June 2023",
+    "family_updated": "8/11/12",
+    "metric_expression": "4.895+",
+    "metric_symbol": "s",
+    "metric_value": 4.895,
+    "reference_text": "40. | | s = 4.895+ | Found by Sigvart Brendberg | in June 2023.",
+    "source_image": "40.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/40.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squindom@40",
+      "credit": "Sigvart Brendberg",
+      "date": "June 2023",
+      "family_updated": "8/11/12",
+      "metric_expression": "4.895+",
+      "metric_symbol": "s",
+      "metric_value": 4.895,
+      "reference_text": "40. | | s = 4.895+ | Found by Sigvart Brendberg | in June 2023.",
+      "source_image": "40.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/40.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "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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+      "y": 1.971732199504646
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+    {
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+    },
+    {
+      "id": 36,
+      "rotation_radians": 2.9363774677913947,
+      "x": -0.423435426691801,
+      "y": -0.7886633012585123
+    },
+    {
+      "id": 37,
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+      "y": 1.980967307723659
+    },
+    {
+      "id": 38,
+      "rotation_radians": 5.497790713589981,
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+    },
+    {
+      "id": 39,
+      "rotation_radians": 2.90894568999357,
+      "x": 3.4497212983108865,
+      "y": -0.7137861509295649
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+    {
+      "id": 40,
+      "rotation_radians": 1.3734158969262789,
+      "x": -3.025642807771795,
+      "y": -0.7875698081746138
+    }
+  ],
+  "problem": "40 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/40.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_041_0c31d560a372d60c.json b/data/solutions/generated/squindom_041_0c31d560a372d60c.json
new file mode 100644
index 0000000000000000000000000000000000000000..a85c4cb8b65a4a9ab496c51d1de3710625ea4094
--- /dev/null
+++ b/data/solutions/generated/squindom_041_0c31d560a372d60c.json
@@ -0,0 +1,306 @@
+{
+  "case": "squindom@41",
+  "container": {
+    "height": 5.00016360709587,
+    "type": "rectangle",
+    "width": 10.00032721419174
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squindom@41",
+    "credit": "Sigvart Brendberg",
+    "date": "June 2023",
+    "family_updated": "8/11/12",
+    "metric_expression": "4.927+",
+    "metric_symbol": "s",
+    "metric_value": 4.927,
+    "reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.",
+    "source_image": "41.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squindom@41",
+      "credit": "Sigvart Brendberg",
+      "date": "June 2023",
+      "family_updated": "8/11/12",
+      "metric_expression": "4.927+",
+      "metric_symbol": "s",
+      "metric_value": 4.927,
+      "reference_text": "41. | | s = 4.927+ | Found by Sigvart Brendberg | in June 2023.",
+      "source_image": "41.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/41.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/squindom/",
+    "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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+      "x": 4.4868401998928835,
+      "y": 2.0000695974319647
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+  ],
+  "problem": "41 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/41.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_042_487471a1c6b8324e.json b/data/solutions/generated/squindom_042_487471a1c6b8324e.json
new file mode 100644
index 0000000000000000000000000000000000000000..1d17e9b00fc4208e33f0e9968dbdb6be10e6bf29
--- /dev/null
+++ b/data/solutions/generated/squindom_042_487471a1c6b8324e.json
@@ -0,0 +1,312 @@
+{
+  "case": "squindom@42",
+  "container": {
+    "height": 5.000184535387125,
+    "type": "rectangle",
+    "width": 10.00036907077425
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squindom@42",
+    "credit": "David W",
+    "date": "August 2012",
+    "family_updated": "8/11/12",
+    "metric_expression": "4.989+",
+    "metric_symbol": "s",
+    "metric_value": 4.989,
+    "reference_text": "42. | | s = 4.989+ | Found by David W. Cantrell | in August 2012.",
+    "source_image": "42.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/42.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squindom@42",
+      "credit": "David W",
+      "date": "August 2012",
+      "family_updated": "8/11/12",
+      "metric_expression": "4.989+",
+      "metric_symbol": "s",
+      "metric_value": 4.989,
+      "reference_text": "42. | | s = 4.989+ | Found by David W. Cantrell | in August 2012.",
+      "source_image": "42.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/42.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
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+  ],
+  "problem": "42 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/42.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_043_7f9527ccddc9d648.json b/data/solutions/generated/squindom_043_7f9527ccddc9d648.json
new file mode 100644
index 0000000000000000000000000000000000000000..9f84e01248c745a79ceaecba39e34c030210a8e1
--- /dev/null
+++ b/data/solutions/generated/squindom_043_7f9527ccddc9d648.json
@@ -0,0 +1,318 @@
+{
+  "case": "squindom@43",
+  "container": {
+    "height": 5.000325272095715,
+    "type": "rectangle",
+    "width": 10.00065054419143
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squindom@43",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "8/11/12",
+    "metric_expression": "5",
+    "metric_symbol": "s",
+    "metric_value": 5.0,
+    "reference_text": "43-50. | | s = 5 | Trivial. |",
+    "source_image": "50.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squindom@43",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "8/11/12",
+      "metric_expression": "5",
+      "metric_symbol": "s",
+      "metric_value": 5.0,
+      "reference_text": "43-50. | | s = 5 | Trivial. |",
+      "source_image": "50.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/50.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_044_1ffd758f1f058de5.json b/data/solutions/generated/squindom_044_1ffd758f1f058de5.json
new file mode 100644
index 0000000000000000000000000000000000000000..15890e1d5931f1ef73abaa1f3a359849c6cd7a97
--- /dev/null
+++ b/data/solutions/generated/squindom_044_1ffd758f1f058de5.json
@@ -0,0 +1,324 @@
+{
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+    "family_updated": "8/11/12",
+    "metric_expression": "5",
+    "metric_symbol": "s",
+    "metric_value": 5.0,
+    "reference_text": "43-50. | | s = 5 | Trivial. |",
+    "source_image": "50.gif",
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+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
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+      "metric_expression": "5",
+      "metric_symbol": "s",
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+      "reference_text": "43-50. | | s = 5 | Trivial. |",
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+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
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+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_045_d085ed9682ca2968.json b/data/solutions/generated/squindom_045_d085ed9682ca2968.json
new file mode 100644
index 0000000000000000000000000000000000000000..f3ceac8bc9a8090bc1c578fe100c04e4a93c1193
--- /dev/null
+++ b/data/solutions/generated/squindom_045_d085ed9682ca2968.json
@@ -0,0 +1,330 @@
+{
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+    "credit": "Trivial",
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+    "family_updated": "8/11/12",
+    "metric_expression": "5",
+    "metric_symbol": "s",
+    "metric_value": 5.0,
+    "reference_text": "43-50. | | s = 5 | Trivial. |",
+    "source_image": "50.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
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+      "family_updated": "8/11/12",
+      "metric_expression": "5",
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+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/50.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_046_3b408e84cd206068.json b/data/solutions/generated/squindom_046_3b408e84cd206068.json
new file mode 100644
index 0000000000000000000000000000000000000000..fdb7844b9375794857db26831e591ee8748644f7
--- /dev/null
+++ b/data/solutions/generated/squindom_046_3b408e84cd206068.json
@@ -0,0 +1,336 @@
+{
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+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "8/11/12",
+    "metric_expression": "5",
+    "metric_symbol": "s",
+    "metric_value": 5.0,
+    "reference_text": "43-50. | | s = 5 | Trivial. |",
+    "source_image": "50.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
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+      "family_updated": "8/11/12",
+      "metric_expression": "5",
+      "metric_symbol": "s",
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+      "reference_text": "43-50. | | s = 5 | Trivial. |",
+      "source_image": "50.gif",
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+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
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+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/50.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_047_1d33d4d710718c8f.json b/data/solutions/generated/squindom_047_1d33d4d710718c8f.json
new file mode 100644
index 0000000000000000000000000000000000000000..7af53f06fd71d21b2fa2cf911d2e6944c6a903bc
--- /dev/null
+++ b/data/solutions/generated/squindom_047_1d33d4d710718c8f.json
@@ -0,0 +1,342 @@
+{
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+    "family_updated": "8/11/12",
+    "metric_expression": "5",
+    "metric_symbol": "s",
+    "metric_value": 5.0,
+    "reference_text": "43-50. | | s = 5 | Trivial. |",
+    "source_image": "50.gif",
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+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
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+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
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+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_048_0433c6294c4f3fe7.json b/data/solutions/generated/squindom_048_0433c6294c4f3fe7.json
new file mode 100644
index 0000000000000000000000000000000000000000..05338d6ea52d907012c6ce98854a88b5858b0c7b
--- /dev/null
+++ b/data/solutions/generated/squindom_048_0433c6294c4f3fe7.json
@@ -0,0 +1,348 @@
+{
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+    "family_updated": "8/11/12",
+    "metric_expression": "5",
+    "metric_symbol": "s",
+    "metric_value": 5.0,
+    "reference_text": "43-50. | | s = 5 | Trivial. |",
+    "source_image": "50.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
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+  "setup": "squindom",
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+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_049_7b7595adf7fbed15.json b/data/solutions/generated/squindom_049_7b7595adf7fbed15.json
new file mode 100644
index 0000000000000000000000000000000000000000..f93249dc4b2d9386ed47006c7b2485592445a52a
--- /dev/null
+++ b/data/solutions/generated/squindom_049_7b7595adf7fbed15.json
@@ -0,0 +1,354 @@
+{
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+    "family_updated": "8/11/12",
+    "metric_expression": "5",
+    "metric_symbol": "s",
+    "metric_value": 5.0,
+    "reference_text": "43-50. | | s = 5 | Trivial. |",
+    "source_image": "50.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
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+      "family_updated": "8/11/12",
+      "metric_expression": "5",
+      "metric_symbol": "s",
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+      "reference_text": "43-50. | | s = 5 | Trivial. |",
+      "source_image": "50.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
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+  ],
+  "problem": "49 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/50.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squindom_050_1dc2963cf23fe9ee.json b/data/solutions/generated/squindom_050_1dc2963cf23fe9ee.json
new file mode 100644
index 0000000000000000000000000000000000000000..609aa108d4f142ef399f96949dd905c526b98d9d
--- /dev/null
+++ b/data/solutions/generated/squindom_050_1dc2963cf23fe9ee.json
@@ -0,0 +1,360 @@
+{
+  "case": "squindom@50",
+  "container": {
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+    "type": "rectangle",
+    "width": 11.179318571407277
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squindom@50",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "8/11/12",
+    "metric_expression": "5",
+    "metric_symbol": "s",
+    "metric_value": 5.0,
+    "reference_text": "43-50. | | s = 5 | Trivial. |",
+    "source_image": "50.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squindom/",
+    "title": "Squares in Dominoes"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squindom@50",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "8/11/12",
+      "metric_expression": "5",
+      "metric_symbol": "s",
+      "metric_value": 5.0,
+      "reference_text": "43-50. | | s = 5 | Trivial. |",
+      "source_image": "50.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squindom/50.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squindom/",
+      "title": "Squares in Dominoes"
+    },
+    "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/squindom/",
+    "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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+    },
+    {
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+    },
+    {
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+    },
+    {
+      "id": 48,
+      "rotation_radians": -0.9498121598057938,
+      "x": 4.436428142008383,
+      "y": 2.2188115107164332
+    },
+    {
+      "id": 49,
+      "rotation_radians": -0.7779240203353868,
+      "x": -4.861802712841794,
+      "y": 2.2910754408562224
+    },
+    {
+      "id": 50,
+      "rotation_radians": -0.7861988635049835,
+      "x": -3.8074642367586793,
+      "y": 2.2939795020960068
+    }
+  ],
+  "problem": "50 equal items for Squares in Dominoes",
+  "setup": "squindom",
+  "source_image": "https://erich-friedman.github.io/packing/squindom/50.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squindom/"
+}
diff --git a/data/solutions/generated/squinhex_021_3a812c823f86feb7.json b/data/solutions/generated/squinhex_021_3a812c823f86feb7.json
new file mode 100644
index 0000000000000000000000000000000000000000..bf048f8a4a2808adf98ae1db8f5082411d4d7d34
--- /dev/null
+++ b/data/solutions/generated/squinhex_021_3a812c823f86feb7.json
@@ -0,0 +1,188 @@
+{
+  "case": "squinhex@21",
+  "container": {
+    "circumradius": 3.2462224555515258,
+    "orientation_radians": 0.0,
+    "side_length": 3.2462224555515253,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@21",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.23496+",
+    "metric_symbol": "s",
+    "metric_value": 3.23496,
+    "reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.",
+    "source_image": "21.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@21",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.23496+",
+      "metric_symbol": "s",
+      "metric_value": 3.23496,
+      "reference_text": "s = 3.23496+ | Found by Ian Watson | in April 2026.",
+      "source_image": "21.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/21.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/squinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.6759240989550092,
+      "x": -0.07587297937859891,
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+      "y": -0.27909313715812467
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+      "y": -1.1035697163668023
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+    {
+      "id": 16,
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+      "x": 2.104896610035874,
+      "y": -0.6591553524003289
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.5919790692758753,
+      "x": -2.1018935734566218,
+      "y": 0.6622933407417531
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.5994880386002699,
+      "x": -1.0596370221563791,
+      "y": 0.294181191798912
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.7835644652682807,
+      "x": 0.49050279323765017,
+      "y": 2.3099156472449804
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.5920751269654153,
+      "x": -2.2414008305638244,
+      "y": -0.32946169425028865
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.5994899865278116,
+      "x": -1.2873524371802179,
+      "y": -0.6805551281860684
+    }
+  ],
+  "problem": "21 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/21.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_022_a1e7eaf12003fa2e.json b/data/solutions/generated/squinhex_022_a1e7eaf12003fa2e.json
new file mode 100644
index 0000000000000000000000000000000000000000..2f39d3f0a4982d48b5d93dd3f9ccde448c6b51ce
--- /dev/null
+++ b/data/solutions/generated/squinhex_022_a1e7eaf12003fa2e.json
@@ -0,0 +1,194 @@
+{
+  "case": "squinhex@22",
+  "container": {
+    "circumradius": 3.3150640439651093,
+    "orientation_radians": 0.0,
+    "side_length": 3.315064043965109,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@22",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.31573+",
+    "metric_symbol": "s",
+    "metric_value": 3.31573,
+    "reference_text": "s = 3.31573+ | Found by Ian Watson | in April 2026.",
+    "source_image": "22.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/22.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@22",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.31573+",
+      "metric_symbol": "s",
+      "metric_value": 3.31573,
+      "reference_text": "s = 3.31573+ | Found by Ian Watson | in April 2026.",
+      "source_image": "22.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/22.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.6601036144467448,
+      "x": 0.6358047708826399,
+      "y": 2.312326692472868
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+      "x": -1.5751214236951503,
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+    {
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+      "y": -1.049263159240478
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+    {
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+    {
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+    {
+      "id": 16,
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+      "x": 0.18135227030891102,
+      "y": -1.055989733034629
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.26180175497973496,
+      "x": -2.5751504575372675,
+      "y": 0.28153452321818
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.7089967574045609,
+      "x": 0.43300547491689234,
+      "y": -2.285994732858188
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.6673664126403278,
+      "x": -0.3744883803876888,
+      "y": 2.3155123642576414
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.26208723095774017,
+      "x": 1.0500425532713564,
+      "y": -0.5568849444206228
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.7089953329196208,
+      "x": -0.5734514389418056,
+      "y": -2.3317203103841493
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.2618016969744831,
+      "x": 1.6318833874363712,
+      "y": -1.9153225308004769
+    }
+  ],
+  "problem": "22 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/22.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_023_c418f25bcf52655a.json b/data/solutions/generated/squinhex_023_c418f25bcf52655a.json
new file mode 100644
index 0000000000000000000000000000000000000000..3cf5d36126a13235e97483ea244b53b2a2f6a653
--- /dev/null
+++ b/data/solutions/generated/squinhex_023_c418f25bcf52655a.json
@@ -0,0 +1,200 @@
+{
+  "case": "squinhex@23",
+  "container": {
+    "circumradius": 3.395398866190117,
+    "orientation_radians": 0.0,
+    "side_length": 3.3953988661901167,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@23",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.36437+",
+    "metric_symbol": "s",
+    "metric_value": 3.36437,
+    "reference_text": "s = 3.36437+ | Found by Ian Watson | in April 2026.",
+    "source_image": "23.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/23.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@23",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.36437+",
+      "metric_symbol": "s",
+      "metric_value": 3.36437,
+      "reference_text": "s = 3.36437+ | Found by Ian Watson | in April 2026.",
+      "source_image": "23.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/23.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.33418685516124375,
+      "x": -1.5964710125183386,
+      "y": -2.0450814473773296
+    },
+    {
+      "id": 2,
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+      "x": -0.6803470159262169,
+      "y": -1.6397339553140213
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+    {
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+      "x": 0.3614315083368069,
+      "y": -2.226381879009547
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+    {
+      "id": 4,
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+      "y": -1.3921756288835367
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+      "x": -2.1802090927627513,
+      "y": -1.0897989774314611
+    },
+    {
+      "id": 7,
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+      "x": -1.1900588122309004,
+      "y": -0.7511538380225387
+    },
+    {
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+      "y": -0.7035878564830326
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+    {
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+    },
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+      "x": 2.5142812492434734,
+      "y": -0.5261087362647413
+    },
+    {
+      "id": 11,
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+      "x": -2.6159553802276814,
+      "y": -0.06796949131380596
+    },
+    {
+      "id": 12,
+      "rotation_radians": -0.36996203873038286,
+      "x": -1.5955149426471467,
+      "y": 0.1668795704944947
+    },
+    {
+      "id": 13,
+      "rotation_radians": -0.40330754376031147,
+      "x": -0.5398568604586487,
+      "y": 0.34274747154755325
+    },
+    {
+      "id": 14,
+      "rotation_radians": -0.4622584136413668,
+      "x": 0.5268535049664124,
+      "y": 0.44328447792450215
+    },
+    {
+      "id": 15,
+      "rotation_radians": 0.2617895194880204,
+      "x": 1.5262500096578901,
+      "y": -0.23734274641783926
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.38108718874459807,
+      "x": -1.9458374784740722,
+      "y": 1.1107566936342372
+    },
+    {
+      "id": 17,
+      "rotation_radians": -0.42164596703246376,
+      "x": -0.9189812039667721,
+      "y": 1.2805386119304571
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.4622627682541183,
+      "x": 0.17109980205626193,
+      "y": 1.378770197208382
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.4416942307088022,
+      "x": 1.2696207274186797,
+      "y": 1.3658860494943297
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.3296186814200756,
+      "x": 2.323027519341803,
+      "y": 0.709757535408642
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.788683629202163,
+      "x": -1.2278870791465517,
+      "y": 2.3893662546026384
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.7853889737388728,
+      "x": -0.22620025090555446,
+      "y": 2.440486610881553
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.4437380625751952,
+      "x": 0.9139830742856148,
+      "y": 2.3018558323946148
+    }
+  ],
+  "problem": "23 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/23.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_024_94da47c0085910e3.json b/data/solutions/generated/squinhex_024_94da47c0085910e3.json
new file mode 100644
index 0000000000000000000000000000000000000000..387d3ce06eba9e5b5f6ed3b23b586f45f91e7960
--- /dev/null
+++ b/data/solutions/generated/squinhex_024_94da47c0085910e3.json
@@ -0,0 +1,206 @@
+{
+  "case": "squinhex@24",
+  "container": {
+    "circumradius": 3.429719391564235,
+    "orientation_radians": 0.0,
+    "side_length": 3.4297193915642348,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@24",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.41524+",
+    "metric_symbol": "s",
+    "metric_value": 3.41524,
+    "reference_text": "s = 3.41524+ | Found by Ian Watson | in April 2026.",
+    "source_image": "24.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/24.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@24",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.41524+",
+      "metric_symbol": "s",
+      "metric_value": 3.41524,
+      "reference_text": "s = 3.41524+ | Found by Ian Watson | in April 2026.",
+      "source_image": "24.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/24.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
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+      "y": 1.379500507342525
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+      "y": 1.3807534655202558
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+    {
+      "id": 20,
+      "rotation_radians": 1.1081463564809602,
+      "x": 1.8731691853468804,
+      "y": 1.5052805051238272
+    },
+    {
+      "id": 21,
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+      "x": -1.8644515822152579,
+      "y": 1.7110902195831283
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+    {
+      "id": 22,
+      "rotation_radians": -0.7853985071413445,
+      "x": -0.8131906659983374,
+      "y": 2.470209599129643
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+    {
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+      "rotation_radians": -0.7853960114868349,
+      "x": 0.18684458126215528,
+      "y": 2.4702070897898487
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.7853902669851293,
+      "x": 1.18688070653436,
+      "y": 2.4702175520886995
+    }
+  ],
+  "problem": "24 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/24.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_025_e42cc21b7cb42f7c.json b/data/solutions/generated/squinhex_025_e42cc21b7cb42f7c.json
new file mode 100644
index 0000000000000000000000000000000000000000..b3ade021b727e32bd41e268e0dd2b6299938671b
--- /dev/null
+++ b/data/solutions/generated/squinhex_025_e42cc21b7cb42f7c.json
@@ -0,0 +1,212 @@
+{
+  "case": "squinhex@25",
+  "container": {
+    "circumradius": 3.472530980948481,
+    "orientation_radians": 0.0,
+    "side_length": 3.4725309809484806,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squinhex@25",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "4/29/26",
+    "metric_expression": "2\u221a3 = 3.46410+",
+    "metric_symbol": "s",
+    "metric_value": 3.4641,
+    "reference_text": "s = 2\u221a3 = 3.46410+ | Trivial. |",
+    "source_image": "25.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/25.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squinhex@25",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "4/29/26",
+      "metric_expression": "2\u221a3 = 3.46410+",
+      "metric_symbol": "s",
+      "metric_value": 3.4641,
+      "reference_text": "s = 2\u221a3 = 3.46410+ | Trivial. |",
+      "source_image": "25.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/25.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "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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+    {
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+      "y": -2.5072828800483653
+    },
+    {
+      "id": 21,
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+      "x": 1.7827405946155575,
+      "y": 1.926776687296748
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+    {
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+      "x": 2.784550328891165,
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+    {
+      "id": 23,
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+      "x": -1.9722525703875513,
+      "y": -1.583701524133338
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.10837422011133627,
+      "x": 1.793694698631801,
+      "y": -1.7666792781290273
+    },
+    {
+      "id": 25,
+      "rotation_radians": -0.26178248229595175,
+      "x": 2.2842931566125193,
+      "y": 1.057551540429897
+    }
+  ],
+  "problem": "25 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/25.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_026_ffb43ba6e2cd5818.json b/data/solutions/generated/squinhex_026_ffb43ba6e2cd5818.json
new file mode 100644
index 0000000000000000000000000000000000000000..444794d394cc097df6ec33d54f1d49155c189569
--- /dev/null
+++ b/data/solutions/generated/squinhex_026_ffb43ba6e2cd5818.json
@@ -0,0 +1,218 @@
+{
+  "case": "squinhex@26",
+  "container": {
+    "circumradius": 3.5188698735793666,
+    "orientation_radians": 0.0,
+    "side_length": 3.518869873579366,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@26",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.4939927+",
+    "metric_symbol": "s",
+    "metric_value": 3.4939927,
+    "reference_text": "s = 3.4939927+ | Found by Ian Watson | in April 2026.",
+    "source_image": "26.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/26.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@26",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.4939927+",
+      "metric_symbol": "s",
+      "metric_value": 3.4939927,
+      "reference_text": "s = 3.4939927+ | Found by Ian Watson | in April 2026.",
+      "source_image": "26.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/26.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "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": -0.2236952806450043,
+      "y": -1.4818039627585737
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+    },
+    {
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+    {
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+      "x": -2.2547831823664004,
+      "y": 0.8243498007333331
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.2618523452156667,
+      "x": 1.5797926302511065,
+      "y": -2.358525517733128
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.3116291751907658,
+      "x": -1.7595104721215462,
+      "y": -0.04448992859711446
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.30066240534142674,
+      "x": -0.7290047742227257,
+      "y": -2.3666258054672986
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.26225662342141237,
+      "x": 0.4443468392804607,
+      "y": -2.3252010782558674
+    },
+    {
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+      "y": 2.5417220354227466
+    },
+    {
+      "id": 26,
+      "rotation_radians": 1.3116270781305925,
+      "x": -1.2595019356321053,
+      "y": -0.9105771944936614
+    }
+  ],
+  "problem": "26 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/26.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_027_1daf4383b04cfd35.json b/data/solutions/generated/squinhex_027_1daf4383b04cfd35.json
new file mode 100644
index 0000000000000000000000000000000000000000..6b435918f511016d4848728357ec85a4e82ae385
--- /dev/null
+++ b/data/solutions/generated/squinhex_027_1daf4383b04cfd35.json
@@ -0,0 +1,224 @@
+{
+  "case": "squinhex@27",
+  "container": {
+    "circumradius": 3.557305397891923,
+    "orientation_radians": 0.0,
+    "side_length": 3.5573053978919225,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squinhex@27",
+    "credit": "Erich Friedman",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "(9+7\u221a3)/6 = 3.52072+",
+    "metric_symbol": "s",
+    "metric_value": 3.52072,
+    "reference_text": "s = (9+7\u221a3)/6 = 3.52072+ | Found by Erich Friedman | in April 2026.",
+    "source_image": "27.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/27.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squinhex@27",
+      "credit": "Erich Friedman",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "(9+7\u221a3)/6 = 3.52072+",
+      "metric_symbol": "s",
+      "metric_value": 3.52072,
+      "reference_text": "s = (9+7\u221a3)/6 = 3.52072+ | Found by Erich Friedman | in April 2026.",
+      "source_image": "27.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/27.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.2640188872778935,
+      "x": -1.903294586368045,
+      "y": -1.8514143191767494
+    },
+    {
+      "id": 2,
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+      "x": -0.7985635649433911,
+      "y": -2.5807079997133346
+    },
+    {
+      "id": 3,
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+      "x": 0.20147179358422904,
+      "y": -2.580705381030683
+    },
+    {
+      "id": 4,
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+      "x": 1.2147282207729728,
+      "y": -2.551873449402318
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+    {
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+      "x": 2.0188314330907318,
+      "y": -1.6564004217598154
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+    {
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+      "x": 2.524324514600553,
+      "y": -0.7890589650598597
+    },
+    {
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+      "x": -2.3828671607962377,
+      "y": -0.9736242086539342
+    },
+    {
+      "id": 8,
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+      "x": -0.8899339451037592,
+      "y": -1.4233961136784739
+    },
+    {
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+      "y": -1.3997009064883592
+    },
+    {
+      "id": 10,
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+      "x": 1.1419036498818702,
+      "y": -0.8165226911838326
+    },
+    {
+      "id": 11,
+      "rotation_radians": -0.2606910702928018,
+      "x": 1.7498726817804977,
+      "y": 0.12936739870770728
+    },
+    {
+      "id": 12,
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+      "x": 2.701997091233083,
+      "y": 0.48140600081961576
+    },
+    {
+      "id": 13,
+      "rotation_radians": -0.2640185458082449,
+      "x": -2.8041601947054935,
+      "y": -0.06236086285459175
+    },
+    {
+      "id": 14,
+      "rotation_radians": -0.3771942123608246,
+      "x": -1.414042358335974,
+      "y": -0.5602653356728349
+    },
+    {
+      "id": 15,
+      "rotation_radians": -0.2727105323587102,
+      "x": -0.185463893738879,
+      "y": -0.5350116840220922
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.3034900396164544,
+      "x": 0.6345276877701667,
+      "y": 0.051293230009029106
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.3133693335600711,
+      "x": 1.2471097950997518,
+      "y": 0.995722678346475
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.3133684401208363,
+      "x": 2.179815636046675,
+      "y": 1.381481748061737
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.2617962512488223,
+      "x": -2.0880880477145802,
+      "y": 1.5447345603612548
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.3771908911853956,
+      "x": -1.8339207445553993,
+      "y": 0.3476953601177456
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.2727123655696819,
+      "x": -0.6837634944064233,
+      "y": 0.3320670802741167
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.2725935765776087,
+      "x": 0.12497774868019547,
+      "y": 0.9340987260353547
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.261798680326908,
+      "x": 0.7483401918272712,
+      "y": 1.8651934355429205
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.26179857404183454,
+      "x": 1.598406744021639,
+      "y": 2.3928871046251055
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.26179826839337095,
+      "x": -1.5653717092242971,
+      "y": 2.3976845202594124
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.1846824576502043,
+      "x": -0.8795530380987648,
+      "y": 1.5638395526126467
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.18468174988463998,
+      "x": -0.30965023163627964,
+      "y": 2.385612919637205
+    }
+  ],
+  "problem": "27 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/27.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_028_a261c762e391859b.json b/data/solutions/generated/squinhex_028_a261c762e391859b.json
new file mode 100644
index 0000000000000000000000000000000000000000..3f142b6965254d8a0960475e2005034002ef0b72
--- /dev/null
+++ b/data/solutions/generated/squinhex_028_a261c762e391859b.json
@@ -0,0 +1,230 @@
+{
+  "case": "squinhex@28",
+  "container": {
+    "circumradius": 3.636771972861152,
+    "orientation_radians": 0.0,
+    "side_length": 3.6367719728611516,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@28",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.62565+",
+    "metric_symbol": "s",
+    "metric_value": 3.62565,
+    "reference_text": "s = 3.62565+ | Found by Ian Watson | in April 2026.",
+    "source_image": "28.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/28.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@28",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.62565+",
+      "metric_symbol": "s",
+      "metric_value": 3.62565,
+      "reference_text": "s = 3.62565+ | Found by Ian Watson | in April 2026.",
+      "source_image": "28.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/28.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.8675427526577613,
+      "x": -0.32873444752825787,
+      "y": 0.529054423661594
+    },
+    {
+      "id": 2,
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+      "y": -0.5166786160088567
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+    {
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+      "x": 0.40366368089773347,
+      "y": -0.5278408650393269
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+    {
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+    },
+    {
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+      "x": -1.3411929993534009,
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+    },
+    {
+      "id": 11,
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+    },
+    {
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+    {
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+      "x": 1.4218625261719402,
+      "y": -0.6452262944708561
+    },
+    {
+      "id": 14,
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+      "x": -2.8449728660417906,
+      "y": -0.32571851571671506
+    },
+    {
+      "id": 15,
+      "rotation_radians": -0.8991336727791007,
+      "x": 2.0784117739504353,
+      "y": 1.3003767413101393
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.9197345818990067,
+      "x": 1.8908080372519784,
+      "y": -1.7193949193425118
+    },
+    {
+      "id": 17,
+      "rotation_radians": -1.300592994475529,
+      "x": -2.4975610350703725,
+      "y": 0.8287830124535467
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.9197380218844484,
+      "x": -1.1066016699288665,
+      "y": -1.4979777426218202
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.9197392969151065,
+      "x": -0.11165226649223381,
+      "y": -1.6027630972831735
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.7434164527321151,
+      "x": 0.11039318029597867,
+      "y": 2.607672623749594
+    },
+    {
+      "id": 21,
+      "rotation_radians": -1.2995121690379798,
+      "x": -2.0557581095170256,
+      "y": 1.728655944576992
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.9142388701557191,
+      "x": 0.7673820549022843,
+      "y": -2.5894228198007596
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.8203517046545201,
+      "x": 2.7025523784286407,
+      "y": 0.24008124364200573
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.7854057100598857,
+      "x": -1.1251712430475982,
+      "y": 2.64952507926819
+    },
+    {
+      "id": 25,
+      "rotation_radians": -0.8382515909820373,
+      "x": -0.3207213777369373,
+      "y": -2.623202718317398
+    },
+    {
+      "id": 26,
+      "rotation_radians": -0.902476272523705,
+      "x": 2.4233374944608284,
+      "y": -0.773609357303761
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.6510564267538171,
+      "x": -2.08656185720669,
+      "y": -1.2823005955437827
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.9834992916966624,
+      "x": 1.3302732131015198,
+      "y": 2.5075573217528415
+    }
+  ],
+  "problem": "28 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/28.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_029_b4f34cc71652a9b5.json b/data/solutions/generated/squinhex_029_b4f34cc71652a9b5.json
new file mode 100644
index 0000000000000000000000000000000000000000..3b9129443cdbdc8b5d105c2042c945786113376d
--- /dev/null
+++ b/data/solutions/generated/squinhex_029_b4f34cc71652a9b5.json
@@ -0,0 +1,236 @@
+{
+  "case": "squinhex@29",
+  "container": {
+    "circumradius": 3.699888460728492,
+    "orientation_radians": 0.0,
+    "side_length": 3.6998884607284914,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@29",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.66437+",
+    "metric_symbol": "s",
+    "metric_value": 3.66437,
+    "reference_text": "s = 3.66437+ | Found by Ian Watson | in April 2026.",
+    "source_image": "29.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/29.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@29",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.66437+",
+      "metric_symbol": "s",
+      "metric_value": 3.66437,
+      "reference_text": "s = 3.66437+ | Found by Ian Watson | in April 2026.",
+      "source_image": "29.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/29.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.7436499457828721,
+      "x": -0.5068341019297985,
+      "y": 0.4824355815444562
+    },
+    {
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+      "y": 1.6611001493434727
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+      "x": -1.5126479237068526,
+      "y": 0.4129516569279208
+    },
+    {
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+      "x": 0.4862490492345076,
+      "y": 0.6706691169447925
+    },
+    {
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+      "y": -1.313267369614534
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+    {
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+      "x": -1.0823333021539268,
+      "y": 1.4866917921427585
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+    {
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+    },
+    {
+      "id": 10,
+      "rotation_radians": -0.771363427610657,
+      "x": -1.4088531478112436,
+      "y": -2.6070383056314026
+    },
+    {
+      "id": 11,
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+      "y": 0.3593824053581815
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.7376588645113508,
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+      "y": -1.5802987442091787
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+    {
+      "id": 19,
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+      "y": -1.578867913661784
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+    {
+      "id": 20,
+      "rotation_radians": -0.7553261530187827,
+      "x": -0.2654020508213184,
+      "y": 2.6671573051234136
+    },
+    {
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+      "y": 1.4746369911706123
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+    {
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+      "y": -2.6760355605425405
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+    {
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+      "x": 2.485721951614913,
+      "y": 0.7525531575972345
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.5417175594830764,
+      "x": -1.4049644777524106,
+      "y": 2.540468341589634
+    },
+    {
+      "id": 25,
+      "rotation_radians": -0.7660885294166588,
+      "x": -0.40532183672516026,
+      "y": -2.611449964496363
+    },
+    {
+      "id": 26,
+      "rotation_radians": -0.8368503951726683,
+      "x": 2.755994849656018,
+      "y": -0.2893777681300581
+    },
+    {
+      "id": 27,
+      "rotation_radians": -0.26181491807329277,
+      "x": -2.1727396466809776,
+      "y": -1.6450714822931995
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.7802536445380738,
+      "x": 0.7595835349246867,
+      "y": 2.7016229431665244
+    },
+    {
+      "id": 29,
+      "rotation_radians": -0.7385082122559332,
+      "x": 1.9204852529277634,
+      "y": 1.7340239234383645
+    }
+  ],
+  "problem": "29 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/29.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_030_622f4b213176ff50.json b/data/solutions/generated/squinhex_030_622f4b213176ff50.json
new file mode 100644
index 0000000000000000000000000000000000000000..fe03f55b7d7df06a27cb7aaa1041a68486d7f892
--- /dev/null
+++ b/data/solutions/generated/squinhex_030_622f4b213176ff50.json
@@ -0,0 +1,242 @@
+{
+  "case": "squinhex@30",
+  "container": {
+    "circumradius": 3.713897533893604,
+    "orientation_radians": 0.0,
+    "side_length": 3.7138975338936038,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@30",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.69554+",
+    "metric_symbol": "s",
+    "metric_value": 3.69554,
+    "reference_text": "s = 3.69554+ | Found by Ian Watson | in April 2026.",
+    "source_image": "30.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/30.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@30",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.69554+",
+      "metric_symbol": "s",
+      "metric_value": 3.69554,
+      "reference_text": "s = 3.69554+ | Found by Ian Watson | in April 2026.",
+      "source_image": "30.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/30.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.19401199721413637,
+      "x": -1.9481005771793396,
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+      "x": 1.3148544383076848,
+      "y": -0.8452399498679434
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+      "x": 2.523492725587881,
+      "y": -1.0618117598703067
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+    {
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+      "x": -0.5367753169273953,
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+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.4269709015633363,
+      "x": -0.6955572341800743,
+      "y": 0.06886842348730783
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.2621248805380167,
+      "x": 3.0253767243308225,
+      "y": -0.19213800861214614
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.7853969907563457,
+      "x": -1.0269300488452207,
+      "y": 2.71630637658691
+    },
+    {
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+      "rotation_radians": 1.3157726780956438,
+      "x": -3.027749625593595,
+      "y": -0.17513041050132336
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+    {
+      "id": 23,
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+      "x": 1.3620046414433167,
+      "y": 2.530625037824825
+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.4336441216309257,
+      "x": 0.7256197926858059,
+      "y": -0.03703184039542095
+    },
+    {
+      "id": 25,
+      "rotation_radians": 1.4092998531604908,
+      "x": -1.3641197134206229,
+      "y": -0.7762120576148431
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.7396946032920813,
+      "x": -0.040515059616341706,
+      "y": -2.693201064453702
+    },
+    {
+      "id": 27,
+      "rotation_radians": 1.4615068110115839,
+      "x": 1.3102041936699658,
+      "y": 0.9444809889993263
+    },
+    {
+      "id": 28,
+      "rotation_radians": 0.7235402674231664,
+      "x": 0.9740663914625523,
+      "y": -2.6863514106165547
+    },
+    {
+      "id": 29,
+      "rotation_radians": 1.4478132201851077,
+      "x": 0.6479530180708619,
+      "y": 1.7067681439828852
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.460000640939602,
+      "x": 1.8790849860357535,
+      "y": 0.1179462520002707
+    }
+  ],
+  "problem": "30 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/30.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_031_5ef6ed65925f4bf8.json b/data/solutions/generated/squinhex_031_5ef6ed65925f4bf8.json
new file mode 100644
index 0000000000000000000000000000000000000000..0083bd8f6c0c6bc6b1eb4935a8f7978b733be2d0
--- /dev/null
+++ b/data/solutions/generated/squinhex_031_5ef6ed65925f4bf8.json
@@ -0,0 +1,248 @@
+{
+  "case": "squinhex@31",
+  "container": {
+    "circumradius": 3.7949472665360036,
+    "orientation_radians": 0.0,
+    "side_length": 3.794947266536003,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@31",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.78410+",
+    "metric_symbol": "s",
+    "metric_value": 3.7841,
+    "reference_text": "s = 3.78410+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "31.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/31.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@31",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.78410+",
+      "metric_symbol": "s",
+      "metric_value": 3.7841,
+      "reference_text": "s = 3.78410+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "31.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/31.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.6232020945453554,
+      "x": -0.47944955142440593,
+      "y": 0.5318362612629399
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+    {
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+    {
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+      "x": 2.1714766492510336,
+      "y": 1.806387541943984
+    },
+    {
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+    },
+    {
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+      "y": -2.7056569137734092
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+    {
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+      "x": 2.671497558282095,
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+    {
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+      "rotation_radians": 0.7853777161646324,
+      "x": 1.278109165973934,
+      "y": -2.7865028614121
+    },
+    {
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+      "y": 2.5566303250921574
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+    {
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+      "x": 3.1083272205572507,
+      "y": -0.16921880411414458
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.6338848381450235,
+      "x": 1.394249439039491,
+      "y": -0.7701439955501879
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.9047295548861715,
+      "x": 1.4605555870777776,
+      "y": 2.730537288058612
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.6077108659043665,
+      "x": -0.958581926304321,
+      "y": 1.6327961809592275
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.24153092442608085,
+      "x": 2.1067658904648154,
+      "y": -1.900891966506724
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.6343377421299399,
+      "x": 0.9679914375738498,
+      "y": -1.7169168670364758
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.6500576279311151,
+      "x": 1.0445579597556698,
+      "y": 1.3581417232879234
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.5075083036173315,
+      "x": -1.5207271822375121,
+      "y": 0.7011279164063284
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.6724251803253376,
+      "x": 0.5546011993739556,
+      "y": 0.400751208720049
+    },
+    {
+      "id": 27,
+      "rotation_radians": 1.3176318540021597,
+      "x": -2.4031641938085095,
+      "y": -1.3767406243310982
+    },
+    {
+      "id": 28,
+      "rotation_radians": 0.6192785410839695,
+      "x": 0.04654762285029467,
+      "y": 1.545123115285953
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.26582670738945735,
+      "x": -2.2343810957839434,
+      "y": 1.6841775692580045
+    },
+    {
+      "id": 30,
+      "rotation_radians": 0.24153985155170743,
+      "x": 2.5705766036434756,
+      "y": -1.012701783095858
+    },
+    {
+      "id": 31,
+      "rotation_radians": 0.623123696864899,
+      "x": -0.6194315655974678,
+      "y": -0.4593436669355711
+    }
+  ],
+  "problem": "31 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/31.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_032_3fefe3c7860a7042.json b/data/solutions/generated/squinhex_032_3fefe3c7860a7042.json
new file mode 100644
index 0000000000000000000000000000000000000000..a8dd7ff2d9f95b5cbe84758cc961e0dfaced4ea4
--- /dev/null
+++ b/data/solutions/generated/squinhex_032_3fefe3c7860a7042.json
@@ -0,0 +1,254 @@
+{
+  "case": "squinhex@32",
+  "container": {
+    "circumradius": 3.8900498740505967,
+    "orientation_radians": 0.0,
+    "side_length": 3.890049874050596,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@32",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.84795+",
+    "metric_symbol": "s",
+    "metric_value": 3.84795,
+    "reference_text": "s = 3.84795+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "32.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/32.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@32",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.84795+",
+      "metric_symbol": "s",
+      "metric_value": 3.84795,
+      "reference_text": "s = 3.84795+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "32.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/32.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
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+      "y": -0.8446858866262057
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+    {
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+    {
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+    {
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+    {
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+      "y": 1.830265701808273
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+    {
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+    {
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+    {
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+      "x": 0.7820942104094442,
+      "y": 1.8440891094798708
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+    {
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+      "rotation_radians": -0.2617799013609324,
+      "x": -2.70530727479185,
+      "y": -0.8982758037326155
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.2618221394268681,
+      "x": -2.1644415975044136,
+      "y": -1.7407694840175978
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.7770890926376783,
+      "x": -0.4569472452065946,
+      "y": 2.8466999140448723
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.7855480672480207,
+      "x": -0.5887875753105072,
+      "y": -2.866825725596241
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.2029118513746155,
+      "x": 3.189076148723064,
+      "y": -0.1280122162271791
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.25325670489371005,
+      "x": -2.639946352446856,
+      "y": 1.0047157986471962
+    },
+    {
+      "id": 26,
+      "rotation_radians": -0.31471369896323753,
+      "x": 2.7096464687928683,
+      "y": 0.9541889197279688
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.20293583644194552,
+      "x": 2.65492845632743,
+      "y": -0.9736397300095935
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.777095947443721,
+      "x": 0.5429926108901456,
+      "y": 2.862462041764315
+    },
+    {
+      "id": 29,
+      "rotation_radians": -0.7770980357797608,
+      "x": -1.4570119555250614,
+      "y": 2.8450822139309904
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.235587411368013,
+      "x": 1.7102090740587372,
+      "y": 2.7011144040710384
+    },
+    {
+      "id": 31,
+      "rotation_radians": 0.20298679378872103,
+      "x": 1.6038666398262842,
+      "y": -2.6762831009310903
+    },
+    {
+      "id": 32,
+      "rotation_radians": 1.3089891695260387,
+      "x": -1.7718323506879212,
+      "y": -2.6688273718325735
+    }
+  ],
+  "problem": "32 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/32.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_033_75f6c6042636af47.json b/data/solutions/generated/squinhex_033_75f6c6042636af47.json
new file mode 100644
index 0000000000000000000000000000000000000000..0b55e6561013188693a5629b115b2ee90b1148aa
--- /dev/null
+++ b/data/solutions/generated/squinhex_033_75f6c6042636af47.json
@@ -0,0 +1,260 @@
+{
+  "case": "squinhex@33",
+  "container": {
+    "circumradius": 3.927959792359783,
+    "orientation_radians": 0.0,
+    "side_length": 3.9279597923597827,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@33",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.88897+",
+    "metric_symbol": "s",
+    "metric_value": 3.88897,
+    "reference_text": "s = 3.88897+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "33.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/33.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@33",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.88897+",
+      "metric_symbol": "s",
+      "metric_value": 3.88897,
+      "reference_text": "s = 3.88897+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "33.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/33.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.3177698260262038,
+      "x": -2.2702221674958647,
+      "y": -1.8625497118625736
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+    {
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+    {
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+      "x": 1.0564075878462675,
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+    {
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+      "x": -3.1881501370864713,
+      "y": -0.08070391592806608
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+    {
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+      "y": -0.8687866409625343
+    },
+    {
+      "id": 17,
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+    },
+    {
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+      "rotation_radians": 0.08242665770936074,
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+      "y": -0.05253578027125007
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+    {
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+      "rotation_radians": 1.2865881098732213,
+      "x": -1.119473323063807,
+      "y": 0.3600021853508474
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.288139672882527,
+      "x": -0.2427740313799709,
+      "y": 0.8426910311608554
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.3255600289781848,
+      "x": 0.8512280726516791,
+      "y": 0.3112662622743921
+    },
+    {
+      "id": 23,
+      "rotation_radians": 1.3168798534188098,
+      "x": 1.5088770247002397,
+      "y": 1.1674862536593447
+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.3090171710719232,
+      "x": 2.761682681955151,
+      "y": 1.0200112471816134
+    },
+    {
+      "id": 25,
+      "rotation_radians": 1.2905487379756562,
+      "x": -2.5818868491092006,
+      "y": 0.9589143544956058
+    },
+    {
+      "id": 26,
+      "rotation_radians": 1.2881367659576388,
+      "x": -1.6047482135564286,
+      "y": 1.259854023018822
+    },
+    {
+      "id": 27,
+      "rotation_radians": 1.2881202688276978,
+      "x": -0.7179765476215271,
+      "y": 1.7226311562520464
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.2966026823017518,
+      "x": 0.4359105375387677,
+      "y": 1.7083637388467596
+    },
+    {
+      "id": 29,
+      "rotation_radians": 1.168303933502857,
+      "x": 1.5034378686254308,
+      "y": 2.729865436695391
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.3295721409025665,
+      "x": 2.242223303611809,
+      "y": 1.8993909614489113
+    },
+    {
+      "id": 31,
+      "rotation_radians": 0.3463066767391965,
+      "x": -1.8615640454555498,
+      "y": 2.497254032134373
+    },
+    {
+      "id": 32,
+      "rotation_radians": 0.7854006952663074,
+      "x": -0.695532197688094,
+      "y": 2.9017004079937414
+    },
+    {
+      "id": 33,
+      "rotation_radians": 0.8460326322093822,
+      "x": 0.33615014104987917,
+      "y": 2.872324140225201
+    }
+  ],
+  "problem": "33 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/33.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_034_9936488a40de24d9.json b/data/solutions/generated/squinhex_034_9936488a40de24d9.json
new file mode 100644
index 0000000000000000000000000000000000000000..5d274b6cce9767fa6983667443438688d9c98a14
--- /dev/null
+++ b/data/solutions/generated/squinhex_034_9936488a40de24d9.json
@@ -0,0 +1,266 @@
+{
+  "case": "squinhex@34",
+  "container": {
+    "circumradius": 4.041605513522111,
+    "orientation_radians": 0.0,
+    "side_length": 4.04160551352211,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@34",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.92704+",
+    "metric_symbol": "s",
+    "metric_value": 3.92704,
+    "reference_text": "s = 3.92704+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "34.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/34.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@34",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.92704+",
+      "metric_symbol": "s",
+      "metric_value": 3.92704,
+      "reference_text": "s = 3.92704+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "34.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/34.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.26181102382037114,
+      "x": -0.5349809884748912,
+      "y": -0.926616173299781
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.2618062699935313,
+      "x": -0.8823370383732594,
+      "y": 0.471828349778321
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.2618084626727145,
+      "x": -0.034645864678592125,
+      "y": -0.060001104210558896
+    },
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+    {
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+      "y": 2.792995035782568
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.26165729821653866,
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+      "y": 2.8151090187680006
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+    {
+      "id": 30,
+      "rotation_radians": 0.1149524510115695,
+      "x": 2.0105143294557357,
+      "y": 2.220123366895351
+    },
+    {
+      "id": 31,
+      "rotation_radians": 0.33273980517423274,
+      "x": 1.7963074273759274,
+      "y": -2.8205514978013086
+    },
+    {
+      "id": 32,
+      "rotation_radians": 1.6447165772233083,
+      "x": -1.4957770026784751,
+      "y": -2.7914491948785147
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+    {
+      "id": 33,
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+      "x": 1.1917687998091058,
+      "y": 2.797724042992161
+    },
+    {
+      "id": 34,
+      "rotation_radians": 0.3579492767944718,
+      "x": 0.6758448456212706,
+      "y": -2.83781206345245
+    }
+  ],
+  "problem": "34 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/34.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_035_af16853a8ef97483.json b/data/solutions/generated/squinhex_035_af16853a8ef97483.json
new file mode 100644
index 0000000000000000000000000000000000000000..39fe005bb20b504a9942c810506a93553730c461
--- /dev/null
+++ b/data/solutions/generated/squinhex_035_af16853a8ef97483.json
@@ -0,0 +1,272 @@
+{
+  "case": "squinhex@35",
+  "container": {
+    "circumradius": 4.041546349022975,
+    "orientation_radians": 0.0,
+    "side_length": 4.041546349022974,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@35",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.99833+",
+    "metric_symbol": "s",
+    "metric_value": 3.99833,
+    "reference_text": "s = 3.99833+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "35.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/35.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@35",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.99833+",
+      "metric_symbol": "s",
+      "metric_value": 3.99833,
+      "reference_text": "s = 3.99833+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "35.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/35.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "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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+    },
+    {
+      "id": 29,
+      "rotation_radians": 1.3089855163552748,
+      "x": 1.2721802343030049,
+      "y": 1.7966448999567923
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.3090021292683123,
+      "x": 2.795455000392118,
+      "y": 1.1582691072705174
+    },
+    {
+      "id": 31,
+      "rotation_radians": 0.7251238890615036,
+      "x": -1.5936138013464938,
+      "y": 2.880360189745615
+    },
+    {
+      "id": 32,
+      "rotation_radians": 0.7020663689190887,
+      "x": -0.5688666804492639,
+      "y": 2.831811678371126
+    },
+    {
+      "id": 33,
+      "rotation_radians": 0.7755704871843266,
+      "x": 0.521309593256484,
+      "y": 2.9676247858214415
+    },
+    {
+      "id": 34,
+      "rotation_radians": 0.8003151653706714,
+      "x": 1.534716942551905,
+      "y": 2.9814277559911218
+    },
+    {
+      "id": 35,
+      "rotation_radians": 1.308993946630558,
+      "x": 2.2880766873936325,
+      "y": 2.0370903955590087
+    }
+  ],
+  "problem": "35 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/35.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_036_a763846075248773.json b/data/solutions/generated/squinhex_036_a763846075248773.json
new file mode 100644
index 0000000000000000000000000000000000000000..66a788a672bdc5c39e50eb5ed602d22497316600
--- /dev/null
+++ b/data/solutions/generated/squinhex_036_a763846075248773.json
@@ -0,0 +1,278 @@
+{
+  "case": "squinhex@36",
+  "container": {
+    "circumradius": 4.041514991863541,
+    "orientation_radians": 0.0,
+    "side_length": 4.04151499186354,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@36",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "4.03258+",
+    "metric_symbol": "s",
+    "metric_value": 4.03258,
+    "reference_text": "s = 4.03258+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "36.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@36",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "4.03258+",
+      "metric_symbol": "s",
+      "metric_value": 4.03258,
+      "reference_text": "s = 4.03258+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "36.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/36.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/squinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.309000735601914,
+      "x": -2.3507648489836384,
+      "y": -1.9284506133779784
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+    },
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+      "x": 0.9587468525657121,
+      "y": 0.33944446356093494
+    },
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+      "y": 1.9075549787236907
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+    {
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+      "x": 2.8432394688829725,
+      "y": 1.075457804943358
+    },
+    {
+      "id": 31,
+      "rotation_radians": 1.3113675121973194,
+      "x": -2.1970784015335645,
+      "y": 1.8294629023159537
+    },
+    {
+      "id": 32,
+      "rotation_radians": 1.2141796071356765,
+      "x": -1.5725103443489137,
+      "y": 2.8374139658475475
+    },
+    {
+      "id": 33,
+      "rotation_radians": 0.916397933744418,
+      "x": -0.3463678743528085,
+      "y": 2.9389930476672697
+    },
+    {
+      "id": 34,
+      "rotation_radians": 0.9161386806008969,
+      "x": 0.6632459363766589,
+      "y": 2.933482837604914
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+    {
+      "id": 35,
+      "rotation_radians": 1.3090010347066232,
+      "x": 1.8431474464190802,
+      "y": 2.8076645213000617
+    },
+    {
+      "id": 36,
+      "rotation_radians": 1.3089991518686204,
+      "x": 2.343214331500626,
+      "y": 1.9415321504578595
+    }
+  ],
+  "problem": "36 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/36.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_037_a455ecb05be301ad.json b/data/solutions/generated/squinhex_037_a455ecb05be301ad.json
new file mode 100644
index 0000000000000000000000000000000000000000..d65afd752dd6251c88cfce235de1cfd1c1794ca4
--- /dev/null
+++ b/data/solutions/generated/squinhex_037_a455ecb05be301ad.json
@@ -0,0 +1,284 @@
+{
+  "case": "squinhex@37",
+  "container": {
+    "circumradius": 4.041527942684514,
+    "orientation_radians": 0.0,
+    "side_length": 4.041527942684513,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squinhex@37",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "4/29/26",
+    "metric_expression": "7/\u221a3 = 4.04145+",
+    "metric_symbol": "s",
+    "metric_value": 4.04145,
+    "reference_text": "s = 7/\u221a3 = 4.04145+ | Trivial. |",
+    "source_image": "37.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/37.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squinhex@37",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "4/29/26",
+      "metric_expression": "7/\u221a3 = 4.04145+",
+      "metric_symbol": "s",
+      "metric_value": 4.04145,
+      "reference_text": "s = 7/\u221a3 = 4.04145+ | Trivial. |",
+      "source_image": "37.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/37.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "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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+    },
+    {
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+      "x": -0.47157519736346487,
+      "y": -3.000062315889956
+    },
+    {
+      "id": 32,
+      "rotation_radians": 0.24178375468479765,
+      "x": 1.829823170494721,
+      "y": -2.8109294192746472
+    },
+    {
+      "id": 33,
+      "rotation_radians": 0.785394363078345,
+      "x": 0.49194188498194313,
+      "y": 3.0000569769265573
+    },
+    {
+      "id": 34,
+      "rotation_radians": -0.7854026258556154,
+      "x": -1.519475505195225,
+      "y": 3.0000624735193764
+    },
+    {
+      "id": 35,
+      "rotation_radians": -0.7853963680869186,
+      "x": -1.484490932874944,
+      "y": -3.000063088919368
+    },
+    {
+      "id": 36,
+      "rotation_radians": 0.2637312538246711,
+      "x": 2.3473610716930486,
+      "y": -1.9314452726600404
+    },
+    {
+      "id": 37,
+      "rotation_radians": -0.7853976281782127,
+      "x": 1.5000241858001895,
+      "y": 3.0000554806008446
+    }
+  ],
+  "problem": "37 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/37.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_038_bcbfc88586b3e923.json b/data/solutions/generated/squinhex_038_bcbfc88586b3e923.json
new file mode 100644
index 0000000000000000000000000000000000000000..499ed5bfa5bab31f05aae482212e180c9adf6f11
--- /dev/null
+++ b/data/solutions/generated/squinhex_038_bcbfc88586b3e923.json
@@ -0,0 +1,290 @@
+{
+  "case": "squinhex@38",
+  "container": {
+    "circumradius": 4.18516437963387,
+    "orientation_radians": 0.0,
+    "side_length": 4.185164379633869,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@38",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "4.18476+",
+    "metric_symbol": "s",
+    "metric_value": 4.18476,
+    "reference_text": "s = 4.18476+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "38.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/38.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@38",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "4.18476+",
+      "metric_symbol": "s",
+      "metric_value": 4.18476,
+      "reference_text": "s = 4.18476+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "38.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/38.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "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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+      "y": 1.2772650769284335
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+    {
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+      "y": 3.1229647942846266
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+    {
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+    {
+      "id": 36,
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+      "x": -2.952081978760646,
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+    {
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+      "rotation_radians": -0.26490366720677067,
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+      "y": -0.9653259764075124
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+    {
+      "id": 38,
+      "rotation_radians": 0.7824339376620221,
+      "x": -0.7817710144197046,
+      "y": 3.115365517415636
+    }
+  ],
+  "problem": "38 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/38.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_039_85e7e9eb3b3b7f5f.json b/data/solutions/generated/squinhex_039_85e7e9eb3b3b7f5f.json
new file mode 100644
index 0000000000000000000000000000000000000000..689539947d08724b7f642587ed4b081b59d0c296
--- /dev/null
+++ b/data/solutions/generated/squinhex_039_85e7e9eb3b3b7f5f.json
@@ -0,0 +1,296 @@
+{
+  "case": "squinhex@39",
+  "container": {
+    "circumradius": 4.259104243334675,
+    "orientation_radians": 0.0,
+    "side_length": 4.259104243334674,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@39",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "4.25744+",
+    "metric_symbol": "s",
+    "metric_value": 4.25744,
+    "reference_text": "s = 4.25744+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "39.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/39.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@39",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "4.25744+",
+      "metric_symbol": "s",
+      "metric_value": 4.25744,
+      "reference_text": "s = 4.25744+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "39.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/39.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "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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+    {
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+    {
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+      "x": -3.1483537688228673,
+      "y": -0.9185275551186056
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+  ],
+  "problem": "39 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/39.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinhex_040_f7dadd815b6542ca.json b/data/solutions/generated/squinhex_040_f7dadd815b6542ca.json
new file mode 100644
index 0000000000000000000000000000000000000000..1318e99c6f7263884dc9a5a46f00369fda452e4f
--- /dev/null
+++ b/data/solutions/generated/squinhex_040_f7dadd815b6542ca.json
@@ -0,0 +1,302 @@
+{
+  "case": "squinhex@40",
+  "container": {
+    "circumradius": 4.310076553764806,
+    "orientation_radians": 0.0,
+    "side_length": 4.310076553764805,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinhex@40",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "4.31157+",
+    "metric_symbol": "s",
+    "metric_value": 4.31157,
+    "reference_text": "s = 4.31157+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "40.png",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinhex/40.png",
+    "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+    "title": "Squares in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinhex@40",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "4.31157+",
+      "metric_symbol": "s",
+      "metric_value": 4.31157,
+      "reference_text": "s = 4.31157+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "40.png",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinhex/40.png",
+      "source_page": "https://erich-friedman.github.io/packing/squinhex/",
+      "title": "Squares in Hexagons"
+    },
+    "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/squinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "y": -3.231319459465292
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+      "x": -2.251499948042222,
+      "y": 0.7587351665355193
+    },
+    {
+      "id": 35,
+      "rotation_radians": -0.2618026854868864,
+      "x": 2.772494184771399,
+      "y": 1.66313052963374
+    },
+    {
+      "id": 36,
+      "rotation_radians": -0.22538009258444697,
+      "x": 2.7357173534336914,
+      "y": -1.3750196888466997
+    },
+    {
+      "id": 37,
+      "rotation_radians": -0.2833661681882933,
+      "x": -3.3197992567315375,
+      "y": -0.6938400792287159
+    },
+    {
+      "id": 38,
+      "rotation_radians": -0.7827498586296029,
+      "x": 1.6631089447919363,
+      "y": -3.217639297903268
+    },
+    {
+      "id": 39,
+      "rotation_radians": -0.2833700956566908,
+      "x": -2.319533195991495,
+      "y": -2.4263538089133725
+    },
+    {
+      "id": 40,
+      "rotation_radians": 0.785427118346575,
+      "x": 1.1248080645973597,
+      "y": 3.2326158236160936
+    }
+  ],
+  "problem": "40 equal items for Squares in Hexagons",
+  "setup": "squinhex",
+  "source_image": "https://erich-friedman.github.io/packing/squinhex/40.png",
+  "source_page": "https://erich-friedman.github.io/packing/squinhex/"
+}
diff --git a/data/solutions/generated/squinoct_021_a3759fa0325bb184.json b/data/solutions/generated/squinoct_021_a3759fa0325bb184.json
new file mode 100644
index 0000000000000000000000000000000000000000..1c2eca6abbc7f84774aa5fc8b626ffd91e12c29b
--- /dev/null
+++ b/data/solutions/generated/squinoct_021_a3759fa0325bb184.json
@@ -0,0 +1,188 @@
+{
+  "case": "squinoct@21",
+  "container": {
+    "circumradius": 3.0291659094838175,
+    "orientation_radians": 0.0,
+    "side_length": 2.3184232148891724,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinoct@21",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/17/26",
+    "metric_expression": "2.32167+",
+    "metric_symbol": "s",
+    "metric_value": 2.32167,
+    "reference_text": "s = 2.32167+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "21.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinoct/21.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+    "title": "Squares in Octagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinoct@21",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/17/26",
+      "metric_expression": "2.32167+",
+      "metric_symbol": "s",
+      "metric_value": 2.32167,
+      "reference_text": "s = 2.32167+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "21.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinoct/21.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+      "title": "Squares in Octagons"
+    },
+    "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/squinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 2.956527647065093,
+      "x": 1.7810728269463767,
+      "y": -1.2050855215718992
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+    {
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+      "x": 0.5647752295691564,
+      "y": -0.8258191946667547
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+    {
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+      "x": 3.4570704063305765e-07,
+      "y": -2.2350792414619803e-05
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+    {
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+      "x": 1.067061965237415,
+      "y": -1.9323808599030627
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+    {
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+    {
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+      "y": -0.26090731222764746
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+    {
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+    },
+    {
+      "id": 15,
+      "rotation_radians": 4.527254458301183,
+      "x": 2.3341333089093292,
+      "y": 0.13016594383147248
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.3856533360648677,
+      "x": -0.1301749222921998,
+      "y": 2.3341335056577166
+    },
+    {
+      "id": 17,
+      "rotation_radians": 4.527248810418394,
+      "x": -1.9412901842392447,
+      "y": -1.0731241338800646
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.3856518865088379,
+      "x": -2.334132746553628,
+      "y": -0.13016321200355618
+    },
+    {
+      "id": 19,
+      "rotation_radians": 4.527259170281439,
+      "x": 0.13016592640818112,
+      "y": -2.334131413671467
+    },
+    {
+      "id": 20,
+      "rotation_radians": 4.527246587479797,
+      "x": -1.054009091937133,
+      "y": 1.9133513740282104
+    },
+    {
+      "id": 21,
+      "rotation_radians": 6.098057125706489,
+      "x": -1.2050969965524445,
+      "y": -1.7810576809869567
+    }
+  ],
+  "problem": "21 equal items for Squares in Octagons",
+  "setup": "squinoct",
+  "source_image": "https://erich-friedman.github.io/packing/squinoct/21.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinoct/"
+}
diff --git a/data/solutions/generated/squinoct_022_bebb10254b247f18.json b/data/solutions/generated/squinoct_022_bebb10254b247f18.json
new file mode 100644
index 0000000000000000000000000000000000000000..a4066f2abd6328620d851089b0429192ab493df4
--- /dev/null
+++ b/data/solutions/generated/squinoct_022_bebb10254b247f18.json
@@ -0,0 +1,194 @@
+{
+  "case": "squinoct@22",
+  "container": {
+    "circumradius": 3.1630603675860054,
+    "orientation_radians": 0.0,
+    "side_length": 2.42090159649159,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinoct@22",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/17/26",
+    "metric_expression": "2.41811+",
+    "metric_symbol": "s",
+    "metric_value": 2.41811,
+    "reference_text": "s = 2.41811+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "22.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinoct/22.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+    "title": "Squares in Octagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinoct@22",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/17/26",
+      "metric_expression": "2.41811+",
+      "metric_symbol": "s",
+      "metric_value": 2.41811,
+      "reference_text": "s = 2.41811+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "22.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinoct/22.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+      "title": "Squares in Octagons"
+    },
+    "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/squinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.1781006071265916,
+      "x": -2.111727039453408,
+      "y": -1.2315428788954894
+    },
+    {
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+      "x": -1.182677654666231,
+      "y": -2.12319214492005
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+    {
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+      "y": -2.5046974697645026
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+    },
+    {
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+      "x": 2.233176772539928,
+      "y": -0.37121765599259665
+    },
+    {
+      "id": 11,
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+      "x": -2.243458211185525,
+      "y": 0.8907844907075221
+    },
+    {
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+      "x": -1.3402445264228073,
+      "y": -0.09018841125956968
+    },
+    {
+      "id": 13,
+      "rotation_radians": -0.6019584330870646,
+      "x": 0.11656025345403088,
+      "y": -0.19178490503799128
+    },
+    {
+      "id": 14,
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+      "x": 1.1854416194847899,
+      "y": 0.3647854923373607
+    },
+    {
+      "id": 15,
+      "rotation_radians": -0.49723589255597794,
+      "x": 2.2633639973101696,
+      "y": 0.6834830225216709
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.6246655657996293,
+      "x": -1.0551230923358725,
+      "y": 0.9691396642031987
+    },
+    {
+      "id": 17,
+      "rotation_radians": -0.6153301656453696,
+      "x": -0.011011870210787098,
+      "y": 0.8077784120884286
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.49855003425103983,
+      "x": 0.4252818534679418,
+      "y": 2.225808023048239
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.4985456190113111,
+      "x": 0.934041053841458,
+      "y": 1.3332540272970852
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.4978291142023739,
+      "x": 1.8936792625440149,
+      "y": 1.6174916271339521
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.0907784606542825,
+      "x": -1.5794688605342118,
+      "y": 1.9224903341108979
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.4974236188283168,
+      "x": -0.6241802792988146,
+      "y": 2.2469879470303473
+    }
+  ],
+  "problem": "22 equal items for Squares in Octagons",
+  "setup": "squinoct",
+  "source_image": "https://erich-friedman.github.io/packing/squinoct/22.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinoct/"
+}
diff --git a/data/solutions/generated/squinoct_023_004d1c5d4d7bca47.json b/data/solutions/generated/squinoct_023_004d1c5d4d7bca47.json
new file mode 100644
index 0000000000000000000000000000000000000000..fe4a82fcbbf5d1f5a426e833047095b11b9b320d
--- /dev/null
+++ b/data/solutions/generated/squinoct_023_004d1c5d4d7bca47.json
@@ -0,0 +1,200 @@
+{
+  "case": "squinoct@23",
+  "container": {
+    "circumradius": 3.23354946432725,
+    "orientation_radians": 0.0,
+    "side_length": 2.4748516154620988,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinoct@23",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/17/26",
+    "metric_expression": "2.47329+",
+    "metric_symbol": "s",
+    "metric_value": 2.47329,
+    "reference_text": "s = 2.47329+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "23.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinoct/23.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+    "title": "Squares in Octagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinoct@23",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/17/26",
+      "metric_expression": "2.47329+",
+      "metric_symbol": "s",
+      "metric_value": 2.47329,
+      "reference_text": "s = 2.47329+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "23.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinoct/23.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+      "title": "Squares in Octagons"
+    },
+    "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/squinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.6433898007734999,
+      "x": -0.017021160145811242,
+      "y": 0.48055256683088565
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+    {
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+    },
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+      "y": 1.0347546184523981
+    },
+    {
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+      "x": -1.2936618033605467,
+      "y": 2.0911642764218903
+    },
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+      "y": -1.2904125059503926
+    },
+    {
+      "id": 11,
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+      "x": 2.1816275460588073,
+      "y": -0.2508767210183338
+    },
+    {
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+      "rotation_radians": -0.647268812082345,
+      "x": 1.0620638685139996,
+      "y": -2.1133340961673777
+    },
+    {
+      "id": 13,
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+      "x": -0.9938073064125954,
+      "y": -2.076442591603827
+    },
+    {
+      "id": 14,
+      "rotation_radians": -0.6743688632424203,
+      "x": 0.7955424875972639,
+      "y": 2.124608521452016
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+    {
+      "id": 15,
+      "rotation_radians": -0.6434397331050161,
+      "x": -0.028999148743666863,
+      "y": -1.541570407475375
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+    {
+      "id": 16,
+      "rotation_radians": -0.6518800629770172,
+      "x": 1.857638204899261,
+      "y": 1.7239082708438147
+    },
+    {
+      "id": 17,
+      "rotation_radians": -0.6433857291361952,
+      "x": -0.2640627283602128,
+      "y": 2.46563205753977
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.6434393216090645,
+      "x": -1.1077463179753528,
+      "y": -1.0619138734756464
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.8857119144250023,
+      "x": -2.4949646931678213,
+      "y": -0.08648680895114726
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.6901193051298071,
+      "x": -2.104974031905981,
+      "y": 0.957910295132944
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.03394681464121,
+      "x": -2.1627321095996526,
+      "y": -1.1044529904522764
+    },
+    {
+      "id": 22,
+      "rotation_radians": -2.2135369222826733,
+      "x": 0.10055739476114507,
+      "y": -2.533600528540566
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.6513184892818402,
+      "x": 2.207328844673403,
+      "y": 0.7616913263373658
+    }
+  ],
+  "problem": "23 equal items for Squares in Octagons",
+  "setup": "squinoct",
+  "source_image": "https://erich-friedman.github.io/packing/squinoct/23.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinoct/"
+}
diff --git a/data/solutions/generated/squinoct_024_4f255616aca5e547.json b/data/solutions/generated/squinoct_024_4f255616aca5e547.json
new file mode 100644
index 0000000000000000000000000000000000000000..d2a6343c32a7ea5133a6f9cd073539ba6c318ef3
--- /dev/null
+++ b/data/solutions/generated/squinoct_024_4f255616aca5e547.json
@@ -0,0 +1,206 @@
+{
+  "case": "squinoct@24",
+  "container": {
+    "circumradius": 3.2472346584110547,
+    "orientation_radians": 0.0,
+    "side_length": 2.4853258095512447,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squinoct@24",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "3/17/26",
+    "metric_expression": "6\u221a2 \u2013 6 = 2.48528+",
+    "metric_symbol": "s",
+    "metric_value": 2.48528,
+    "reference_text": "s = 6\u221a2 \u2013 6 = 2.48528+ | Trivial.",
+    "source_image": "24.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinoct/24.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+    "title": "Squares in Octagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squinoct@24",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "3/17/26",
+      "metric_expression": "6\u221a2 \u2013 6 = 2.48528+",
+      "metric_symbol": "s",
+      "metric_value": 2.48528,
+      "reference_text": "s = 6\u221a2 \u2013 6 = 2.48528+ | Trivial.",
+      "source_image": "24.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinoct/24.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+      "title": "Squares in Octagons"
+    },
+    "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/squinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.3492828380185447,
+      "x": -0.08257771262920585,
+      "y": 2.445482731144791
+    },
+    {
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+      "y": -1.1358704876045376
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+      "y": -0.653288236767267
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+    {
+      "id": 11,
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+      "x": -2.190550960410662,
+      "y": 1.244471651480701
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+    {
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+      "x": -0.34511395850575,
+      "y": 1.4132235220836413
+    },
+    {
+      "id": 13,
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+      "x": 0.7919534756842531,
+      "y": 1.295583093087502
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+    {
+      "id": 14,
+      "rotation_radians": 1.963496959316567,
+      "x": -1.3165029391328726,
+      "y": 0.7414328620014606
+    },
+    {
+      "id": 15,
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+      "x": 1.535818220763199,
+      "y": -0.21198026691781074
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.1780906824125261,
+      "x": 0.8947327386439516,
+      "y": -2.33541938450635
+    },
+    {
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+      "rotation_radians": 5.105089473947284,
+      "x": -1.699384493821064,
+      "y": -0.1829019107889565
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.07169656906392713,
+      "x": -1.300421706442141,
+      "y": 1.9735628287370641
+    },
+    {
+      "id": 19,
+      "rotation_radians": 3.534288780977769,
+      "x": -1.2357453355696972,
+      "y": -2.194163859499145
+    },
+    {
+      "id": 20,
+      "rotation_radians": 5.1050905054539735,
+      "x": 2.0705295174028273,
+      "y": -1.5342363791345508
+    },
+    {
+      "id": 21,
+      "rotation_radians": 6.675885621671456,
+      "x": -2.5753971717181288,
+      "y": 0.315382389365522
+    },
+    {
+      "id": 22,
+      "rotation_radians": 3.5342940486490653,
+      "x": -0.5462302551324523,
+      "y": -0.012131269849587742
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.39270145914177207,
+      "x": -0.11208262443540579,
+      "y": -1.5771839004353312
+    },
+    {
+      "id": 24,
+      "rotation_radians": 2.748893572118971,
+      "x": -2.169756292139018,
+      "y": -1.2946677301024392
+    }
+  ],
+  "problem": "24 equal items for Squares in Octagons",
+  "setup": "squinoct",
+  "source_image": "https://erich-friedman.github.io/packing/squinoct/24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinoct/"
+}
diff --git a/data/solutions/generated/squinoct_025_cf47f0214a5dc773.json b/data/solutions/generated/squinoct_025_cf47f0214a5dc773.json
new file mode 100644
index 0000000000000000000000000000000000000000..f523605eb610f0ef6c8fc035a0cf6944ace4ff6c
--- /dev/null
+++ b/data/solutions/generated/squinoct_025_cf47f0214a5dc773.json
@@ -0,0 +1,212 @@
+{
+  "case": "squinoct@25",
+  "container": {
+    "circumradius": 3.2868590368735426,
+    "orientation_radians": 0.0,
+    "side_length": 2.515652995861961,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squinoct@25",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/17/26",
+    "metric_expression": "11/(3+\u221a2) = 2.49195+",
+    "metric_symbol": "s",
+    "metric_value": 2.49195,
+    "reference_text": "s = 11/(3+\u221a2) = 2.49195+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "25.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinoct/25.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+    "title": "Squares in Octagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squinoct@25",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/17/26",
+      "metric_expression": "11/(3+\u221a2) = 2.49195+",
+      "metric_symbol": "s",
+      "metric_value": 2.49195,
+      "reference_text": "s = 11/(3+\u221a2) = 2.49195+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "25.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinoct/25.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+      "title": "Squares in Octagons"
+    },
+    "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/squinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.39019881146312685,
+      "x": -0.4305109716056136,
+      "y": 0.17507683059224005
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+    },
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+      "x": -0.042605236482287825,
+      "y": 1.1084971794911507
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+    {
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+    {
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+      "x": 2.1671872093012676,
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+    },
+    {
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+      "y": 1.214059694161527
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+    {
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+      "x": -1.9584388930880883,
+      "y": 1.7102581617365227
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.3926769894753441,
+      "x": 2.1830513146980737,
+      "y": -1.3581757536326713
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.39268211904536127,
+      "x": 1.644819652269161,
+      "y": -0.044373477830351296
+    },
+    {
+      "id": 15,
+      "rotation_radians": 0.3923693167054084,
+      "x": 1.1892633668303059,
+      "y": -2.028878006462261
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.4026314923918605,
+      "x": -0.4246403517087193,
+      "y": 2.345624448423991
+    },
+    {
+      "id": 17,
+      "rotation_radians": -0.39269908772381695,
+      "x": -2.1181941844202012,
+      "y": -1.5147921602597036
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.39302352810231794,
+      "x": -0.1761114247000605,
+      "y": -2.5944071314719674
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.9632021110865465,
+      "x": -2.364897629182713,
+      "y": 0.7961965016208669
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.3931802303472799,
+      "x": -1.1058835783532799,
+      "y": -2.225650422937175
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.39237948979533616,
+      "x": -1.4230229361377646,
+      "y": -0.4962130380169088
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.3925277291847716,
+      "x": 0.7026252120417938,
+      "y": 2.454446362929871
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.39268924137721695,
+      "x": 2.5657622390559625,
+      "y": -0.4342670521102708
+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.9631955263424632,
+      "x": -2.4107213043205005,
+      "y": -0.26737166120643174
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.3925095123921338,
+      "x": 1.626563028372262,
+      "y": 2.071792843521872
+    }
+  ],
+  "problem": "25 equal items for Squares in Octagons",
+  "setup": "squinoct",
+  "source_image": "https://erich-friedman.github.io/packing/squinoct/25.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinoct/"
+}
diff --git a/data/solutions/generated/squinoct_026_5b23f9a6c0d60139.json b/data/solutions/generated/squinoct_026_5b23f9a6c0d60139.json
new file mode 100644
index 0000000000000000000000000000000000000000..04ab5c85556398ba82a82c9630773fca486c3f22
--- /dev/null
+++ b/data/solutions/generated/squinoct_026_5b23f9a6c0d60139.json
@@ -0,0 +1,218 @@
+{
+  "case": "squinoct@26",
+  "container": {
+    "circumradius": 3.374092830355374,
+    "orientation_radians": 0.0,
+    "side_length": 2.58241885087767,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinoct@26",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/17/26",
+    "metric_expression": "2.52841+",
+    "metric_symbol": "s",
+    "metric_value": 2.52841,
+    "reference_text": "s = 2.52841+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "26.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinoct/26.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+    "title": "Squares in Octagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinoct@26",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/17/26",
+      "metric_expression": "2.52841+",
+      "metric_symbol": "s",
+      "metric_value": 2.52841,
+      "reference_text": "s = 2.52841+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "26.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinoct/26.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+      "title": "Squares in Octagons"
+    },
+    "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/squinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.1788068979241297,
+      "x": -2.2397118942951146,
+      "y": -1.425280557267727
+    },
+    {
+      "id": 2,
+      "rotation_radians": 1.1764908621350023,
+      "x": -1.7155570307208012,
+      "y": 2.1213940177534902
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+    {
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+      "x": -1.3360311653450017,
+      "y": -0.9667244187829825
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+    {
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+      "x": -2.6717635673601023,
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+    {
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+      "x": -0.2850634387532692,
+      "y": -2.7148040115549184
+    },
+    {
+      "id": 6,
+      "rotation_radians": 1.1699334456455006,
+      "x": -1.2980812252153813,
+      "y": 1.2082830170447052
+    },
+    {
+      "id": 7,
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+      "x": -1.2535882012195119,
+      "y": -2.224385865190219
+    },
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+    {
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+    {
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+    {
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+      "y": 2.350762543717049
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+    {
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+    {
+      "id": 22,
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+      "y": -0.2909698300093025
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+    {
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+      "x": 0.8935352084839479,
+      "y": -2.4255241412570756
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+    {
+      "id": 24,
+      "rotation_radians": -0.2599961048141366,
+      "x": 0.9553814263641143,
+      "y": 1.374127052015411
+    },
+    {
+      "id": 25,
+      "rotation_radians": 1.1714437071079782,
+      "x": -0.8013722396026718,
+      "y": 0.3298661014784011
+    },
+    {
+      "id": 26,
+      "rotation_radians": -0.25996133238906005,
+      "x": 1.8315583506467914,
+      "y": 1.8567820636449395
+    }
+  ],
+  "problem": "26 equal items for Squares in Octagons",
+  "setup": "squinoct",
+  "source_image": "https://erich-friedman.github.io/packing/squinoct/26.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinoct/"
+}
diff --git a/data/solutions/generated/squinoct_027_7199a9fabf8295f3.json b/data/solutions/generated/squinoct_027_7199a9fabf8295f3.json
new file mode 100644
index 0000000000000000000000000000000000000000..809f266273f0582ff2fb2867c1d5d4a293d2426c
--- /dev/null
+++ b/data/solutions/generated/squinoct_027_7199a9fabf8295f3.json
@@ -0,0 +1,224 @@
+{
+  "case": "squinoct@27",
+  "container": {
+    "circumradius": 3.4367269794343693,
+    "orientation_radians": 0.0,
+    "side_length": 2.6303569531833038,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinoct@27",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/17/26",
+    "metric_expression": "2.58695+",
+    "metric_symbol": "s",
+    "metric_value": 2.58695,
+    "reference_text": "s = 2.58695+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "27.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinoct/27.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+    "title": "Squares in Octagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinoct@27",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/17/26",
+      "metric_expression": "2.58695+",
+      "metric_symbol": "s",
+      "metric_value": 2.58695,
+      "reference_text": "s = 2.58695+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "27.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinoct/27.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+      "title": "Squares in Octagons"
+    },
+    "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/squinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.2764653917499169,
+      "x": -0.7200659105650664,
+      "y": 0.262491203508768
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+    {
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+    {
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+      "x": -0.1441075071246886,
+      "y": -2.681031963377917
+    },
+    {
+      "id": 17,
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+      "x": -2.756285749685689,
+      "y": -0.19276626661638097
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.2761659774924435,
+      "x": -0.752968115358304,
+      "y": -1.7272613182509462
+    },
+    {
+      "id": 19,
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+      "x": 1.7798078052323347,
+      "y": 1.9392981306575534
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.056647297584236,
+      "x": -2.3125963297582084,
+      "y": 0.9682321780913333
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.2758564674647773,
+      "x": -1.7801743100268357,
+      "y": -1.939198405664745
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.2773358412991588,
+      "x": -2.3217232621587467,
+      "y": -1.09540128608903
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.36752142798739845,
+      "x": -1.6543025039541563,
+      "y": 2.1639178808059185
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.2764662261985929,
+      "x": 2.3703913389795344,
+      "y": 1.1236558508949082
+    },
+    {
+      "id": 25,
+      "rotation_radians": -1.0490588834036536,
+      "x": 0.6713514597890915,
+      "y": 2.5458111940803674
+    },
+    {
+      "id": 26,
+      "rotation_radians": -0.32356917192359125,
+      "x": 1.0347175117447402,
+      "y": -2.417132637621435
+    },
+    {
+      "id": 27,
+      "rotation_radians": -0.27734336572005996,
+      "x": 2.7566268244151964,
+      "y": 0.19361390070351422
+    }
+  ],
+  "problem": "27 equal items for Squares in Octagons",
+  "setup": "squinoct",
+  "source_image": "https://erich-friedman.github.io/packing/squinoct/27.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinoct/"
+}
diff --git a/data/solutions/generated/squinoct_028_ad6175b5666f3771.json b/data/solutions/generated/squinoct_028_ad6175b5666f3771.json
new file mode 100644
index 0000000000000000000000000000000000000000..72c3e552eca7013972dd9d18ef02c3b12ec30c66
--- /dev/null
+++ b/data/solutions/generated/squinoct_028_ad6175b5666f3771.json
@@ -0,0 +1,230 @@
+{
+  "case": "squinoct@28",
+  "container": {
+    "circumradius": 3.4413786679914873,
+    "orientation_radians": 0.0,
+    "side_length": 2.6339172014699663,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinoct@28",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/17/26",
+    "metric_expression": "2.63116+",
+    "metric_symbol": "s",
+    "metric_value": 2.63116,
+    "reference_text": "s = 2.63116+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "28.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinoct/28.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+    "title": "Squares in Octagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinoct@28",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/17/26",
+      "metric_expression": "2.63116+",
+      "metric_symbol": "s",
+      "metric_value": 2.63116,
+      "reference_text": "s = 2.63116+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "28.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinoct/28.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+      "title": "Squares in Octagons"
+    },
+    "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/squinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.27912375584933513,
+      "x": -0.15485982721523914,
+      "y": -0.74930503333117
+    },
+    {
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+      "y": 0.1480471649215197
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+    {
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+      "y": -0.2710723383539866
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+    {
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+      "x": -1.2931434450813881,
+      "y": -0.76051036482112
+    },
+    {
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+      "x": 1.2075876135437094,
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+    {
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+    {
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+      "x": 1.7570995124569433,
+      "y": -0.06429359260259221
+    },
+    {
+      "id": 11,
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+      "x": -0.3112819772513961,
+      "y": 1.5972598688990995
+    },
+    {
+      "id": 12,
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+      "x": 0.7856617946111594,
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+    {
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+      "y": 0.8119216140547223
+    },
+    {
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+      "y": 2.1687008551162994
+    },
+    {
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+      "rotation_radians": -0.16743255893335104,
+      "x": 2.295036791389902,
+      "y": -0.9663769579755576
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.3926937976274043,
+      "x": -0.3493548574471953,
+      "y": -2.7554579831283785
+    },
+    {
+      "id": 17,
+      "rotation_radians": -0.28907363363892613,
+      "x": -2.7566297229714927,
+      "y": -0.1847926113533626
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.27501614822121034,
+      "x": 1.7889683663709695,
+      "y": 1.940261094311898
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.30064381949451335,
+      "x": 0.8724803972699618,
+      "y": -2.491305517018328
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.2885870407239016,
+      "x": -1.7803105388199987,
+      "y": 0.11293352715218104
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.28909074503367643,
+      "x": -2.3832358160326317,
+      "y": -1.1198480733952645
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.2891136507364372,
+      "x": -1.792928730332945,
+      "y": -1.9374339814179704
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.275039046966167,
+      "x": 2.760807498481124,
+      "y": 0.19212501494119263
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.3926977411496937,
+      "x": -0.827721796411388,
+      "y": 2.5170394856181
+    },
+    {
+      "id": 25,
+      "rotation_radians": -0.28204890820091727,
+      "x": 1.8049794019030976,
+      "y": -2.0960565528177106
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.4030254300025386,
+      "x": -2.425362415387293,
+      "y": 1.1328393999718926
+    },
+    {
+      "id": 27,
+      "rotation_radians": -0.2750055231400956,
+      "x": 2.372553039824388,
+      "y": 1.1208843452359551
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.2750014611125319,
+      "x": 0.2975494035612449,
+      "y": 2.558027187516629
+    }
+  ],
+  "problem": "28 equal items for Squares in Octagons",
+  "setup": "squinoct",
+  "source_image": "https://erich-friedman.github.io/packing/squinoct/28.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinoct/"
+}
diff --git a/data/solutions/generated/squinoct_029_a7c60552360644b6.json b/data/solutions/generated/squinoct_029_a7c60552360644b6.json
new file mode 100644
index 0000000000000000000000000000000000000000..272337c928ab8aa7581f076b272d9c4bdf49f438
--- /dev/null
+++ b/data/solutions/generated/squinoct_029_a7c60552360644b6.json
@@ -0,0 +1,236 @@
+{
+  "case": "squinoct@29",
+  "container": {
+    "circumradius": 3.5681258139835834,
+    "orientation_radians": 0.0,
+    "side_length": 2.7309252672114352,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinoct@29",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/17/26",
+    "metric_expression": "2.70811+",
+    "metric_symbol": "s",
+    "metric_value": 2.70811,
+    "reference_text": "s = 2.70811+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "29.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinoct/29.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+    "title": "Squares in Octagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinoct@29",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/17/26",
+      "metric_expression": "2.70811+",
+      "metric_symbol": "s",
+      "metric_value": 2.70811,
+      "reference_text": "s = 2.70811+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "29.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinoct/29.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+      "title": "Squares in Octagons"
+    },
+    "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/squinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "y": -0.9824633305231301
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+    {
+      "id": 25,
+      "rotation_radians": 1.2093986094927955,
+      "x": -2.309790118991704,
+      "y": 1.190987732174536
+    },
+    {
+      "id": 26,
+      "rotation_radians": 1.1981758199701253,
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+    {
+      "id": 27,
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+      "x": 0.42501647532614734,
+      "y": 1.037978614800938
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.1834932465044008,
+      "x": -1.2981875525578308,
+      "y": 1.3981697121039431
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.21948325184881534,
+      "x": -2.869713130318831,
+      "y": 0.13402372880817393
+    }
+  ],
+  "problem": "29 equal items for Squares in Octagons",
+  "setup": "squinoct",
+  "source_image": "https://erich-friedman.github.io/packing/squinoct/29.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinoct/"
+}
diff --git a/data/solutions/generated/squinoct_030_8d25a2ea5990135c.json b/data/solutions/generated/squinoct_030_8d25a2ea5990135c.json
new file mode 100644
index 0000000000000000000000000000000000000000..095490d42e719d9230d69e7ee8ffff60038e0af6
--- /dev/null
+++ b/data/solutions/generated/squinoct_030_8d25a2ea5990135c.json
@@ -0,0 +1,242 @@
+{
+  "case": "squinoct@30",
+  "container": {
+    "circumradius": 3.629752802377564,
+    "orientation_radians": 0.0,
+    "side_length": 2.778092522101299,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinoct@30",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/17/26",
+    "metric_expression": "2.74220+",
+    "metric_symbol": "s",
+    "metric_value": 2.7422,
+    "reference_text": "s = 2.74220+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "30.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinoct/30.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+    "title": "Squares in Octagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinoct@30",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/17/26",
+      "metric_expression": "2.74220+",
+      "metric_symbol": "s",
+      "metric_value": 2.7422,
+      "reference_text": "s = 2.74220+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "30.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinoct/30.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinoct/",
+      "title": "Squares in Octagons"
+    },
+    "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/squinoct/",
+    "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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+      "y": 0.8025887094977882
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+    {
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+      "x": -0.3870633333482293,
+      "y": 1.797001114315408
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.39269551615833287,
+      "x": -2.6270707756178737,
+      "y": 1.114082744315379
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+    {
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+    {
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+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.1784838742541708,
+      "x": 1.1183560967152129,
+      "y": -1.5397671085190798
+    },
+    {
+      "id": 25,
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+      "x": -1.2726322897403746,
+      "y": 1.2456312485807406
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.32876723415813636,
+      "x": 1.9675160052360527,
+      "y": 2.1689784928623523
+    },
+    {
+      "id": 27,
+      "rotation_radians": 1.1765021043846227,
+      "x": 1.4894726101350855,
+      "y": -2.4695313287348046
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.1718833739349859,
+      "x": -0.6153678820861982,
+      "y": -2.6094973308268536
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.3287655693513067,
+      "x": 1.735680466558067,
+      "y": 1.16867687037266
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.1718826990077345,
+      "x": -0.41025390138409185,
+      "y": -1.0378906327172985
+    }
+  ],
+  "problem": "30 equal items for Squares in Octagons",
+  "setup": "squinoct",
+  "source_image": "https://erich-friedman.github.io/packing/squinoct/30.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinoct/"
+}
diff --git a/data/solutions/generated/squinpen_021_3fc16f4ddfd45967.json b/data/solutions/generated/squinpen_021_3fc16f4ddfd45967.json
new file mode 100644
index 0000000000000000000000000000000000000000..27f8d951b8ab47ef52a252679d8a956066cc66f4
--- /dev/null
+++ b/data/solutions/generated/squinpen_021_3fc16f4ddfd45967.json
@@ -0,0 +1,188 @@
+{
+  "case": "squinpen@21",
+  "container": {
+    "circumradius": 3.2948553477024034,
+    "orientation_radians": 0.0,
+    "side_length": 3.873334763632923,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@21",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "3.864+",
+    "metric_symbol": "s",
+    "metric_value": 3.864,
+    "reference_text": "s = 3.864+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "21.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/21.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@21",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "3.864+",
+      "metric_symbol": "s",
+      "metric_value": 3.864,
+      "reference_text": "s = 3.864+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "21.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/21.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "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/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
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+      "y": 0.12256793771596418
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+      "y": 2.436764940900869
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.4813212199104229,
+      "x": -1.0853587828912825,
+      "y": 1.9109936348817151
+    },
+    {
+      "id": 17,
+      "rotation_radians": -0.8103056776170912,
+      "x": -2.1532744909455936,
+      "y": -0.44890916344661747
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.481319784828733,
+      "x": -2.038806152846391,
+      "y": 1.6093061094777374
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.1583824982556747,
+      "x": 1.492681985575123,
+      "y": 1.627361368041125
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.4712399514437465,
+      "x": -1.1239820719054026,
+      "y": -1.9118274443243062
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.48132192817608915,
+      "x": -1.6781469813787322,
+      "y": 0.6743724327934054
+    }
+  ],
+  "problem": "21 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/21.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_022_33b95c59890c6cd7.json b/data/solutions/generated/squinpen_022_33b95c59890c6cd7.json
new file mode 100644
index 0000000000000000000000000000000000000000..0042858cde0da60be46a1f33d6c5fe4d320845c8
--- /dev/null
+++ b/data/solutions/generated/squinpen_022_33b95c59890c6cd7.json
@@ -0,0 +1,194 @@
+{
+  "case": "squinpen@22",
+  "container": {
+    "circumradius": 3.351631214801316,
+    "orientation_radians": 0.0,
+    "side_length": 3.9400787983666397,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@22",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "3.937+",
+    "metric_symbol": "s",
+    "metric_value": 3.937,
+    "reference_text": "s = 3.937+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "22.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/22.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@22",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "3.937+",
+      "metric_symbol": "s",
+      "metric_value": 3.937,
+      "reference_text": "s = 3.937+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "22.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/22.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "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/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -1.18312229780343,
+      "x": -0.01821128870843724,
+      "y": -0.1535326006424212
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+    {
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+    {
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+      "y": 0.11121466745450158
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+    {
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+      "rotation_radians": 0.47434931916547796,
+      "x": -1.7020262006267737,
+      "y": -0.6401669682340222
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+    {
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+      "y": -0.8470497256944243
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+    {
+      "id": 13,
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+      "x": 0.8328748449938311,
+      "y": 0.5889537111889724
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+    {
+      "id": 14,
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+      "y": 1.4856590427660725
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+    {
+      "id": 15,
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+      "y": 2.1816676801760533
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.2006556264432885,
+      "x": 1.4781794899808185,
+      "y": -1.6818233553681623
+    },
+    {
+      "id": 17,
+      "rotation_radians": -0.4712224545747266,
+      "x": 0.6777487523077631,
+      "y": 2.5455115866624203
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.762398578939319,
+      "x": -2.181674425115677,
+      "y": 0.4854740045506486
+    },
+    {
+      "id": 19,
+      "rotation_radians": -1.097459566821129,
+      "x": -2.082134567900052,
+      "y": -1.568890576164043
+    },
+    {
+      "id": 20,
+      "rotation_radians": -1.0985465390173124,
+      "x": -1.1472451775814219,
+      "y": -1.9298061882733615
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.15698191222276542,
+      "x": 2.0648495687392714,
+      "y": 0.9202412384766959
+    },
+    {
+      "id": 22,
+      "rotation_radians": -1.0986165609546643,
+      "x": -0.20262930154542017,
+      "y": -2.2589748729713683
+    }
+  ],
+  "problem": "22 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/22.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_023_125d15e1f42d4cc7.json b/data/solutions/generated/squinpen_023_125d15e1f42d4cc7.json
new file mode 100644
index 0000000000000000000000000000000000000000..c3a9e9cfa2bd19c903fbd21dca1e92efb81bf204
--- /dev/null
+++ b/data/solutions/generated/squinpen_023_125d15e1f42d4cc7.json
@@ -0,0 +1,200 @@
+{
+  "case": "squinpen@23",
+  "container": {
+    "circumradius": 3.4051286935340226,
+    "orientation_radians": 0.0,
+    "side_length": 4.00296885643447,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@23",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "4.002+",
+    "metric_symbol": "s",
+    "metric_value": 4.002,
+    "reference_text": "s = 4.002+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "23.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/23.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@23",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "4.002+",
+      "metric_symbol": "s",
+      "metric_value": 4.002,
+      "reference_text": "s = 4.002+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "23.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/23.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "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/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.4083319103408503,
+      "x": -0.004549076931451928,
+      "y": 0.1772367033572422
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+    {
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+      "x": -1.2547679005734291,
+      "y": 0.1215760146005793
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.7784932165195517,
+      "x": -2.2497088041205995,
+      "y": -1.5054603180040884
+    },
+    {
+      "id": 12,
+      "rotation_radians": 1.7279146221100379,
+      "x": 0.9601588313108579,
+      "y": -2.5145058023340043
+    },
+    {
+      "id": 13,
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+      "x": 1.060162509354659,
+      "y": 0.47420939901521103
+    },
+    {
+      "id": 14,
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+      "x": 2.6945977673451633,
+      "y": 0.009421290221088152
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+    {
+      "id": 15,
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+      "x": 1.9716787870794328,
+      "y": -0.6910985227545124
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.4352512972326492,
+      "x": 2.0698335465241273,
+      "y": 0.8671328280435111
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.7854002307613193,
+      "x": -2.254793505018402,
+      "y": -0.49446500791220366
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.47125117513088527,
+      "x": -1.1151476114949403,
+      "y": -2.0085011820749386
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.4137148616950383,
+      "x": -0.4686631507371087,
+      "y": 1.0784612936727918
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.15707737616215117,
+      "x": 1.5479940829502787,
+      "y": -1.7054473150232055
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.7853969266861722,
+      "x": -2.2547938554220672,
+      "y": 0.5105967258500962
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.8466084378199042,
+      "x": 0.7655279928824079,
+      "y": -0.7342171469066978
+    },
+    {
+      "id": 23,
+      "rotation_radians": 1.4137159219303725,
+      "x": -0.058038640016580885,
+      "y": 2.214627448047071
+    }
+  ],
+  "problem": "23 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/23.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_024_5483079483431bd6.json b/data/solutions/generated/squinpen_024_5483079483431bd6.json
new file mode 100644
index 0000000000000000000000000000000000000000..fa7c719c3a09de43715c71a9b1cf197d099c7613
--- /dev/null
+++ b/data/solutions/generated/squinpen_024_5483079483431bd6.json
@@ -0,0 +1,206 @@
+{
+  "case": "squinpen@24",
+  "container": {
+    "circumradius": 3.5217297103103538,
+    "orientation_radians": 0.0,
+    "side_length": 4.140041572561339,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@24",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "4.107+",
+    "metric_symbol": "s",
+    "metric_value": 4.107,
+    "reference_text": "s = 4.107+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "24.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/24.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@24",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "4.107+",
+      "metric_symbol": "s",
+      "metric_value": 4.107,
+      "reference_text": "s = 4.107+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "24.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/24.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "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/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.4146331548732214,
+      "x": -2.1472344919677964,
+      "y": -1.5638230777685964
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+    {
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+      "x": -1.258338007181853,
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+      "y": 0.09990131810536913
+    },
+    {
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+      "x": -2.324287889888269,
+      "y": -0.37618336037660227
+    },
+    {
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+      "y": 0.1848329342235694
+    },
+    {
+      "id": 14,
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+      "x": 1.1060481443799977,
+      "y": 0.768784499562691
+    },
+    {
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+      "rotation_radians": 1.4041089450408732,
+      "x": 2.21136871552694,
+      "y": 0.9447307506377265
+    },
+    {
+      "id": 16,
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+      "y": 0.6244232672309563
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+    {
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+      "x": -1.3192432599182653,
+      "y": 0.37643345448191845
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+    {
+      "id": 18,
+      "rotation_radians": 1.4079722510227826,
+      "x": -0.4072744598082227,
+      "y": 1.1513841281156818
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.408947660039717,
+      "x": 0.5182328169723309,
+      "y": 1.577838705141216
+    },
+    {
+      "id": 20,
+      "rotation_radians": 1.4137172690415163,
+      "x": 1.5890518442689425,
+      "y": 1.809410801581433
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.0907078192647734,
+      "x": -2.2219439605009725,
+      "y": 1.7434213520109751
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.092171482760529,
+      "x": -1.249705516670639,
+      "y": 1.9879328643000949
+    },
+    {
+      "id": 23,
+      "rotation_radians": 1.0995708723521531,
+      "x": -0.31745074965842707,
+      "y": 2.366874764773937
+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.4137174757618867,
+      "x": 0.9940391039348341,
+      "y": 2.628377894807814
+    }
+  ],
+  "problem": "24 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_025_965f543dd3a1a5b2.json b/data/solutions/generated/squinpen_025_965f543dd3a1a5b2.json
new file mode 100644
index 0000000000000000000000000000000000000000..543311550b06b9ef80048ed45a3bf2f972413a8e
--- /dev/null
+++ b/data/solutions/generated/squinpen_025_965f543dd3a1a5b2.json
@@ -0,0 +1,212 @@
+{
+  "case": "squinpen@25",
+  "container": {
+    "circumradius": 3.549365855641956,
+    "orientation_radians": 0.0,
+    "side_length": 4.172529809873594,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@25",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "4.169+",
+    "metric_symbol": "s",
+    "metric_value": 4.169,
+    "reference_text": "s = 4.169+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "25.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/25.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@25",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "4.169+",
+      "metric_symbol": "s",
+      "metric_value": 4.169,
+      "reference_text": "s = 4.169+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "25.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/25.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "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/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.7913686471395188,
+      "x": -2.3643731966258894,
+      "y": -1.5813515520996448
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+    {
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+      "x": -1.1232784395222144,
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+    {
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+      "x": 1.8455267443163488,
+      "y": -0.21078027826207862
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+    {
+      "id": 11,
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+      "y": 0.0021193940772869973
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+      "y": -0.19491516279202561
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+      "id": 13,
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+      "x": 0.6565098687382722,
+      "y": -0.48556210626108187
+    },
+    {
+      "id": 14,
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+      "y": 0.7227585345163104
+    },
+    {
+      "id": 15,
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+      "x": 2.842313739220558,
+      "y": 0.11638325267712148
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.7853978132225019,
+      "x": -2.3714860431583764,
+      "y": 0.4893772978458858
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.7857149236000472,
+      "x": -1.3712934844933036,
+      "y": 1.00425732824288
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.7845887119545628,
+      "x": -0.37096096266403006,
+      "y": 0.805140863919368
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.15708521319190266,
+      "x": 0.5722482597605102,
+      "y": 1.54563906996397
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.1570855592767954,
+      "x": 2.2399432271040784,
+      "y": 0.9515761132764056
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.7853989646573181,
+      "x": -2.371484882056246,
+      "y": 1.537783815402405
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.096400766390279,
+      "x": -1.1034554121742386,
+      "y": 2.133308143922604
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.4748254047366579,
+      "x": -0.14152963883903807,
+      "y": 2.4253507950119944
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.15706974434978674,
+      "x": 1.0137814023254739,
+      "y": 2.6392650838634117
+    },
+    {
+      "id": 25,
+      "rotation_radians": -0.1570829738563012,
+      "x": 1.6197265945705779,
+      "y": 1.805254399518042
+    }
+  ],
+  "problem": "25 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/25.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_026_12ea954c92ca25d9.json b/data/solutions/generated/squinpen_026_12ea954c92ca25d9.json
new file mode 100644
index 0000000000000000000000000000000000000000..a3750c7ac0c571846d2cb6b8be53241a7f1915ef
--- /dev/null
+++ b/data/solutions/generated/squinpen_026_12ea954c92ca25d9.json
@@ -0,0 +1,218 @@
+{
+  "case": "squinpen@26",
+  "container": {
+    "circumradius": 3.593713074674243,
+    "orientation_radians": 0.0,
+    "side_length": 4.224663092528319,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@26",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "4.223+",
+    "metric_symbol": "s",
+    "metric_value": 4.223,
+    "reference_text": "s = 4.223+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "26.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/26.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@26",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "4.223+",
+      "metric_symbol": "s",
+      "metric_value": 4.223,
+      "reference_text": "s = 4.223+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "26.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/26.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "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/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.6144770416291189,
+      "x": 0.6010544817963643,
+      "y": -1.6048829598386134
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+    {
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+    {
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+      "y": -0.8334897691351119
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+      "x": 0.6009089307627735,
+      "y": -0.517399335261046
+    },
+    {
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+    {
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+      "x": -0.4236079834059959,
+      "y": 2.3936122407104192
+    },
+    {
+      "id": 11,
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+      "x": 0.9236946192590073,
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+    {
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+      "y": 0.050824420712315556
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+    {
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+      "rotation_radians": 0.780606215857329,
+      "x": -0.40394747290644684,
+      "y": 0.8901266013417534
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.7805973768439021,
+      "x": -0.3974973967991644,
+      "y": -0.10994976295057943
+    },
+    {
+      "id": 15,
+      "rotation_radians": 1.0995480180712285,
+      "x": -1.3746953915565177,
+      "y": 2.084591830499319
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.7853868659228801,
+      "x": -1.4068882883238842,
+      "y": -0.045467981250062746
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.4371744389576708,
+      "x": 0.5087487685587887,
+      "y": 1.6743041731885824
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.4712468269227371,
+      "x": -1.0948347639439964,
+      "y": -2.1755257120658
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.4712361800843202,
+      "x": -0.14370029318022903,
+      "y": -2.4843994984325803
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.7853826419475666,
+      "x": -2.407094708369398,
+      "y": 0.5374566549516283
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.784274884460863,
+      "x": -2.406506390183513,
+      "y": 1.598667302025473
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.7853860950737279,
+      "x": -1.4065470261586885,
+      "y": 0.9545419421866781
+    },
+    {
+      "id": 23,
+      "rotation_radians": 1.4463330611072804,
+      "x": 0.9942946047465046,
+      "y": 2.6979688404153954
+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.4137268022606229,
+      "x": 2.195170303015151,
+      "y": 1.0629182773841692
+    },
+    {
+      "id": 25,
+      "rotation_radians": 1.4137632909526072,
+      "x": 1.6127086904237988,
+      "y": 1.8759037182834137
+    },
+    {
+      "id": 26,
+      "rotation_radians": 1.4137222586733538,
+      "x": 2.7883664393543426,
+      "y": 0.25779388837941075
+    }
+  ],
+  "problem": "26 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/26.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_027_c69ed1bfb373f6cd.json b/data/solutions/generated/squinpen_027_c69ed1bfb373f6cd.json
new file mode 100644
index 0000000000000000000000000000000000000000..87a3feb5d4ed208fc813909ac795eb6ef6b348de
--- /dev/null
+++ b/data/solutions/generated/squinpen_027_c69ed1bfb373f6cd.json
@@ -0,0 +1,224 @@
+{
+  "case": "squinpen@27",
+  "container": {
+    "circumradius": 3.7175405869881395,
+    "orientation_radians": 0.0,
+    "side_length": 4.370231063660665,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@27",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "4.350+",
+    "metric_symbol": "s",
+    "metric_value": 4.35,
+    "reference_text": "s = 4.350+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "27.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/27.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@27",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "4.350+",
+      "metric_symbol": "s",
+      "metric_value": 4.35,
+      "reference_text": "s = 4.350+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "27.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/27.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "generator": "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/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.3698878141339904,
+      "x": -2.3482375367793096,
+      "y": -1.815937498519039
+    },
+    {
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+      "x": 2.2886630391008618,
+      "y": -1.1010636531778
+    },
+    {
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+      "x": -1.460420931831544,
+      "y": -1.0657872948281015
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+    {
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+    {
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+    {
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+    {
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+      "y": 1.683108672357874
+    },
+    {
+      "id": 23,
+      "rotation_radians": 1.4152630405441524,
+      "x": 1.0436812520586958,
+      "y": 2.8282584293056408
+    },
+    {
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+      "rotation_radians": 1.41372194126819,
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+      "y": 1.9761610070921418
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+    {
+      "id": 25,
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+      "x": -2.3773883465307026,
+      "y": 1.7444703269854058
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+    {
+      "id": 26,
+      "rotation_radians": 1.0995996656370377,
+      "x": -1.461352535343699,
+      "y": 2.1617516463834257
+    },
+    {
+      "id": 27,
+      "rotation_radians": 1.3366187362557334,
+      "x": 0.010104140441791797,
+      "y": 2.520310680226431
+    }
+  ],
+  "problem": "27 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/27.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_028_117dfd2e5e6c3a3f.json b/data/solutions/generated/squinpen_028_117dfd2e5e6c3a3f.json
new file mode 100644
index 0000000000000000000000000000000000000000..b137a0e1f7659f041e746c3918709ba6a5dbd509
--- /dev/null
+++ b/data/solutions/generated/squinpen_028_117dfd2e5e6c3a3f.json
@@ -0,0 +1,230 @@
+{
+  "case": "squinpen@28",
+  "container": {
+    "circumradius": 3.785621919941396,
+    "orientation_radians": 0.0,
+    "side_length": 4.45026547059334,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@28",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "4.421+",
+    "metric_symbol": "s",
+    "metric_value": 4.421,
+    "reference_text": "s = 4.421+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "28.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/28.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@28",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "4.421+",
+      "metric_symbol": "s",
+      "metric_value": 4.421,
+      "reference_text": "s = 4.421+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "28.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/28.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "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/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.4712416003877584,
+      "x": -2.4291012089464235,
+      "y": -1.9052183581263686
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+    {
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+      "y": -2.2579366078323155
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+    {
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+      "x": -0.340265624399387,
+      "y": -2.583933269895215
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+      "y": 0.421932638015013
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+      "x": 0.78768369590849,
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+    },
+    {
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+      "y": -0.10830093022075793
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+    {
+      "id": 18,
+      "rotation_radians": 0.4712318693566605,
+      "x": 2.702542542087848,
+      "y": -0.4181085231767726
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+    {
+      "id": 19,
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+      "y": 0.9653871436221975
+    },
+    {
+      "id": 20,
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+      "x": -0.5337237363033763,
+      "y": 1.4544089060241998
+    },
+    {
+      "id": 21,
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+      "x": 0.2843949962026153,
+      "y": 2.7868993564192133
+    },
+    {
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+      "y": 1.7732292417970186
+    },
+    {
+      "id": 23,
+      "rotation_radians": -1.099564541604153,
+      "x": 1.436736433653882,
+      "y": 1.0446889064523022
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.47123177794547577,
+      "x": 2.387834872943213,
+      "y": 0.7356600924605611
+    },
+    {
+      "id": 25,
+      "rotation_radians": -0.7853974214622796,
+      "x": -2.562609466709928,
+      "y": 1.371576917289352
+    },
+    {
+      "id": 26,
+      "rotation_radians": -0.4459582308007448,
+      "x": -1.630059905022047,
+      "y": 2.149239355321753
+    },
+    {
+      "id": 27,
+      "rotation_radians": -0.47123668553887804,
+      "x": -0.670657035905686,
+      "y": 2.4765771912886625
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.15705908926051937,
+      "x": 1.5104454319327625,
+      "y": 2.2808408842669485
+    }
+  ],
+  "problem": "28 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/28.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_029_c1c4dc57f8cd7d32.json b/data/solutions/generated/squinpen_029_c1c4dc57f8cd7d32.json
new file mode 100644
index 0000000000000000000000000000000000000000..8f5082f079a18862f20c6809e1d93d8bf1e31d9c
--- /dev/null
+++ b/data/solutions/generated/squinpen_029_c1c4dc57f8cd7d32.json
@@ -0,0 +1,236 @@
+{
+  "case": "squinpen@29",
+  "container": {
+    "circumradius": 3.86034546200736,
+    "orientation_radians": 0.0,
+    "side_length": 4.5381082626442,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@29",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "4.499+",
+    "metric_symbol": "s",
+    "metric_value": 4.499,
+    "reference_text": "s = 4.499+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "29.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/29.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@29",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "4.499+",
+      "metric_symbol": "s",
+      "metric_value": 4.499,
+      "reference_text": "s = 4.499+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "29.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/29.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "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/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
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+      "x": -1.9643744161431782,
+      "y": -2.119795627860861
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+    {
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+    {
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+      "x": -2.6130132402534176,
+      "y": 0.017132196312779447
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+    {
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+    {
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+      "x": 0.17835522788913546,
+      "y": 0.6183052278266711
+    },
+    {
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+      "x": 1.7668402327875703,
+      "y": 0.1214706101556768
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.11934185409428462,
+      "x": 2.936954776540884,
+      "y": 0.3468598082654404
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.8043593298078382,
+      "x": -2.5909213026387135,
+      "y": 1.0169278098072287
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.42154786713531744,
+      "x": -1.3790641724784045,
+      "y": 1.1695883222867678
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.4269068392208273,
+      "x": -0.4284688299447912,
+      "y": 1.4989204093946908
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.43373228604551467,
+      "x": 0.537601750587438,
+      "y": 1.8116786507147797
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.32290889503073844,
+      "x": 1.2010989210660319,
+      "y": 0.9588898971482188
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.13073544643627158,
+      "x": 2.3040719147539854,
+      "y": 1.222352761493128
+    },
+    {
+      "id": 25,
+      "rotation_radians": 1.0995325903954196,
+      "x": -1.9018558757255348,
+      "y": 2.14010680213291
+    },
+    {
+      "id": 26,
+      "rotation_radians": -0.4712525226817066,
+      "x": -0.9399090726833708,
+      "y": 2.415758120417466
+    },
+    {
+      "id": 27,
+      "rotation_radians": -0.47124975466817687,
+      "x": 0.013366472806676024,
+      "y": 2.7181422901439642
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.15708478889587765,
+      "x": 1.1483743811912255,
+      "y": 2.8820160432334574
+    },
+    {
+      "id": 29,
+      "rotation_radians": -0.1413434300505571,
+      "x": 1.7329595326688227,
+      "y": 2.0597590549215354
+    }
+  ],
+  "problem": "29 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/29.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_030_3b632d53270924b9.json b/data/solutions/generated/squinpen_030_3b632d53270924b9.json
new file mode 100644
index 0000000000000000000000000000000000000000..e5471604bdabd952c5145eb69f90f071baf1422a
--- /dev/null
+++ b/data/solutions/generated/squinpen_030_3b632d53270924b9.json
@@ -0,0 +1,242 @@
+{
+  "case": "squinpen@30",
+  "container": {
+    "circumradius": 3.9400985755907008,
+    "orientation_radians": 0.0,
+    "side_length": 4.6318636706215885,
+    "sides": 5,
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+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@30",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "4.550+",
+    "metric_symbol": "s",
+    "metric_value": 4.55,
+    "reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "30.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@30",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "4.550+",
+      "metric_symbol": "s",
+      "metric_value": 4.55,
+      "reference_text": "s = 4.550+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "30.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/30.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+    {
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+      "x": -2.5836002518822796,
+      "y": 1.7896070602847804
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+    {
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+      "y": -1.7011326124343549
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+    {
+      "id": 28,
+      "rotation_radians": 0.3809517261357379,
+      "x": -1.3647326783875935,
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+    {
+      "id": 29,
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+      "x": 2.64086488825888,
+      "y": -0.9026135881928236
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+    {
+      "id": 30,
+      "rotation_radians": -1.0880609397882117,
+      "x": -2.560781584531864,
+      "y": 0.4409635528201759
+    }
+  ],
+  "problem": "30 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/30.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_031_4553b8253edc54ee.json b/data/solutions/generated/squinpen_031_4553b8253edc54ee.json
new file mode 100644
index 0000000000000000000000000000000000000000..b29f8af4d590cd6f5dd161e768971e24a3a63d54
--- /dev/null
+++ b/data/solutions/generated/squinpen_031_4553b8253edc54ee.json
@@ -0,0 +1,248 @@
+{
+  "case": "squinpen@31",
+  "container": {
+    "circumradius": 3.955682348404072,
+    "orientation_radians": 0.0,
+    "side_length": 4.650183494291141,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@31",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "4.63041+",
+    "metric_symbol": "s",
+    "metric_value": 4.63041,
+    "reference_text": "s = 4.63041+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "31.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/31.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@31",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "4.63041+",
+      "metric_symbol": "s",
+      "metric_value": 4.63041,
+      "reference_text": "s = 4.63041+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "31.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/31.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "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/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "y": 3.0941640957926664
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+    {
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+      "y": -0.7134363512382542
+    },
+    {
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+      "y": -1.0772496766854247
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+    {
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+      "y": -0.005966651854075765
+    },
+    {
+      "id": 25,
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+      "x": 1.3835875458855253,
+      "y": 0.9881218328446747
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.1578356009861051,
+      "x": 2.2308519499509583,
+      "y": -1.5226785113207422
+    },
+    {
+      "id": 27,
+      "rotation_radians": 1.4137278080099933,
+      "x": 2.0235316712299776,
+      "y": 0.10732538591135327
+    },
+    {
+      "id": 28,
+      "rotation_radians": 0.5882440685897783,
+      "x": -2.561863511419486,
+      "y": -1.948853265188123
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.4712387455396941,
+      "x": 0.7578270540146763,
+      "y": -3.08538809890942
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.234619423967945,
+      "x": -1.3804776749249468,
+      "y": -2.1627492286394316
+    },
+    {
+      "id": 31,
+      "rotation_radians": 1.4135930039719515,
+      "x": 0.7922102204157947,
+      "y": 1.8019639931987081
+    }
+  ],
+  "problem": "31 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/31.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_032_b157990acac8fece.json b/data/solutions/generated/squinpen_032_b157990acac8fece.json
new file mode 100644
index 0000000000000000000000000000000000000000..f2e6146a0e4f5f98e58ac4872efb1e519748381d
--- /dev/null
+++ b/data/solutions/generated/squinpen_032_b157990acac8fece.json
@@ -0,0 +1,254 @@
+{
+  "case": "squinpen@32",
+  "container": {
+    "circumradius": 4.016949776157224,
+    "orientation_radians": 0.0,
+    "side_length": 4.7222076752495346,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@32",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "4.70774+",
+    "metric_symbol": "s",
+    "metric_value": 4.70774,
+    "reference_text": "s = 4.70774+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "32.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/32.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@32",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "4.70774+",
+      "metric_symbol": "s",
+      "metric_value": 4.70774,
+      "reference_text": "s = 4.70774+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "32.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/32.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "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/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.4137072744389956,
+      "x": 0.30656920875768784,
+      "y": 0.85353094451549
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+    {
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+      "y": -1.275577179927078
+    },
+    {
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+    {
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+      "x": -1.7494600277808874,
+      "y": -1.1343856348015404
+    },
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+    {
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+    {
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+    {
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+      "x": 2.11081543610995,
+      "y": -0.18616612021009712
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+  ],
+  "problem": "32 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/32.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_033_84c8eef1219afe3a.json b/data/solutions/generated/squinpen_033_84c8eef1219afe3a.json
new file mode 100644
index 0000000000000000000000000000000000000000..2df876dce18efe9a53d0cde514768a009ec71ce3
--- /dev/null
+++ b/data/solutions/generated/squinpen_033_84c8eef1219afe3a.json
@@ -0,0 +1,260 @@
+{
+  "case": "squinpen@33",
+  "container": {
+    "circumradius": 4.0834167411679925,
+    "orientation_radians": 0.0,
+    "side_length": 4.800344278845474,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@33",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "4.75774+",
+    "metric_symbol": "s",
+    "metric_value": 4.75774,
+    "reference_text": "s = 4.75774+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "33.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/33.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@33",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "4.75774+",
+      "metric_symbol": "s",
+      "metric_value": 4.75774,
+      "reference_text": "s = 4.75774+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "33.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/33.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "generator": "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/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "y": 1.6785294561894475
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+    {
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+      "y": 3.1610198989599514
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+    {
+      "id": 29,
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+      "y": 2.0305955951627475
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+    {
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+      "y": 2.4422600813741857
+    },
+    {
+      "id": 31,
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+      "x": -2.2222491163427813,
+      "y": 2.225760273669865
+    },
+    {
+      "id": 32,
+      "rotation_radians": -0.48685550903010016,
+      "x": -1.2492298511573532,
+      "y": 2.5284815449924194
+    },
+    {
+      "id": 33,
+      "rotation_radians": -0.47125460700053173,
+      "x": -0.2834889885420195,
+      "y": 2.8167936057646474
+    }
+  ],
+  "problem": "33 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/33.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_034_01337f10c6d18cd5.json b/data/solutions/generated/squinpen_034_01337f10c6d18cd5.json
new file mode 100644
index 0000000000000000000000000000000000000000..842fde7796b518079750a682dbc4297f27a5b237
--- /dev/null
+++ b/data/solutions/generated/squinpen_034_01337f10c6d18cd5.json
@@ -0,0 +1,266 @@
+{
+  "case": "squinpen@34",
+  "container": {
+    "circumradius": 4.133864857777755,
+    "orientation_radians": 0.0,
+    "side_length": 4.859649596743772,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@34",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "4.81817+",
+    "metric_symbol": "s",
+    "metric_value": 4.81817,
+    "reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "34.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@34",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "4.81817+",
+      "metric_symbol": "s",
+      "metric_value": 4.81817,
+      "reference_text": "s = 4.81817+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "34.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/34.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "generator": "polygon_packer_c",
+    "generator_profile": "best of cg/steepest/sa seed profiles",
+    "notes": "Generated seed layout for frontend figures with polygon-packer-c.",
+    "profile": "sa",
+    "source_url": "https://erich-friedman.github.io/packing/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+    {
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+      "rotation_radians": 1.413716893558685,
+      "x": 1.7505729687271192,
+      "y": 2.4296271666324665
+    },
+    {
+      "id": 29,
+      "rotation_radians": 1.6012224385282066,
+      "x": 1.5665154929398029,
+      "y": 0.839432189985201
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.4764090834499033,
+      "x": 2.34207074855973,
+      "y": 1.5629947238757522
+    },
+    {
+      "id": 31,
+      "rotation_radians": 1.09954742974702,
+      "x": -2.588462552805399,
+      "y": 2.149687596027564
+    },
+    {
+      "id": 32,
+      "rotation_radians": 1.680396315269111,
+      "x": -1.1769794750982374,
+      "y": 2.4060181785847834
+    },
+    {
+      "id": 33,
+      "rotation_radians": -0.03882331720839513,
+      "x": -0.022818158062079544,
+      "y": 2.8099446320782877
+    },
+    {
+      "id": 34,
+      "rotation_radians": 1.3811642118889318,
+      "x": 1.1195686430255436,
+      "y": 3.228880585054155
+    }
+  ],
+  "problem": "34 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/34.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_035_18582601dada9f12.json b/data/solutions/generated/squinpen_035_18582601dada9f12.json
new file mode 100644
index 0000000000000000000000000000000000000000..2d68c12b7572c7f190f4a449aa12d9b713ceccdf
--- /dev/null
+++ b/data/solutions/generated/squinpen_035_18582601dada9f12.json
@@ -0,0 +1,272 @@
+{
+  "case": "squinpen@35",
+  "container": {
+    "circumradius": 4.200750960842055,
+    "orientation_radians": 0.0,
+    "side_length": 4.938278926672792,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@35",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "4.86994+",
+    "metric_symbol": "s",
+    "metric_value": 4.86994,
+    "reference_text": "s = 4.86994+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "35.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/35.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@35",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "4.86994+",
+      "metric_symbol": "s",
+      "metric_value": 4.86994,
+      "reference_text": "s = 4.86994+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "35.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/35.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "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/squinpen/",
+    "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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+    {
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+    {
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+    {
+      "id": 29,
+      "rotation_radians": 1.0995664843965944,
+      "x": -0.8942955457402963,
+      "y": 2.701629540067827
+    },
+    {
+      "id": 30,
+      "rotation_radians": 4.161378194704665,
+      "x": 0.714685352095719,
+      "y": 2.1880962695729647
+    },
+    {
+      "id": 31,
+      "rotation_radians": 4.788694161357987,
+      "x": 2.5484747863025228,
+      "y": -1.3047834418256665
+    },
+    {
+      "id": 32,
+      "rotation_radians": 3.7701026232329755,
+      "x": -0.6112764348268811,
+      "y": 1.560724522377967
+    },
+    {
+      "id": 33,
+      "rotation_radians": 3.61283207748082,
+      "x": 0.09265657689228265,
+      "y": -3.052642497128583
+    },
+    {
+      "id": 34,
+      "rotation_radians": 5.81196579908999,
+      "x": 0.040507149131119025,
+      "y": 3.060775135124965
+    },
+    {
+      "id": 35,
+      "rotation_radians": 0.4555189672771835,
+      "x": -0.8130006531848475,
+      "y": -0.6722383921296162
+    }
+  ],
+  "problem": "35 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/35.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_036_106a35f9dda2ef3a.json b/data/solutions/generated/squinpen_036_106a35f9dda2ef3a.json
new file mode 100644
index 0000000000000000000000000000000000000000..857274c07857613008ce80af35cbf0bcba9db07f
--- /dev/null
+++ b/data/solutions/generated/squinpen_036_106a35f9dda2ef3a.json
@@ -0,0 +1,278 @@
+{
+  "case": "squinpen@36",
+  "container": {
+    "circumradius": 4.212447621939824,
+    "orientation_radians": 0.0,
+    "side_length": 4.952029176461456,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@36",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "4.93902+",
+    "metric_symbol": "s",
+    "metric_value": 4.93902,
+    "reference_text": "s = 4.93902+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "36.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/36.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@36",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "4.93902+",
+      "metric_symbol": "s",
+      "metric_value": 4.93902,
+      "reference_text": "s = 4.93902+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "36.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/36.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "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/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 5.817572383043886,
+      "x": 0.9842402070388308,
+      "y": 3.374432230187003
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+    {
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+    {
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+    {
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+      "x": 1.7764337543709072,
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+    {
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+      "y": -2.1861854676845565
+    },
+    {
+      "id": 27,
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+      "x": -0.8761510773090724,
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+    },
+    {
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+      "x": 0.0748577333011107,
+      "y": -3.0809441531018864
+    },
+    {
+      "id": 29,
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+      "x": 0.46868140007352826,
+      "y": 1.0567938749136498
+    },
+    {
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+      "rotation_radians": 6.12899883811191,
+      "x": 2.338106819098574,
+      "y": 1.72666823472107
+    },
+    {
+      "id": 31,
+      "rotation_radians": 2.7281638253872913,
+      "x": -0.7532826996983107,
+      "y": 1.7306327611053995
+    },
+    {
+      "id": 32,
+      "rotation_radians": 1.1625896838239338,
+      "x": -1.6889309845278762,
+      "y": 1.3701321296149063
+    },
+    {
+      "id": 33,
+      "rotation_radians": 2.988022521090385,
+      "x": 3.5136458005163345,
+      "y": 0.10815726899377415
+    },
+    {
+      "id": 34,
+      "rotation_radians": 1.2324414404305724,
+      "x": -0.9368576409498935,
+      "y": -0.5753952876063091
+    },
+    {
+      "id": 35,
+      "rotation_radians": 3.4376833608398143,
+      "x": -0.575560777286188,
+      "y": -1.732931984362165
+    },
+    {
+      "id": 36,
+      "rotation_radians": 2.98802060931093,
+      "x": 2.92476898869663,
+      "y": 0.9164152127886697
+    }
+  ],
+  "problem": "36 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/36.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_037_118ed6265867ee6d.json b/data/solutions/generated/squinpen_037_118ed6265867ee6d.json
new file mode 100644
index 0000000000000000000000000000000000000000..b0f0de180f77659445da97603af688236c39980e
--- /dev/null
+++ b/data/solutions/generated/squinpen_037_118ed6265867ee6d.json
@@ -0,0 +1,284 @@
+{
+  "case": "squinpen@37",
+  "container": {
+    "circumradius": 4.273823861671925,
+    "orientation_radians": 0.0,
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+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@37",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "4.98234+",
+    "metric_symbol": "s",
+    "metric_value": 4.98234,
+    "reference_text": "s = 4.98234+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "37.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/37.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@37",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "4.98234+",
+      "metric_symbol": "s",
+      "metric_value": 4.98234,
+      "reference_text": "s = 4.98234+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "37.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/37.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "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/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
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+    },
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+    {
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+    {
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+    {
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+      "x": 0.06983062172830677,
+      "y": 3.1181685019082703
+    }
+  ],
+  "problem": "37 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/37.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_038_05c73c36e688b1e7.json b/data/solutions/generated/squinpen_038_05c73c36e688b1e7.json
new file mode 100644
index 0000000000000000000000000000000000000000..e0cd012f2a9badba0a04ae12ffb1f60e0249e024
--- /dev/null
+++ b/data/solutions/generated/squinpen_038_05c73c36e688b1e7.json
@@ -0,0 +1,290 @@
+{
+  "case": "squinpen@38",
+  "container": {
+    "circumradius": 4.331676404502069,
+    "orientation_radians": 0.0,
+    "side_length": 5.0921910165392035,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@38",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "5.05233+",
+    "metric_symbol": "s",
+    "metric_value": 5.05233,
+    "reference_text": "s = 5.05233+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "38.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/38.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@38",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "5.05233+",
+      "metric_symbol": "s",
+      "metric_value": 5.05233,
+      "reference_text": "s = 5.05233+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "38.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/38.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "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/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+    {
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+      "x": 2.437600570572254,
+      "y": -1.7562297129546545
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+    },
+    {
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+      "x": -1.2382980334075506,
+      "y": -1.7051397370098675
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+    {
+      "id": 32,
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+      "x": -3.0043871971894744,
+      "y": -1.1043934329615257
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+    {
+      "id": 33,
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+      "y": 1.5150906009009264
+    },
+    {
+      "id": 34,
+      "rotation_radians": 1.0997914819131047,
+      "x": -2.75398959323987,
+      "y": 0.16101366059234481
+    },
+    {
+      "id": 35,
+      "rotation_radians": 0.15774201920536923,
+      "x": 1.3726633740786993,
+      "y": -1.5200910955747893
+    },
+    {
+      "id": 36,
+      "rotation_radians": 0.1609275994934875,
+      "x": -0.0729150665611485,
+      "y": -1.7715017578843486
+    },
+    {
+      "id": 37,
+      "rotation_radians": 1.413722861360904,
+      "x": 1.8249890319310758,
+      "y": 2.599480813429025
+    },
+    {
+      "id": 38,
+      "rotation_radians": 1.4519703404298911,
+      "x": -0.09153381199792288,
+      "y": 1.7520815280293518
+    }
+  ],
+  "problem": "38 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/38.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squinpen_040_9fbb25ae252614ca.json b/data/solutions/generated/squinpen_040_9fbb25ae252614ca.json
new file mode 100644
index 0000000000000000000000000000000000000000..e9b2bcc9d29f82e4e027da9bbb1a855bb6f5d216
--- /dev/null
+++ b/data/solutions/generated/squinpen_040_9fbb25ae252614ca.json
@@ -0,0 +1,302 @@
+{
+  "case": "squinpen@40",
+  "container": {
+    "circumradius": 4.414740213841796,
+    "orientation_radians": 0.0,
+    "side_length": 5.189838380797454,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squinpen@40",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/8/26",
+    "metric_expression": "5.17250+",
+    "metric_symbol": "s",
+    "metric_value": 5.1725,
+    "reference_text": "s = 5.17250+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "40.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squinpen/40.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+    "title": "Squares in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squinpen@40",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/8/26",
+      "metric_expression": "5.17250+",
+      "metric_symbol": "s",
+      "metric_value": 5.1725,
+      "reference_text": "s = 5.17250+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "40.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squinpen/40.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squinpen/",
+      "title": "Squares in Pentagons"
+    },
+    "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/squinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
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+      "y": -0.9548051884175996
+    },
+    {
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+    },
+    {
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+      "y": -0.0845319952768984
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+    {
+      "id": 37,
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+    },
+    {
+      "id": 38,
+      "rotation_radians": 1.0995683809219317,
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+    },
+    {
+      "id": 39,
+      "rotation_radians": 1.3703341338800799,
+      "x": 3.1273601580265162,
+      "y": 0.885078809266491
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+    {
+      "id": 40,
+      "rotation_radians": 0.7853819373194761,
+      "x": -3.071568679119248,
+      "y": -0.9197279880339723
+    }
+  ],
+  "problem": "40 equal items for Squares in Pentagons",
+  "setup": "squinpen",
+  "source_image": "https://erich-friedman.github.io/packing/squinpen/40.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squinpen/"
+}
diff --git a/data/solutions/generated/squintri_021_a2e24601c2557198.json b/data/solutions/generated/squintri_021_a2e24601c2557198.json
new file mode 100644
index 0000000000000000000000000000000000000000..072c6ce16c765013815a5b32b7e2de60cf795d40
--- /dev/null
+++ b/data/solutions/generated/squintri_021_a2e24601c2557198.json
@@ -0,0 +1,188 @@
+{
+  "case": "squintri@21",
+  "container": {
+    "circumradius": 4.398847304000316,
+    "orientation_radians": 0.0,
+    "side_length": 7.619027025265926,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squintri@21",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "4/28/26",
+    "metric_expression": "3 + 8 / \u221a3 = 7.618+",
+    "metric_symbol": "s",
+    "metric_value": 7.618,
+    "reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.",
+    "source_image": "ts21.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squintri@21",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "4/28/26",
+      "metric_expression": "3 + 8 / \u221a3 = 7.618+",
+      "metric_symbol": "s",
+      "metric_value": 7.618,
+      "reference_text": "s = 3 + 8 / \u221a3 = 7.618+ | Found by Erich Friedman | in 1997.",
+      "source_image": "ts21.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts21.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.7853944264720535,
+      "x": -0.699381802692831,
+      "y": -9.23228881165581e-06
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+    {
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+    {
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+      "x": 2.2322052277580475,
+      "y": -0.6735399205887409
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.2617978314355014,
+      "x": -0.6503494997848538,
+      "y": 2.3377857454858844
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.2484259756921845,
+      "x": -0.5124316851652589,
+      "y": -2.2140409247673696
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.2617980173920209,
+      "x": 0.2157017358736772,
+      "y": 1.8377719999258157
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.3090046295264732,
+      "x": 1.295954035000609,
+      "y": -1.2140926952380455
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.26177705911968907,
+      "x": 2.2157510848694484,
+      "y": 0.4717248940685765
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.3089828888255435,
+      "x": 3.1674340838546478,
+      "y": -0.13357708927013334
+    }
+  ],
+  "problem": "21 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts21.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_022_bbb028380d997350.json b/data/solutions/generated/squintri_022_bbb028380d997350.json
new file mode 100644
index 0000000000000000000000000000000000000000..d1a499f82f23b4af95ef859c1602a9777aa2bfe8
--- /dev/null
+++ b/data/solutions/generated/squintri_022_bbb028380d997350.json
@@ -0,0 +1,194 @@
+{
+  "case": "squintri@22",
+  "container": {
+    "circumradius": 4.708276091307807,
+    "orientation_radians": 0.0,
+    "side_length": 8.154973406206924,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squintri@22",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "4/28/26",
+    "metric_expression": "7 + 2 / \u221a3 = 8.154+",
+    "metric_symbol": "s",
+    "metric_value": 8.154,
+    "reference_text": "s = 7 + 2 / \u221a3 = 8.154+ | Found by Erich Friedman | in 1997.",
+    "source_image": "ts22.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts22.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squintri@22",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "4/28/26",
+      "metric_expression": "7 + 2 / \u221a3 = 8.154+",
+      "metric_symbol": "s",
+      "metric_value": 8.154,
+      "reference_text": "s = 7 + 2 / \u221a3 = 8.154+ | Found by Erich Friedman | in 1997.",
+      "source_image": "ts22.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts22.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
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+      "x": -1.6711139577794896,
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+    {
+      "id": 17,
+      "rotation_radians": 0.7436379853691125,
+      "x": -0.820542827799026,
+      "y": 1.418773730008984
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.7456046419751388,
+      "x": 0.188869897290301,
+      "y": 1.5481084756087884
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.7214974290006289,
+      "x": 1.2298084346751397,
+      "y": 1.2346813688013198
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.39116593945579997,
+      "x": 2.335076863151971,
+      "y": 0.7148971576307457
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.7663365576814679,
+      "x": -1.8334741942620134,
+      "y": 2.7185231412153774
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.7436821112063875,
+      "x": -0.833351245767635,
+      "y": 2.4202489520046617
+    }
+  ],
+  "problem": "22 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts22.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_023_23ac4c9fa2eea010.json b/data/solutions/generated/squintri_023_23ac4c9fa2eea010.json
new file mode 100644
index 0000000000000000000000000000000000000000..19ffb452934ae3e4cadb6f05cacd5d98923936cf
--- /dev/null
+++ b/data/solutions/generated/squintri_023_23ac4c9fa2eea010.json
@@ -0,0 +1,200 @@
+{
+  "case": "squintri@23",
+  "container": {
+    "circumradius": 4.842577628843471,
+    "orientation_radians": 0.0,
+    "side_length": 8.387590492753313,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squintri@23",
+    "credit": "David W",
+    "date": "July 2002",
+    "family_updated": "4/28/26",
+    "metric_expression": "8.301+",
+    "metric_symbol": "s",
+    "metric_value": 8.301,
+    "reference_text": "s = 8.301+ | Found by David W. Cantrell | in July 2002.",
+    "source_image": "ts23.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts23.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squintri@23",
+      "credit": "David W",
+      "date": "July 2002",
+      "family_updated": "4/28/26",
+      "metric_expression": "8.301+",
+      "metric_symbol": "s",
+      "metric_value": 8.301,
+      "reference_text": "s = 8.301+ | Found by David W. Cantrell | in July 2002.",
+      "source_image": "ts23.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts23.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "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": -1.8635584487081114,
+      "y": -0.5705044289350163
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+    {
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+      "x": -1.9194036177132467,
+      "y": 2.116349161626416
+    },
+    {
+      "id": 14,
+      "rotation_radians": -1.360097931425882,
+      "x": 3.6436774588471352,
+      "y": 0.08534773064584804
+    },
+    {
+      "id": 15,
+      "rotation_radians": 0.2475230199603095,
+      "x": -1.7354217497507345,
+      "y": -3.012015504089858
+    },
+    {
+      "id": 16,
+      "rotation_radians": -1.2892432153449904,
+      "x": -0.7391377795970582,
+      "y": 2.633665159829661
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.777051497575726,
+      "x": -1.898915863016624,
+      "y": -1.5932153070996327
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.6791556004013636,
+      "x": 0.24369539061184045,
+      "y": -1.8478583847951928
+    },
+    {
+      "id": 19,
+      "rotation_radians": -1.2892212647399315,
+      "x": 0.0994730673242546,
+      "y": 2.0832279264668156
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.7853879918698295,
+      "x": -1.9212795756342143,
+      "y": 1.1162852095743474
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.2458560154098625,
+      "x": 1.6592688516525629,
+      "y": -1.0526681725906821
+    },
+    {
+      "id": 22,
+      "rotation_radians": -1.289146318706407,
+      "x": 0.9778869292484552,
+      "y": 1.603878713885732
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.7854230177465833,
+      "x": -1.9212609398641631,
+      "y": 3.1163975466170837
+    }
+  ],
+  "problem": "23 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts23.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_024_841c613875887f20.json b/data/solutions/generated/squintri_024_841c613875887f20.json
new file mode 100644
index 0000000000000000000000000000000000000000..11af583ca9b98e3791d423b3493413a7284dfaf3
--- /dev/null
+++ b/data/solutions/generated/squintri_024_841c613875887f20.json
@@ -0,0 +1,206 @@
+{
+  "case": "squintri@24",
+  "container": {
+    "circumradius": 4.888596117676278,
+    "orientation_radians": 0.0,
+    "side_length": 8.467296853499276,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squintri@24",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "4/28/26",
+    "metric_expression": "6 + 4 / \u221a3 = 8.309+",
+    "metric_symbol": "s",
+    "metric_value": 8.309,
+    "reference_text": "s = 6 + 4 / \u221a3 = 8.309+ | Found by Erich Friedman | in 1997.",
+    "source_image": "ts24.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts24.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squintri@24",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "4/28/26",
+      "metric_expression": "6 + 4 / \u221a3 = 8.309+",
+      "metric_symbol": "s",
+      "metric_value": 8.309,
+      "reference_text": "s = 6 + 4 / \u221a3 = 8.309+ | Found by Erich Friedman | in 1997.",
+      "source_image": "ts24.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts24.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.7913115511359317,
+      "x": -0.659545929894677,
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+      "y": 2.036686932601894
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+    {
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+      "y": 0.6045507516420957
+    },
+    {
+      "id": 15,
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+    },
+    {
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+    {
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+      "x": -1.837446872215432,
+      "y": -0.4637035080549026
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.3088481376146135,
+      "x": -0.910304782036361,
+      "y": -2.7352532936983165
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.26507257406764667,
+      "x": 1.0865526665510152,
+      "y": 1.5730161143756427
+    },
+    {
+      "id": 20,
+      "rotation_radians": 1.3090086458323644,
+      "x": -0.028837870234534112,
+      "y": -2.2617211755407114
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.30896541877095,
+      "x": 0.8305898099961285,
+      "y": -1.7501356289628134
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.2618289504139927,
+      "x": 3.70536136687951,
+      "y": 0.10558434923560024
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.7862033900330864,
+      "x": -0.9433814070921981,
+      "y": 1.5784757794870008
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.3841037877950146,
+      "x": 1.1838364288184116,
+      "y": 0.3197297843881803
+    }
+  ],
+  "problem": "24 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_025_b4f5fafd19e47950.json b/data/solutions/generated/squintri_025_b4f5fafd19e47950.json
new file mode 100644
index 0000000000000000000000000000000000000000..9ba9ea825b806fae7513e4d7613de265fd7294c0
--- /dev/null
+++ b/data/solutions/generated/squintri_025_b4f5fafd19e47950.json
@@ -0,0 +1,212 @@
+{
+  "case": "squintri@25",
+  "container": {
+    "circumradius": 4.931501385026837,
+    "orientation_radians": 0.0,
+    "side_length": 8.541610956462769,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squintri@25",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "4/28/26",
+    "metric_expression": "5 + 2 \u221a3 = 8.464+",
+    "metric_symbol": "s",
+    "metric_value": 8.464,
+    "reference_text": "s = 5 + 2 \u221a3 = 8.464+ | Found by Erich Friedman | in 1997.",
+    "source_image": "ts25.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts25.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squintri@25",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "4/28/26",
+      "metric_expression": "5 + 2 \u221a3 = 8.464+",
+      "metric_symbol": "s",
+      "metric_value": 8.464,
+      "reference_text": "s = 5 + 2 \u221a3 = 8.464+ | Found by Erich Friedman | in 1997.",
+      "source_image": "ts25.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts25.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "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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+  "problem": "25 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts25.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_026_029d10bebacbb7a8.json b/data/solutions/generated/squintri_026_029d10bebacbb7a8.json
new file mode 100644
index 0000000000000000000000000000000000000000..c7fcc2cc7ce2f8d59d1110fb3622112f417dc8ec
--- /dev/null
+++ b/data/solutions/generated/squintri_026_029d10bebacbb7a8.json
@@ -0,0 +1,218 @@
+{
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+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squintri@26",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "4/28/26",
+    "metric_expression": "4 + 8 / \u221a3 = 8.618+",
+    "metric_symbol": "s",
+    "metric_value": 8.618,
+    "reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.",
+    "source_image": "ts27.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
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+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
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+    "friedman_reference": {
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+      "case": "squintri@26",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "4/28/26",
+      "metric_expression": "4 + 8 / \u221a3 = 8.618+",
+      "metric_symbol": "s",
+      "metric_value": 8.618,
+      "reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.",
+      "source_image": "ts27.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
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+  "problem": "26 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts27.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_027_d80877f3b5e3e559.json b/data/solutions/generated/squintri_027_d80877f3b5e3e559.json
new file mode 100644
index 0000000000000000000000000000000000000000..61d0ecf9de07cedab3a1a45b7ab432994fedc1e1
--- /dev/null
+++ b/data/solutions/generated/squintri_027_d80877f3b5e3e559.json
@@ -0,0 +1,224 @@
+{
+  "case": "squintri@27",
+  "container": {
+    "circumradius": 5.025432216641772,
+    "orientation_radians": 0.0,
+    "side_length": 8.704303929217035,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squintri@27",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "4/28/26",
+    "metric_expression": "4 + 8 / \u221a3 = 8.618+",
+    "metric_symbol": "s",
+    "metric_value": 8.618,
+    "reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.",
+    "source_image": "ts27.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
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+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
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+    "friedman_reference": {
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+      "case": "squintri@27",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "4/28/26",
+      "metric_expression": "4 + 8 / \u221a3 = 8.618+",
+      "metric_symbol": "s",
+      "metric_value": 8.618,
+      "reference_text": "s = 4 + 8 / \u221a3 = 8.618+ | Found by Erich Friedman | in 1997.",
+      "source_image": "ts27.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts27.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "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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+      "x": 1.9762567734357976,
+      "y": 1.1830799054376544
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+    {
+      "id": 27,
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+      "x": -1.0126617119127665,
+      "y": -1.6615845276964625
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+  ],
+  "problem": "27 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts27.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_028_0d20b359435ed501.json b/data/solutions/generated/squintri_028_0d20b359435ed501.json
new file mode 100644
index 0000000000000000000000000000000000000000..71c744552637608419f752852cea2f86d93e5379
--- /dev/null
+++ b/data/solutions/generated/squintri_028_0d20b359435ed501.json
@@ -0,0 +1,230 @@
+{
+  "case": "squintri@28",
+  "container": {
+    "circumradius": 5.065536966965852,
+    "orientation_radians": 0.0,
+    "side_length": 8.773767394403205,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squintri@28",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "4/28/26",
+    "metric_expression": "3 + 10 / \u221a3 = 8.773+",
+    "metric_symbol": "s",
+    "metric_value": 8.773,
+    "reference_text": "s = 3 + 10 / \u221a3 = 8.773+ | Found by Erich Friedman | in 1997.",
+    "source_image": "ts28.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts28.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squintri@28",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "4/28/26",
+      "metric_expression": "3 + 10 / \u221a3 = 8.773+",
+      "metric_symbol": "s",
+      "metric_value": 8.773,
+      "reference_text": "s = 3 + 10 / \u221a3 = 8.773+ | Found by Erich Friedman | in 1997.",
+      "source_image": "ts28.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts28.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "x": -0.032693738420043875,
+      "y": 2.658429355226733e-06
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+    {
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+      "y": 2.366990558771269
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+    {
+      "id": 24,
+      "rotation_radians": -0.26161511106412627,
+      "x": 0.1235680878056009,
+      "y": -2.2757841466385265
+    },
+    {
+      "id": 25,
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+      "x": -2.032756408314115,
+      "y": -0.06483393115160445
+    },
+    {
+      "id": 26,
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+      "x": -2.032762074417656,
+      "y": 1.0110459287763678
+    },
+    {
+      "id": 27,
+      "rotation_radians": -0.7853941891160412,
+      "x": -2.0327524543071895,
+      "y": -1.0961515312674086
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.7436592061996831,
+      "x": -1.985711348172965,
+      "y": 2.101871273749641
+    }
+  ],
+  "problem": "28 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts28.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_029_3947aab39c0a1a92.json b/data/solutions/generated/squintri_029_3947aab39c0a1a92.json
new file mode 100644
index 0000000000000000000000000000000000000000..f7b0482a2b9e98e1c822daad729f11048978f381
--- /dev/null
+++ b/data/solutions/generated/squintri_029_3947aab39c0a1a92.json
@@ -0,0 +1,236 @@
+{
+  "case": "squintri@29",
+  "container": {
+    "circumradius": 5.2855679241308415,
+    "orientation_radians": 0.0,
+    "side_length": 9.154872191450979,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squintri@29",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "4/28/26",
+    "metric_expression": "8 + 2 / \u221a3 = 9.154+",
+    "metric_symbol": "s",
+    "metric_value": 9.154,
+    "reference_text": "s = 8 + 2 / \u221a3 = 9.154+ | Found by Erich Friedman | in 1997.",
+    "source_image": "ts29.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts29.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squintri@29",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "4/28/26",
+      "metric_expression": "8 + 2 / \u221a3 = 9.154+",
+      "metric_symbol": "s",
+      "metric_value": 9.154,
+      "reference_text": "s = 8 + 2 / \u221a3 = 9.154+ | Found by Erich Friedman | in 1997.",
+      "source_image": "ts29.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts29.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "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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+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.3032882938880377,
+      "x": 3.1242003651876913,
+      "y": 0.6429605033685268
+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.5424506632172008,
+      "x": -0.01079436191366425,
+      "y": 2.3257771319358396
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.785397565428284,
+      "x": -2.1427674118742055,
+      "y": -0.5000046563871942
+    },
+    {
+      "id": 26,
+      "rotation_radians": 1.23758604608232,
+      "x": -0.788916371551253,
+      "y": 0.6055203723050497
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.895114160736621,
+      "x": 2.9595809798905663,
+      "y": -0.579093188780199
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.3169393338895201,
+      "x": 1.1412172492951886,
+      "y": -1.8083234603518155
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.35163579386831445,
+      "x": -0.9771788465760711,
+      "y": 2.988965394395821
+    }
+  ],
+  "problem": "29 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts29.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_030_e0b7505d8b6b1d46.json b/data/solutions/generated/squintri_030_e0b7505d8b6b1d46.json
new file mode 100644
index 0000000000000000000000000000000000000000..f7af16bd328cbc717a67b129a4657ab51fc51581
--- /dev/null
+++ b/data/solutions/generated/squintri_030_e0b7505d8b6b1d46.json
@@ -0,0 +1,242 @@
+{
+  "case": "squintri@30",
+  "container": {
+    "circumradius": 5.375274403108803,
+    "orientation_radians": 0.0,
+    "side_length": 9.310248370808917,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squintri@30",
+    "credit": "David W",
+    "date": "July 2002",
+    "family_updated": "4/28/26",
+    "metric_expression": "9.301+",
+    "metric_symbol": "s",
+    "metric_value": 9.301,
+    "reference_text": "s = 9.301+ | Found by David W. Cantrell | in July 2002.",
+    "source_image": "ts30.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts30.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squintri@30",
+      "credit": "David W",
+      "date": "July 2002",
+      "family_updated": "4/28/26",
+      "metric_expression": "9.301+",
+      "metric_symbol": "s",
+      "metric_value": 9.301,
+      "reference_text": "s = 9.301+ | Found by David W. Cantrell | in July 2002.",
+      "source_image": "ts30.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts30.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
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+    {
+      "id": 26,
+      "rotation_radians": -0.7857345245392593,
+      "x": -2.187457939884805,
+      "y": 3.577737674692676
+    },
+    {
+      "id": 27,
+      "rotation_radians": -1.0882197721320193,
+      "x": 3.024154233213898,
+      "y": 0.6516358448504519
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.7849742966647789,
+      "x": -2.1767038060467985,
+      "y": -0.42275978613861354
+    },
+    {
+      "id": 29,
+      "rotation_radians": 1.3092552232668024,
+      "x": -2.0001448173063014,
+      "y": -3.680011505883223
+    },
+    {
+      "id": 30,
+      "rotation_radians": 0.03591087702870068,
+      "x": -0.9121328880447881,
+      "y": 2.8759376140951174
+    }
+  ],
+  "problem": "30 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts30.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_031_2fc342f23897d355.json b/data/solutions/generated/squintri_031_2fc342f23897d355.json
new file mode 100644
index 0000000000000000000000000000000000000000..2900378f5221f939c092e6cbdabf68e4e2b14354
--- /dev/null
+++ b/data/solutions/generated/squintri_031_2fc342f23897d355.json
@@ -0,0 +1,248 @@
+{
+  "case": "squintri@31",
+  "container": {
+    "circumradius": 5.508478825555405,
+    "orientation_radians": 0.0,
+    "side_length": 9.540965198279299,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squintri@31",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "4/28/26",
+    "metric_expression": "7 + 4 / \u221a3 = 9.309+",
+    "metric_symbol": "s",
+    "metric_value": 9.309,
+    "reference_text": "s = 7 + 4 / \u221a3 = 9.309+ | Found by Erich Friedman | in 1997.",
+    "source_image": "ts31.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts31.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squintri@31",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "4/28/26",
+      "metric_expression": "7 + 4 / \u221a3 = 9.309+",
+      "metric_symbol": "s",
+      "metric_value": 9.309,
+      "reference_text": "s = 7 + 4 / \u221a3 = 9.309+ | Found by Erich Friedman | in 1997.",
+      "source_image": "ts31.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts31.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "y": -0.2503028121000422
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+    {
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+    {
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+      "y": -0.10361973055903193
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+    {
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+      "x": -2.0451648549932444,
+      "y": -3.716807696904948
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.2617713166380925,
+      "x": -0.22994113483269432,
+      "y": 2.735708166486303
+    },
+    {
+      "id": 27,
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+      "x": -2.2542228253663943,
+      "y": 0.5174364319576816
+    },
+    {
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+      "x": 3.3035283750540487,
+      "y": 0.4921416435382336
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.1839226174015743,
+      "x": 0.94297757960705,
+      "y": 0.7978395850216418
+    },
+    {
+      "id": 30,
+      "rotation_radians": 0.2547833769523714,
+      "x": 0.6009576479574182,
+      "y": 2.1670450033147435
+    },
+    {
+      "id": 31,
+      "rotation_radians": 0.9196994628018442,
+      "x": 0.9341439026563605,
+      "y": -1.8876981107822588
+    }
+  ],
+  "problem": "31 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts31.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_032_5dfb790e771f9b5e.json b/data/solutions/generated/squintri_032_5dfb790e771f9b5e.json
new file mode 100644
index 0000000000000000000000000000000000000000..8926795b0a89b4aabc628593b108c1549f6d0e8b
--- /dev/null
+++ b/data/solutions/generated/squintri_032_5dfb790e771f9b5e.json
@@ -0,0 +1,254 @@
+{
+  "case": "squintri@32",
+  "container": {
+    "circumradius": 5.510102584692577,
+    "orientation_radians": 0.0,
+    "side_length": 9.543777631604135,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squintri@32",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "4/28/26",
+    "metric_expression": "6 + 2 \u221a3 = 9.464+",
+    "metric_symbol": "s",
+    "metric_value": 9.464,
+    "reference_text": "s = 6 + 2 \u221a3 = 9.464+ | Found by Erich Friedman | in 1997.",
+    "source_image": "ts32.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts32.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squintri@32",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "4/28/26",
+      "metric_expression": "6 + 2 \u221a3 = 9.464+",
+      "metric_symbol": "s",
+      "metric_value": 9.464,
+      "reference_text": "s = 6 + 2 \u221a3 = 9.464+ | Found by Erich Friedman | in 1997.",
+      "source_image": "ts32.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts32.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "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": -2.2407542559872247
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+      "y": 1.196337097549669
+    },
+    {
+      "id": 23,
+      "rotation_radians": 1.3137247543645016,
+      "x": -1.1415716339618642,
+      "y": -3.253647098178029
+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.309006475735594,
+      "x": 4.327042376295499,
+      "y": -0.1056628786404486
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.2607976955393425,
+      "x": -0.29462120434116007,
+      "y": 1.2571182424020224
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.7824190090528631,
+      "x": -1.2535089380558975,
+      "y": 1.9614054063511615
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.26180183497223153,
+      "x": 3.3202822159963468,
+      "y": 0.6869320443208317
+    },
+    {
+      "id": 28,
+      "rotation_radians": 0.7854097377069359,
+      "x": -2.255043709719149,
+      "y": -3.694519898908288
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.29049559954327875,
+      "x": -1.064663877240957,
+      "y": 3.1986709098532105
+    },
+    {
+      "id": 30,
+      "rotation_radians": 0.5878057247013376,
+      "x": -2.1510336394992056,
+      "y": 3.6871602863844886
+    },
+    {
+      "id": 31,
+      "rotation_radians": 0.2607998228588448,
+      "x": 0.6217584829829231,
+      "y": 0.844049155735927
+    },
+    {
+      "id": 32,
+      "rotation_radians": -0.2570618431627363,
+      "x": 2.3255267902557275,
+      "y": -1.2585167340503198
+    }
+  ],
+  "problem": "32 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts32.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_033_3a2374dab53b1d0d.json b/data/solutions/generated/squintri_033_3a2374dab53b1d0d.json
new file mode 100644
index 0000000000000000000000000000000000000000..edc3ae000e7511aee7d7bc3cae4c60c4334d4aa5
--- /dev/null
+++ b/data/solutions/generated/squintri_033_3a2374dab53b1d0d.json
@@ -0,0 +1,260 @@
+{
+  "case": "squintri@33",
+  "container": {
+    "circumradius": 5.5995131789179275,
+    "orientation_radians": 0.0,
+    "side_length": 9.698641323537368,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squintri@33",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "4/28/26",
+    "metric_expression": "5 + 8 / \u221a3 = 9.618+",
+    "metric_symbol": "s",
+    "metric_value": 9.618,
+    "reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.",
+    "source_image": "ts34.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squintri@33",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "4/28/26",
+      "metric_expression": "5 + 8 / \u221a3 = 9.618+",
+      "metric_symbol": "s",
+      "metric_value": 9.618,
+      "reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.",
+      "source_image": "ts34.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
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+    "profile": "cg",
+    "source_url": "https://erich-friedman.github.io/packing/squintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
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+  ],
+  "problem": "33 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts34.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_034_3661302cdd9d0eb0.json b/data/solutions/generated/squintri_034_3661302cdd9d0eb0.json
new file mode 100644
index 0000000000000000000000000000000000000000..daeadeda384fc5522a0f75c3f9ddab69c945a6bd
--- /dev/null
+++ b/data/solutions/generated/squintri_034_3661302cdd9d0eb0.json
@@ -0,0 +1,266 @@
+{
+  "case": "squintri@34",
+  "container": {
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+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squintri@34",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "4/28/26",
+    "metric_expression": "5 + 8 / \u221a3 = 9.618+",
+    "metric_symbol": "s",
+    "metric_value": 9.618,
+    "reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.",
+    "source_image": "ts34.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
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+    "type": "regular_polygon"
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+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "4/28/26",
+      "metric_expression": "5 + 8 / \u221a3 = 9.618+",
+      "metric_symbol": "s",
+      "metric_value": 9.618,
+      "reference_text": "s = 5 + 8 / \u221a3 = 9.618+ | Found by Erich Friedman | in 1997.",
+      "source_image": "ts34.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts34.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
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+  ],
+  "problem": "34 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts34.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_035_767d03b8ae8b30a8.json b/data/solutions/generated/squintri_035_767d03b8ae8b30a8.json
new file mode 100644
index 0000000000000000000000000000000000000000..30ac41cf33bf2a77424138a00eadda8efcb2123f
--- /dev/null
+++ b/data/solutions/generated/squintri_035_767d03b8ae8b30a8.json
@@ -0,0 +1,272 @@
+{
+  "case": "squintri@35",
+  "container": {
+    "circumradius": 5.732394484953724,
+    "orientation_radians": 0.0,
+    "side_length": 9.928798496967476,
+    "sides": 3,
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+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squintri@35",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "4/28/26",
+    "metric_expression": "4 + 10 / \u221a3 = 9.773+",
+    "metric_symbol": "s",
+    "metric_value": 9.773,
+    "reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.",
+    "source_image": "ts36.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
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+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
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+    "friedman_reference": {
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+      "case": "squintri@35",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "4/28/26",
+      "metric_expression": "4 + 10 / \u221a3 = 9.773+",
+      "metric_symbol": "s",
+      "metric_value": 9.773,
+      "reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.",
+      "source_image": "ts36.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
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+    {
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+      "rotation_radians": 3.927319522387243,
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+      "y": -1.727749053263182
+    },
+    {
+      "id": 31,
+      "rotation_radians": 6.021385099838004,
+      "x": 0.7062321359341411,
+      "y": -1.169754580148915
+    },
+    {
+      "id": 32,
+      "rotation_radians": 0.14771515429365953,
+      "x": 3.491656615304342,
+      "y": 0.6530416509558987
+    },
+    {
+      "id": 33,
+      "rotation_radians": 7.068602805780719,
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+      "y": 3.3260189412834915
+    },
+    {
+      "id": 34,
+      "rotation_radians": 1.7939710512494638,
+      "x": 2.5219119867720923,
+      "y": 0.08165082435398824
+    },
+    {
+      "id": 35,
+      "rotation_radians": 2.356346943066762,
+      "x": -0.3658854938591536,
+      "y": 1.7321103363336767
+    }
+  ],
+  "problem": "35 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts36.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_036_8dffe8c81eb0e47e.json b/data/solutions/generated/squintri_036_8dffe8c81eb0e47e.json
new file mode 100644
index 0000000000000000000000000000000000000000..1b0ac3de72aac2ddf4b6f6694801881c5acb7c8e
--- /dev/null
+++ b/data/solutions/generated/squintri_036_8dffe8c81eb0e47e.json
@@ -0,0 +1,278 @@
+{
+  "case": "squintri@36",
+  "container": {
+    "circumradius": 5.66788852135307,
+    "orientation_radians": 0.0,
+    "side_length": 9.817070890619954,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "squintri@36",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "4/28/26",
+    "metric_expression": "4 + 10 / \u221a3 = 9.773+",
+    "metric_symbol": "s",
+    "metric_value": 9.773,
+    "reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.",
+    "source_image": "ts36.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "squintri@36",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "4/28/26",
+      "metric_expression": "4 + 10 / \u221a3 = 9.773+",
+      "metric_symbol": "s",
+      "metric_value": 9.773,
+      "reference_text": "s = 4 + 10 / \u221a3 = 9.773+ | Found by Erich Friedman | in 1997.",
+      "source_image": "ts36.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts36.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "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": 32,
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+      "x": -2.333904163089193,
+      "y": 0.6494222294815905
+    },
+    {
+      "id": 33,
+      "rotation_radians": -0.26177860426624544,
+      "x": 0.5584116180295355,
+      "y": -2.372564036005666
+    },
+    {
+      "id": 34,
+      "rotation_radians": -0.2822255738344907,
+      "x": -2.153676006073244,
+      "y": -2.743858144795499
+    },
+    {
+      "id": 35,
+      "rotation_radians": -0.26180029213350875,
+      "x": -1.2480017117611386,
+      "y": -3.415518594402171
+    },
+    {
+      "id": 36,
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+      "x": -2.2713377645090054,
+      "y": 3.786840659434135
+    }
+  ],
+  "problem": "36 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts36.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_037_8530be000ac2e9ed.json b/data/solutions/generated/squintri_037_8530be000ac2e9ed.json
new file mode 100644
index 0000000000000000000000000000000000000000..ffc757de9335969997e282664f85f625d045aff9
--- /dev/null
+++ b/data/solutions/generated/squintri_037_8530be000ac2e9ed.json
@@ -0,0 +1,284 @@
+{
+  "case": "squintri@37",
+  "container": {
+    "circumradius": 5.863073513456338,
+    "orientation_radians": 0.0,
+    "side_length": 10.155141213817744,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squintri@37",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/28/26",
+    "metric_expression": "10.154+",
+    "metric_symbol": "s",
+    "metric_value": 10.154,
+    "reference_text": "s = 10.154+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "ts37.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts37.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squintri@37",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/28/26",
+      "metric_expression": "10.154+",
+      "metric_symbol": "s",
+      "metric_value": 10.154,
+      "reference_text": "s = 10.154+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "ts37.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts37.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "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": 4.680010040809672,
+      "y": -0.10566255215437766
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+  ],
+  "problem": "37 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts37.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_038_896b636f9d899bf5.json b/data/solutions/generated/squintri_038_896b636f9d899bf5.json
new file mode 100644
index 0000000000000000000000000000000000000000..4f8ff9ebb7bdcb6699c4accf9c2d4c25c5ce5d19
--- /dev/null
+++ b/data/solutions/generated/squintri_038_896b636f9d899bf5.json
@@ -0,0 +1,290 @@
+{
+  "case": "squintri@38",
+  "container": {
+    "circumradius": 5.952347755555162,
+    "orientation_radians": 0.0,
+    "side_length": 10.309768736940113,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squintri@38",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/28/26",
+    "metric_expression": "10.309+",
+    "metric_symbol": "s",
+    "metric_value": 10.309,
+    "reference_text": "s = 10.309+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "ts38.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts38.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squintri@38",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/28/26",
+      "metric_expression": "10.309+",
+      "metric_symbol": "s",
+      "metric_value": 10.309,
+      "reference_text": "s = 10.309+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "ts38.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts38.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
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+      "y": 2.123373447951235
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+  ],
+  "problem": "38 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts38.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/squintri_039_306f80d621673198.json b/data/solutions/generated/squintri_039_306f80d621673198.json
new file mode 100644
index 0000000000000000000000000000000000000000..d7a8bfefeeee31acb893536ac7bb2b7516153589
--- /dev/null
+++ b/data/solutions/generated/squintri_039_306f80d621673198.json
@@ -0,0 +1,296 @@
+{
+  "case": "squintri@39",
+  "container": {
+    "circumradius": 5.952496868392292,
+    "orientation_radians": 0.0,
+    "side_length": 10.310027007950083,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "squintri@39",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/28/26",
+    "metric_expression": "10.310+",
+    "metric_symbol": "s",
+    "metric_value": 10.31,
+    "reference_text": "s = 10.310+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "ts39.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts39.gif",
+    "source_page": "https://erich-friedman.github.io/packing/squintri/",
+    "title": "Squares in Triangles"
+  },
+  "item": {
+    "circumradius": 0.7071067811865476,
+    "side_length": 1.0,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "squintri@39",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/28/26",
+      "metric_expression": "10.310+",
+      "metric_symbol": "s",
+      "metric_value": 10.31,
+      "reference_text": "s = 10.310+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "ts39.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/squintri/ts39.gif",
+      "source_page": "https://erich-friedman.github.io/packing/squintri/",
+      "title": "Squares in Triangles"
+    },
+    "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/squintri/",
+    "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": -2.922586972479528
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+    {
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+      "x": 4.769463270054349,
+      "y": 0.10565745865769235
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+    {
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+      "rotation_radians": 1.3085304319983009,
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+      "y": -2.148970671534464
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+    {
+      "id": 35,
+      "rotation_radians": 0.7854029952173371,
+      "x": -2.4629467812775476,
+      "y": -1.9225527462676923
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+    {
+      "id": 36,
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+      "x": 1.81421539846532,
+      "y": 0.5983140946887701
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+    {
+      "id": 37,
+      "rotation_radians": 1.308562700219963,
+      "x": -0.6164442978048414,
+      "y": -3.0872037626108884
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+    {
+      "id": 38,
+      "rotation_radians": 1.3085277906905683,
+      "x": 2.0300551259375084,
+      "y": -1.6709534563937005
+    },
+    {
+      "id": 39,
+      "rotation_radians": 1.0585794694885209,
+      "x": 0.6726653747455642,
+      "y": 1.0733728152750808
+    }
+  ],
+  "problem": "39 equal items for Squares in Triangles",
+  "setup": "squintri",
+  "source_image": "https://erich-friedman.github.io/packing/squintri/ts39.gif",
+  "source_page": "https://erich-friedman.github.io/packing/squintri/"
+}
diff --git a/data/solutions/generated/triincir_021_26dd3deb629b6129.json b/data/solutions/generated/triincir_021_26dd3deb629b6129.json
new file mode 100644
index 0000000000000000000000000000000000000000..49bd5bb2627b28b7c713dddc43c0a16cc9a5d520
--- /dev/null
+++ b/data/solutions/generated/triincir_021_26dd3deb629b6129.json
@@ -0,0 +1,185 @@
+{
+  "case": "triincir@21",
+  "container": {
+    "radius": 1.9254374587796521,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triincir@21",
+    "credit": "Maurizio Morandi",
+    "date": "May 2008",
+    "family_updated": "8/31/19",
+    "metric_expression": "1.910+",
+    "metric_symbol": "r",
+    "metric_value": 1.91,
+    "reference_text": "r = 1.910+ | Found by Maurizio Morandi | in May 2008.",
+    "source_image": "tc21.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc21.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triincir/",
+    "title": "Triangles in Circles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triincir@21",
+      "credit": "Maurizio Morandi",
+      "date": "May 2008",
+      "family_updated": "8/31/19",
+      "metric_expression": "1.910+",
+      "metric_symbol": "r",
+      "metric_value": 1.91,
+      "reference_text": "r = 1.910+ | Found by Maurizio Morandi | in May 2008.",
+      "source_image": "tc21.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc21.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triincir/",
+      "title": "Triangles in Circles"
+    },
+    "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/triincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.26374378200271614,
+      "x": -1.0726810080128928,
+      "y": -0.9307867561786684
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+    {
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+    {
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+      "y": 0.15370736393377746
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+    {
+      "id": 16,
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+      "y": 0.4302757983078603
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+    {
+      "id": 17,
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+      "x": -0.8056979652515669,
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+    {
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+      "rotation_radians": -0.913601154290898,
+      "x": 0.025192698434193275,
+      "y": 1.3746075479085607
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+    {
+      "id": 19,
+      "rotation_radians": 0.1335910974319412,
+      "x": 0.5972485798035476,
+      "y": 1.4526898218520414
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.7838595405570334,
+      "x": 1.0208985269365964,
+      "y": 0.9716750188445961
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.7837016312762978,
+      "x": -0.83111554562575,
+      "y": 1.2424331802242992
+    }
+  ],
+  "problem": "21 equal items for Triangles in Circles",
+  "setup": "triincir",
+  "source_image": "https://erich-friedman.github.io/packing/triincir/tc21.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triincir/"
+}
diff --git a/data/solutions/generated/triincir_022_0907be89df20a3ff.json b/data/solutions/generated/triincir_022_0907be89df20a3ff.json
new file mode 100644
index 0000000000000000000000000000000000000000..f5dbf8866bc164bc59851cd187d27959546924fe
--- /dev/null
+++ b/data/solutions/generated/triincir_022_0907be89df20a3ff.json
@@ -0,0 +1,191 @@
+{
+  "case": "triincir@22",
+  "container": {
+    "radius": 1.962348742244891,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triincir@22",
+    "credit": "Maurizio Morandi",
+    "date": "June 2008",
+    "family_updated": "8/31/19",
+    "metric_expression": "1.943+",
+    "metric_symbol": "r",
+    "metric_value": 1.943,
+    "reference_text": "r = 1.943+ | Found by Maurizio Morandi | in June 2008.",
+    "source_image": "tc22.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc22.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triincir/",
+    "title": "Triangles in Circles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triincir@22",
+      "credit": "Maurizio Morandi",
+      "date": "June 2008",
+      "family_updated": "8/31/19",
+      "metric_expression": "1.943+",
+      "metric_symbol": "r",
+      "metric_value": 1.943,
+      "reference_text": "r = 1.943+ | Found by Maurizio Morandi | in June 2008.",
+      "source_image": "tc22.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc22.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triincir/",
+      "title": "Triangles in Circles"
+    },
+    "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/triincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.3005165711321491,
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+      "y": 0.2220512187803285
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+    {
+      "id": 16,
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+      "y": 1.0029748014930342
+    },
+    {
+      "id": 17,
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+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.3854948608777832,
+      "x": -0.05326945819454621,
+      "y": 0.6564034278706272
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+    {
+      "id": 19,
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+      "y": 1.3969977697937244
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+    {
+      "id": 20,
+      "rotation_radians": -0.6589742263311141,
+      "x": 1.0360029404578428,
+      "y": 1.043458862311533
+    },
+    {
+      "id": 21,
+      "rotation_radians": -1.7028944776436694,
+      "x": -0.7129343405550485,
+      "y": 1.221760002216375
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.6590212130589046,
+      "x": 0.023905193372182356,
+      "y": 1.2299520368871253
+    }
+  ],
+  "problem": "22 equal items for Triangles in Circles",
+  "setup": "triincir",
+  "source_image": "https://erich-friedman.github.io/packing/triincir/tc22.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triincir/"
+}
diff --git a/data/solutions/generated/triincir_023_973cadfcac9f0399.json b/data/solutions/generated/triincir_023_973cadfcac9f0399.json
new file mode 100644
index 0000000000000000000000000000000000000000..2d0d97396ad04ce40d268cfde36315280c1dee2a
--- /dev/null
+++ b/data/solutions/generated/triincir_023_973cadfcac9f0399.json
@@ -0,0 +1,197 @@
+{
+  "case": "triincir@23",
+  "container": {
+    "radius": 2.0008339506934125,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triincir@23",
+    "credit": "Maurizio Morandi",
+    "date": "June 2008",
+    "family_updated": "8/31/19",
+    "metric_expression": "1.988+",
+    "metric_symbol": "r",
+    "metric_value": 1.988,
+    "reference_text": "r = 1.988+ | Found by Maurizio Morandi | in June 2008.",
+    "source_image": "tc23.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc23.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triincir/",
+    "title": "Triangles in Circles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triincir@23",
+      "credit": "Maurizio Morandi",
+      "date": "June 2008",
+      "family_updated": "8/31/19",
+      "metric_expression": "1.988+",
+      "metric_symbol": "r",
+      "metric_value": 1.988,
+      "reference_text": "r = 1.988+ | Found by Maurizio Morandi | in June 2008.",
+      "source_image": "tc23.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc23.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triincir/",
+      "title": "Triangles in Circles"
+    },
+    "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/triincir/",
+    "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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+      "y": 0.4653432740133446
+    },
+    {
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+      "rotation_radians": -0.7841138086689299,
+      "x": 0.41339348095354506,
+      "y": 0.9901174852337328
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.261438003741591,
+      "x": 0.97156380054221,
+      "y": 1.1409408129916339
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+    {
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+      "rotation_radians": -0.7857701811601262,
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+      "y": 0.7325359759618063
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.7656583407078588,
+      "x": -1.188565571460426,
+      "y": 1.142546920028473
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.7841140813910691,
+      "x": -0.3704436526411201,
+      "y": 1.4306260569048217
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.2630836155662819,
+      "x": 0.18705855166121116,
+      "y": 1.5807765807316472
+    }
+  ],
+  "problem": "23 equal items for Triangles in Circles",
+  "setup": "triincir",
+  "source_image": "https://erich-friedman.github.io/packing/triincir/tc23.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triincir/"
+}
diff --git a/data/solutions/generated/triincir_024_9ebf7fbae73f62a7.json b/data/solutions/generated/triincir_024_9ebf7fbae73f62a7.json
new file mode 100644
index 0000000000000000000000000000000000000000..1aad6f878cdb717543ca6c675ba0d15d31401cbf
--- /dev/null
+++ b/data/solutions/generated/triincir_024_9ebf7fbae73f62a7.json
@@ -0,0 +1,203 @@
+{
+  "case": "triincir@24",
+  "container": {
+    "radius": 2.072188814075174,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triincir@24",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "8/31/19",
+    "metric_expression": "2",
+    "metric_symbol": "r",
+    "metric_value": 2.0,
+    "reference_text": "r = 2 | Trivial.",
+    "source_image": "tc24.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc24.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triincir/",
+    "title": "Triangles in Circles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triincir@24",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "8/31/19",
+      "metric_expression": "2",
+      "metric_symbol": "r",
+      "metric_value": 2.0,
+      "reference_text": "r = 2 | Trivial.",
+      "source_image": "tc24.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc24.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triincir/",
+      "title": "Triangles in Circles"
+    },
+    "generator": "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/triincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
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+      "x": -0.6311965574463366,
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+    {
+      "id": 18,
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+    {
+      "id": 19,
+      "rotation_radians": 1.9888170193764034,
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+      "y": 0.6006641736823788
+    },
+    {
+      "id": 20,
+      "rotation_radians": 1.0111665066421123,
+      "x": 1.1847051122789898,
+      "y": 0.949536419916745
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+    {
+      "id": 21,
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+      "x": -1.1294295446597185,
+      "y": 1.014997570498015
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+    {
+      "id": 22,
+      "rotation_radians": 7.138486070738375,
+      "x": -0.5349683258580942,
+      "y": 1.6305150790459284
+    },
+    {
+      "id": 23,
+      "rotation_radians": 6.090963934276114,
+      "x": 0.032308260982600596,
+      "y": 1.520395925785306
+    },
+    {
+      "id": 24,
+      "rotation_radians": 6.247282007145419,
+      "x": 0.9141283112808571,
+      "y": 1.4596649062702969
+    }
+  ],
+  "problem": "24 equal items for Triangles in Circles",
+  "setup": "triincir",
+  "source_image": "https://erich-friedman.github.io/packing/triincir/tc24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triincir/"
+}
diff --git a/data/solutions/generated/triincir_025_460bfc63493e0a99.json b/data/solutions/generated/triincir_025_460bfc63493e0a99.json
new file mode 100644
index 0000000000000000000000000000000000000000..9558d10b0238296ebeec5904418cca465b59787f
--- /dev/null
+++ b/data/solutions/generated/triincir_025_460bfc63493e0a99.json
@@ -0,0 +1,209 @@
+{
+  "case": "triincir@25",
+  "container": {
+    "radius": 2.0564599742843677,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triincir@25",
+    "credit": "David W",
+    "date": "July 2005",
+    "family_updated": "8/31/19",
+    "metric_expression": "2.055+",
+    "metric_symbol": "r",
+    "metric_value": 2.055,
+    "reference_text": "r = 2.055+ | Found by David W. Cantrell | in July 2005.",
+    "source_image": "tc25.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc25.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triincir/",
+    "title": "Triangles in Circles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triincir@25",
+      "credit": "David W",
+      "date": "July 2005",
+      "family_updated": "8/31/19",
+      "metric_expression": "2.055+",
+      "metric_symbol": "r",
+      "metric_value": 2.055,
+      "reference_text": "r = 2.055+ | Found by David W. Cantrell | in July 2005.",
+      "source_image": "tc25.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc25.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triincir/",
+      "title": "Triangles in Circles"
+    },
+    "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/triincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 4.55075338666295,
+      "x": -1.1451614497650053,
+      "y": -1.072166601947836
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+    {
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+    {
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+    },
+    {
+      "id": 20,
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+      "y": 0.8846947578163628
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.4186788100706809,
+      "x": -1.2196988839033867,
+      "y": 1.1460199642593092
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.3714812826362563,
+      "x": -0.681711935422134,
+      "y": 1.3556027568858433
+    },
+    {
+      "id": 23,
+      "rotation_radians": 2.47070973760969,
+      "x": 0.12474834922547678,
+      "y": 1.6712923158171111
+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.4235120205638025,
+      "x": 0.3703986454488955,
+      "y": 1.0520882247416434
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.37631371189299834,
+      "x": 0.9155041244997592,
+      "y": 1.2436396621434709
+    }
+  ],
+  "problem": "25 equal items for Triangles in Circles",
+  "setup": "triincir",
+  "source_image": "https://erich-friedman.github.io/packing/triincir/tc25.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triincir/"
+}
diff --git a/data/solutions/generated/triincir_026_297d48c1e4300be9.json b/data/solutions/generated/triincir_026_297d48c1e4300be9.json
new file mode 100644
index 0000000000000000000000000000000000000000..50d6f491486b4e975fc24751e8352c1c4cbb242a
--- /dev/null
+++ b/data/solutions/generated/triincir_026_297d48c1e4300be9.json
@@ -0,0 +1,215 @@
+{
+  "case": "triincir@26",
+  "container": {
+    "radius": 2.1662963643931503,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triincir@26",
+    "credit": "Maurizio Morandi",
+    "date": "April 2008",
+    "family_updated": "8/31/19",
+    "metric_expression": "2.109+",
+    "metric_symbol": "r",
+    "metric_value": 2.109,
+    "reference_text": "r = 2.109+ | Found by Maurizio Morandi | in April 2008.",
+    "source_image": "tc26.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc26.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triincir/",
+    "title": "Triangles in Circles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triincir@26",
+      "credit": "Maurizio Morandi",
+      "date": "April 2008",
+      "family_updated": "8/31/19",
+      "metric_expression": "2.109+",
+      "metric_symbol": "r",
+      "metric_value": 2.109,
+      "reference_text": "r = 2.109+ | Found by Maurizio Morandi | in April 2008.",
+      "source_image": "tc26.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc26.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triincir/",
+      "title": "Triangles in Circles"
+    },
+    "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/triincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
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+      "y": -1.2414533133751962
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+    {
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+      "x": -0.28237764905392476,
+      "y": 1.578688753109616
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+  ],
+  "problem": "26 equal items for Triangles in Circles",
+  "setup": "triincir",
+  "source_image": "https://erich-friedman.github.io/packing/triincir/tc26.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triincir/"
+}
diff --git a/data/solutions/generated/triincir_027_0b682f2ff7f493f4.json b/data/solutions/generated/triincir_027_0b682f2ff7f493f4.json
new file mode 100644
index 0000000000000000000000000000000000000000..31cf9b37333f5bb11aad5063f1b591c551bb99a9
--- /dev/null
+++ b/data/solutions/generated/triincir_027_0b682f2ff7f493f4.json
@@ -0,0 +1,221 @@
+{
+  "case": "triincir@27",
+  "container": {
+    "radius": 2.1683865525945683,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triincir@27",
+    "credit": "David W",
+    "date": "July 2005",
+    "family_updated": "8/31/19",
+    "metric_expression": "2.138+",
+    "metric_symbol": "r",
+    "metric_value": 2.138,
+    "reference_text": "r = 2.138+ | Found by David W. Cantrell | in July 2005.",
+    "source_image": "tc27.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc27.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triincir/",
+    "title": "Triangles in Circles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triincir@27",
+      "credit": "David W",
+      "date": "July 2005",
+      "family_updated": "8/31/19",
+      "metric_expression": "2.138+",
+      "metric_symbol": "r",
+      "metric_value": 2.138,
+      "reference_text": "r = 2.138+ | Found by David W. Cantrell | in July 2005.",
+      "source_image": "tc27.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc27.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triincir/",
+      "title": "Triangles in Circles"
+    },
+    "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/triincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "y": -0.8482321011420866
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+    {
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+    {
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+    {
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+    {
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+    {
+      "id": 25,
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+      "y": 1.0961421874587556
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+    {
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+    {
+      "id": 27,
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+      "x": 0.5169916216023114,
+      "y": 1.7463440668498451
+    }
+  ],
+  "problem": "27 equal items for Triangles in Circles",
+  "setup": "triincir",
+  "source_image": "https://erich-friedman.github.io/packing/triincir/tc27.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triincir/"
+}
diff --git a/data/solutions/generated/triincir_028_f7e451634cc50a5c.json b/data/solutions/generated/triincir_028_f7e451634cc50a5c.json
new file mode 100644
index 0000000000000000000000000000000000000000..9b9d25bef2948edf76c0c5de00cb21e8278c8430
--- /dev/null
+++ b/data/solutions/generated/triincir_028_f7e451634cc50a5c.json
@@ -0,0 +1,227 @@
+{
+  "case": "triincir@28",
+  "container": {
+    "radius": 2.2195935862420257,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triincir@28",
+    "credit": "David W",
+    "date": "July 2005",
+    "family_updated": "8/31/19",
+    "metric_expression": "2.191+",
+    "metric_symbol": "r",
+    "metric_value": 2.191,
+    "reference_text": "r = 2.191+ | Found by David W. Cantrell | in July 2005.",
+    "source_image": "tc28.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc28.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triincir/",
+    "title": "Triangles in Circles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triincir@28",
+      "credit": "David W",
+      "date": "July 2005",
+      "family_updated": "8/31/19",
+      "metric_expression": "2.191+",
+      "metric_symbol": "r",
+      "metric_value": 2.191,
+      "reference_text": "r = 2.191+ | Found by David W. Cantrell | in July 2005.",
+      "source_image": "tc28.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc28.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triincir/",
+      "title": "Triangles in Circles"
+    },
+    "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/triincir/",
+    "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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+    {
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+      "x": -0.7641615144069672,
+      "y": 0.7729683641300008
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+    {
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+      "x": -0.10049991425723973,
+      "y": 1.0614981900797578
+    },
+    {
+      "id": 22,
+      "rotation_radians": 3.7496518067373388,
+      "x": 0.6264668996616122,
+      "y": 0.8565590355321941
+    },
+    {
+      "id": 23,
+      "rotation_radians": 4.795301297938196,
+      "x": 1.0728010739974092,
+      "y": 1.227332404211655
+    },
+    {
+      "id": 24,
+      "rotation_radians": 3.668552556692403,
+      "x": 1.6196687694570442,
+      "y": 0.942342405783455
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.8817287647381836,
+      "x": -1.4050870708245522,
+      "y": 0.9186228638988659
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.9960631169571769,
+      "x": -0.905720205622389,
+      "y": 1.6225497960683248
+    },
+    {
+      "id": 27,
+      "rotation_radians": 4.137658410559489,
+      "x": -0.329102100782787,
+      "y": 1.5931222228252546
+    },
+    {
+      "id": 28,
+      "rotation_radians": 2.3592846351360213,
+      "x": 0.47938942190929995,
+      "y": 1.8114971840785425
+    }
+  ],
+  "problem": "28 equal items for Triangles in Circles",
+  "setup": "triincir",
+  "source_image": "https://erich-friedman.github.io/packing/triincir/tc28.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triincir/"
+}
diff --git a/data/solutions/generated/triincir_029_73bcaf90b9fd2226.json b/data/solutions/generated/triincir_029_73bcaf90b9fd2226.json
new file mode 100644
index 0000000000000000000000000000000000000000..744293489cf32db6e652e9e0feb9feb4bafb2a63
--- /dev/null
+++ b/data/solutions/generated/triincir_029_73bcaf90b9fd2226.json
@@ -0,0 +1,233 @@
+{
+  "case": "triincir@29",
+  "container": {
+    "radius": 2.210219413194693,
+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triincir@29",
+    "credit": "Maurizio Morandi",
+    "date": "June 2008",
+    "family_updated": "8/31/19",
+    "metric_expression": "2.215+",
+    "metric_symbol": "r",
+    "metric_value": 2.215,
+    "reference_text": "r = 2.215+ | Found by Maurizio Morandi | in June 2008.",
+    "source_image": "tc29.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc29.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triincir/",
+    "title": "Triangles in Circles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triincir@29",
+      "credit": "Maurizio Morandi",
+      "date": "June 2008",
+      "family_updated": "8/31/19",
+      "metric_expression": "2.215+",
+      "metric_symbol": "r",
+      "metric_value": 2.215,
+      "reference_text": "r = 2.215+ | Found by Maurizio Morandi | in June 2008.",
+      "source_image": "tc29.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc29.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triincir/",
+      "title": "Triangles in Circles"
+    },
+    "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/triincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
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+  "problem": "29 equal items for Triangles in Circles",
+  "setup": "triincir",
+  "source_image": "https://erich-friedman.github.io/packing/triincir/tc29.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triincir/"
+}
diff --git a/data/solutions/generated/triincir_030_05c2ceb22d6802af.json b/data/solutions/generated/triincir_030_05c2ceb22d6802af.json
new file mode 100644
index 0000000000000000000000000000000000000000..82ed1b72ea5c40a7a1505bd721ce54d387f60139
--- /dev/null
+++ b/data/solutions/generated/triincir_030_05c2ceb22d6802af.json
@@ -0,0 +1,239 @@
+{
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+    "analytical_or_proved": false,
+    "case": "triincir@30",
+    "credit": "Maurizio Morandi",
+    "date": "July 2008",
+    "family_updated": "8/31/19",
+    "metric_expression": "2.258+",
+    "metric_symbol": "r",
+    "metric_value": 2.258,
+    "reference_text": "r = 2.258+ | Found by Maurizio Morandi | in July 2008.",
+    "source_image": "tc30.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc30.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triincir/",
+    "title": "Triangles in Circles"
+  },
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+      "case": "triincir@30",
+      "credit": "Maurizio Morandi",
+      "date": "July 2008",
+      "family_updated": "8/31/19",
+      "metric_expression": "2.258+",
+      "metric_symbol": "r",
+      "metric_value": 2.258,
+      "reference_text": "r = 2.258+ | Found by Maurizio Morandi | in July 2008.",
+      "source_image": "tc30.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc30.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triincir/",
+      "title": "Triangles in Circles"
+    },
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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/triincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
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+  ],
+  "problem": "30 equal items for Triangles in Circles",
+  "setup": "triincir",
+  "source_image": "https://erich-friedman.github.io/packing/triincir/tc30.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triincir/"
+}
diff --git a/data/solutions/generated/triincir_031_d099d25f47dd541c.json b/data/solutions/generated/triincir_031_d099d25f47dd541c.json
new file mode 100644
index 0000000000000000000000000000000000000000..0f325e78f3f91287af05d7ffab9e3488d213ab99
--- /dev/null
+++ b/data/solutions/generated/triincir_031_d099d25f47dd541c.json
@@ -0,0 +1,245 @@
+{
+  "case": "triincir@31",
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+    "type": "circle"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triincir@31",
+    "credit": "Maurizio Morandi",
+    "date": "July 2008",
+    "family_updated": "8/31/19",
+    "metric_expression": "2.272+",
+    "metric_symbol": "r",
+    "metric_value": 2.272,
+    "reference_text": "r = 2.272+ | Found by Maurizio Morandi | in July 2008.",
+    "source_image": "tc31.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc31.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triincir/",
+    "title": "Triangles in Circles"
+  },
+  "item": {
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+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
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+      "case": "triincir@31",
+      "credit": "Maurizio Morandi",
+      "date": "July 2008",
+      "family_updated": "8/31/19",
+      "metric_expression": "2.272+",
+      "metric_symbol": "r",
+      "metric_value": 2.272,
+      "reference_text": "r = 2.272+ | Found by Maurizio Morandi | in July 2008.",
+      "source_image": "tc31.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triincir/tc31.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triincir/",
+      "title": "Triangles in Circles"
+    },
+    "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/triincir/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
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+    {
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+      "y": 0.9419652705958971
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+    {
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+      "x": -0.18216856777375023,
+      "y": 1.732952265691758
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+    {
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+    {
+      "id": 29,
+      "rotation_radians": -0.7210486202852934,
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+      "y": 1.5426881096355258
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+    {
+      "id": 30,
+      "rotation_radians": -0.5193823630479477,
+      "x": 1.6912880357675322,
+      "y": 0.9814371697927989
+    },
+    {
+      "id": 31,
+      "rotation_radians": 0.3249966431186758,
+      "x": -1.0753844680277318,
+      "y": 1.323726804311345
+    }
+  ],
+  "problem": "31 equal items for Triangles in Circles",
+  "setup": "triincir",
+  "source_image": "https://erich-friedman.github.io/packing/triincir/tc31.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triincir/"
+}
diff --git a/data/solutions/generated/triinhex_021_96f74df50573bb81.json b/data/solutions/generated/triinhex_021_96f74df50573bb81.json
new file mode 100644
index 0000000000000000000000000000000000000000..ad9a527e3d48e51d8b859a79ab3b9b8963a5382c
--- /dev/null
+++ b/data/solutions/generated/triinhex_021_96f74df50573bb81.json
@@ -0,0 +1,188 @@
+{
+  "case": "triinhex@21",
+  "container": {
+    "circumradius": 2.0000540227066215,
+    "orientation_radians": 0.0,
+    "side_length": 2.000054022706621,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinhex@21",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "1.99878+",
+    "metric_symbol": "s",
+    "metric_value": 1.99878,
+    "reference_text": "s = 1.99878+ | Found by Ian Watson | in April 2026.",
+    "source_image": "21.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/21.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinhex@21",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "1.99878+",
+      "metric_symbol": "s",
+      "metric_value": 1.99878,
+      "reference_text": "s = 1.99878+ | Found by Ian Watson | in April 2026.",
+      "source_image": "21.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/21.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles in Hexagons"
+    },
+    "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/triinhex/",
+    "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": -0.5000189652150768,
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+    {
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+      "y": -1.443408049832474
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+    {
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+      "x": 1.0000302566994834,
+      "y": -1.154722510205806
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+    {
+      "id": 20,
+      "rotation_radians": 1.5707787806223275,
+      "x": -3.2248462468927874e-06,
+      "y": 1.1547326857029792
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.5235810846108432,
+      "x": 1.4613537579750626,
+      "y": -0.22166511722871504
+    }
+  ],
+  "problem": "21 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/21.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinhex_022_38182a59461da74e.json b/data/solutions/generated/triinhex_022_38182a59461da74e.json
new file mode 100644
index 0000000000000000000000000000000000000000..bee3f498093c91f755562efbfed267eabbe6e3ed
--- /dev/null
+++ b/data/solutions/generated/triinhex_022_38182a59461da74e.json
@@ -0,0 +1,194 @@
+{
+  "case": "triinhex@22",
+  "container": {
+    "circumradius": 2.0000562934901334,
+    "orientation_radians": 0.0,
+    "side_length": 2.000056293490133,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triinhex@22",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "4/29/26",
+    "metric_expression": "2",
+    "metric_symbol": "s",
+    "metric_value": 2.0,
+    "reference_text": "s = 2 | Trivial. |",
+    "source_image": "24.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triinhex@22",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "4/29/26",
+      "metric_expression": "2",
+      "metric_symbol": "s",
+      "metric_value": 2.0,
+      "reference_text": "s = 2 | Trivial. |",
+      "source_image": "24.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles in Hexagons"
+    },
+    "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/triinhex/",
+    "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": -1.1547257940366111
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+    {
+      "id": 22,
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+      "x": -0.5000119169834393,
+      "y": 1.4434100848469182
+    }
+  ],
+  "problem": "22 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinhex_023_dcd331994270a997.json b/data/solutions/generated/triinhex_023_dcd331994270a997.json
new file mode 100644
index 0000000000000000000000000000000000000000..37814fda3462d04b70d10e6e8fbf0cd7e50fda00
--- /dev/null
+++ b/data/solutions/generated/triinhex_023_dcd331994270a997.json
@@ -0,0 +1,200 @@
+{
+  "case": "triinhex@23",
+  "container": {
+    "circumradius": 2.0000568124706115,
+    "orientation_radians": 0.0,
+    "side_length": 2.000056812470611,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triinhex@23",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "4/29/26",
+    "metric_expression": "2",
+    "metric_symbol": "s",
+    "metric_value": 2.0,
+    "reference_text": "s = 2 | Trivial. |",
+    "source_image": "24.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triinhex@23",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "4/29/26",
+      "metric_expression": "2",
+      "metric_symbol": "s",
+      "metric_value": 2.0,
+      "reference_text": "s = 2 | Trivial. |",
+      "source_image": "24.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles in Hexagons"
+    },
+    "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/triinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "id": 19,
+      "rotation_radians": 0.5235836679614261,
+      "x": 0.5000056602813967,
+      "y": 1.443415921328364
+    },
+    {
+      "id": 20,
+      "rotation_radians": -2.618009941833377,
+      "x": -1.5000400555324773,
+      "y": 0.2886815297732877
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.5235835482154719,
+      "x": -1.0000245046513616,
+      "y": -1.1547332053146593
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.5235865408594965,
+      "x": -0.500023394186134,
+      "y": 1.443412376687313
+    },
+    {
+      "id": 23,
+      "rotation_radians": -2.618009325421106,
+      "x": 1.0000217827708595,
+      "y": 1.1547336264295245
+    }
+  ],
+  "problem": "23 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinhex_024_13936a08bfd4d152.json b/data/solutions/generated/triinhex_024_13936a08bfd4d152.json
new file mode 100644
index 0000000000000000000000000000000000000000..5d55683d5d4d2ab108ae1616b0e60950db06692a
--- /dev/null
+++ b/data/solutions/generated/triinhex_024_13936a08bfd4d152.json
@@ -0,0 +1,206 @@
+{
+  "case": "triinhex@24",
+  "container": {
+    "circumradius": 2.000057973379978,
+    "orientation_radians": 0.0,
+    "side_length": 2.0000579733799775,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triinhex@24",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "4/29/26",
+    "metric_expression": "2",
+    "metric_symbol": "s",
+    "metric_value": 2.0,
+    "reference_text": "s = 2 | Trivial. |",
+    "source_image": "24.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triinhex@24",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "4/29/26",
+      "metric_expression": "2",
+      "metric_symbol": "s",
+      "metric_value": 2.0,
+      "reference_text": "s = 2 | Trivial. |",
+      "source_image": "24.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/24.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles in Hexagons"
+    },
+    "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/triinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.5235809751291943,
+      "x": -1.5000379175798173,
+      "y": -0.28868842403581374
+    },
+    {
+      "id": 2,
+      "rotation_radians": -2.618011911476324,
+      "x": -1.5000393959399279,
+      "y": 0.2886773332656754
+    },
+    {
+      "id": 3,
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+      "x": -1.0000275978663102,
+      "y": 0.5773607991450416
+    },
+    {
+      "id": 4,
+      "rotation_radians": -2.618011518018861,
+      "x": -1.0000312336458028,
+      "y": 1.154726485989383
+    },
+    {
+      "id": 5,
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+      "x": -0.5000179405936932,
+      "y": 1.443410651562017
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.5235802525711232,
+      "x": -1.000022243433059,
+      "y": -1.1547332978739324
+    },
+    {
+      "id": 7,
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+      "x": -1.0000226971746415,
+      "y": -0.5773685206072579
+    },
+    {
+      "id": 8,
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+      "x": -0.5000107395304006,
+      "y": -0.2886840254628781
+    },
+    {
+      "id": 9,
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+      "x": -0.5000138071272273,
+      "y": 0.28868021742190925
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+    {
+      "id": 10,
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+      "x": -2.491239012447898e-06,
+      "y": 0.5773645125458193
+    },
+    {
+      "id": 11,
+      "rotation_radians": -2.618013411140186,
+      "x": -5.09322691485787e-06,
+      "y": 1.1547291880736783
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.5235799172221824,
+      "x": 0.5000061243093603,
+      "y": 1.4434144079698499
+    },
+    {
+      "id": 13,
+      "rotation_radians": -2.6180117674058723,
+      "x": -0.5000076524185725,
+      "y": -1.4434154410953357
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.5235794395246794,
+      "x": 3.924241503762102e-06,
+      "y": -1.154729028984474
+    },
+    {
+      "id": 15,
+      "rotation_radians": -2.618013860649882,
+      "x": 2.3431637083189786e-06,
+      "y": -0.5773637714102416
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.5235785182001274,
+      "x": 0.5000134597409054,
+      "y": -0.2886792842605226
+    },
+    {
+      "id": 17,
+      "rotation_radians": -2.618014475734169,
+      "x": 0.5000106433509852,
+      "y": 0.2886849388771347
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.5235788173126468,
+      "x": 1.0000218563884806,
+      "y": 0.5773689014884494
+    },
+    {
+      "id": 19,
+      "rotation_radians": -2.618013739373046,
+      "x": 1.0000212696732418,
+      "y": 1.1547331954941749
+    },
+    {
+      "id": 20,
+      "rotation_radians": -2.6180126634585985,
+      "x": 0.5000169220633622,
+      "y": -1.4434105125023653
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.5235798456657701,
+      "x": 1.0000293586365487,
+      "y": -1.1547260177126049
+    },
+    {
+      "id": 22,
+      "rotation_radians": -2.618013523262758,
+      "x": 1.0000267351866345,
+      "y": -0.5773605171479185
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.523579277991472,
+      "x": 1.5000384429096667,
+      "y": -0.28867719086122556
+    },
+    {
+      "id": 24,
+      "rotation_radians": -2.618013248442663,
+      "x": 1.5000367475800558,
+      "y": 0.28868825604305676
+    }
+  ],
+  "problem": "24 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinhex_025_71a7801cfb4a8d31.json b/data/solutions/generated/triinhex_025_71a7801cfb4a8d31.json
new file mode 100644
index 0000000000000000000000000000000000000000..1fc9e8e0ff932e05765573e29fbc9f11cef3c9ed
--- /dev/null
+++ b/data/solutions/generated/triinhex_025_71a7801cfb4a8d31.json
@@ -0,0 +1,212 @@
+{
+  "case": "triinhex@25",
+  "container": {
+    "circumradius": 2.167152661060189,
+    "orientation_radians": 0.0,
+    "side_length": 2.1671526610601886,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triinhex@25",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "13/6 = 2.166+",
+    "metric_symbol": "s",
+    "metric_value": 2.166,
+    "reference_text": "s = 13/6 = 2.166+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "25.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/25.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triinhex@25",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "13/6 = 2.166+",
+      "metric_symbol": "s",
+      "metric_value": 2.166,
+      "reference_text": "s = 13/6 = 2.166+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "25.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/25.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles in Hexagons"
+    },
+    "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/triinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.5239431923417057,
+      "x": 0.5846194633004307,
+      "y": -0.4309581399683717
+    },
+    {
+      "id": 2,
+      "rotation_radians": -2.6169572341869047,
+      "x": 0.08494910369262285,
+      "y": -0.7209415168600195
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+    {
+      "id": 3,
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+      "x": -0.4151187211163004,
+      "y": 0.14501823417695028
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+    {
+      "id": 4,
+      "rotation_radians": 0.5245326810493743,
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+    {
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+      "x": 0.584268488111201,
+      "y": 0.146700529279995
+    },
+    {
+      "id": 6,
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+      "x": 0.0839668333534887,
+      "y": 0.4353197803502547
+    },
+    {
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+      "x": -0.999689731066698,
+      "y": 0.2873722362785664
+    },
+    {
+      "id": 8,
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+      "x": -0.9151761340168918,
+      "y": -0.7219017590331184
+    },
+    {
+      "id": 9,
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+      "x": 1.0850029534626646,
+      "y": -0.7195803970292691
+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.5246405511902779,
+      "x": 0.08416185620858598,
+      "y": -1.2983152113389438
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.5237724342115734,
+      "x": 1.084788234076963,
+      "y": 0.43539283414388147
+    },
+    {
+      "id": 12,
+      "rotation_radians": -2.617946757880282,
+      "x": 0.2490153736786299,
+      "y": 1.0127747201005624
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.5235944577129802,
+      "x": -1.4997180627045923,
+      "y": -0.5786696062113592
+    },
+    {
+      "id": 14,
+      "rotation_radians": -2.61688081103647,
+      "x": 0.584117403900204,
+      "y": -1.5871749749716209
+    },
+    {
+      "id": 15,
+      "rotation_radians": 0.524391423176793,
+      "x": 1.084227858698467,
+      "y": -1.2974368418035613
+    },
+    {
+      "id": 16,
+      "rotation_radians": -2.6171714501799794,
+      "x": -0.4155778163541667,
+      "y": -1.5877126039120684
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.5238694283194867,
+      "x": 1.5849711383480265,
+      "y": -0.43056960917402776
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.5235951263687915,
+      "x": 0.7490267738400069,
+      "y": 1.3015194130771572
+    },
+    {
+      "id": 19,
+      "rotation_radians": -2.6177236350117874,
+      "x": 1.5852165387999289,
+      "y": 0.14679759358992886
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.5235992060499499,
+      "x": -0.08551824577766805,
+      "y": 1.588130000804978
+    },
+    {
+      "id": 21,
+      "rotation_radians": -2.617988126710399,
+      "x": -0.5855176664245635,
+      "y": 1.2994336321617999
+    },
+    {
+      "id": 22,
+      "rotation_radians": -2.618000825727862,
+      "x": -1.4997103125884166,
+      "y": -0.0013086645350485035
+    },
+    {
+      "id": 23,
+      "rotation_radians": -2.617986878453665,
+      "x": 1.2490457296471944,
+      "y": 1.0128492271762883
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.5244189206780203,
+      "x": -0.9158267369215456,
+      "y": -1.2994373080142863
+    },
+    {
+      "id": 25,
+      "rotation_radians": -2.6179962968568256,
+      "x": -1.3345584043508487,
+      "y": 0.8647395367990971
+    }
+  ],
+  "problem": "25 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/25.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinhex_026_658d7f93b604b663.json b/data/solutions/generated/triinhex_026_658d7f93b604b663.json
new file mode 100644
index 0000000000000000000000000000000000000000..6f1fcb5de99d7529e96ba901b01f69631133487d
--- /dev/null
+++ b/data/solutions/generated/triinhex_026_658d7f93b604b663.json
@@ -0,0 +1,218 @@
+{
+  "case": "triinhex@26",
+  "container": {
+    "circumradius": 2.2210449903788474,
+    "orientation_radians": 0.0,
+    "side_length": 2.221044990378847,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinhex@26",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "2.21991+",
+    "metric_symbol": "s",
+    "metric_value": 2.21991,
+    "reference_text": "s = 2.21991+ | Found by Ian Watson | in April 2026.",
+    "source_image": "26.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/26.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinhex@26",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "2.21991+",
+      "metric_symbol": "s",
+      "metric_value": 2.21991,
+      "reference_text": "s = 2.21991+ | Found by Ian Watson | in April 2026.",
+      "source_image": "26.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/26.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles in Hexagons"
+    },
+    "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/triinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.5708034821994694,
+      "x": -0.3758323515465858,
+      "y": 0.4562962577977996
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.5236055756899153,
+      "x": -0.20000716930940762,
+      "y": -0.12108119320410993
+    },
+    {
+      "id": 3,
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+      "x": 0.12419059267902086,
+      "y": 0.7449864544079625
+    },
+    {
+      "id": 4,
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+      "x": 0.624210493232877,
+      "y": 0.4562964656420306
+    },
+    {
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+      "x": 0.2861784403088791,
+      "y": -0.4340893865630591
+    },
+    {
+      "id": 6,
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+      "x": 0.7861089381313656,
+      "y": -0.14519122596910006
+    },
+    {
+      "id": 7,
+      "rotation_radians": 0.5236057193271365,
+      "x": -0.8621352986644648,
+      "y": 0.7687436901322753
+    },
+    {
+      "id": 8,
+      "rotation_radians": 1.5707737176183252,
+      "x": -0.5206554471702163,
+      "y": -0.7687388021252732
+    },
+    {
+      "id": 9,
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+      "x": 0.12420035229491161,
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+    },
+    {
+      "id": 10,
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+      "x": 0.2863732403119589,
+      "y": -1.0114825890194765
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.5236057312579873,
+      "x": 1.132723282174666,
+      "y": 0.7302776851806888
+    },
+    {
+      "id": 12,
+      "rotation_radians": 1.5711986244880196,
+      "x": 1.2121807375560545,
+      "y": -0.5620832795434783
+    },
+    {
+      "id": 13,
+      "rotation_radians": 1.5708030990659012,
+      "x": -0.8621299994204032,
+      "y": 1.3461136204695554
+    },
+    {
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+      "rotation_radians": 1.9894375595801121,
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+    {
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+      "x": -0.3621071340315953,
+      "y": 1.634795551914293
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+    {
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+      "y": -0.8775211055274816
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+    {
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+      "rotation_radians": 0.5236057934828916,
+      "x": 0.6242698647296332,
+      "y": 1.6109556675202805
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+    {
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+      "y": -1.3461083055737968
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+    {
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+      "x": -0.15115344767655567,
+      "y": -1.6348007568230842
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+    {
+      "id": 20,
+      "rotation_radians": 1.5707963267708611,
+      "x": 1.1319064642222976,
+      "y": 1.3090666888358848
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.5711942960210048,
+      "x": 0.7296931476657662,
+      "y": -1.4283432729676488
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.558120380831009,
+      "x": 1.6331798432973572,
+      "y": 0.4282008393133308
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.5239963983590038,
+      "x": 1.2296024915463575,
+      "y": -1.139456201168338
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.524001083502184,
+      "x": 1.7120859867734202,
+      "y": -0.2731974140006328
+    },
+    {
+      "id": 25,
+      "rotation_radians": 1.5708034820784016,
+      "x": -1.4863481168769184,
+      "y": 0.6951736586807188
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.942209283780388,
+      "x": -1.6468570928350794,
+      "y": -0.06052340290319563
+    }
+  ],
+  "problem": "26 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/26.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinhex_027_11ad91d5c6b8788e.json b/data/solutions/generated/triinhex_027_11ad91d5c6b8788e.json
new file mode 100644
index 0000000000000000000000000000000000000000..37d19a18190c2f93417fb203c22fca1d3376ed64
--- /dev/null
+++ b/data/solutions/generated/triinhex_027_11ad91d5c6b8788e.json
@@ -0,0 +1,224 @@
+{
+  "case": "triinhex@27",
+  "container": {
+    "circumradius": 2.3244889604953727,
+    "orientation_radians": 0.0,
+    "side_length": 2.3244889604953722,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinhex@27",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "2.29541+",
+    "metric_symbol": "s",
+    "metric_value": 2.29541,
+    "reference_text": "s = 2.29541+ | Found by Ian Watson | in April 2026.",
+    "source_image": "27.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/27.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000700021000353,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinhex@27",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "2.29541+",
+      "metric_symbol": "s",
+      "metric_value": 2.29541,
+      "reference_text": "s = 2.29541+ | Found by Ian Watson | in April 2026.",
+      "source_image": "27.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/27.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles in Hexagons"
+    },
+    "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/triinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.6316279211074862,
+      "x": 0.029358846464989045,
+      "y": -0.01814588558702195
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+    {
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+      "x": -0.7821937764681951,
+      "y": -0.08030777656835522
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+    {
+      "id": 3,
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+      "x": 0.7285444910892458,
+      "y": 0.019324309008832682
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+    {
+      "id": 4,
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+      "y": 0.8281222797524859
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+    {
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+    {
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+      "y": 0.8578642483821504
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+    {
+      "id": 16,
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+      "x": 1.765351003228341,
+      "y": -0.16475628642078077
+    },
+    {
+      "id": 17,
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+      "x": -1.7219806003384108,
+      "y": -0.10276175020896648
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.4791751853559103,
+      "x": 1.6422937847830736,
+      "y": 0.5151219995005437
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.5651521396759631,
+      "x": -1.6610333530125028,
+      "y": 0.5654590450732594
+    },
+    {
+      "id": 20,
+      "rotation_radians": 1.5062014435024642,
+      "x": 0.007737016855220386,
+      "y": 1.4092757946630545
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.4896113608413144,
+      "x": 1.1154325996403696,
+      "y": 1.4375859252650072
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.5646173159706258,
+      "x": -1.1163120155529835,
+      "y": 1.4356434293451832
+    },
+    {
+      "id": 23,
+      "rotation_radians": -1.6121915689441197,
+      "x": 0.5773474752569709,
+      "y": 1.7039238369802667
+    },
+    {
+      "id": 24,
+      "rotation_radians": -1.6019645895150547,
+      "x": -0.5608979282199662,
+      "y": 1.7086067456845728
+    },
+    {
+      "id": 25,
+      "rotation_radians": -1.5100865712966838,
+      "x": -0.561088389434101,
+      "y": -1.4367233921860367
+    },
+    {
+      "id": 26,
+      "rotation_radians": -1.5096814319124432,
+      "x": 0.5650061888433319,
+      "y": -1.436538939238513
+    },
+    {
+      "id": 27,
+      "rotation_radians": 1.628006806924602,
+      "x": -0.011733440905370308,
+      "y": -1.6960514663489132
+    }
+  ],
+  "problem": "27 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/27.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinhex_028_2b319174d63885b4.json b/data/solutions/generated/triinhex_028_2b319174d63885b4.json
new file mode 100644
index 0000000000000000000000000000000000000000..980a4070a14dfadeb04071148121d0eac2b84cbd
--- /dev/null
+++ b/data/solutions/generated/triinhex_028_2b319174d63885b4.json
@@ -0,0 +1,230 @@
+{
+  "case": "triinhex@28",
+  "container": {
+    "circumradius": 2.366084749635803,
+    "orientation_radians": 0.0,
+    "side_length": 2.3660847496358026,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinhex@28",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "2.32289+",
+    "metric_symbol": "s",
+    "metric_value": 2.32289,
+    "reference_text": "s = 2.32289+ | Found by Ian Watson | in April 2026.",
+    "source_image": "28.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/28.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinhex@28",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "2.32289+",
+      "metric_symbol": "s",
+      "metric_value": 2.32289,
+      "reference_text": "s = 2.32289+ | Found by Ian Watson | in April 2026.",
+      "source_image": "28.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/28.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles in Hexagons"
+    },
+    "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/triinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.5260154642507973,
+      "x": -0.5026860706050721,
+      "y": 0.33989918385252355
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+    {
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+    {
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+      "x": 0.0024461516005378826,
+      "y": 0.05244234739564818
+    },
+    {
+      "id": 4,
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+      "x": 0.6872946448127951,
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+    {
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+      "x": 0.6808050180865404,
+      "y": 0.6068301812260313
+    },
+    {
+      "id": 7,
+      "rotation_radians": -1.6262194718304737,
+      "x": -0.7133684549771446,
+      "y": -0.5541408804904934
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+    {
+      "id": 8,
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+      "x": 0.1779922964998723,
+      "y": -0.7067493058504907
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+    {
+      "id": 9,
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+      "x": -1.2453941826554136,
+      "y": 0.7863652917916951
+    },
+    {
+      "id": 10,
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+      "x": -1.0038835903388499,
+      "y": 0.05040669208362889
+    },
+    {
+      "id": 11,
+      "rotation_radians": 1.51542185888866,
+      "x": -1.2294221645021932,
+      "y": -0.8146738907495598
+    },
+    {
+      "id": 12,
+      "rotation_radians": -2.6235864774969704,
+      "x": 1.1881539786810669,
+      "y": -0.2691813762519486
+    },
+    {
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+      "x": -0.22563001500167904,
+      "y": -1.3945880526148582
+    },
+    {
+      "id": 14,
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+      "x": 0.2575733109332851,
+      "y": -1.7604083278363043
+    },
+    {
+      "id": 15,
+      "rotation_radians": -2.6130890428234994,
+      "x": 0.17669907148503697,
+      "y": 1.4717313877249116
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.49682199210758204,
+      "x": -0.6911865323225441,
+      "y": 1.746164223479137
+    },
+    {
+      "id": 17,
+      "rotation_radians": -2.617993895167547,
+      "x": -1.1997774978785711,
+      "y": 1.442736259285058
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.5322319371116799,
+      "x": 1.185167888493558,
+      "y": 0.890737064626825
+    },
+    {
+      "id": 19,
+      "rotation_radians": -2.2300686955047313,
+      "x": 0.7525606497019234,
+      "y": -0.9714573126695769
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.5235983258873963,
+      "x": 1.5423747482657733,
+      "y": -0.8493403865035722
+    },
+    {
+      "id": 21,
+      "rotation_radians": -2.613435568448256,
+      "x": 1.1809733860891047,
+      "y": 1.4707471944197028
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.5287019947806615,
+      "x": 0.6793262701098134,
+      "y": 1.7571475962500867
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.5180093749880462,
+      "x": 1.6897680609071501,
+      "y": 0.016707042308758288
+    },
+    {
+      "id": 24,
+      "rotation_radians": -2.6196204488828783,
+      "x": 1.6876526381391614,
+      "y": 0.5960641880097028
+    },
+    {
+      "id": 25,
+      "rotation_radians": -2.673405253450262,
+      "x": -0.7127510179999113,
+      "y": -1.7107188346686006
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.9004766228894976,
+      "x": 0.97007202176731,
+      "y": -1.5122386582100849
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.8435093635832122,
+      "x": -1.7806545655345762,
+      "y": -0.11576930307611563
+    },
+    {
+      "id": 28,
+      "rotation_radians": -1.6261676290924334,
+      "x": -1.1960289006460592,
+      "y": -1.3947803348833083
+    }
+  ],
+  "problem": "28 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/28.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinhex_029_64c6a497fdd4bc1d.json b/data/solutions/generated/triinhex_029_64c6a497fdd4bc1d.json
new file mode 100644
index 0000000000000000000000000000000000000000..2ac9b22abe8335ad2f4995a10fe0103b64e0ead1
--- /dev/null
+++ b/data/solutions/generated/triinhex_029_64c6a497fdd4bc1d.json
@@ -0,0 +1,236 @@
+{
+  "case": "triinhex@29",
+  "container": {
+    "circumradius": 2.402316870538761,
+    "orientation_radians": 0.0,
+    "side_length": 2.4023168705387605,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triinhex@29",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "7/3 = 2.333+",
+    "metric_symbol": "s",
+    "metric_value": 2.333,
+    "reference_text": "s = 7/3 = 2.333+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "29.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/29.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triinhex@29",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "7/3 = 2.333+",
+      "metric_symbol": "s",
+      "metric_value": 2.333,
+      "reference_text": "s = 7/3 = 2.333+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "29.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/29.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles in Hexagons"
+    },
+    "generator": "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/triinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.5224984031922542,
+      "x": 0.08027753333470412,
+      "y": -0.04939422438662173
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+    {
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+    {
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+      "y": 0.9258521077075634
+    },
+    {
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+      "x": 1.599162422273485,
+      "y": 0.8042029853304743
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.5696210517927613,
+      "x": 0.5204327059875647,
+      "y": -1.7883527478643815
+    },
+    {
+      "id": 19,
+      "rotation_radians": -1.5141256325612016,
+      "x": -0.018030925535036334,
+      "y": -1.504010042113499
+    },
+    {
+      "id": 20,
+      "rotation_radians": -1.5814461415885004,
+      "x": 1.1015235653957627,
+      "y": 1.098378339729898
+    },
+    {
+      "id": 21,
+      "rotation_radians": -1.6028875349355582,
+      "x": 1.6281256004745468,
+      "y": 0.18668275814597635
+    },
+    {
+      "id": 22,
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+      "x": 1.144290514199243,
+      "y": -1.5030988644934806
+    },
+    {
+      "id": 23,
+      "rotation_radians": -1.5473358822979582,
+      "x": -1.5927235352279137,
+      "y": -0.8015720194949999
+    },
+    {
+      "id": 24,
+      "rotation_radians": -1.5862457038364366,
+      "x": -0.6588225232501673,
+      "y": 1.7840751418959504
+    },
+    {
+      "id": 25,
+      "rotation_radians": -1.5004006855034968,
+      "x": -0.9831066407425632,
+      "y": -1.504541565141096
+    },
+    {
+      "id": 26,
+      "rotation_radians": -1.5751363463098005,
+      "x": 0.5020434355495096,
+      "y": 1.7896001438436324
+    },
+    {
+      "id": 27,
+      "rotation_radians": 1.6411994860021315,
+      "x": -0.9847788037526414,
+      "y": -0.9258597449886306
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.564866414286383,
+      "x": -0.00016223280715842964,
+      "y": 1.5031190877871392
+    },
+    {
+      "id": 29,
+      "rotation_radians": 1.565419003070704,
+      "x": -1.1703270872527454,
+      "y": 1.5031000847692892
+    }
+  ],
+  "problem": "29 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/29.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinhex_030_11d17f9e12268b02.json b/data/solutions/generated/triinhex_030_11d17f9e12268b02.json
new file mode 100644
index 0000000000000000000000000000000000000000..70fa60db2dc5b45efe0b920006f93fdc9cd93386
--- /dev/null
+++ b/data/solutions/generated/triinhex_030_11d17f9e12268b02.json
@@ -0,0 +1,242 @@
+{
+  "case": "triinhex@30",
+  "container": {
+    "circumradius": 2.463631266870014,
+    "orientation_radians": 0.0,
+    "side_length": 2.4636312668700135,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triinhex@30",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "19/8 = 2.375",
+    "metric_symbol": "s",
+    "metric_value": 2.375,
+    "reference_text": "s = 19/8 = 2.375 | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "30.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/30.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triinhex@30",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "19/8 = 2.375",
+      "metric_symbol": "s",
+      "metric_value": 2.375,
+      "reference_text": "s = 19/8 = 2.375 | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "30.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/30.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles in Hexagons"
+    },
+    "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/triinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.4717331535806748,
+      "x": 0.27165816450823743,
+      "y": -0.15538645829091274
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+      "x": -0.1437387669930932,
+      "y": -0.984425357476941
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+    {
+      "id": 11,
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+      "x": 1.5692427010488912,
+      "y": -0.9338012967688755
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+    {
+      "id": 12,
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+      "y": -0.981518577797747
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+      "y": -0.19575067897509316
+    },
+    {
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+      "y": 0.7838471453999024
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+      "id": 15,
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+      "x": -1.229366903976787,
+      "y": 0.16226667434030537
+    },
+    {
+      "id": 16,
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+      "x": -1.0363701665232945,
+      "y": 0.9953654800509092
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.472200576258727,
+      "x": 1.6966219473955182,
+      "y": 0.6554941126461542
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.4800730138556224,
+      "x": 0.35903614800956923,
+      "y": -1.7987540482800346
+    },
+    {
+      "id": 19,
+      "rotation_radians": -1.6698571978479935,
+      "x": -0.2001926137165086,
+      "y": -1.5590295806721635
+    },
+    {
+      "id": 20,
+      "rotation_radians": -1.6737223474831076,
+      "x": 1.2256261318772255,
+      "y": 0.9956690880096222
+    },
+    {
+      "id": 21,
+      "rotation_radians": -1.836930900653502,
+      "x": 1.8745499379488701,
+      "y": -0.09375166587783343
+    },
+    {
+      "id": 22,
+      "rotation_radians": -1.6698183549864642,
+      "x": 0.8974123133100509,
+      "y": -1.5590320741433308
+    },
+    {
+      "id": 23,
+      "rotation_radians": -1.620025326288678,
+      "x": -1.709280908055299,
+      "y": -0.6807071485249871
+    },
+    {
+      "id": 24,
+      "rotation_radians": -1.6084418123934214,
+      "x": -0.4659954365333926,
+      "y": 1.7655164504169514
+    },
+    {
+      "id": 25,
+      "rotation_radians": -1.6373359870596669,
+      "x": -1.1584386512251872,
+      "y": -1.557477226826506
+    },
+    {
+      "id": 26,
+      "rotation_radians": -1.6192047543744004,
+      "x": 0.7243266947164125,
+      "y": 1.8209688636791406
+    },
+    {
+      "id": 27,
+      "rotation_radians": 1.5042891082278915,
+      "x": -1.2023935436079447,
+      "y": -0.9758842809374233
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.5097457965573036,
+      "x": 0.16744193747369807,
+      "y": 1.557282045143679
+    },
+    {
+      "id": 29,
+      "rotation_radians": 1.737526548490473,
+      "x": -1.1351187583797713,
+      "y": 1.5642212443376091
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.4806094363418891,
+      "x": -1.7533495328524085,
+      "y": -0.0802065614110586
+    }
+  ],
+  "problem": "30 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/30.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinhex_031_1ce8108c850d5941.json b/data/solutions/generated/triinhex_031_1ce8108c850d5941.json
new file mode 100644
index 0000000000000000000000000000000000000000..58cf431f43e284752bbe4de78fdf4639bf73fcbc
--- /dev/null
+++ b/data/solutions/generated/triinhex_031_1ce8108c850d5941.json
@@ -0,0 +1,248 @@
+{
+  "case": "triinhex@31",
+  "container": {
+    "circumradius": 2.464592896722666,
+    "orientation_radians": 0.0,
+    "side_length": 2.4645928967226656,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triinhex@31",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "12/5 = 2.400",
+    "metric_symbol": "s",
+    "metric_value": 2.4,
+    "reference_text": "s = 12/5 = 2.400 | Found by Emerson Connelly | in April 2026.",
+    "source_image": "31.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/31.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triinhex@31",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "12/5 = 2.400",
+      "metric_symbol": "s",
+      "metric_value": 2.4,
+      "reference_text": "s = 12/5 = 2.400 | Found by Emerson Connelly | in April 2026.",
+      "source_image": "31.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/31.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles in Hexagons"
+    },
+    "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/triinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.4631795917070878,
+      "x": 0.275896354074456,
+      "y": -0.15296623989953792
+    },
+    {
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+    {
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+      "x": 0.44998327367469443,
+      "y": -0.765166626914554
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+    {
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+      "x": -0.6581631853769423,
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+    },
+    {
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+      "y": 0.7485571512466759
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+    {
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+      "x": -0.10829720724953823,
+      "y": -0.9819648260429528
+    },
+    {
+      "id": 11,
+      "rotation_radians": -1.5987018021138235,
+      "x": 1.618398032084736,
+      "y": -0.8407400272357006
+    },
+    {
+      "id": 12,
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+      "y": -0.9826792104933673
+    },
+    {
+      "id": 13,
+      "rotation_radians": 1.4633837779181178,
+      "x": 1.2241638809294748,
+      "y": -0.1339520370490229
+    },
+    {
+      "id": 14,
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+      "x": -1.5776540525589222,
+      "y": 0.8790477502661027
+    },
+    {
+      "id": 15,
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+      "x": -1.2688343416187535,
+      "y": 0.16515650305834859
+    },
+    {
+      "id": 16,
+      "rotation_radians": -1.6537825400974604,
+      "x": -0.9805230281485272,
+      "y": 0.9833214373209419
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.4789474815220025,
+      "x": 1.6791259767790083,
+      "y": 0.693802849330045
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.492561990300683,
+      "x": 0.4316290272956739,
+      "y": -1.798030554234476
+    },
+    {
+      "id": 19,
+      "rotation_radians": -1.6333249703278967,
+      "x": -0.1451817497702155,
+      "y": -1.5581647629715427
+    },
+    {
+      "id": 20,
+      "rotation_radians": -1.6650170992302225,
+      "x": 1.2071100296512973,
+      "y": 1.028368861435095
+    },
+    {
+      "id": 21,
+      "rotation_radians": -1.6782224815585567,
+      "x": 1.778145878784986,
+      "y": 0.04088027467632755
+    },
+    {
+      "id": 22,
+      "rotation_radians": -1.6393005114495596,
+      "x": 0.976751726408699,
+      "y": -1.5583738350034153
+    },
+    {
+      "id": 23,
+      "rotation_radians": -1.5871378956367752,
+      "x": -1.7280684116697715,
+      "y": -0.6820519908807204
+    },
+    {
+      "id": 24,
+      "rotation_radians": -1.6443913657754918,
+      "x": -0.4085735606541805,
+      "y": 1.8095363413250716
+    },
+    {
+      "id": 25,
+      "rotation_radians": -1.5724279908440382,
+      "x": -1.2313597437042747,
+      "y": -1.5570259700854079
+    },
+    {
+      "id": 26,
+      "rotation_radians": -1.6883803815097735,
+      "x": 0.6943513291951394,
+      "y": 1.789046887076436
+    },
+    {
+      "id": 27,
+      "rotation_radians": 1.5497042744392837,
+      "x": -1.22470541178336,
+      "y": -0.9699787997798245
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.4685019455574475,
+      "x": 0.14031638703740246,
+      "y": 1.5600319315052213
+    },
+    {
+      "id": 29,
+      "rotation_radians": 1.354781731590356,
+      "x": -1.8329067131687398,
+      "y": 0.03378751461789998
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.4877941715812408,
+      "x": -0.9363419032134261,
+      "y": 1.559020559387938
+    },
+    {
+      "id": 31,
+      "rotation_radians": 1.5165718618890391,
+      "x": -0.6649166053424114,
+      "y": -1.819035184281666
+    }
+  ],
+  "problem": "31 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/31.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinhex_032_8674581436e5e74d.json b/data/solutions/generated/triinhex_032_8674581436e5e74d.json
new file mode 100644
index 0000000000000000000000000000000000000000..d249cabbb895da96b83724005b7a353f31ad2d30
--- /dev/null
+++ b/data/solutions/generated/triinhex_032_8674581436e5e74d.json
@@ -0,0 +1,254 @@
+{
+  "case": "triinhex@32",
+  "container": {
+    "circumradius": 2.466336368233779,
+    "orientation_radians": 0.0,
+    "side_length": 2.4663363682337787,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinhex@32",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "2.465+",
+    "metric_symbol": "s",
+    "metric_value": 2.465,
+    "reference_text": "s = 2.465+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "32.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/32.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinhex@32",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "2.465+",
+      "metric_symbol": "s",
+      "metric_value": 2.465,
+      "reference_text": "s = 2.465+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "32.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/32.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles in Hexagons"
+    },
+    "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/triinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.4972085030667401,
+      "x": -0.2524850802063715,
+      "y": -0.14876753894782999
+    },
+    {
+      "id": 2,
+      "rotation_radians": 0.4501342822204236,
+      "x": 0.2477208685112531,
+      "y": 0.14321816855371963
+    },
+    {
+      "id": 3,
+      "rotation_radians": 0.4771763070128756,
+      "x": -0.8325666367664102,
+      "y": 0.04167669720677916
+    },
+    {
+      "id": 4,
+      "rotation_radians": 0.45001059789425835,
+      "x": -0.2515844165861629,
+      "y": -0.727757539526812
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+    {
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+      "x": -0.29596955430383404,
+      "y": 0.959533254260141
+    },
+    {
+      "id": 6,
+      "rotation_radians": 0.4925206200664781,
+      "x": 0.7757581156835559,
+      "y": -0.6198212322878617
+    },
+    {
+      "id": 7,
+      "rotation_radians": 1.5616175375402264,
+      "x": 0.8503048839114905,
+      "y": -0.0336130576655623
+    },
+    {
+      "id": 8,
+      "rotation_radians": 1.4973332316037533,
+      "x": 0.2530276976724155,
+      "y": 0.7217484558091258
+    },
+    {
+      "id": 9,
+      "rotation_radians": 1.5353269933256637,
+      "x": 0.30326275859134183,
+      "y": -0.9650016590667542
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+    {
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+      "rotation_radians": 1.5330274137586104,
+      "x": -0.775600077538587,
+      "y": 0.6214265283718401
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.513981728827474,
+      "x": -1.618258613375815,
+      "y": -0.8818899468762516
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+    {
+      "id": 12,
+      "rotation_radians": 1.2741340277727804,
+      "x": -0.856612371277246,
+      "y": -1.0404837985074897
+    },
+    {
+      "id": 13,
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+      "x": -1.3060704886992391,
+      "y": -0.3001049098596222
+    },
+    {
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+      "x": 1.6145016554972142,
+      "y": 0.8958692063549825
+    },
+    {
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+      "x": 0.8644012833870183,
+      "y": 1.039079841269402
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.5204458387835666,
+      "x": 1.3171582072358652,
+      "y": 0.31896487522930583
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.551023705458993,
+      "x": -0.34503132392596453,
+      "y": -1.8372823884168916
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.5243252762900705,
+      "x": -1.778971452516936,
+      "y": 0.5673418058971706
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.5155064415233309,
+      "x": 0.22927797505523514,
+      "y": -1.5585598010921815
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.4858314009584768,
+      "x": -1.259044596974377,
+      "y": 0.937209387111876
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.47757549964668494,
+      "x": -1.808429665975862,
+      "y": -0.013964319013462761
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.22693278932726002,
+      "x": -1.0543171935232123,
+      "y": -1.5837766227525636
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.5498329594879396,
+      "x": 0.31995587203362963,
+      "y": 1.8263564645040928
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.5304093205902745,
+      "x": 1.775339714308086,
+      "y": -0.6126499394618808
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.5256530857803342,
+      "x": -0.7280732484190708,
+      "y": 1.8462019203444642
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.49906797844650147,
+      "x": 1.2493800020681494,
+      "y": -1.504056494198503
+    },
+    {
+      "id": 27,
+      "rotation_radians": 1.5710820189657384,
+      "x": -0.2234246807264309,
+      "y": 1.5585431557281402
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.5397157460985003,
+      "x": 1.2666948811581256,
+      "y": -0.9236756871021673
+    },
+    {
+      "id": 29,
+      "rotation_radians": 1.567642758657688,
+      "x": 1.8166269196853653,
+      "y": 0.02936640662120255
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.2558887694087884,
+      "x": 1.0465994058708084,
+      "y": 1.5869469748035243
+    },
+    {
+      "id": 31,
+      "rotation_radians": 1.5693886583976013,
+      "x": 0.7335612756432012,
+      "y": -1.8465265837286984
+    },
+    {
+      "id": 32,
+      "rotation_radians": 1.5767089542034438,
+      "x": -1.2303841493145933,
+      "y": 1.5574635776083017
+    }
+  ],
+  "problem": "32 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/32.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinhex_033_5b836a27d2bb958c.json b/data/solutions/generated/triinhex_033_5b836a27d2bb958c.json
new file mode 100644
index 0000000000000000000000000000000000000000..232fa49900fd65f4b1fb9a981c42c7c179ee2e80
--- /dev/null
+++ b/data/solutions/generated/triinhex_033_5b836a27d2bb958c.json
@@ -0,0 +1,260 @@
+{
+  "case": "triinhex@33",
+  "container": {
+    "circumradius": 2.5000789881797005,
+    "orientation_radians": 0.0,
+    "side_length": 2.5000789881797,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinhex@33",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "2.498+",
+    "metric_symbol": "s",
+    "metric_value": 2.498,
+    "reference_text": "s = 2.498+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "33.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/33.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinhex@33",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "2.498+",
+      "metric_symbol": "s",
+      "metric_value": 2.498,
+      "reference_text": "s = 2.498+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "33.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/33.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles in Hexagons"
+    },
+    "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/triinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.5707770751601016,
+      "x": 0.2500156973660663,
+      "y": -0.14434889316592578
+    },
+    {
+      "id": 2,
+      "rotation_radians": -1.5708176910366125,
+      "x": -0.25000631636601084,
+      "y": 0.14431796565031502
+    },
+    {
+      "id": 3,
+      "rotation_radians": -1.5708179122799417,
+      "x": 0.25006511009412474,
+      "y": -0.7217149520378406
+    },
+    {
+      "id": 4,
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+      "x": 0.5000170561290674,
+      "y": 0.5773881474369261
+    },
+    {
+      "id": 5,
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+      "x": -0.7499797631021614,
+      "y": -0.7217309921563239
+    },
+    {
+      "id": 6,
+      "rotation_radians": -1.5707990559128056,
+      "x": -0.2500235378871011,
+      "y": 1.0103924876127863
+    },
+    {
+      "id": 7,
+      "rotation_radians": 1.5707935800276542,
+      "x": -0.7500290753918958,
+      "y": 0.7216940555381167
+    },
+    {
+      "id": 8,
+      "rotation_radians": 1.5707717054990569,
+      "x": -0.7500220960890742,
+      "y": -0.14436398730115696
+    },
+    {
+      "id": 9,
+      "rotation_radians": 1.5707777673304832,
+      "x": 0.5000185756530843,
+      "y": 1.154752873864966
+    },
+    {
+      "id": 10,
+      "rotation_radians": 1.5707736684082454,
+      "x": -0.2499520453974799,
+      "y": -1.0103964730382264
+    },
+    {
+      "id": 11,
+      "rotation_radians": -1.5708218113883445,
+      "x": 1.0000768950963856,
+      "y": -0.2886538982949825
+    },
+    {
+      "id": 12,
+      "rotation_radians": 1.5707754808264145,
+      "x": 0.7500785621708439,
+      "y": -1.0103974335088426
+    },
+    {
+      "id": 13,
+      "rotation_radians": 1.570770631592737,
+      "x": 1.0000291745411132,
+      "y": 0.2887074227542645
+    },
+    {
+      "id": 14,
+      "rotation_radians": 1.5707968397028786,
+      "x": -1.750067758429221,
+      "y": 0.7216954489344684
+    },
+    {
+      "id": 15,
+      "rotation_radians": -1.5708204724682917,
+      "x": -1.2500359251578823,
+      "y": 0.14431666684596708
+    },
+    {
+      "id": 16,
+      "rotation_radians": -1.5707973154408494,
+      "x": -1.250048278817636,
+      "y": 1.0103755018697895
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.570796328257971,
+      "x": 1.999890497120144,
+      "y": 0.2889830030003739
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.5707822017370927,
+      "x": 0.25015882718073107,
+      "y": -1.8764441981996351
+    },
+    {
+      "id": 19,
+      "rotation_radians": -1.5708172362633948,
+      "x": -0.24986584634577635,
+      "y": -1.5877642572651876
+    },
+    {
+      "id": 20,
+      "rotation_radians": -1.5708223169087385,
+      "x": 1.4476184333941988,
+      "y": 0.6681924505910759
+    },
+    {
+      "id": 21,
+      "rotation_radians": -1.5709329353886192,
+      "x": 1.9999779836306033,
+      "y": -0.28854355163108525
+    },
+    {
+      "id": 22,
+      "rotation_radians": -1.5708167935386075,
+      "x": 0.7501842294713792,
+      "y": -1.5877658506781742
+    },
+    {
+      "id": 23,
+      "rotation_radians": -1.5708228717145511,
+      "x": -1.7500284108609772,
+      "y": -0.7217321836167834
+    },
+    {
+      "id": 24,
+      "rotation_radians": -1.5707991585017929,
+      "x": -0.7500313818255453,
+      "y": 1.8764472015301183
+    },
+    {
+      "id": 25,
+      "rotation_radians": -1.5708277183841632,
+      "x": -1.249934707957427,
+      "y": -1.5877720623183635
+    },
+    {
+      "id": 26,
+      "rotation_radians": -1.5708012556323496,
+      "x": 0.2500023949097152,
+      "y": 1.8764467200773371
+    },
+    {
+      "id": 27,
+      "rotation_radians": 1.570767719407883,
+      "x": -1.2500033577949117,
+      "y": -1.0104070247225372
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.5707938608730982,
+      "x": -0.250018199643472,
+      "y": 1.5877617685437269
+    },
+    {
+      "id": 29,
+      "rotation_radians": 1.5707938412291593,
+      "x": -1.2500476372655613,
+      "y": 1.5877481478038626
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.5707720971766495,
+      "x": -1.7500508395042431,
+      "y": -0.14436111469474186
+    },
+    {
+      "id": 31,
+      "rotation_radians": 1.570785188721765,
+      "x": -0.7498940333096495,
+      "y": -1.8764431184955923
+    },
+    {
+      "id": 32,
+      "rotation_radians": 1.570796299400043,
+      "x": 1.2950364953645823,
+      "y": 1.5098339311710902
+    },
+    {
+      "id": 33,
+      "rotation_radians": -1.570798931168478,
+      "x": 1.5001320051220346,
+      "y": -1.154600379070531
+    }
+  ],
+  "problem": "33 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/33.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinhex_034_a712744ff3b5bcc9.json b/data/solutions/generated/triinhex_034_a712744ff3b5bcc9.json
new file mode 100644
index 0000000000000000000000000000000000000000..56e8a37412ceba59aa1f78706a6f3f98741d7890
--- /dev/null
+++ b/data/solutions/generated/triinhex_034_a712744ff3b5bcc9.json
@@ -0,0 +1,266 @@
+{
+  "case": "triinhex@34",
+  "container": {
+    "circumradius": 2.5000778510013064,
+    "orientation_radians": 0.0,
+    "side_length": 2.500077851001306,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triinhex@34",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "5/2 = 2.500",
+    "metric_symbol": "s",
+    "metric_value": 2.5,
+    "reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.",
+    "source_image": "35.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triinhex@34",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "5/2 = 2.500",
+      "metric_symbol": "s",
+      "metric_value": 2.5,
+      "reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.",
+      "source_image": "35.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles 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/triinhex/",
+    "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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+    {
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+      "x": 1.2500568910921024,
+      "y": 1.5877324038717813
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+    {
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+      "x": 1.5000650938916413,
+      "y": -1.1547072894263115
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+    {
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+      "x": 1.500052836819845,
+      "y": -0.5773455358291418
+    }
+  ],
+  "problem": "34 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/35.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinhex_035_6c433acba2e3b71c.json b/data/solutions/generated/triinhex_035_6c433acba2e3b71c.json
new file mode 100644
index 0000000000000000000000000000000000000000..2da99760b49fa70557d728e097557ddf8ee84676
--- /dev/null
+++ b/data/solutions/generated/triinhex_035_6c433acba2e3b71c.json
@@ -0,0 +1,272 @@
+{
+  "case": "triinhex@35",
+  "container": {
+    "circumradius": 2.576905263846017,
+    "orientation_radians": 0.0,
+    "side_length": 2.5769052638460166,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triinhex@35",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "5/2 = 2.500",
+    "metric_symbol": "s",
+    "metric_value": 2.5,
+    "reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.",
+    "source_image": "35.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triinhex@35",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "5/2 = 2.500",
+      "metric_symbol": "s",
+      "metric_value": 2.5,
+      "reference_text": "s = 5/2 = 2.500 | Found by Emerson Connelly | in April 2026.",
+      "source_image": "35.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/35.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles 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/triinhex/",
+    "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": 0.04758683000230462,
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+    {
+      "id": 25,
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+    },
+    {
+      "id": 26,
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+    },
+    {
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+      "y": -0.9398388050034157
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+    {
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+      "y": 1.6543237568323605
+    },
+    {
+      "id": 29,
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+      "x": -1.1915780373365839,
+      "y": 1.654308926334819
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.4651017229804646,
+      "x": -1.9193211394293834,
+      "y": 0.009306195885348785
+    },
+    {
+      "id": 31,
+      "rotation_radians": 1.5119567056164442,
+      "x": -0.8160051740154726,
+      "y": -1.897218626362677
+    },
+    {
+      "id": 32,
+      "rotation_radians": 1.5574269959305198,
+      "x": 1.0461183896336834,
+      "y": 1.6543494718618608
+    },
+    {
+      "id": 33,
+      "rotation_radians": -1.5707874074877601,
+      "x": 1.486558725215498,
+      "y": -1.3111565305809845
+    },
+    {
+      "id": 34,
+      "rotation_radians": -1.5704167024079048,
+      "x": 1.9863570841818954,
+      "y": -0.44510924754765707
+    },
+    {
+      "id": 35,
+      "rotation_radians": 1.5711809364727247,
+      "x": 1.486233657753099,
+      "y": -0.7336020136410033
+    }
+  ],
+  "problem": "35 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/35.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinhex_038_76fd196e8c79a5c9.json b/data/solutions/generated/triinhex_038_76fd196e8c79a5c9.json
new file mode 100644
index 0000000000000000000000000000000000000000..53c38c48c7accfa7ea4d2df1c852c9ae88c6294b
--- /dev/null
+++ b/data/solutions/generated/triinhex_038_76fd196e8c79a5c9.json
@@ -0,0 +1,290 @@
+{
+  "case": "triinhex@38",
+  "container": {
+    "circumradius": 2.6664956329108493,
+    "orientation_radians": 0.0,
+    "side_length": 2.666495632910849,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triinhex@38",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "8/3 = 2.666+",
+    "metric_symbol": "s",
+    "metric_value": 2.666,
+    "reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "39.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triinhex@38",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "8/3 = 2.666+",
+      "metric_symbol": "s",
+      "metric_value": 2.666,
+      "reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "39.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles 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/triinhex/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.5753472447414623,
+      "x": -0.0031588914886749564,
+      "y": 0.0033403261277854565
+    },
+    {
+      "id": 2,
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+      "x": -0.5045975748372464,
+      "y": 0.2895480537388663
+    },
+    {
+      "id": 3,
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+    {
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+    {
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+      "y": 1.7318979461253057
+    },
+    {
+      "id": 33,
+      "rotation_radians": -1.566239063200628,
+      "x": 1.4974839229811034,
+      "y": -1.442874226607535
+    },
+    {
+      "id": 34,
+      "rotation_radians": -1.566227984306913,
+      "x": 1.9988337190732146,
+      "y": -0.5745042158254369
+    },
+    {
+      "id": 35,
+      "rotation_radians": 1.575358853318183,
+      "x": 1.5001327966453464,
+      "y": -0.8654690673737815
+    },
+    {
+      "id": 36,
+      "rotation_radians": 1.5753532181661452,
+      "x": 0.9987863266363068,
+      "y": -1.7338349711362522
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+    {
+      "id": 37,
+      "rotation_radians": 1.5753677436388236,
+      "x": 2.0016415437375206,
+      "y": 0.003151057328621403
+    },
+    {
+      "id": 38,
+      "rotation_radians": -0.5236003205312204,
+      "x": -1.5110817041280482,
+      "y": 1.4238667957661695
+    }
+  ],
+  "problem": "38 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/39.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinhex_039_cf1c7ccbe8f975b2.json b/data/solutions/generated/triinhex_039_cf1c7ccbe8f975b2.json
new file mode 100644
index 0000000000000000000000000000000000000000..51b0b2008166b358965ca33f5c4d4ac31fe44dd6
--- /dev/null
+++ b/data/solutions/generated/triinhex_039_cf1c7ccbe8f975b2.json
@@ -0,0 +1,296 @@
+{
+  "case": "triinhex@39",
+  "container": {
+    "circumradius": 2.7126247045795115,
+    "orientation_radians": 0.0,
+    "side_length": 2.712624704579511,
+    "sides": 6,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triinhex@39",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "8/3 = 2.666+",
+    "metric_symbol": "s",
+    "metric_value": 2.666,
+    "reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "39.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+    "title": "Triangles in Hexagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triinhex@39",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "8/3 = 2.666+",
+      "metric_symbol": "s",
+      "metric_value": 2.666,
+      "reference_text": "s = 8/3 = 2.666+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "39.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinhex/39.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinhex/",
+      "title": "Triangles 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/triinhex/",
+    "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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+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.6568092876947906,
+      "x": 0.18981243459187744,
+      "y": 1.7739611629174805
+    },
+    {
+      "id": 29,
+      "rotation_radians": 1.601956164629881,
+      "x": -0.8767568956317713,
+      "y": 1.7721296594767137
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.5844535774074076,
+      "x": -1.9810841122481821,
+      "y": -0.11243258946080799
+    },
+    {
+      "id": 31,
+      "rotation_radians": 1.564000214563339,
+      "x": -0.763335638777901,
+      "y": -2.057130327401946
+    },
+    {
+      "id": 32,
+      "rotation_radians": 1.6544503049553596,
+      "x": 1.2906117018015906,
+      "y": 1.7738488460825876
+    },
+    {
+      "id": 33,
+      "rotation_radians": -1.5593042783621982,
+      "x": 1.5481008705979573,
+      "y": -1.4281829986603798
+    },
+    {
+      "id": 34,
+      "rotation_radians": -1.5416466374595743,
+      "x": 2.0609870005881366,
+      "y": -0.5223886650178067
+    },
+    {
+      "id": 35,
+      "rotation_radians": 1.6061967417491954,
+      "x": 1.5678897629359385,
+      "y": -0.8287112517372669
+    },
+    {
+      "id": 36,
+      "rotation_radians": 1.5822292682100731,
+      "x": 1.049150224492305,
+      "y": -1.7265678349260722
+    },
+    {
+      "id": 37,
+      "rotation_radians": 1.6201793171642076,
+      "x": 2.107025498138696,
+      "y": 0.10440744903632561
+    },
+    {
+      "id": 38,
+      "rotation_radians": 0.5235987683498997,
+      "x": -1.6163046041825335,
+      "y": 0.7441496838988427
+    },
+    {
+      "id": 39,
+      "rotation_radians": 1.570799090489449,
+      "x": -1.6163079815636106,
+      "y": 1.3215148269515073
+    }
+  ],
+  "problem": "39 equal items for Triangles in Hexagons",
+  "setup": "triinhex",
+  "source_image": "https://erich-friedman.github.io/packing/triinhex/39.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinhex/"
+}
diff --git a/data/solutions/generated/triinoct_021_550235b8e64c906b.json b/data/solutions/generated/triinoct_021_550235b8e64c906b.json
new file mode 100644
index 0000000000000000000000000000000000000000..ddb2af313fd0fce677aae37d717fa6f2936a3db1
--- /dev/null
+++ b/data/solutions/generated/triinoct_021_550235b8e64c906b.json
@@ -0,0 +1,188 @@
+{
+  "case": "triinoct@21",
+  "container": {
+    "circumradius": 2.003890517624121,
+    "orientation_radians": 0.0,
+    "side_length": 1.5337114027365102,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinoct@21",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/22/26",
+    "metric_expression": "1.52615+",
+    "metric_symbol": "s",
+    "metric_value": 1.52615,
+    "reference_text": "s = 1.52615+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "21.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinoct/21.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+    "title": "Triangles in Octagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinoct@21",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/22/26",
+      "metric_expression": "1.52615+",
+      "metric_symbol": "s",
+      "metric_value": 1.52615,
+      "reference_text": "s = 1.52615+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "21.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinoct/21.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+      "title": "Triangles in Octagons"
+    },
+    "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/triinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.14323619222473416,
+      "x": -0.6718622304451457,
+      "y": -0.06118214063421832
+    },
+    {
+      "id": 2,
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+      "x": 0.4717828397973261,
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+    {
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+    {
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+      "y": 0.545080976473041
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+      "y": 0.47011502560995055
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+    {
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+      "x": 0.3149992860060556,
+      "y": -0.5975545876278664
+    },
+    {
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+      "y": -0.04972560441828116
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+    {
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+    {
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+    {
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+      "y": -1.470526605708177
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+    {
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+      "y": 1.4623084474976336
+    },
+    {
+      "id": 17,
+      "rotation_radians": -3.266714664099441,
+      "x": 1.245466075631171,
+      "y": 0.5287831193454707
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.39270805433890027,
+      "x": -1.3562671401383641,
+      "y": -0.80914393120235
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.39270099043504086,
+      "x": -1.4361730027367337,
+      "y": 0.6162211372968012
+    },
+    {
+      "id": 20,
+      "rotation_radians": -3.5342868302224075,
+      "x": 1.4234158577914355,
+      "y": -0.6470272187750782
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.13273910027829322,
+      "x": 1.02199948713717,
+      "y": 1.0652834164023122
+    }
+  ],
+  "problem": "21 equal items for Triangles in Octagons",
+  "setup": "triinoct",
+  "source_image": "https://erich-friedman.github.io/packing/triinoct/21.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinoct/"
+}
diff --git a/data/solutions/generated/triinoct_022_a1924650c6f006ea.json b/data/solutions/generated/triinoct_022_a1924650c6f006ea.json
new file mode 100644
index 0000000000000000000000000000000000000000..128110f445575400426ae7b9d8eb5039cd845854
--- /dev/null
+++ b/data/solutions/generated/triinoct_022_a1924650c6f006ea.json
@@ -0,0 +1,194 @@
+{
+  "case": "triinoct@22",
+  "container": {
+    "circumradius": 2.036940808566546,
+    "orientation_radians": 0.0,
+    "side_length": 1.5590070002935343,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinoct@22",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/22/26",
+    "metric_expression": "1.55545+",
+    "metric_symbol": "s",
+    "metric_value": 1.55545,
+    "reference_text": "s = 1.55545+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "22.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinoct/22.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+    "title": "Triangles in Octagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinoct@22",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/22/26",
+      "metric_expression": "1.55545+",
+      "metric_symbol": "s",
+      "metric_value": 1.55545,
+      "reference_text": "s = 1.55545+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "22.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinoct/22.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+      "title": "Triangles in Octagons"
+    },
+    "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/triinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.9088027236181184,
+      "x": 0.4898648327039741,
+      "y": 0.044767542041637104
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+    {
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+      "y": -0.9921559809786146
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+    {
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+    {
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+      "x": -0.6610408880934154,
+      "y": -1.0630146604397772
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.9250346719769075,
+      "x": -0.22569264309928602,
+      "y": -1.5054436307706995
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.9084873300187775,
+      "x": -0.3563667522834625,
+      "y": 1.5726407044052535
+    },
+    {
+      "id": 19,
+      "rotation_radians": -2.2252175753084913,
+      "x": 0.3513530665183454,
+      "y": -1.5788258533374862
+    },
+    {
+      "id": 20,
+      "rotation_radians": -2.2331737871355095,
+      "x": 0.21674496682534763,
+      "y": 1.501798698409567
+    },
+    {
+      "id": 21,
+      "rotation_radians": -2.4870924057817256,
+      "x": -1.4432431955360827,
+      "y": 0.6789512089915085
+    },
+    {
+      "id": 22,
+      "rotation_radians": -1.7016913457467449,
+      "x": -1.4153273439204141,
+      "y": -0.7463362205599944
+    }
+  ],
+  "problem": "22 equal items for Triangles in Octagons",
+  "setup": "triinoct",
+  "source_image": "https://erich-friedman.github.io/packing/triinoct/22.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinoct/"
+}
diff --git a/data/solutions/generated/triinoct_023_4ca1a825a22b1f04.json b/data/solutions/generated/triinoct_023_4ca1a825a22b1f04.json
new file mode 100644
index 0000000000000000000000000000000000000000..5c1583e565b4638d435b859d7fb5b18c5f8c633e
--- /dev/null
+++ b/data/solutions/generated/triinoct_023_4ca1a825a22b1f04.json
@@ -0,0 +1,200 @@
+{
+  "case": "triinoct@23",
+  "container": {
+    "circumradius": 2.0708388330217105,
+    "orientation_radians": 0.0,
+    "side_length": 1.5849514249913303,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinoct@23",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/22/26",
+    "metric_expression": "1.58458+",
+    "metric_symbol": "s",
+    "metric_value": 1.58458,
+    "reference_text": "s = 1.58458+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "23.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinoct/23.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+    "title": "Triangles in Octagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinoct@23",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/22/26",
+      "metric_expression": "1.58458+",
+      "metric_symbol": "s",
+      "metric_value": 1.58458,
+      "reference_text": "s = 1.58458+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "23.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinoct/23.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+      "title": "Triangles in Octagons"
+    },
+    "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/triinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.42752391980528215,
+      "x": 0.05777659962307684,
+      "y": 0.6212030402700558
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+      "x": 1.1028230287600964,
+      "y": 0.6315210905833348
+    },
+    {
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+      "x": -0.999024690987579,
+      "y": -0.4857422994205837
+    },
+    {
+      "id": 12,
+      "rotation_radians": 1.4746987924206971,
+      "x": 1.030220633213545,
+      "y": -0.5010835413654589
+    },
+    {
+      "id": 13,
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+      "x": 1.600822261528121,
+      "y": 0.33541028471680434
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.42751381446843423,
+      "x": 1.5454167964384138,
+      "y": -0.23931857443793084
+    },
+    {
+      "id": 15,
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+      "x": -1.6006620849860769,
+      "y": -0.33500281879172866
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.4749442072853074,
+      "x": -1.5454033406826755,
+      "y": 0.23972053403072577
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.4275648233759445,
+      "x": -0.5148158014127981,
+      "y": 1.3276024783839324
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.13055356873679433,
+      "x": 0.7728777559537089,
+      "y": 1.4380440820022422
+    },
+    {
+      "id": 19,
+      "rotation_radians": 1.4730032612069277,
+      "x": -0.5085329693252447,
+      "y": -1.4039148929614318
+    },
+    {
+      "id": 20,
+      "rotation_radians": 1.4747182696168855,
+      "x": 0.5267997220435172,
+      "y": -1.3226322583330616
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.4747561608059319,
+      "x": -1.040216984244298,
+      "y": 1.0881911792511438
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.4275027911575632,
+      "x": 1.0522127038087863,
+      "y": -1.0832422759719538
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.42774341508298,
+      "x": -0.9790874846845073,
+      "y": -1.0676893028848453
+    }
+  ],
+  "problem": "23 equal items for Triangles in Octagons",
+  "setup": "triinoct",
+  "source_image": "https://erich-friedman.github.io/packing/triinoct/23.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinoct/"
+}
diff --git a/data/solutions/generated/triinoct_024_e197b92ecac28558.json b/data/solutions/generated/triinoct_024_e197b92ecac28558.json
new file mode 100644
index 0000000000000000000000000000000000000000..76346dccc97a477166e67ffb2c7c9520f811e57c
--- /dev/null
+++ b/data/solutions/generated/triinoct_024_e197b92ecac28558.json
@@ -0,0 +1,206 @@
+{
+  "case": "triinoct@24",
+  "container": {
+    "circumradius": 2.094763549694726,
+    "orientation_radians": 0.0,
+    "side_length": 1.6032626103809142,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinoct@24",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/22/26",
+    "metric_expression": "1.60261+",
+    "metric_symbol": "s",
+    "metric_value": 1.60261,
+    "reference_text": "s = 1.60261+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "24.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinoct/24.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+    "title": "Triangles in Octagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinoct@24",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/22/26",
+      "metric_expression": "1.60261+",
+      "metric_symbol": "s",
+      "metric_value": 1.60261,
+      "reference_text": "s = 1.60261+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "24.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinoct/24.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+      "title": "Triangles in Octagons"
+    },
+    "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/triinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.9580452782185809,
+      "x": 0.5767449169696428,
+      "y": -0.029527674743214587
+    },
+    {
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+    {
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+      "y": -0.5029456292723087
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+    {
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+      "x": -0.33319894000675654,
+      "y": -0.49400488448670404
+    },
+    {
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+      "x": -0.24518492905853911,
+      "y": 0.5027527927922512
+    },
+    {
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+      "x": 1.154952610939419,
+      "y": -0.04586578284416638
+    },
+    {
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+      "y": 0.04740729376135834
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+    {
+      "id": 15,
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+      "y": 1.0264720728589662
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+    {
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+    {
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+      "x": 0.3310559471451874,
+      "y": -1.6219342172619868
+    },
+    {
+      "id": 20,
+      "rotation_radians": -2.176922060290676,
+      "x": 0.24649587378916124,
+      "y": 1.5726479090612178
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+    {
+      "id": 21,
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+      "y": 0.5706174639115749
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+    {
+      "id": 22,
+      "rotation_radians": -2.173973138364147,
+      "x": -1.3541663504980321,
+      "y": -0.5217974948384793
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.9580549102079876,
+      "x": -1.066408150074295,
+      "y": 1.0429532341027192
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.9676202143401137,
+      "x": -1.1061365995247867,
+      "y": -1.0431767180645293
+    }
+  ],
+  "problem": "24 equal items for Triangles in Octagons",
+  "setup": "triinoct",
+  "source_image": "https://erich-friedman.github.io/packing/triinoct/24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinoct/"
+}
diff --git a/data/solutions/generated/triinoct_025_4e1b861b138850ae.json b/data/solutions/generated/triinoct_025_4e1b861b138850ae.json
new file mode 100644
index 0000000000000000000000000000000000000000..68651c6e9d3dc0c3df8db56abca1ab72505984bd
--- /dev/null
+++ b/data/solutions/generated/triinoct_025_4e1b861b138850ae.json
@@ -0,0 +1,212 @@
+{
+  "case": "triinoct@25",
+  "container": {
+    "circumradius": 2.1595921206683837,
+    "orientation_radians": 0.0,
+    "side_length": 1.6528802504919604,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinoct@25",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/22/26",
+    "metric_expression": "1.63797+",
+    "metric_symbol": "s",
+    "metric_value": 1.63797,
+    "reference_text": "s = 1.63797+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "25.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinoct/25.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+    "title": "Triangles in Octagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000700021000353,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinoct@25",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/22/26",
+      "metric_expression": "1.63797+",
+      "metric_symbol": "s",
+      "metric_value": 1.63797,
+      "reference_text": "s = 1.63797+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "25.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinoct/25.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+      "title": "Triangles in Octagons"
+    },
+    "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/triinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.6607090227708314,
+      "x": -0.15301413940911507,
+      "y": -0.4704968226682609
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+    {
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+    {
+      "id": 15,
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+      "x": 0.9943601248306615,
+      "y": 0.5350368210798753
+    },
+    {
+      "id": 16,
+      "rotation_radians": -3.8023935083239944,
+      "x": -1.1486641862579015,
+      "y": 0.6063722631138659
+    },
+    {
+      "id": 17,
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+      "x": -1.6192775435912548,
+      "y": 0.23089957123273894
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.6606373080956158,
+      "x": 1.6581779408915442,
+      "y": 0.4481628952759825
+    },
+    {
+      "id": 19,
+      "rotation_radians": -3.8021512807702393,
+      "x": 1.5863445387427708,
+      "y": -0.12482489783355051
+    },
+    {
+      "id": 20,
+      "rotation_radians": -3.8023594661220836,
+      "x": -1.698240352622639,
+      "y": -0.341085296268838
+    },
+    {
+      "id": 21,
+      "rotation_radians": -3.806866739232915,
+      "x": 0.6205778119250358,
+      "y": 1.465415092571935
+    },
+    {
+      "id": 22,
+      "rotation_radians": -3.802512113476881,
+      "x": -0.5327852281499631,
+      "y": 1.395679405077183
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.6608784215973745,
+      "x": -1.0676472256174847,
+      "y": 1.1780991400021346
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.6651939489658798,
+      "x": 1.0748823464534767,
+      "y": 1.1090022815166833
+    },
+    {
+      "id": 25,
+      "rotation_radians": -0.027018010362686112,
+      "x": 0.30209158982651385,
+      "y": -1.6675536364496693
+    }
+  ],
+  "problem": "25 equal items for Triangles in Octagons",
+  "setup": "triinoct",
+  "source_image": "https://erich-friedman.github.io/packing/triinoct/25.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinoct/"
+}
diff --git a/data/solutions/generated/triinoct_026_cbcb6c755dc046de.json b/data/solutions/generated/triinoct_026_cbcb6c755dc046de.json
new file mode 100644
index 0000000000000000000000000000000000000000..3d97bf316686a828a3166a8410a2233aa9dec7a5
--- /dev/null
+++ b/data/solutions/generated/triinoct_026_cbcb6c755dc046de.json
@@ -0,0 +1,218 @@
+{
+  "case": "triinoct@26",
+  "container": {
+    "circumradius": 2.210014693893155,
+    "orientation_radians": 0.0,
+    "side_length": 1.6914720172726316,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinoct@26",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/22/26",
+    "metric_expression": "1.67666+",
+    "metric_symbol": "s",
+    "metric_value": 1.67666,
+    "reference_text": "s = 1.67666+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "26.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinoct/26.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+    "title": "Triangles in Octagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinoct@26",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/22/26",
+      "metric_expression": "1.67666+",
+      "metric_symbol": "s",
+      "metric_value": 1.67666,
+      "reference_text": "s = 1.67666+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "26.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinoct/26.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+      "title": "Triangles in Octagons"
+    },
+    "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/triinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.6598128025579123,
+      "x": -0.09306103219506309,
+      "y": -0.5851284382427087
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+    {
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+    {
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+      "x": -0.4677428666729768,
+      "y": -1.1206503258876577
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+      "x": 1.0673385892509004,
+      "y": -0.25905233636253083
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+    {
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+      "x": -1.0182641049305468,
+      "y": -1.3429934274911812
+    },
+    {
+      "id": 11,
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+      "x": 0.7182270010425329,
+      "y": -1.068577925345008
+    },
+    {
+      "id": 12,
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+    },
+    {
+      "id": 13,
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+      "x": -1.480156608023904,
+      "y": -0.9948765355330171
+    },
+    {
+      "id": 14,
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+      "x": 0.05742596331988651,
+      "y": 1.2805068311635492
+    },
+    {
+      "id": 15,
+      "rotation_radians": -3.796359574789445,
+      "x": 0.9875680536459087,
+      "y": 0.591944230047088
+    },
+    {
+      "id": 16,
+      "rotation_radians": -3.7454671751597215,
+      "x": -1.0316971994960318,
+      "y": 0.6297161620013061
+    },
+    {
+      "id": 17,
+      "rotation_radians": -0.48161034269533926,
+      "x": -1.657949140634742,
+      "y": 0.46542320034952717
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.6488371864496076,
+      "x": 1.6745317965815023,
+      "y": 0.5292809694146718
+    },
+    {
+      "id": 19,
+      "rotation_radians": -3.7880473355240065,
+      "x": 1.6064139185574247,
+      "y": -0.051433149610052235
+    },
+    {
+      "id": 20,
+      "rotation_radians": -3.6232370131773806,
+      "x": -1.6337173444175546,
+      "y": -0.11144529620443991
+    },
+    {
+      "id": 21,
+      "rotation_radians": -3.836154228382814,
+      "x": 0.6023679214666333,
+      "y": 1.5366650934705983
+    },
+    {
+      "id": 22,
+      "rotation_radians": -3.7454475633042814,
+      "x": -0.5453136120002856,
+      "y": 1.4594363930260028
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.6038756036050995,
+      "x": -1.0668799340071138,
+      "y": 1.2117736536777917
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.6548731452548425,
+      "x": 1.0686280691922914,
+      "y": 1.1636715720132582
+    },
+    {
+      "id": 25,
+      "rotation_radians": -0.7411173611362156,
+      "x": -0.19819945475221235,
+      "y": -1.7259084044976911
+    },
+    {
+      "id": 26,
+      "rotation_radians": -4.050898321951963,
+      "x": 0.4449430707751367,
+      "y": -1.580747068050869
+    }
+  ],
+  "problem": "26 equal items for Triangles in Octagons",
+  "setup": "triinoct",
+  "source_image": "https://erich-friedman.github.io/packing/triinoct/26.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinoct/"
+}
diff --git a/data/solutions/generated/triinoct_027_836b5a3b2c412e9b.json b/data/solutions/generated/triinoct_027_836b5a3b2c412e9b.json
new file mode 100644
index 0000000000000000000000000000000000000000..97811a4d0a803230efd752fccfa5ca959c008b6d
--- /dev/null
+++ b/data/solutions/generated/triinoct_027_836b5a3b2c412e9b.json
@@ -0,0 +1,224 @@
+{
+  "case": "triinoct@27",
+  "container": {
+    "circumradius": 2.271564118212042,
+    "orientation_radians": 0.0,
+    "side_length": 1.7385799071895256,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinoct@27",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/22/26",
+    "metric_expression": "1.70882+",
+    "metric_symbol": "s",
+    "metric_value": 1.70882,
+    "reference_text": "s = 1.70882+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "27.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinoct/27.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+    "title": "Triangles in Octagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinoct@27",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/22/26",
+      "metric_expression": "1.70882+",
+      "metric_symbol": "s",
+      "metric_value": 1.70882,
+      "reference_text": "s = 1.70882+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "27.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinoct/27.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+      "title": "Triangles in Octagons"
+    },
+    "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/triinoct/",
+    "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": 1.4486347565462603
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+    {
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+    {
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+      "x": 0.14562523126686902,
+      "y": -1.0418369412532307
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+  ],
+  "problem": "27 equal items for Triangles in Octagons",
+  "setup": "triinoct",
+  "source_image": "https://erich-friedman.github.io/packing/triinoct/27.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinoct/"
+}
diff --git a/data/solutions/generated/triinoct_028_728bf65e8a483e5e.json b/data/solutions/generated/triinoct_028_728bf65e8a483e5e.json
new file mode 100644
index 0000000000000000000000000000000000000000..8b872da1802c253d590b01fa860e2b14e98abd16
--- /dev/null
+++ b/data/solutions/generated/triinoct_028_728bf65e8a483e5e.json
@@ -0,0 +1,230 @@
+{
+  "case": "triinoct@28",
+  "container": {
+    "circumradius": 2.2912021670970564,
+    "orientation_radians": 0.0,
+    "side_length": 1.753610219094067,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinoct@28",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/22/26",
+    "metric_expression": "1.73954+",
+    "metric_symbol": "s",
+    "metric_value": 1.73954,
+    "reference_text": "s = 1.73954+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "28.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinoct/28.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+    "title": "Triangles in Octagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinoct@28",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/22/26",
+      "metric_expression": "1.73954+",
+      "metric_symbol": "s",
+      "metric_value": 1.73954,
+      "reference_text": "s = 1.73954+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "28.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinoct/28.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+      "title": "Triangles in Octagons"
+    },
+    "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/triinoct/",
+    "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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+      "x": -1.0946998483176973,
+      "y": 1.3794815324508347
+    },
+    {
+      "id": 23,
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+      "x": -1.661069293865027,
+      "y": -0.442605770705713
+    },
+    {
+      "id": 24,
+      "rotation_radians": -2.47592853860686,
+      "x": -1.7428090048266305,
+      "y": 0.12894926659310194
+    },
+    {
+      "id": 25,
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+    },
+    {
+      "id": 26,
+      "rotation_radians": 1.7217027476065057,
+      "x": 0.25185961942251356,
+      "y": -1.753913969483781
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.805349420528651,
+      "x": 1.2200920817003724,
+      "y": 1.2038018870566238
+    },
+    {
+      "id": 28,
+      "rotation_radians": 0.8081101383542635,
+      "x": 1.7804829172483045,
+      "y": -0.14743907300587059
+    }
+  ],
+  "problem": "28 equal items for Triangles in Octagons",
+  "setup": "triinoct",
+  "source_image": "https://erich-friedman.github.io/packing/triinoct/28.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinoct/"
+}
diff --git a/data/solutions/generated/triinoct_029_f6d5bdc33f1fd083.json b/data/solutions/generated/triinoct_029_f6d5bdc33f1fd083.json
new file mode 100644
index 0000000000000000000000000000000000000000..9f39edb01c0938ec4e30b04962cbb3870fecce4b
--- /dev/null
+++ b/data/solutions/generated/triinoct_029_f6d5bdc33f1fd083.json
@@ -0,0 +1,236 @@
+{
+  "case": "triinoct@29",
+  "container": {
+    "circumradius": 2.3452354327508447,
+    "orientation_radians": 0.0,
+    "side_length": 1.7949654902186398,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinoct@29",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/22/26",
+    "metric_expression": "1.75576+",
+    "metric_symbol": "s",
+    "metric_value": 1.75576,
+    "reference_text": "s = 1.75576+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "29.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinoct/29.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+    "title": "Triangles in Octagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinoct@29",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/22/26",
+      "metric_expression": "1.75576+",
+      "metric_symbol": "s",
+      "metric_value": 1.75576,
+      "reference_text": "s = 1.75576+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "29.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinoct/29.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+      "title": "Triangles in Octagons"
+    },
+    "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/triinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "x": -0.5082496267037514,
+      "y": 1.347436139356641
+    },
+    {
+      "id": 26,
+      "rotation_radians": 1.1846812306858028,
+      "x": 0.2940501071263739,
+      "y": -1.2111828049882098
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.393028148592449,
+      "x": -0.5389863356335013,
+      "y": -1.156390580730917
+    },
+    {
+      "id": 28,
+      "rotation_radians": 0.137486369637589,
+      "x": 0.22603165596450464,
+      "y": -1.80680137966306
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.9162960103932338,
+      "x": -1.0629500552445856,
+      "y": 1.592471925497142
+    }
+  ],
+  "problem": "29 equal items for Triangles in Octagons",
+  "setup": "triinoct",
+  "source_image": "https://erich-friedman.github.io/packing/triinoct/29.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinoct/"
+}
diff --git a/data/solutions/generated/triinoct_030_55871e661d418192.json b/data/solutions/generated/triinoct_030_55871e661d418192.json
new file mode 100644
index 0000000000000000000000000000000000000000..b5845e75183f46e2bc1229d2c2abc7c31aaee3cf
--- /dev/null
+++ b/data/solutions/generated/triinoct_030_55871e661d418192.json
@@ -0,0 +1,242 @@
+{
+  "case": "triinoct@30",
+  "container": {
+    "circumradius": 2.360619667060012,
+    "orientation_radians": 0.0,
+    "side_length": 1.8067400733981216,
+    "sides": 8,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinoct@30",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "3/22/26",
+    "metric_expression": "1.78101+",
+    "metric_symbol": "s",
+    "metric_value": 1.78101,
+    "reference_text": "s = 1.78101+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "30.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinoct/30.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+    "title": "Triangles in Octagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinoct@30",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "3/22/26",
+      "metric_expression": "1.78101+",
+      "metric_symbol": "s",
+      "metric_value": 1.78101,
+      "reference_text": "s = 1.78101+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "30.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinoct/30.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinoct/",
+      "title": "Triangles in Octagons"
+    },
+    "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/triinoct/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.24969534573711746,
+      "x": -0.08993251452553454,
+      "y": 0.2954226015530591
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+      "x": -1.882429842771135,
+      "y": -0.24255342219183512
+    },
+    {
+      "id": 18,
+      "rotation_radians": -2.89332721317214,
+      "x": 0.4679738201215797,
+      "y": -1.1850119193066877
+    },
+    {
+      "id": 19,
+      "rotation_radians": -3.125127011240319,
+      "x": 1.371238829654129,
+      "y": 1.1717924332508955
+    },
+    {
+      "id": 20,
+      "rotation_radians": -3.1442947496737497,
+      "x": 1.4509234332953087,
+      "y": -1.0017484277320865
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.0034638306053475596,
+      "x": 1.160520169616587,
+      "y": -1.5012035053364443
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.16021728804821925,
+      "x": 0.8899833841023518,
+      "y": 1.6637351110260483
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.5216500894060352,
+      "x": -0.9970688491729824,
+      "y": 1.4510924859429533
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.2520890369324395,
+      "x": -0.5542425175546466,
+      "y": -1.3732847365780363
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.016441645571059156,
+      "x": 1.783336304933647,
+      "y": -0.009484805802504695
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.2520999105905954,
+      "x": -1.5176258565827476,
+      "y": -1.1051578693308344
+    },
+    {
+      "id": 27,
+      "rotation_radians": -2.8894985968996556,
+      "x": -1.113343286626549,
+      "y": -1.5173514847096035
+    },
+    {
+      "id": 28,
+      "rotation_radians": -2.891886597185326,
+      "x": -0.2484224650734644,
+      "y": -1.8833124204105738
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.24826219519634962,
+      "x": 0.3118317827977145,
+      "y": -1.7408595406020355
+    },
+    {
+      "id": 30,
+      "rotation_radians": -0.5247750321200261,
+      "x": -1.4978698219710285,
+      "y": 1.1630133553352155
+    }
+  ],
+  "problem": "30 equal items for Triangles in Octagons",
+  "setup": "triinoct",
+  "source_image": "https://erich-friedman.github.io/packing/triinoct/30.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinoct/"
+}
diff --git a/data/solutions/generated/triinpen_021_115c20fad199fe9d.json b/data/solutions/generated/triinpen_021_115c20fad199fe9d.json
new file mode 100644
index 0000000000000000000000000000000000000000..02925887979edd38fdbb7263e3124eab7cdfdeb1
--- /dev/null
+++ b/data/solutions/generated/triinpen_021_115c20fad199fe9d.json
@@ -0,0 +1,188 @@
+{
+  "case": "triinpen@21",
+  "container": {
+    "circumradius": 2.1100378608614,
+    "orientation_radians": 0.0,
+    "side_length": 2.4804982727861766,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@21",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "2.479+",
+    "metric_symbol": "s",
+    "metric_value": 2.479,
+    "reference_text": "s = 2.479+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "21.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/21.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@21",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "2.479+",
+      "metric_symbol": "s",
+      "metric_value": 2.479,
+      "reference_text": "s = 2.479+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "21.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/21.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "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/triinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 2.0929265681804674,
+      "x": -0.5523268053297729,
+      "y": -0.009266160753280307
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+    {
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+      "x": -0.2756405493599927,
+      "y": 0.49771220059329696
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+    {
+      "id": 4,
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+      "y": 0.003305522759426516
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+      "y": 0.865734151220734
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+    {
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+    {
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+      "x": -0.5524777928343507,
+      "y": 1.0112127510417457
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.012559493429466217,
+      "x": -0.5524265090949693,
+      "y": -1.0176871463603008
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.004601776425474523,
+      "x": -1.4160686997768472,
+      "y": -0.5185876917791443
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+    {
+      "id": 13,
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+      "x": -1.4136839086373825,
+      "y": 0.5135025544329922
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+    {
+      "id": 14,
+      "rotation_radians": 1.0457279420740928,
+      "x": -1.129692091284093,
+      "y": -0.008552273288658279
+    },
+    {
+      "id": 15,
+      "rotation_radians": 1.0597569343746958,
+      "x": -1.1297355063948378,
+      "y": -1.0259294969972683
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.0338482917730798,
+      "x": -1.12973039558134,
+      "y": 1.024565979956189
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.0310519111681091,
+      "x": -0.04448758724372389,
+      "y": 1.3815684478441386
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.0624272584737393,
+      "x": -0.03679351080720229,
+      "y": -1.3836554776690217
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.015230847947360054,
+      "x": 0.5405054484717287,
+      "y": -1.3744778805059525
+    },
+    {
+      "id": 20,
+      "rotation_radians": 2.0867979341642635,
+      "x": 0.5371156537442312,
+      "y": 1.3746633381730475
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.4192229852387899,
+      "x": 1.4929156079572072,
+      "y": -0.32824810095480844
+    }
+  ],
+  "problem": "21 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/21.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_022_b3ecf4aa9beda411.json b/data/solutions/generated/triinpen_022_b3ecf4aa9beda411.json
new file mode 100644
index 0000000000000000000000000000000000000000..bc3523a26fc41ce9224eb6bd73b05834c8cfa88f
--- /dev/null
+++ b/data/solutions/generated/triinpen_022_b3ecf4aa9beda411.json
@@ -0,0 +1,194 @@
+{
+  "case": "triinpen@22",
+  "container": {
+    "circumradius": 2.188269840341113,
+    "orientation_radians": 0.0,
+    "side_length": 2.572465480377822,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@22",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "2.56740+",
+    "metric_symbol": "s",
+    "metric_value": 2.5674,
+    "reference_text": "s = 2.56740+ | Found by Ian Watson | in April 2026.",
+    "source_image": "22.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/22.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@22",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "2.56740+",
+      "metric_symbol": "s",
+      "metric_value": 2.5674,
+      "reference_text": "s = 2.56740+ | Found by Ian Watson | in April 2026.",
+      "source_image": "22.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/22.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "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/triinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.18027810414089152,
+      "x": -0.6362903403132092,
+      "y": -0.07822963900486395
+    },
+    {
+      "id": 2,
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+      "x": -0.21834679194560214,
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+    {
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+    {
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+      "x": 0.3753214554719906,
+      "y": -0.4971692677663237
+    },
+    {
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+    },
+    {
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+      "x": 0.729160670372139,
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+    },
+    {
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+    },
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+      "x": -0.6048210189219044,
+      "y": 1.0559954472888675
+    },
+    {
+      "id": 11,
+      "rotation_radians": -0.030494144748831303,
+      "x": -0.5769930744587211,
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+    {
+      "id": 13,
+      "rotation_radians": -0.18190826426215123,
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+      "y": 0.5823206248891016
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+    {
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+    {
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+      "y": 1.171042453647064
+    },
+    {
+      "id": 17,
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+      "y": 1.4872114436742332
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+    {
+      "id": 18,
+      "rotation_radians": -3.161445462175335,
+      "x": -0.02855592982416945,
+      "y": -1.4370778771506916
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.020448922760262875,
+      "x": 0.5490066354297298,
+      "y": -1.4487217076482235
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.20758763891847576,
+      "x": 0.35485846755561856,
+      "y": 1.3696785680122292
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.3844742077392061,
+      "x": 1.4643432783801555,
+      "y": -0.4762936976442672
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.20758534910790197,
+      "x": 1.1218783468496178,
+      "y": 0.8091519815751489
+    }
+  ],
+  "problem": "22 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/22.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_023_b2f9cfacd50b72e9.json b/data/solutions/generated/triinpen_023_b2f9cfacd50b72e9.json
new file mode 100644
index 0000000000000000000000000000000000000000..26ad89481e0c1959e1c95e5ee102e7181c132a5f
--- /dev/null
+++ b/data/solutions/generated/triinpen_023_b2f9cfacd50b72e9.json
@@ -0,0 +1,200 @@
+{
+  "case": "triinpen@23",
+  "container": {
+    "circumradius": 2.2386395885701447,
+    "orientation_radians": 0.0,
+    "side_length": 2.6316786707192414,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@23",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "2.61831+",
+    "metric_symbol": "s",
+    "metric_value": 2.61831,
+    "reference_text": "s = 2.61831+ | Found by Ian Watson | in April 2026.",
+    "source_image": "23.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/23.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@23",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "2.61831+",
+      "metric_symbol": "s",
+      "metric_value": 2.61831,
+      "reference_text": "s = 2.61831+ | Found by Ian Watson | in April 2026.",
+      "source_image": "23.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/23.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "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/triinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.08078543416610404,
+      "x": -0.6601424763753608,
+      "y": -0.010272511413577512
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+    {
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+    },
+    {
+      "id": 17,
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+      "x": -0.06763193781136742,
+      "y": 1.5718125583368474
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+    {
+      "id": 18,
+      "rotation_radians": -2.7592081290462596,
+      "x": 0.05049778097478714,
+      "y": -1.5027730821662992
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.41496332481246767,
+      "x": 0.7351902566509882,
+      "y": -1.5488706301152257
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.41985744984614265,
+      "x": 0.7417489596342642,
+      "y": 1.5468936168837195
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.4188799860035302,
+      "x": 1.3432844885623834,
+      "y": -0.7412162233135663
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.41145797253434135,
+      "x": 1.3730249142382902,
+      "y": 0.6939784989725916
+    },
+    {
+      "id": 23,
+      "rotation_radians": -3.5538772795943583,
+      "x": 1.4478735689409024,
+      "y": 0.10565559753032688
+    }
+  ],
+  "problem": "23 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/23.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_024_76211a17aba30b36.json b/data/solutions/generated/triinpen_024_76211a17aba30b36.json
new file mode 100644
index 0000000000000000000000000000000000000000..f317e5ad6a19580bb82246403d1d489507f615f2
--- /dev/null
+++ b/data/solutions/generated/triinpen_024_76211a17aba30b36.json
@@ -0,0 +1,206 @@
+{
+  "case": "triinpen@24",
+  "container": {
+    "circumradius": 2.3082818217361782,
+    "orientation_radians": 0.0,
+    "side_length": 2.713548025902658,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@24",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "2.66641+",
+    "metric_symbol": "s",
+    "metric_value": 2.66641,
+    "reference_text": "s = 2.66641+ | Found by Ian Watson | in April 2026.",
+    "source_image": "24.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/24.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@24",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "2.66641+",
+      "metric_symbol": "s",
+      "metric_value": 2.66641,
+      "reference_text": "s = 2.66641+ | Found by Ian Watson | in April 2026.",
+      "source_image": "24.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/24.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "generator": "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/triinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 7.459293048575174e-05,
+      "x": -0.6822883192044209,
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+      "x": -0.9031550410641106,
+      "y": -1.3610378189819359
+    },
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+    {
+      "id": 13,
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+      "x": -1.548381893007028,
+      "y": 0.866650436910066
+    },
+    {
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+      "rotation_radians": 1.0472811352471048,
+      "x": -1.2596615615166031,
+      "y": 0.3666637180355881
+    },
+    {
+      "id": 15,
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+      "x": -0.3352848076835116,
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+    },
+    {
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+      "y": 1.3365604215361542
+    },
+    {
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+      "y": 1.7355101533150739
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.270084395707679,
+      "x": 0.05690454159399992,
+      "y": -1.6714573627802891
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.460778727700991,
+      "x": 0.7495458262227315,
+      "y": -1.6190761655531436
+    },
+    {
+      "id": 20,
+      "rotation_radians": 1.6976544986036266,
+      "x": 0.8525692042645487,
+      "y": 1.493780329596002
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.5480801241626019,
+      "x": 0.850796335711167,
+      "y": -1.027081428198389
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.6793925224704078,
+      "x": 1.4582708108551765,
+      "y": 0.6755194593700196
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.6321950228996794,
+      "x": 1.5208261283164612,
+      "y": 0.10155289416789177
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.470921875526154,
+      "x": 1.3745256893948732,
+      "y": -0.7504859421873863
+    }
+  ],
+  "problem": "24 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_025_cc904cb82492c4b0.json b/data/solutions/generated/triinpen_025_cc904cb82492c4b0.json
new file mode 100644
index 0000000000000000000000000000000000000000..56325bab5bf098b049ba2ce54ff819354eef927d
--- /dev/null
+++ b/data/solutions/generated/triinpen_025_cc904cb82492c4b0.json
@@ -0,0 +1,212 @@
+{
+  "case": "triinpen@25",
+  "container": {
+    "circumradius": 2.360578355429412,
+    "orientation_radians": 0.0,
+    "side_length": 2.7750262884044563,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@25",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "2.720+",
+    "metric_symbol": "s",
+    "metric_value": 2.72,
+    "reference_text": "s = 2.720+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "25.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/25.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@25",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "2.720+",
+      "metric_symbol": "s",
+      "metric_value": 2.72,
+      "reference_text": "s = 2.720+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "25.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/25.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles 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/triinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.32800471976914847,
+      "x": -0.28146817211522257,
+      "y": -0.18196237014777292
+    },
+    {
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+      "y": -1.7086293060175952
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+    {
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+      "x": 0.7197564631953696,
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+      "x": 1.2043348219546115,
+      "y": 0.34280505809771067
+    },
+    {
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+    {
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+      "x": -1.6190054920351642,
+      "y": 0.830317414420908
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+      "id": 14,
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+      "x": 0.9204987889033934,
+      "y": -1.443824080771277
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+    {
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+      "y": -0.9565836352842663
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+    {
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+      "x": -1.3323846513834452,
+      "y": 0.3259390754704834
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+    {
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+      "y": 1.43953860833152
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+    {
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+    {
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+      "rotation_radians": 1.375206899162783,
+      "x": -1.3631548520393646,
+      "y": -1.2015054611373999
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+    {
+      "id": 20,
+      "rotation_radians": 1.884960223012151,
+      "x": -0.25066651488882846,
+      "y": 1.3194959381904556
+    },
+    {
+      "id": 21,
+      "rotation_radians": 1.5423396159313256,
+      "x": 1.0239448588060196,
+      "y": -0.8602971448204895
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.884966691082685,
+      "x": 0.7002974995937592,
+      "y": 1.6279144382942816
+    },
+    {
+      "id": 23,
+      "rotation_radians": 1.5466296677545601,
+      "x": 1.2182785500306854,
+      "y": 0.9200096153697425
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.4702771328295224,
+      "x": 1.5463167563495441,
+      "y": -0.5865314359007054
+    },
+    {
+      "id": 25,
+      "rotation_radians": 0.8377571139218656,
+      "x": 0.1356730730485045,
+      "y": 1.7485691465082949
+    }
+  ],
+  "problem": "25 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/25.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_026_810173856676a6fb.json b/data/solutions/generated/triinpen_026_810173856676a6fb.json
new file mode 100644
index 0000000000000000000000000000000000000000..c1e48f5a680f82b74a0df7d8bef71d07fb4d71e1
--- /dev/null
+++ b/data/solutions/generated/triinpen_026_810173856676a6fb.json
@@ -0,0 +1,218 @@
+{
+  "case": "triinpen@26",
+  "container": {
+    "circumradius": 2.39024467844567,
+    "orientation_radians": 0.0,
+    "side_length": 2.8099011427218588,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@26",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "2.771+",
+    "metric_symbol": "s",
+    "metric_value": 2.771,
+    "reference_text": "s = 2.771+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "26.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/26.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@26",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "2.771+",
+      "metric_symbol": "s",
+      "metric_value": 2.771,
+      "reference_text": "s = 2.771+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "26.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/26.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "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/triinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.7295951293785414,
+      "x": 0.528399443379336,
+      "y": 0.08250450117013546
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+      "y": 1.6315206630485755
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+    {
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+      "x": -0.075211889248136,
+      "y": 1.6760967324869847
+    },
+    {
+      "id": 17,
+      "rotation_radians": -2.3868988835828158,
+      "x": -0.500347564483488,
+      "y": 1.2657078513558768
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.7559066440147054,
+      "x": -1.3806942815027,
+      "y": 0.3646472377069053
+    },
+    {
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+      "rotation_radians": 0.7597354586647201,
+      "x": -1.097248248106529,
+      "y": 1.3287367455259238
+    },
+    {
+      "id": 20,
+      "rotation_radians": -2.381402822786204,
+      "x": -1.5146871749766508,
+      "y": 0.9287166659689178
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.8186881840361966,
+      "x": -0.5787155315967846,
+      "y": -1.3473803925389833
+    },
+    {
+      "id": 22,
+      "rotation_radians": -2.4118465736630696,
+      "x": 0.0195386147014584,
+      "y": -1.514869334292812
+    },
+    {
+      "id": 23,
+      "rotation_radians": -2.505386855454872,
+      "x": 1.8609583088372774,
+      "y": 0.23067781961509398
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.41888118279991265,
+      "x": 0.8528294320627969,
+      "y": -1.6249358457598775
+    },
+    {
+      "id": 25,
+      "rotation_radians": -2.2915002662213833,
+      "x": -1.5527288892411462,
+      "y": -0.3177270774248698
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.8187019378903987,
+      "x": -1.3713926540777555,
+      "y": -0.8823229752865801
+    }
+  ],
+  "problem": "26 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/26.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_027_8b8ba91284e47068.json b/data/solutions/generated/triinpen_027_8b8ba91284e47068.json
new file mode 100644
index 0000000000000000000000000000000000000000..9d94898bde5041db3483bde792f114ae5f873790
--- /dev/null
+++ b/data/solutions/generated/triinpen_027_8b8ba91284e47068.json
@@ -0,0 +1,224 @@
+{
+  "case": "triinpen@27",
+  "container": {
+    "circumradius": 2.4307965626670343,
+    "orientation_radians": 0.0,
+    "side_length": 2.8575727417178385,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@27",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "2.81761+",
+    "metric_symbol": "s",
+    "metric_value": 2.81761,
+    "reference_text": "s = 2.81761+ | Found by Ian Watson | in April 2026.",
+    "source_image": "27.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/27.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@27",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "2.81761+",
+      "metric_symbol": "s",
+      "metric_value": 2.81761,
+      "reference_text": "s = 2.81761+ | Found by Ian Watson | in April 2026.",
+      "source_image": "27.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/27.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "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/triinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.8948777673505975,
+      "x": 0.41524780705936654,
+      "y": 0.07930471049280649
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+    {
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+    {
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+      "y": -0.1004291135099167
+    },
+    {
+      "id": 8,
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+      "x": 0.2565994196203766,
+      "y": -0.9036050598956396
+    },
+    {
+      "id": 9,
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+      "x": -0.7959198360978204,
+      "y": -0.9823253154179785
+    },
+    {
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+      "x": 0.6008730511429639,
+      "y": 1.0468328808505472
+    },
+    {
+      "id": 11,
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+      "x": 1.2956729997268854,
+      "y": 1.05144538693321
+    },
+    {
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+      "y": 0.47014191032467695
+    },
+    {
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+    },
+    {
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+      "x": 1.0353747335462886,
+      "y": -0.9379606378039914
+    },
+    {
+      "id": 15,
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+      "x": -0.02148648010488625,
+      "y": 1.4536947769859014
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.837770440113482,
+      "x": -0.5862401786984025,
+      "y": 1.5737380827701792
+    },
+    {
+      "id": 17,
+      "rotation_radians": -2.2831486351742485,
+      "x": -0.8360471118041929,
+      "y": 1.013012362720721
+    },
+    {
+      "id": 18,
+      "rotation_radians": 0.938350894516595,
+      "x": -1.3926030293897254,
+      "y": -0.04845512947583336
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.8584453006973254,
+      "x": -1.399450401393034,
+      "y": 1.1407216499526633
+    },
+    {
+      "id": 20,
+      "rotation_radians": -2.154409683580248,
+      "x": -1.6477001953977382,
+      "y": 0.5046081145014382
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.9443363656231304,
+      "x": -0.4643586958026151,
+      "y": -1.4664919533652545
+    },
+    {
+      "id": 22,
+      "rotation_radians": -2.243564306714329,
+      "x": 0.1312454113929047,
+      "y": -1.5419482451869082
+    },
+    {
+      "id": 23,
+      "rotation_radians": -2.5132770390848305,
+      "x": 1.9024577288971245,
+      "y": 0.23605895347121986
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.4188757342181556,
+      "x": 0.975130031841355,
+      "y": -1.5124253279002489
+    },
+    {
+      "id": 25,
+      "rotation_radians": -2.182869526280812,
+      "x": -1.633866757361017,
+      "y": -0.6039841595278537
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.9443379691415978,
+      "x": -1.3922438422757695,
+      "y": -1.1362743360887118
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.8377634514322737,
+      "x": 0.3648432751323823,
+      "y": 1.8827588454599906
+    }
+  ],
+  "problem": "27 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/27.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_028_6ad421ad9865e8bf.json b/data/solutions/generated/triinpen_028_6ad421ad9865e8bf.json
new file mode 100644
index 0000000000000000000000000000000000000000..c76182e012d3f34ed9c5e88b30909cc97241d356
--- /dev/null
+++ b/data/solutions/generated/triinpen_028_6ad421ad9865e8bf.json
@@ -0,0 +1,230 @@
+{
+  "case": "triinpen@28",
+  "container": {
+    "circumradius": 2.444390599847763,
+    "orientation_radians": 0.0,
+    "side_length": 2.873553490865734,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@28",
+    "credit": "Ignacio Vallejo",
+    "date": "March 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "2.868+",
+    "metric_symbol": "s",
+    "metric_value": 2.868,
+    "reference_text": "s = 2.868+ | Found by Ignacio Vallejo | in March 2026.",
+    "source_image": "28.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/28.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@28",
+      "credit": "Ignacio Vallejo",
+      "date": "March 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "2.868+",
+      "metric_symbol": "s",
+      "metric_value": 2.868,
+      "reference_text": "s = 2.868+ | Found by Ignacio Vallejo | in March 2026.",
+      "source_image": "28.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/28.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "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/triinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
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+      "y": 0.4306050184040929
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+  ],
+  "problem": "28 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/28.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_029_0d9d40fe56c0f6d4.json b/data/solutions/generated/triinpen_029_0d9d40fe56c0f6d4.json
new file mode 100644
index 0000000000000000000000000000000000000000..f6556ba860bec77d3d4deb36b00636a11e0511e9
--- /dev/null
+++ b/data/solutions/generated/triinpen_029_0d9d40fe56c0f6d4.json
@@ -0,0 +1,236 @@
+{
+  "case": "triinpen@29",
+  "container": {
+    "circumradius": 2.4979502018632167,
+    "orientation_radians": 0.0,
+    "side_length": 2.93651657923241,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@29",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "2.903+",
+    "metric_symbol": "s",
+    "metric_value": 2.903,
+    "reference_text": "s = 2.903+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "29.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/29.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@29",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "2.903+",
+      "metric_symbol": "s",
+      "metric_value": 2.903,
+      "reference_text": "s = 2.903+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "29.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/29.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "generator": "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/triinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
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+    },
+    {
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+      "y": -1.0465347063191741
+    },
+    {
+      "id": 29,
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+      "x": 1.896904378400056,
+      "y": -0.16991796667871872
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+  ],
+  "problem": "29 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/29.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_030_2b832e7a9fa0a7c5.json b/data/solutions/generated/triinpen_030_2b832e7a9fa0a7c5.json
new file mode 100644
index 0000000000000000000000000000000000000000..c246e01d3970d3bf970d30b05ee10c0810cb0975
--- /dev/null
+++ b/data/solutions/generated/triinpen_030_2b832e7a9fa0a7c5.json
@@ -0,0 +1,242 @@
+{
+  "case": "triinpen@30",
+  "container": {
+    "circumradius": 2.5506930813371196,
+    "orientation_radians": 0.0,
+    "side_length": 2.998519552668809,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@30",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "2.952+",
+    "metric_symbol": "s",
+    "metric_value": 2.952,
+    "reference_text": "s = 2.952+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "30.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/30.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@30",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "2.952+",
+      "metric_symbol": "s",
+      "metric_value": 2.952,
+      "reference_text": "s = 2.952+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "30.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/30.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "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/triinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "rotation_radians": -3.9767245723486693,
+      "x": -0.6961335669781518,
+      "y": -1.3350993800807072
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.6663401664109224,
+      "x": -1.2498350918926222,
+      "y": 0.2470844054431193
+    },
+    {
+      "id": 24,
+      "rotation_radians": -3.787759907184156,
+      "x": -1.2793307417923672,
+      "y": -0.3411123096165282
+    },
+    {
+      "id": 25,
+      "rotation_radians": -0.8377591395607266,
+      "x": -1.2620226197086841,
+      "y": -1.456146362921727
+    },
+    {
+      "id": 26,
+      "rotation_radians": -3.3510254559459147,
+      "x": -1.47492125688063,
+      "y": 1.3869752447747687
+    },
+    {
+      "id": 27,
+      "rotation_radians": -3.7275038786364125,
+      "x": 0.8168783804321725,
+      "y": -1.8472380723649788
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.5842427417175718,
+      "x": 0.7531891395159444,
+      "y": 1.8495473046985789
+    },
+    {
+      "id": 29,
+      "rotation_radians": -4.1887916869148265,
+      "x": -1.77486822536632,
+      "y": 0.7806999738923265
+    },
+    {
+      "id": 30,
+      "rotation_radians": -0.007856019687155056,
+      "x": -1.7709480532176514,
+      "y": -1.0015224041150217
+    }
+  ],
+  "problem": "30 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/30.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_031_579de3c893a5a64c.json b/data/solutions/generated/triinpen_031_579de3c893a5a64c.json
new file mode 100644
index 0000000000000000000000000000000000000000..a44f391be0278f11a0b976217ea1c6c443b940df
--- /dev/null
+++ b/data/solutions/generated/triinpen_031_579de3c893a5a64c.json
@@ -0,0 +1,248 @@
+{
+  "case": "triinpen@31",
+  "container": {
+    "circumradius": 2.567236156337147,
+    "orientation_radians": 0.0,
+    "side_length": 3.017967103693978,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@31",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "2.992+",
+    "metric_symbol": "s",
+    "metric_value": 2.992,
+    "reference_text": "s = 2.992+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "31.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/31.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000700021000353,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@31",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "2.992+",
+      "metric_symbol": "s",
+      "metric_value": 2.992,
+      "reference_text": "s = 2.992+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "31.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/31.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "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/triinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.8935030506301695,
+      "x": 0.4532937867023691,
+      "y": 0.167438483757637
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+      "y": 0.32931170103238405
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+      "y": 1.3910463365827253
+    },
+    {
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+      "x": -1.7195702828331183,
+      "y": 0.8083361243247826
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.899786982303614,
+      "x": -0.9850619619194987,
+      "y": -1.3956646561950132
+    },
+    {
+      "id": 22,
+      "rotation_radians": -2.2337662950843526,
+      "x": -0.4064679923043528,
+      "y": -1.4812112970427587
+    },
+    {
+      "id": 23,
+      "rotation_radians": -2.513260642428597,
+      "x": 1.8427007928337205,
+      "y": 0.5060784035297514
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.40859516811630797,
+      "x": 0.9210103025631564,
+      "y": -1.76596000337839
+    },
+    {
+      "id": 25,
+      "rotation_radians": -2.238222632727295,
+      "x": -1.7195560588186027,
+      "y": -0.12417969491866782
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.9033694427018225,
+      "x": -1.3605160908395233,
+      "y": -0.6025523166745265
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.8577369645644248,
+      "x": 0.4173261837490415,
+      "y": 2.002549583307421
+    },
+    {
+      "id": 28,
+      "rotation_radians": -2.2382322769048586,
+      "x": -1.7179028600690753,
+      "y": -1.0560413457487796
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.9111029657518505,
+      "x": 1.7833816386984256,
+      "y": -0.24401391571537223
+    },
+    {
+      "id": 30,
+      "rotation_radians": -2.228498164482336,
+      "x": 1.4293567411270276,
+      "y": -0.7013909984892107
+    },
+    {
+      "id": 31,
+      "rotation_radians": 1.2566368860932997,
+      "x": 0.2789849756041042,
+      "y": -1.9709194693408627
+    }
+  ],
+  "problem": "31 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/31.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_032_70ed9a5e30a88f24.json b/data/solutions/generated/triinpen_032_70ed9a5e30a88f24.json
new file mode 100644
index 0000000000000000000000000000000000000000..1f5b63663276701d2e7a2ea5c6442d394619fdab
--- /dev/null
+++ b/data/solutions/generated/triinpen_032_70ed9a5e30a88f24.json
@@ -0,0 +1,254 @@
+{
+  "case": "triinpen@32",
+  "container": {
+    "circumradius": 2.616201147217181,
+    "orientation_radians": 0.0,
+    "side_length": 3.0755289027298165,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@32",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.029+",
+    "metric_symbol": "s",
+    "metric_value": 3.029,
+    "reference_text": "s = 3.029+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "32.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/32.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@32",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.029+",
+      "metric_symbol": "s",
+      "metric_value": 3.029,
+      "reference_text": "s = 3.029+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "32.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/32.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "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/triinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.20345020306896672,
+      "x": -0.06980373844107203,
+      "y": -0.26748981105308156
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+    {
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+      "x": -0.8846468992296858,
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+    {
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+    {
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+      "x": 0.035039036800810316,
+      "y": 0.7157407544262284
+    },
+    {
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+    {
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+    {
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+      "x": 0.42030871336825615,
+      "y": 1.1469860809779893
+    },
+    {
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+    {
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+    {
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+      "y": -0.3136968122751157
+    },
+    {
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+      "y": -0.15580834879433345
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.07101824752346501,
+      "x": -1.7931206816035727,
+      "y": 0.8750400733535868
+    },
+    {
+      "id": 17,
+      "rotation_radians": -3.212609363262855,
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+      "y": 0.36192846113506927
+    },
+    {
+      "id": 18,
+      "rotation_radians": -3.3450154545375725,
+      "x": -1.3654246279291071,
+      "y": -0.6604362593823029
+    },
+    {
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+      "rotation_radians": -3.348806902048219,
+      "x": -1.4804482906724346,
+      "y": 1.43958197265592
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.20944772935193498,
+      "x": -0.9119414170130129,
+      "y": 1.3179607822607695
+    },
+    {
+      "id": 21,
+      "rotation_radians": -2.9321541907920787,
+      "x": 0.016287833892636588,
+      "y": -1.927225664926239
+    },
+    {
+      "id": 22,
+      "rotation_radians": -0.41886967549582227,
+      "x": 1.1817088538690155,
+      "y": 1.4832613451601997
+    },
+    {
+      "id": 23,
+      "rotation_radians": -3.56046072352557,
+      "x": 1.2420640345342409,
+      "y": 0.9090518188322783
+    },
+    {
+      "id": 24,
+      "rotation_radians": -3.351030562666984,
+      "x": -0.5289641335648076,
+      "y": 1.750062822346057
+    },
+    {
+      "id": 25,
+      "rotation_radians": -0.20942894565158612,
+      "x": 0.03578796440057218,
+      "y": 1.6300150213570064
+    },
+    {
+      "id": 26,
+      "rotation_radians": -0.05316959405610084,
+      "x": 1.6349778856566815,
+      "y": -0.5263100052268675
+    },
+    {
+      "id": 27,
+      "rotation_radians": -0.2034497376720678,
+      "x": -1.732794002033515,
+      "y": -1.1064041872569057
+    },
+    {
+      "id": 28,
+      "rotation_radians": -3.3510256746961833,
+      "x": 0.4221205410021622,
+      "y": 2.0590873067529745
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.028649497083099405,
+      "x": 0.6768687673395247,
+      "y": -1.8482110563222631
+    },
+    {
+      "id": 30,
+      "rotation_radians": -3.195110165445245,
+      "x": 1.0138005330666098,
+      "y": -1.3308134751434426
+    },
+    {
+      "id": 31,
+      "rotation_radians": -0.4188718209550834,
+      "x": 1.769520074945422,
+      "y": 0.6742174984014365
+    },
+    {
+      "id": 32,
+      "rotation_radians": -3.227137405500322,
+      "x": 1.9666161089078127,
+      "y": -0.03413657215138326
+    }
+  ],
+  "problem": "32 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/32.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_033_13357e078d1002ad.json b/data/solutions/generated/triinpen_033_13357e078d1002ad.json
new file mode 100644
index 0000000000000000000000000000000000000000..14f1f6bef68606b924f0daa7907dc2302107daf5
--- /dev/null
+++ b/data/solutions/generated/triinpen_033_13357e078d1002ad.json
@@ -0,0 +1,260 @@
+{
+  "case": "triinpen@33",
+  "container": {
+    "circumradius": 2.6242009419018393,
+    "orientation_radians": 0.0,
+    "side_length": 3.0849332254038364,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@33",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.078+",
+    "metric_symbol": "s",
+    "metric_value": 3.078,
+    "reference_text": "s = 3.078+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "33.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/33.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@33",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.078+",
+      "metric_symbol": "s",
+      "metric_value": 3.078,
+      "reference_text": "s = 3.078+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "33.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/33.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "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/triinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+    {
+      "id": 29,
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+    {
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+      "y": -1.8045600542201712
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+    {
+      "id": 32,
+      "rotation_radians": -2.2903690892722337,
+      "x": 0.6145844360120045,
+      "y": -1.8740850202357224
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+    {
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+      "rotation_radians": -2.3106319202105996,
+      "x": 0.8883851041640313,
+      "y": 1.7368638451532974
+    }
+  ],
+  "problem": "33 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/33.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_034_9cac5218ebb67cb5.json b/data/solutions/generated/triinpen_034_9cac5218ebb67cb5.json
new file mode 100644
index 0000000000000000000000000000000000000000..799747cecde7a54c09a3256d5af0fca6ad024b39
--- /dev/null
+++ b/data/solutions/generated/triinpen_034_9cac5218ebb67cb5.json
@@ -0,0 +1,266 @@
+{
+  "case": "triinpen@34",
+  "container": {
+    "circumradius": 2.6681701272786396,
+    "orientation_radians": 0.0,
+    "side_length": 3.1366221028434307,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@34",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.114+",
+    "metric_symbol": "s",
+    "metric_value": 3.114,
+    "reference_text": "s = 3.114+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "34.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/34.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@34",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.114+",
+      "metric_symbol": "s",
+      "metric_value": 3.114,
+      "reference_text": "s = 3.114+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "34.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/34.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "generator": "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/triinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+    },
+    {
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+      "x": 1.9670085440081178,
+      "y": 0.3477808060756826
+    },
+    {
+      "id": 29,
+      "rotation_radians": -0.005404774601815486,
+      "x": -1.8672131003483796,
+      "y": 0.937695020606509
+    },
+    {
+      "id": 30,
+      "rotation_radians": -2.706359138937151,
+      "x": 0.19902864067831638,
+      "y": -1.8785618891434706
+    },
+    {
+      "id": 31,
+      "rotation_radians": 0.4223269570448134,
+      "x": 2.1182737073410647,
+      "y": -0.262796838023602
+    },
+    {
+      "id": 32,
+      "rotation_radians": 0.00794804732509929,
+      "x": -1.862668474182186,
+      "y": -1.0696673234497758
+    },
+    {
+      "id": 33,
+      "rotation_radians": -3.117896096628018,
+      "x": -1.132295060845967,
+      "y": -1.4943422872729129
+    },
+    {
+      "id": 34,
+      "rotation_radians": -3.2913017203863215,
+      "x": 0.466279050992203,
+      "y": 2.0837483638126817
+    }
+  ],
+  "problem": "34 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/34.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_035_e568d5830b049327.json b/data/solutions/generated/triinpen_035_e568d5830b049327.json
new file mode 100644
index 0000000000000000000000000000000000000000..65eb8b12796b6047253919ef279396339c60a09c
--- /dev/null
+++ b/data/solutions/generated/triinpen_035_e568d5830b049327.json
@@ -0,0 +1,272 @@
+{
+  "case": "triinpen@35",
+  "container": {
+    "circumradius": 2.7145882145907416,
+    "orientation_radians": 0.0,
+    "side_length": 3.1911898371667866,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@35",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.150+",
+    "metric_symbol": "s",
+    "metric_value": 3.15,
+    "reference_text": "s = 3.150+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "35.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/35.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@35",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.150+",
+      "metric_symbol": "s",
+      "metric_value": 3.15,
+      "reference_text": "s = 3.150+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "35.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/35.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "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/triinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.4981254849708943,
+      "x": -0.05585674723117419,
+      "y": 0.18634010978903667
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+    {
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+    {
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+      "x": -1.878481929141269,
+      "y": -0.1298349896851387
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+  ],
+  "problem": "35 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/35.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_036_94f98697d38e8534.json b/data/solutions/generated/triinpen_036_94f98697d38e8534.json
new file mode 100644
index 0000000000000000000000000000000000000000..27b43872d43058e177491b86c0d367bd4c56cbe0
--- /dev/null
+++ b/data/solutions/generated/triinpen_036_94f98697d38e8534.json
@@ -0,0 +1,278 @@
+{
+  "case": "triinpen@36",
+  "container": {
+    "circumradius": 2.7058446228521733,
+    "orientation_radians": 0.0,
+    "side_length": 3.180911128614793,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@36",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.177+",
+    "metric_symbol": "s",
+    "metric_value": 3.177,
+    "reference_text": "s = 3.177+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "36.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/36.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@36",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.177+",
+      "metric_symbol": "s",
+      "metric_value": 3.177,
+      "reference_text": "s = 3.177+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "36.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/36.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "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/triinpen/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
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+    {
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+    {
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+      "x": 1.6253099016902777,
+      "y": 0.504928512547504
+    }
+  ],
+  "problem": "36 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/36.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinpen_039_67a6bbf24108966a.json b/data/solutions/generated/triinpen_039_67a6bbf24108966a.json
new file mode 100644
index 0000000000000000000000000000000000000000..b166cca800082da2da618868f191492ff4015a61
--- /dev/null
+++ b/data/solutions/generated/triinpen_039_67a6bbf24108966a.json
@@ -0,0 +1,296 @@
+{
+  "case": "triinpen@39",
+  "container": {
+    "circumradius": 2.805326444569377,
+    "orientation_radians": 0.0,
+    "side_length": 3.2978590239679155,
+    "sides": 5,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinpen@39",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.295+",
+    "metric_symbol": "s",
+    "metric_value": 3.295,
+    "reference_text": "s = 3.295+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "39.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinpen/39.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+    "title": "Triangles in Pentagons"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinpen@39",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.295+",
+      "metric_symbol": "s",
+      "metric_value": 3.295,
+      "reference_text": "s = 3.295+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "39.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinpen/39.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinpen/",
+      "title": "Triangles in Pentagons"
+    },
+    "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/triinpen/",
+    "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": 38,
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+      "y": -0.04675500911103437
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+    {
+      "id": 39,
+      "rotation_radians": 2.0943961466495704,
+      "x": -1.9808695502537894,
+      "y": -1.0467975427007814
+    }
+  ],
+  "problem": "39 equal items for Triangles in Pentagons",
+  "setup": "triinpen",
+  "source_image": "https://erich-friedman.github.io/packing/triinpen/39.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinpen/"
+}
diff --git a/data/solutions/generated/triinsqu_021_3debb201d272befe.json b/data/solutions/generated/triinsqu_021_3debb201d272befe.json
new file mode 100644
index 0000000000000000000000000000000000000000..3b2691236e58d18dfbcf085dd3df66e685a60375
--- /dev/null
+++ b/data/solutions/generated/triinsqu_021_3debb201d272befe.json
@@ -0,0 +1,188 @@
+{
+  "case": "triinsqu@21",
+  "container": {
+    "circumradius": 2.3550370139002608,
+    "orientation_radians": 0.0,
+    "side_length": 3.3305252849483837,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@21",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.3111+",
+    "metric_symbol": "s",
+    "metric_value": 3.3111,
+    "reference_text": "s = 3.3111+ | Found by Ian Watson | in April 2026.",
+    "source_image": "t21.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t21.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@21",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.3111+",
+      "metric_symbol": "s",
+      "metric_value": 3.3111,
+      "reference_text": "s = 3.3111+ | Found by Ian Watson | in April 2026.",
+      "source_image": "t21.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t21.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
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+      "x": 0.26826754958743465,
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+    {
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+      "y": -1.144109067134925
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+    {
+      "id": 17,
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+      "x": -1.1893435526178953,
+      "y": -0.3577659589910713
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+    {
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+      "rotation_radians": 0.6427737498858352,
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+      "y": -0.9169057253445022
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+    {
+      "id": 19,
+      "rotation_radians": 0.7084822268922311,
+      "x": -0.07948594128048662,
+      "y": -1.7608496875127968
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.669300989708314,
+      "x": -1.7364874621670543,
+      "y": -0.13111724890960377
+    },
+    {
+      "id": 21,
+      "rotation_radians": -2.8797947648421918,
+      "x": -0.57826472978507,
+      "y": 1.3685145791416333
+    }
+  ],
+  "problem": "21 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t21.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_022_470a866027c799dc.json b/data/solutions/generated/triinsqu_022_470a866027c799dc.json
new file mode 100644
index 0000000000000000000000000000000000000000..f9e958247576989f43b4795fe696e458291c2ef1
--- /dev/null
+++ b/data/solutions/generated/triinsqu_022_470a866027c799dc.json
@@ -0,0 +1,194 @@
+{
+  "case": "triinsqu@22",
+  "container": {
+    "circumradius": 2.392653511861857,
+    "orientation_radians": 0.0,
+    "side_length": 3.383723046534653,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@22",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.3757+",
+    "metric_symbol": "s",
+    "metric_value": 3.3757,
+    "reference_text": "22. | | s = 3.3757+ | Found by Ian Watson | in April 2026.",
+    "source_image": "t22.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t22.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@22",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.3757+",
+      "metric_symbol": "s",
+      "metric_value": 3.3757,
+      "reference_text": "22. | | s = 3.3757+ | Found by Ian Watson | in April 2026.",
+      "source_image": "t22.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t22.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.27773966709036535,
+      "x": 0.320367001334884,
+      "y": -0.4392801049363519
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+      "y": 0.43931029630038665
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+      "y": 1.3992604558722153
+    },
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+      "x": -0.14917063026860872,
+      "y": -1.8348927288979524
+    },
+    {
+      "id": 11,
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+      "x": 0.14941855440923482,
+      "y": 1.834966325351728
+    },
+    {
+      "id": 12,
+      "rotation_radians": 0.27422540638884646,
+      "x": 0.5595024863761555,
+      "y": -1.4063826400741954
+    },
+    {
+      "id": 13,
+      "rotation_radians": -3.4034144776646214,
+      "x": 0.2980020846990225,
+      "y": 1.277049395543136
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.2777309286006157,
+      "x": -0.7352258396187893,
+      "y": 0.8410162129016115
+    },
+    {
+      "id": 15,
+      "rotation_radians": -0.26227642701807696,
+      "x": -0.29835501088903144,
+      "y": -1.277132666437672
+    },
+    {
+      "id": 16,
+      "rotation_radians": -2.8638510064027027,
+      "x": 0.72896708444173,
+      "y": -0.8472899752718988
+    },
+    {
+      "id": 17,
+      "rotation_radians": 0.2885544700803307,
+      "x": 1.4564534153849362,
+      "y": -0.5090986923848075
+    },
+    {
+      "id": 18,
+      "rotation_radians": -2.8858930373229885,
+      "x": -1.4525435282844237,
+      "y": 0.5265392071059943
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.26258415742476604,
+      "x": 0.8561226246775607,
+      "y": 1.1277125343992835
+    },
+    {
+      "id": 20,
+      "rotation_radians": -3.403879359274387,
+      "x": -0.8561099693401039,
+      "y": -1.1279084737342855
+    },
+    {
+      "id": 21,
+      "rotation_radians": -2.7753936190161674,
+      "x": 1.6561563888650428,
+      "y": 0.07576160094570257
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.3664223095302104,
+      "x": -1.656314236414293,
+      "y": -0.07571110420713804
+    }
+  ],
+  "problem": "22 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t22.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_023_23d97af9efc6a19d.json b/data/solutions/generated/triinsqu_023_23d97af9efc6a19d.json
new file mode 100644
index 0000000000000000000000000000000000000000..c5fe77244990c7a1d4a4ce74ff8f94784f0fd41f
--- /dev/null
+++ b/data/solutions/generated/triinsqu_023_23d97af9efc6a19d.json
@@ -0,0 +1,200 @@
+{
+  "case": "triinsqu@23",
+  "container": {
+    "circumradius": 2.456611836703044,
+    "orientation_radians": 0.0,
+    "side_length": 3.4741737769517234,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@23",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.4311+",
+    "metric_symbol": "s",
+    "metric_value": 3.4311,
+    "reference_text": "23. | | s = 3.4311+ | Found by Ian Watson | in April 2026.",
+    "source_image": "t23.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t23.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@23",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.4311+",
+      "metric_symbol": "s",
+      "metric_value": 3.4311,
+      "reference_text": "23. | | s = 3.4311+ | Found by Ian Watson | in April 2026.",
+      "source_image": "t23.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t23.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -2.3312228125873977,
+      "x": 0.23282866852782716,
+      "y": 0.5697353514502567
+    },
+    {
+      "id": 2,
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+      "x": 0.3780977715888406,
+      "y": 0.010625694470650118
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+    {
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+      "x": -0.651481408707311,
+      "y": -0.16872260298663855
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+    {
+      "id": 4,
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+      "x": -0.09547653399111529,
+      "y": -0.3357603553548743
+    },
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+    {
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+      "y": 0.1328750369917141
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+    {
+      "id": 19,
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+    {
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+    {
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+      "y": -1.8779983618741725
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+    {
+      "id": 22,
+      "rotation_radians": -2.328638718389717,
+      "x": -1.1227673325945464,
+      "y": -0.5176386645476726
+    },
+    {
+      "id": 23,
+      "rotation_radians": -2.3312560805859754,
+      "x": -0.37787505697274804,
+      "y": -1.262468807939402
+    }
+  ],
+  "problem": "23 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t23.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_024_aa931802df351f6b.json b/data/solutions/generated/triinsqu_024_aa931802df351f6b.json
new file mode 100644
index 0000000000000000000000000000000000000000..c4aacfdfc8b3f9cb8a85a6665175e5544ecf258d
--- /dev/null
+++ b/data/solutions/generated/triinsqu_024_aa931802df351f6b.json
@@ -0,0 +1,206 @@
+{
+  "case": "triinsqu@24",
+  "container": {
+    "circumradius": 2.461618332064436,
+    "orientation_radians": 0.0,
+    "side_length": 3.4812540305917623,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@24",
+    "credit": "Maurizio Morandi",
+    "date": "August 2008",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.468+",
+    "metric_symbol": "s",
+    "metric_value": 3.468,
+    "reference_text": "24. | | s = 3.468+ | Found by Maurizio Morandi | in August 2008.",
+    "source_image": "t24.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t24.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000700021000353,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@24",
+      "credit": "Maurizio Morandi",
+      "date": "August 2008",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.468+",
+      "metric_symbol": "s",
+      "metric_value": 3.468,
+      "reference_text": "24. | | s = 3.468+ | Found by Maurizio Morandi | in August 2008.",
+      "source_image": "t24.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t24.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.7792561781871442,
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+    {
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+    {
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+      "y": -1.3454835161697625
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+    {
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+    {
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+      "y": -1.1952583718936824
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.7840089342382535,
+      "x": -0.1486648780747331,
+      "y": -1.903707107268735
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.7839082357262006,
+      "x": -1.5609154656297826,
+      "y": -0.49139302796105805
+    },
+    {
+      "id": 21,
+      "rotation_radians": -2.879791543966929,
+      "x": -0.26490944665891797,
+      "y": 1.7884314294113774
+    },
+    {
+      "id": 22,
+      "rotation_radians": -1.8326005558406282,
+      "x": 1.4936769227030153,
+      "y": -0.5596712698281162
+    },
+    {
+      "id": 23,
+      "rotation_radians": 0.2619795033498067,
+      "x": 0.5596766133677276,
+      "y": -1.4935621824672067
+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.3089940976699717,
+      "x": -1.7899840098991577,
+      "y": 0.2633636685627326
+    }
+  ],
+  "problem": "24 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t24.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_025_16117b2f4cd0a5a0.json b/data/solutions/generated/triinsqu_025_16117b2f4cd0a5a0.json
new file mode 100644
index 0000000000000000000000000000000000000000..27fa3d77c6b101dc8b167833a2aea15ad0c763a2
--- /dev/null
+++ b/data/solutions/generated/triinsqu_025_16117b2f4cd0a5a0.json
@@ -0,0 +1,212 @@
+{
+  "case": "triinsqu@25",
+  "container": {
+    "circumradius": 2.512742609832427,
+    "orientation_radians": 0.0,
+    "side_length": 3.553554677577784,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@25",
+    "credit": "David W",
+    "date": "August 2012",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.537+",
+    "metric_symbol": "s",
+    "metric_value": 3.537,
+    "reference_text": "25. | | s = 3.537+ | Found by David W. Cantrell | in August 2012.",
+    "source_image": "t25.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t25.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@25",
+      "credit": "David W",
+      "date": "August 2012",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.537+",
+      "metric_symbol": "s",
+      "metric_value": 3.537,
+      "reference_text": "25. | | s = 3.537+ | Found by David W. Cantrell | in August 2012.",
+      "source_image": "t25.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t25.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -2.356151309543716,
+      "x": 0.24337416341832513,
+      "y": 0.6341058607449663
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+    {
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+      "y": 1.6013798019072145
+    },
+    {
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+      "x": 0.6511816950837432,
+      "y": 1.0434502128097882
+    },
+    {
+      "id": 12,
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+      "y": 0.3367863824725788
+    },
+    {
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+      "y": 1.341911667640739
+    },
+    {
+      "id": 14,
+      "rotation_radians": 0.26179824883144487,
+      "x": -1.3681497856902722,
+      "y": 0.3280697685213937
+    },
+    {
+      "id": 15,
+      "rotation_radians": 0.7864267433760727,
+      "x": -0.05537926019151877,
+      "y": 1.7506449069784473
+    },
+    {
+      "id": 16,
+      "rotation_radians": 0.7875412767802992,
+      "x": 1.1980977057842495,
+      "y": -0.6047415043207348
+    },
+    {
+      "id": 17,
+      "rotation_radians": -2.354055246409157,
+      "x": 0.7916624470455447,
+      "y": -1.0148309770167767
+    },
+    {
+      "id": 18,
+      "rotation_radians": -2.2497851824891955,
+      "x": 1.9423310363539625,
+      "y": 0.0893542757868404
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.7854024870387706,
+      "x": -0.8564931757552623,
+      "y": -1.2479031370799198
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.7853958549629642,
+      "x": -1.5636473725908844,
+      "y": -0.5408420888077635
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.7854068956215488,
+      "x": -0.1494283691148304,
+      "y": -1.9550532241836047
+    },
+    {
+      "id": 22,
+      "rotation_radians": -2.3561897338613953,
+      "x": -1.0059291824532028,
+      "y": -0.6902043042156463
+    },
+    {
+      "id": 23,
+      "rotation_radians": -2.3561892746143616,
+      "x": -0.29878825246890284,
+      "y": -1.3973375978211524
+    },
+    {
+      "id": 24,
+      "rotation_radians": -2.879791173327523,
+      "x": -1.9258525122522103,
+      "y": 0.17863077139117392
+    },
+    {
+      "id": 25,
+      "rotation_radians": 1.3089960771874332,
+      "x": -1.2187116089690089,
+      "y": 0.8857691070964497
+    }
+  ],
+  "problem": "25 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t25.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_026_ebfed25c219baa0e.json b/data/solutions/generated/triinsqu_026_ebfed25c219baa0e.json
new file mode 100644
index 0000000000000000000000000000000000000000..3b19ff2252bcbe94926456ffee36551086d97753
--- /dev/null
+++ b/data/solutions/generated/triinsqu_026_ebfed25c219baa0e.json
@@ -0,0 +1,218 @@
+{
+  "case": "triinsqu@26",
+  "container": {
+    "circumradius": 2.5636623001700425,
+    "orientation_radians": 0.0,
+    "side_length": 3.625565994245078,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@26",
+    "credit": "Maurizio Morandi",
+    "date": "September 2008",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.575+",
+    "metric_symbol": "s",
+    "metric_value": 3.575,
+    "reference_text": "26. | | s = 3.575+ | Found by Maurizio Morandi | in September 2008.",
+    "source_image": "t26.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t26.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@26",
+      "credit": "Maurizio Morandi",
+      "date": "September 2008",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.575+",
+      "metric_symbol": "s",
+      "metric_value": 3.575,
+      "reference_text": "26. | | s = 3.575+ | Found by Maurizio Morandi | in September 2008.",
+      "source_image": "t26.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t26.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
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+  ],
+  "problem": "26 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t26.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_027_dbdb303c3aa850bb.json b/data/solutions/generated/triinsqu_027_dbdb303c3aa850bb.json
new file mode 100644
index 0000000000000000000000000000000000000000..3b6e96288ea3be32e20f910747a3f4104ee4f499
--- /dev/null
+++ b/data/solutions/generated/triinsqu_027_dbdb303c3aa850bb.json
@@ -0,0 +1,224 @@
+{
+  "case": "triinsqu@27",
+  "container": {
+    "circumradius": 2.62266883631111,
+    "orientation_radians": 0.0,
+    "side_length": 3.7090138379244344,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@27",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.6726+",
+    "metric_symbol": "s",
+    "metric_value": 3.6726,
+    "reference_text": "27. | | s = 3.6726+ | Found by Ian Watson | in April 2026.",
+    "source_image": "t27.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t27.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@27",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.6726+",
+      "metric_symbol": "s",
+      "metric_value": 3.6726,
+      "reference_text": "27. | | s = 3.6726+ | Found by Ian Watson | in April 2026.",
+      "source_image": "t27.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t27.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "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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+      "x": 1.592655379696305,
+      "y": 0.6211293106324474
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+  ],
+  "problem": "27 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t27.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_028_d660009be45656fb.json b/data/solutions/generated/triinsqu_028_d660009be45656fb.json
new file mode 100644
index 0000000000000000000000000000000000000000..7c8064cc47142033030c0206ce45cf77cfdd5979
--- /dev/null
+++ b/data/solutions/generated/triinsqu_028_d660009be45656fb.json
@@ -0,0 +1,230 @@
+{
+  "case": "triinsqu@28",
+  "container": {
+    "circumradius": 2.6848666494771205,
+    "orientation_radians": 0.0,
+    "side_length": 3.796974828853754,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@28",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.7571+",
+    "metric_symbol": "s",
+    "metric_value": 3.7571,
+    "reference_text": "28. | | s = 3.7571+ | Found by Ian Watson | in April 2026.",
+    "source_image": "t28.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t28.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@28",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.7571+",
+      "metric_symbol": "s",
+      "metric_value": 3.7571,
+      "reference_text": "28. | | s = 3.7571+ | Found by Ian Watson | in April 2026.",
+      "source_image": "t28.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t28.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+    {
+      "id": 27,
+      "rotation_radians": -0.2617987255182068,
+      "x": 1.736133352910546,
+      "y": 0.5404768765512388
+    },
+    {
+      "id": 28,
+      "rotation_radians": -3.408625123509356,
+      "x": -1.786057610860823,
+      "y": -0.48685339751008405
+    }
+  ],
+  "problem": "28 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t28.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_029_580739cf26075b25.json b/data/solutions/generated/triinsqu_029_580739cf26075b25.json
new file mode 100644
index 0000000000000000000000000000000000000000..496615d323e0527928ef86431da126a82e196d07
--- /dev/null
+++ b/data/solutions/generated/triinsqu_029_580739cf26075b25.json
@@ -0,0 +1,236 @@
+{
+  "case": "triinsqu@29",
+  "container": {
+    "circumradius": 2.7160111792156925,
+    "orientation_radians": 0.0,
+    "side_length": 3.8410198452037747,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@29",
+    "credit": "Ignacio Vallejo",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.818+",
+    "metric_symbol": "s",
+    "metric_value": 3.818,
+    "reference_text": "29. | | s = 3.818+ | Found by Ignacio Vallejo | in April 2026.",
+    "source_image": "t29.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t29.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@29",
+      "credit": "Ignacio Vallejo",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.818+",
+      "metric_symbol": "s",
+      "metric_value": 3.818,
+      "reference_text": "29. | | s = 3.818+ | Found by Ignacio Vallejo | in April 2026.",
+      "source_image": "t29.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t29.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.7402621829134104,
+      "x": 0.541746194532084,
+      "y": 0.3638220421576771
+    },
+    {
+      "id": 2,
+      "rotation_radians": -0.7982196579732586,
+      "x": -0.9284839625391739,
+      "y": 0.12635776930617107
+    },
+    {
+      "id": 3,
+      "rotation_radians": -3.881861188811825,
+      "x": 0.7731754622626958,
+      "y": -0.2783118754560333
+    },
+    {
+      "id": 4,
+      "rotation_radians": -3.923087146282463,
+      "x": -0.7915784181400638,
+      "y": -0.5154805856219505
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+    {
+      "id": 5,
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+      "x": 0.07156966800726118,
+      "y": -0.39638013791376825
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+    {
+      "id": 6,
+      "rotation_radians": -3.917416441880899,
+      "x": -0.35449676898673105,
+      "y": 0.2648966555599465
+    },
+    {
+      "id": 7,
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+      "x": -0.24253724868434917,
+      "y": 0.8394523732192858
+    },
+    {
+      "id": 8,
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+      "x": 0.000990638952871284,
+      "y": -0.9794416631658399
+    },
+    {
+      "id": 9,
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+      "y": -0.3471519687033311
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+    {
+      "id": 10,
+      "rotation_radians": -0.7785895469718744,
+      "x": -1.9113141315958,
+      "y": 0.3896566872552752
+    },
+    {
+      "id": 11,
+      "rotation_radians": -0.32253902905410825,
+      "x": 1.849330663903782,
+      "y": 0.4162619901783749
+    },
+    {
+      "id": 12,
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+      "x": -1.7617014616492037,
+      "y": -0.24879619124402494
+    },
+    {
+      "id": 13,
+      "rotation_radians": -0.785400037661081,
+      "x": 1.4028964639131913,
+      "y": -0.4965887254205656
+    },
+    {
+      "id": 14,
+      "rotation_radians": -3.4641422766298495,
+      "x": 1.280076248688517,
+      "y": 0.5344930269950752
+    },
+    {
+      "id": 15,
+      "rotation_radians": -3.9273477572329307,
+      "x": -1.3465074289257069,
+      "y": 0.5373478364075929
+    },
+    {
+      "id": 16,
+      "rotation_radians": -0.7814891981166848,
+      "x": -1.3518449510584085,
+      "y": -0.6554608900989074
+    },
+    {
+      "id": 17,
+      "rotation_radians": -3.926994250148288,
+      "x": 1.2534643158798253,
+      "y": -1.0542874174038568
+    },
+    {
+      "id": 18,
+      "rotation_radians": -0.28306251997211984,
+      "x": 1.1713341676390732,
+      "y": 1.1214842612830702
+    },
+    {
+      "id": 19,
+      "rotation_radians": -3.4283488634534915,
+      "x": -0.9193735198486628,
+      "y": -1.3708606811698352
+    },
+    {
+      "id": 20,
+      "rotation_radians": -0.7853956372375852,
+      "x": -1.2092620439292703,
+      "y": 1.0984911418204557
+    },
+    {
+      "id": 21,
+      "rotation_radians": -3.9244028878085975,
+      "x": 0.3168720169633382,
+      "y": 0.9862124423423946
+    },
+    {
+      "id": 22,
+      "rotation_radians": -3.9262989627448683,
+      "x": -0.651076737709528,
+      "y": 1.2474382429175668
+    },
+    {
+      "id": 23,
+      "rotation_radians": -0.32736847163497884,
+      "x": -0.3497712108042813,
+      "y": -1.551476187039063
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.7853966358687331,
+      "x": 0.6957660836284069,
+      "y": -1.2037248326499477
+    },
+    {
+      "id": 25,
+      "rotation_radians": -0.7828682432616785,
+      "x": 0.4658555178335178,
+      "y": 1.5440585072465456
+    },
+    {
+      "id": 26,
+      "rotation_radians": -3.9269939645222847,
+      "x": 0.5463325471554483,
+      "y": -1.7614222260949146
+    },
+    {
+      "id": 27,
+      "rotation_radians": -3.4075071771321532,
+      "x": -0.17195214512281298,
+      "y": -2.1328898306365365
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.7846984960443584,
+      "x": -0.5020243400467866,
+      "y": 1.8052345173453213
+    },
+    {
+      "id": 29,
+      "rotation_radians": -3.9262944073718997,
+      "x": 0.05629721779398683,
+      "y": 1.9523152250351734
+    }
+  ],
+  "problem": "29 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t29.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_030_c1d8c0f9af9cd320.json b/data/solutions/generated/triinsqu_030_c1d8c0f9af9cd320.json
new file mode 100644
index 0000000000000000000000000000000000000000..83a75c1be2d1badfd4ff124144f3955d5f5f9046
--- /dev/null
+++ b/data/solutions/generated/triinsqu_030_c1d8c0f9af9cd320.json
@@ -0,0 +1,242 @@
+{
+  "case": "triinsqu@30",
+  "container": {
+    "circumradius": 2.771828067295217,
+    "orientation_radians": 0.0,
+    "side_length": 3.9199568453352995,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@30",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.8662+",
+    "metric_symbol": "s",
+    "metric_value": 3.8662,
+    "reference_text": "30. | | s = 3.8662+ | Found by Ian Watson | in April 2026.",
+    "source_image": "t30.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t30.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@30",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.8662+",
+      "metric_symbol": "s",
+      "metric_value": 3.8662,
+      "reference_text": "30. | | s = 3.8662+ | Found by Ian Watson | in April 2026.",
+      "source_image": "t30.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t30.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 1.5782598343756162,
+      "x": -0.6769023553814485,
+      "y": 0.2670187356130129
+    },
+    {
+      "id": 2,
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+      "x": 0.6292628809626871,
+      "y": -0.48014343325134784
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+    {
+      "id": 3,
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+      "x": -0.7115877659455107,
+      "y": -0.4271061794148453
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+    {
+      "id": 4,
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+      "x": 0.6397707719876253,
+      "y": 0.20012842213745585
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+    {
+      "id": 5,
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+      "x": 0.0030452009436609667,
+      "y": 0.25095260973587813
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+    {
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+      "x": -0.1538694415394255,
+      "y": -0.5766312736592164
+    },
+    {
+      "id": 7,
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+      "y": 0.8283310111846918
+    },
+    {
+      "id": 8,
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+      "x": -0.004423805225672709,
+      "y": -1.134338199370372
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+    {
+      "id": 9,
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+    },
+    {
+      "id": 10,
+      "rotation_radians": 0.2618039345415621,
+      "x": 2.100230770400298,
+      "y": -0.26333058980665125
+    },
+    {
+      "id": 11,
+      "rotation_radians": 0.7796989196483626,
+      "x": -2.049986599945601,
+      "y": -0.3095605639791225
+    },
+    {
+      "id": 12,
+      "rotation_radians": 1.684584257568325,
+      "x": 1.814283904712171,
+      "y": 0.4494735390264576
+    },
+    {
+      "id": 13,
+      "rotation_radians": 0.38086401426158,
+      "x": -1.2800649295851902,
+      "y": 0.5189930059801793
+    },
+    {
+      "id": 14,
+      "rotation_radians": 1.3090042017612935,
+      "x": 1.5425263311435364,
+      "y": -0.41276663005620295
+    },
+    {
+      "id": 15,
+      "rotation_radians": 0.5396625956032979,
+      "x": 1.1492018690307173,
+      "y": 0.48657937753738845
+    },
+    {
+      "id": 16,
+      "rotation_radians": 1.8276482799711409,
+      "x": -1.4927618632752266,
+      "y": -0.4622050426409771
+    },
+    {
+      "id": 17,
+      "rotation_radians": 1.4174506214198137,
+      "x": -1.1941303813981372,
+      "y": 1.0952951323904643
+    },
+    {
+      "id": 18,
+      "rotation_radians": 1.5868593106964908,
+      "x": 1.13992517039324,
+      "y": 1.0638788967494042
+    },
+    {
+      "id": 19,
+      "rotation_radians": 0.261805978320169,
+      "x": 1.3930884125203746,
+      "y": -0.970469146608394
+    },
+    {
+      "id": 20,
+      "rotation_radians": 0.785387364556237,
+      "x": -1.3415669630330906,
+      "y": -1.0219847848668413
+    },
+    {
+      "id": 21,
+      "rotation_radians": 0.5255725121589533,
+      "x": 0.5013511965395401,
+      "y": 1.1180202643392678
+    },
+    {
+      "id": 22,
+      "rotation_radians": 0.525580734703107,
+      "x": -0.5007258873691914,
+      "y": 1.1124909414751842
+    },
+    {
+      "id": 23,
+      "rotation_radians": 1.8325869325451085,
+      "x": -0.783866287873137,
+      "y": -1.171436651288188
+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.3090047900811415,
+      "x": 0.8353886300557908,
+      "y": -1.1199115732139906
+    },
+    {
+      "id": 25,
+      "rotation_radians": 1.5655097934015587,
+      "x": -0.5040330630868219,
+      "y": 1.6934904524733603
+    },
+    {
+      "id": 26,
+      "rotation_radians": 1.5727636964986957,
+      "x": 0.5001965751569333,
+      "y": 1.6953984298270457
+    },
+    {
+      "id": 27,
+      "rotation_radians": 0.2618110435820182,
+      "x": 0.6859530640854432,
+      "y": -1.6776170750700812
+    },
+    {
+      "id": 28,
+      "rotation_radians": 0.785400929558274,
+      "x": -0.6344258145332671,
+      "y": -1.729141711484104
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.5255129424766509,
+      "x": -0.0004052538731177357,
+      "y": 1.983120643602332
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.8325890830437808,
+      "x": -0.07672286845935548,
+      "y": -1.8785821814304335
+    }
+  ],
+  "problem": "30 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t30.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_031_272c8c45b9a6dd78.json b/data/solutions/generated/triinsqu_031_272c8c45b9a6dd78.json
new file mode 100644
index 0000000000000000000000000000000000000000..d4c85fe0900056abd92fcd034ea319f850341512
--- /dev/null
+++ b/data/solutions/generated/triinsqu_031_272c8c45b9a6dd78.json
@@ -0,0 +1,248 @@
+{
+  "case": "triinsqu@31",
+  "container": {
+    "circumradius": 2.826647264236029,
+    "orientation_radians": 0.0,
+    "side_length": 3.9974828971273975,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@31",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.936+",
+    "metric_symbol": "s",
+    "metric_value": 3.936,
+    "reference_text": "31. | | s = 3.936+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "t31.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t31.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@31",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.936+",
+      "metric_symbol": "s",
+      "metric_value": 3.936,
+      "reference_text": "31. | | s = 3.936+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "t31.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t31.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": -0.2654702201955321,
+      "x": 0.1948679094432062,
+      "y": -0.23445012447514285
+    },
+    {
+      "id": 2,
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+      "x": -0.36398437959433877,
+      "y": -0.08331252222758474
+    },
+    {
+      "id": 3,
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+      "x": 0.2438451622108309,
+      "y": 0.9479336352188569
+    },
+    {
+      "id": 4,
+      "rotation_radians": -3.407253163253123,
+      "x": 0.39104618039020256,
+      "y": 0.38761277544427175
+    },
+    {
+      "id": 5,
+      "rotation_radians": -3.40484399742059,
+      "x": -0.31555622626201674,
+      "y": 1.093950791717042
+    },
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+    {
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+    {
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+    {
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+      "x": -0.5030336368898964,
+      "y": -1.9150663938636259
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+  ],
+  "problem": "31 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t31.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_032_aa2ff1aceeba9dbd.json b/data/solutions/generated/triinsqu_032_aa2ff1aceeba9dbd.json
new file mode 100644
index 0000000000000000000000000000000000000000..e0ea614f44743dcdfdfdcd8e602d214a29c512c7
--- /dev/null
+++ b/data/solutions/generated/triinsqu_032_aa2ff1aceeba9dbd.json
@@ -0,0 +1,254 @@
+{
+  "case": "triinsqu@32",
+  "container": {
+    "circumradius": 2.8839372848069154,
+    "orientation_radians": 0.0,
+    "side_length": 4.078503221207378,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@32",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "3.997+",
+    "metric_symbol": "s",
+    "metric_value": 3.997,
+    "reference_text": "32. | | s = 3.997+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "t32.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t32.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@32",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "3.997+",
+      "metric_symbol": "s",
+      "metric_value": 3.997,
+      "reference_text": "32. | | s = 3.997+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "t32.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t32.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "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": -2.1241855069884514
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+    {
+      "id": 28,
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+      "x": 0.4608979486953227,
+      "y": -1.711861067250365
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+    {
+      "id": 29,
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+      "x": 1.972082825523715,
+      "y": 0.503046367080047
+    },
+    {
+      "id": 30,
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+      "x": 2.1219470493098105,
+      "y": -0.05454380865896381
+    },
+    {
+      "id": 31,
+      "rotation_radians": -3.4060889765320987,
+      "x": -0.6510490399774499,
+      "y": -1.8214793509514409
+    },
+    {
+      "id": 32,
+      "rotation_radians": -0.2595633933231656,
+      "x": -0.8049988994216667,
+      "y": -1.2624242259476655
+    }
+  ],
+  "problem": "32 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t32.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_033_652d6c2cf21c385c.json b/data/solutions/generated/triinsqu_033_652d6c2cf21c385c.json
new file mode 100644
index 0000000000000000000000000000000000000000..43ed09c91a6b7af23d32bb5973cfe94a41d7566a
--- /dev/null
+++ b/data/solutions/generated/triinsqu_033_652d6c2cf21c385c.json
@@ -0,0 +1,260 @@
+{
+  "case": "triinsqu@33",
+  "container": {
+    "circumradius": 2.922285129707092,
+    "orientation_radians": 0.0,
+    "side_length": 4.132735263552989,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@33",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "4.058+",
+    "metric_symbol": "s",
+    "metric_value": 4.058,
+    "reference_text": "33. | | s = 4.058+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "t33.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t33.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@33",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "4.058+",
+      "metric_symbol": "s",
+      "metric_value": 4.058,
+      "reference_text": "33. | | s = 4.058+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "t33.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t33.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "rotation_radians": -2.367453265013262,
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+    {
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+      "y": 1.0533539412412942
+    },
+    {
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+      "y": 0.6449199060494787
+    },
+    {
+      "id": 27,
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+      "x": -0.16198219377737957,
+      "y": 2.3308301413459374
+    },
+    {
+      "id": 28,
+      "rotation_radians": 0.7741380623368475,
+      "x": -2.3553221593729585,
+      "y": -0.1507694763077363
+    },
+    {
+      "id": 29,
+      "rotation_radians": -2.351831958117701,
+      "x": 1.745769961470591,
+      "y": -0.47118626920515483
+    },
+    {
+      "id": 30,
+      "rotation_radians": 0.7901302125098626,
+      "x": 0.9311945160656738,
+      "y": -1.282044053967975
+    },
+    {
+      "id": 31,
+      "rotation_radians": 0.7799189955802932,
+      "x": 2.1577371343872707,
+      "y": -0.059686848528291515
+    },
+    {
+      "id": 32,
+      "rotation_radians": -2.3297396304994886,
+      "x": 0.5218253896685254,
+      "y": -1.7043962677244997
+    },
+    {
+      "id": 33,
+      "rotation_radians": -1.8628816588742274,
+      "x": 0.5959817440029924,
+      "y": 1.631882694642362
+    }
+  ],
+  "problem": "33 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t33.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_034_5f00ff525459125e.json b/data/solutions/generated/triinsqu_034_5f00ff525459125e.json
new file mode 100644
index 0000000000000000000000000000000000000000..411616bfb96c73d13a8125feb00e10257b5689eb
--- /dev/null
+++ b/data/solutions/generated/triinsqu_034_5f00ff525459125e.json
@@ -0,0 +1,266 @@
+{
+  "case": "triinsqu@34",
+  "container": {
+    "circumradius": 2.9504955951110787,
+    "orientation_radians": 0.0,
+    "side_length": 4.172630886328164,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@34",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "4.098+",
+    "metric_symbol": "s",
+    "metric_value": 4.098,
+    "reference_text": "34. | | s = 4.098+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "t34.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t34.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000030000300001,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@34",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "4.098+",
+      "metric_symbol": "s",
+      "metric_value": 4.098,
+      "reference_text": "34. | | s = 4.098+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "t34.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t34.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "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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+    },
+    {
+      "id": 24,
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+      "y": 0.5324380844367061
+    },
+    {
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+      "y": 0.06651031698406451
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+    {
+      "id": 26,
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+      "x": 1.2404076353134315,
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+    {
+      "id": 27,
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+      "y": -1.9973667898389835
+    },
+    {
+      "id": 28,
+      "rotation_radians": 0.2730872796299191,
+      "x": 2.0406958230018284,
+      "y": -0.49358534020539513
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.16162865542701418,
+      "x": -1.0324036658978044,
+      "y": 1.1056880164979752
+    },
+    {
+      "id": 30,
+      "rotation_radians": 0.16162838127866772,
+      "x": -1.8094660049897169,
+      "y": 0.32862110860720734
+    },
+    {
+      "id": 31,
+      "rotation_radians": -0.3506327393885874,
+      "x": 0.09412184531695486,
+      "y": 2.366941312021079
+    },
+    {
+      "id": 32,
+      "rotation_radians": -2.972332268117263,
+      "x": -1.599671215673158,
+      "y": 0.8777544989101429
+    },
+    {
+      "id": 33,
+      "rotation_radians": -2.9775665796227706,
+      "x": -0.8281598629617407,
+      "y": 1.6470013706820985
+    },
+    {
+      "id": 34,
+      "rotation_radians": -3.007969784291189,
+      "x": -2.37055816971197,
+      "y": 0.07071879618315917
+    }
+  ],
+  "problem": "34 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t34.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_035_0fd80a947c5904bb.json b/data/solutions/generated/triinsqu_035_0fd80a947c5904bb.json
new file mode 100644
index 0000000000000000000000000000000000000000..d6c5596c871676da33fffb0784b93d38e4c1addb
--- /dev/null
+++ b/data/solutions/generated/triinsqu_035_0fd80a947c5904bb.json
@@ -0,0 +1,272 @@
+{
+  "case": "triinsqu@35",
+  "container": {
+    "circumradius": 2.971114295635399,
+    "orientation_radians": 0.0,
+    "side_length": 4.201790132248166,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triinsqu@35",
+    "credit": "Erich Friedman",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "9(2\u221a3\u20133) = 4.176+",
+    "metric_symbol": "s",
+    "metric_value": 4.176,
+    "reference_text": "35. | | s = 9(2\u221a3\u20133) = 4.176+ | Found by Erich Friedman | in April 2026.",
+    "source_image": "t35.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t35.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triinsqu@35",
+      "credit": "Erich Friedman",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "9(2\u221a3\u20133) = 4.176+",
+      "metric_symbol": "s",
+      "metric_value": 4.176,
+      "reference_text": "35. | | s = 9(2\u221a3\u20133) = 4.176+ | Found by Erich Friedman | in April 2026.",
+      "source_image": "t35.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t35.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 0.25945225280083234,
+      "x": 0.03860414067806889,
+      "y": -0.0763587712880587
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+    },
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+      "y": 0.039913766621611745
+    },
+    {
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+      "x": 1.261446605264178,
+      "y": -1.2997554199641137
+    },
+    {
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+    },
+    {
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+    {
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+      "y": 1.115616579825169
+    },
+    {
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+      "y": 0.3009614784803664
+    },
+    {
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+      "rotation_radians": 0.24240270447804094,
+      "x": -0.3095771628292645,
+      "y": 1.8451660860146488
+    },
+    {
+      "id": 32,
+      "rotation_radians": -2.8797932364050074,
+      "x": -1.598558403512083,
+      "y": 0.9643047260440056
+    },
+    {
+      "id": 33,
+      "rotation_radians": -2.879791804122578,
+      "x": -0.8751177610486714,
+      "y": 1.6877336364481224
+    },
+    {
+      "id": 34,
+      "rotation_radians": -2.8882608698691485,
+      "x": -2.412173426509581,
+      "y": 0.14470459585110587
+    },
+    {
+      "id": 35,
+      "rotation_radians": -2.8813380740449324,
+      "x": -0.1519164883774582,
+      "y": 2.4098445941556377
+    }
+  ],
+  "problem": "35 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t35.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_036_73acd05c27fe131e.json b/data/solutions/generated/triinsqu_036_73acd05c27fe131e.json
new file mode 100644
index 0000000000000000000000000000000000000000..a3bb1d3f84b50f8ad44b1dc8646134593301dfac
--- /dev/null
+++ b/data/solutions/generated/triinsqu_036_73acd05c27fe131e.json
@@ -0,0 +1,278 @@
+{
+  "case": "triinsqu@36",
+  "container": {
+    "circumradius": 3.000572436839074,
+    "orientation_radians": 0.0,
+    "side_length": 4.243450235060705,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@36",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "4.214+",
+    "metric_symbol": "s",
+    "metric_value": 4.214,
+    "reference_text": "36. | | s = 4.214+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "t36.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t36.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@36",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "4.214+",
+      "metric_symbol": "s",
+      "metric_value": 4.214,
+      "reference_text": "36. | | s = 4.214+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "t36.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t36.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "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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+      "x": -1.8174585956723992,
+      "y": 0.3678040981258096
+    },
+    {
+      "id": 31,
+      "rotation_radians": 0.22615292448572208,
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+      "y": 1.8704820339969461
+    },
+    {
+      "id": 32,
+      "rotation_radians": -2.9321247362610583,
+      "x": -1.6383072688870293,
+      "y": 0.9175748989211251
+    },
+    {
+      "id": 33,
+      "rotation_radians": -2.912138809313208,
+      "x": -0.8690205545519143,
+      "y": 1.7006390498488515
+    },
+    {
+      "id": 34,
+      "rotation_radians": -3.0474844382282176,
+      "x": -2.4073741807509696,
+      "y": 0.0551558802148674
+    },
+    {
+      "id": 35,
+      "rotation_radians": -2.898309128590855,
+      "x": -0.14715360838671782,
+      "y": 2.432130543176579
+    },
+    {
+      "id": 36,
+      "rotation_radians": 0.7853945224534403,
+      "x": -0.8565560058283775,
+      "y": -1.7357570979458437
+    }
+  ],
+  "problem": "36 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t36.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_038_a013f42c7873094a.json b/data/solutions/generated/triinsqu_038_a013f42c7873094a.json
new file mode 100644
index 0000000000000000000000000000000000000000..31e6a68227a91d6b3830e03949ec989ead823795
--- /dev/null
+++ b/data/solutions/generated/triinsqu_038_a013f42c7873094a.json
@@ -0,0 +1,290 @@
+{
+  "case": "triinsqu@38",
+  "container": {
+    "circumradius": 3.075823003347129,
+    "orientation_radians": 0.0,
+    "side_length": 4.349870606792655,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@38",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "4.327+",
+    "metric_symbol": "s",
+    "metric_value": 4.327,
+    "reference_text": "38. | | s = 4.327+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "t38.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t38.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@38",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "4.327+",
+      "metric_symbol": "s",
+      "metric_value": 4.327,
+      "reference_text": "38. | | s = 4.327+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "t38.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t38.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "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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+      "y": -1.6024302334094722
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+    },
+    {
+      "id": 29,
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+    },
+    {
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+      "x": -0.7670430085286071,
+      "y": -0.6757165899598165
+    },
+    {
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+      "x": 0.609084025619551,
+      "y": -0.8323535535790949
+    },
+    {
+      "id": 32,
+      "rotation_radians": 2.8797901122338594,
+      "x": -1.9217200013067348,
+      "y": -0.7458402184557982
+    },
+    {
+      "id": 33,
+      "rotation_radians": 0.7853981634443868,
+      "x": -0.5066332778886725,
+      "y": -2.160922700828484
+    },
+    {
+      "id": 34,
+      "rotation_radians": -0.7849409229909335,
+      "x": 0.9098156477702252,
+      "y": -1.3482693148605664
+    },
+    {
+      "id": 35,
+      "rotation_radians": 3.3990419512790275,
+      "x": -1.7711882529928056,
+      "y": 0.8932346625377247
+    },
+    {
+      "id": 36,
+      "rotation_radians": 2.3421844551839284,
+      "x": 0.35306529747845894,
+      "y": 0.1467154957048997
+    },
+    {
+      "id": 37,
+      "rotation_radians": 6.545265234295749,
+      "x": 2.175030515410515,
+      "y": -0.492335981769974
+    },
+    {
+      "id": 38,
+      "rotation_radians": 3.403674181791824,
+      "x": 1.6173566827782135,
+      "y": -0.6418726052768812
+    }
+  ],
+  "problem": "38 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t38.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_039_5f6780607ec0989b.json b/data/solutions/generated/triinsqu_039_5f6780607ec0989b.json
new file mode 100644
index 0000000000000000000000000000000000000000..4f7e43b228a72480e3089d3cdcc0316430032de6
--- /dev/null
+++ b/data/solutions/generated/triinsqu_039_5f6780607ec0989b.json
@@ -0,0 +1,296 @@
+{
+  "case": "triinsqu@39",
+  "container": {
+    "circumradius": 3.1120014478097833,
+    "orientation_radians": 0.0,
+    "side_length": 4.401034653617303,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@39",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "4.383+",
+    "metric_symbol": "s",
+    "metric_value": 4.383,
+    "reference_text": "39. | | s = 4.383+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "t39.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t39.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@39",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "4.383+",
+      "metric_symbol": "s",
+      "metric_value": 4.383,
+      "reference_text": "39. | | s = 4.383+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "t39.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t39.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "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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+    {
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+    {
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+      "x": -2.146039031707975,
+      "y": -0.5577043603650729
+    }
+  ],
+  "problem": "39 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t39.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triinsqu_040_ccf2360cc8917adc.json b/data/solutions/generated/triinsqu_040_ccf2360cc8917adc.json
new file mode 100644
index 0000000000000000000000000000000000000000..347f330792aec5453e57a1b2427b5ea038fd7045
--- /dev/null
+++ b/data/solutions/generated/triinsqu_040_ccf2360cc8917adc.json
@@ -0,0 +1,302 @@
+{
+  "case": "triinsqu@40",
+  "container": {
+    "circumradius": 3.139086540920165,
+    "orientation_radians": 0.0,
+    "side_length": 4.439338759632142,
+    "sides": 4,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triinsqu@40",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "4/29/26",
+    "metric_expression": "4.437+",
+    "metric_symbol": "s",
+    "metric_value": 4.437,
+    "reference_text": "40. | | s = 4.437+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "t40.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t40.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+    "title": "Triangles in Squares"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triinsqu@40",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "4/29/26",
+      "metric_expression": "4.437+",
+      "metric_symbol": "s",
+      "metric_value": 4.437,
+      "reference_text": "40. | | s = 4.437+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "t40.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triinsqu/t40.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triinsqu/",
+      "title": "Triangles in Squares"
+    },
+    "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/triinsqu/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+    {
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+      "x": -0.9617517668226624,
+      "y": 1.3242495559230765
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+    {
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+      "x": -1.661121583418974,
+      "y": 0.6279661151372248
+    },
+    {
+      "id": 31,
+      "rotation_radians": 0.2900108425448924,
+      "x": -0.2601481417789495,
+      "y": 2.0090231768325055
+    },
+    {
+      "id": 32,
+      "rotation_radians": -2.8538261214512843,
+      "x": -1.5238322814711756,
+      "y": 1.1887792980987817
+    },
+    {
+      "id": 33,
+      "rotation_radians": -2.8537366920200964,
+      "x": -0.8268912020027672,
+      "y": 1.8856520033730757
+    },
+    {
+      "id": 34,
+      "rotation_radians": -2.853826615158589,
+      "x": -2.2224591111090306,
+      "y": 0.4901540692778629
+    },
+    {
+      "id": 35,
+      "rotation_radians": -2.841804063757322,
+      "x": -0.1281399132777514,
+      "y": 2.5761161741386616
+    },
+    {
+      "id": 36,
+      "rotation_radians": 0.2919341363784985,
+      "x": -1.1443346599135655,
+      "y": -1.3002383591186428
+    },
+    {
+      "id": 37,
+      "rotation_radians": -2.8496583342168207,
+      "x": -0.7239537084184194,
+      "y": -1.6960219535476868
+    },
+    {
+      "id": 38,
+      "rotation_radians": -2.8538252813712295,
+      "x": -1.9573202536203045,
+      "y": -0.46427975501759494
+    },
+    {
+      "id": 39,
+      "rotation_radians": 0.2877659288514639,
+      "x": -2.3760459314657516,
+      "y": -0.06674765588688412
+    },
+    {
+      "id": 40,
+      "rotation_radians": 0.293523691839152,
+      "x": 0.13139311065962123,
+      "y": -2.5766530438827044
+    }
+  ],
+  "problem": "40 equal items for Triangles in Squares",
+  "setup": "triinsqu",
+  "source_image": "https://erich-friedman.github.io/packing/triinsqu/t40.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triinsqu/"
+}
diff --git a/data/solutions/generated/triintri_021_51d32dd1bf4348fb.json b/data/solutions/generated/triintri_021_51d32dd1bf4348fb.json
new file mode 100644
index 0000000000000000000000000000000000000000..b4e7e942ad82a6fe65c91e55845d9646dfff1390
--- /dev/null
+++ b/data/solutions/generated/triintri_021_51d32dd1bf4348fb.json
@@ -0,0 +1,188 @@
+{
+  "case": "triintri@21",
+  "container": {
+    "circumradius": 2.886846663972746,
+    "orientation_radians": 0.0,
+    "side_length": 5.000165095661513,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triintri@21",
+    "credit": "Maurizio Morandi",
+    "date": "May 2008",
+    "family_updated": "2/29/26",
+    "metric_expression": "4.923+",
+    "metric_symbol": "s",
+    "metric_value": 4.923,
+    "reference_text": "s = 4.923+ | Found by Maurizio Morandi | in May 2008.",
+    "source_image": "tt21.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt21.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triintri@21",
+      "credit": "Maurizio Morandi",
+      "date": "May 2008",
+      "family_updated": "2/29/26",
+      "metric_expression": "4.923+",
+      "metric_symbol": "s",
+      "metric_value": 4.923,
+      "reference_text": "s = 4.923+ | Found by Maurizio Morandi | in May 2008.",
+      "source_image": "tt21.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt21.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
+      "title": "Triangles in Triangles"
+    },
+    "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/triintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
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+      "x": 0.9260646858161644,
+      "y": -0.4669883894908596
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+  ],
+  "problem": "21 equal items for Triangles in Triangles",
+  "setup": "triintri",
+  "source_image": "https://erich-friedman.github.io/packing/triintri/tt21.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_022_2122d833c6fcab70.json b/data/solutions/generated/triintri_022_2122d833c6fcab70.json
new file mode 100644
index 0000000000000000000000000000000000000000..dd7be53b4118087acbb6ce62d1e9adaf8a81c5ac
--- /dev/null
+++ b/data/solutions/generated/triintri_022_2122d833c6fcab70.json
@@ -0,0 +1,194 @@
+{
+  "case": "triintri@22",
+  "container": {
+    "circumradius": 2.8868751328982873,
+    "orientation_radians": 0.0,
+    "side_length": 5.000214405286989,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triintri@22",
+    "credit": "Maurizio Morandi",
+    "date": "May 2008",
+    "family_updated": "2/29/26",
+    "metric_expression": "4.996+",
+    "metric_symbol": "s",
+    "metric_value": 4.996,
+    "reference_text": "s = 4.996+ | Found by Maurizio Morandi | in May 2008.",
+    "source_image": "tt22.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt22.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triintri@22",
+      "credit": "Maurizio Morandi",
+      "date": "May 2008",
+      "family_updated": "2/29/26",
+      "metric_expression": "4.996+",
+      "metric_symbol": "s",
+      "metric_value": 4.996,
+      "reference_text": "s = 4.996+ | Found by Maurizio Morandi | in May 2008.",
+      "source_image": "tt22.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt22.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
+      "title": "Triangles in Triangles"
+    },
+    "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/triintri/",
+    "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 Triangles in Triangles",
+  "setup": "triintri",
+  "source_image": "https://erich-friedman.github.io/packing/triintri/tt22.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_023_c27df81200778ffb.json b/data/solutions/generated/triintri_023_c27df81200778ffb.json
new file mode 100644
index 0000000000000000000000000000000000000000..9bee78f7e0e62d5d13a251eefa2ef62cbf079df1
--- /dev/null
+++ b/data/solutions/generated/triintri_023_c27df81200778ffb.json
@@ -0,0 +1,200 @@
+{
+  "case": "triintri@23",
+  "container": {
+    "circumradius": 2.886860915368747,
+    "orientation_radians": 0.0,
+    "side_length": 5.000189779803466,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triintri@23",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "2/29/26",
+    "metric_expression": "5",
+    "metric_symbol": "s",
+    "metric_value": 5.0,
+    "reference_text": "s = 5 | Trivial.",
+    "source_image": "tt25.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triintri@23",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "2/29/26",
+      "metric_expression": "5",
+      "metric_symbol": "s",
+      "metric_value": 5.0,
+      "reference_text": "s = 5 | Trivial.",
+      "source_image": "tt25.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
+      "title": "Triangles in Triangles"
+    },
+    "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/triintri/",
+    "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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+      "x": -0.8660528997414253,
+      "y": 1.5000528390892178
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+  ],
+  "problem": "23 equal items for Triangles in Triangles",
+  "setup": "triintri",
+  "source_image": "https://erich-friedman.github.io/packing/triintri/tt25.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_024_c9e2b321b60a0e78.json b/data/solutions/generated/triintri_024_c9e2b321b60a0e78.json
new file mode 100644
index 0000000000000000000000000000000000000000..a83323719ffe62dd1f10f54e92c73ce96c2e1a5d
--- /dev/null
+++ b/data/solutions/generated/triintri_024_c9e2b321b60a0e78.json
@@ -0,0 +1,206 @@
+{
+  "case": "triintri@24",
+  "container": {
+    "circumradius": 2.8868640720639496,
+    "orientation_radians": 0.0,
+    "side_length": 5.000195247359941,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triintri@24",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "2/29/26",
+    "metric_expression": "5",
+    "metric_symbol": "s",
+    "metric_value": 5.0,
+    "reference_text": "s = 5 | Trivial.",
+    "source_image": "tt25.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triintri@24",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "2/29/26",
+      "metric_expression": "5",
+      "metric_symbol": "s",
+      "metric_value": 5.0,
+      "reference_text": "s = 5 | Trivial.",
+      "source_image": "tt25.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
+      "title": "Triangles in Triangles"
+    },
+    "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/triintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+  ],
+  "problem": "24 equal items for Triangles in Triangles",
+  "setup": "triintri",
+  "source_image": "https://erich-friedman.github.io/packing/triintri/tt25.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_025_5092959dfa8a0e27.json b/data/solutions/generated/triintri_025_5092959dfa8a0e27.json
new file mode 100644
index 0000000000000000000000000000000000000000..4156572ea3c55ee064baf11ec08255af29552c52
--- /dev/null
+++ b/data/solutions/generated/triintri_025_5092959dfa8a0e27.json
@@ -0,0 +1,212 @@
+{
+  "case": "triintri@25",
+  "container": {
+    "circumradius": 2.886834884913793,
+    "orientation_radians": 0.0,
+    "side_length": 5.000144693732942,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triintri@25",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "2/29/26",
+    "metric_expression": "5",
+    "metric_symbol": "s",
+    "metric_value": 5.0,
+    "reference_text": "s = 5 | Trivial.",
+    "source_image": "tt25.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triintri@25",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "2/29/26",
+      "metric_expression": "5",
+      "metric_symbol": "s",
+      "metric_value": 5.0,
+      "reference_text": "s = 5 | Trivial.",
+      "source_image": "tt25.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt25.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
+      "title": "Triangles in Triangles"
+    },
+    "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/triintri/",
+    "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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+    {
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+    {
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+    },
+    {
+      "id": 25,
+      "rotation_radians": 3.1415852654764826,
+      "x": -0.8660540675017624,
+      "y": 1.5000428214877144
+    }
+  ],
+  "problem": "25 equal items for Triangles in Triangles",
+  "setup": "triintri",
+  "source_image": "https://erich-friedman.github.io/packing/triintri/tt25.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_026_8db318b73d49217d.json b/data/solutions/generated/triintri_026_8db318b73d49217d.json
new file mode 100644
index 0000000000000000000000000000000000000000..a4f5a91a174a0d985b0dfcedf794d7771bf68569
--- /dev/null
+++ b/data/solutions/generated/triintri_026_8db318b73d49217d.json
@@ -0,0 +1,218 @@
+{
+  "case": "triintri@26",
+  "container": {
+    "circumradius": 3.1458210093572156,
+    "orientation_radians": 0.0,
+    "side_length": 5.448721819724306,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triintri@26",
+    "credit": "Joah Frenzley",
+    "date": "April 2026",
+    "family_updated": "2/29/26",
+    "metric_expression": "5.406+",
+    "metric_symbol": "s",
+    "metric_value": 5.406,
+    "reference_text": "s = 5.406+ | Found by Joah Frenzley | in April 2026.",
+    "source_image": "tt26.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt26.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triintri@26",
+      "credit": "Joah Frenzley",
+      "date": "April 2026",
+      "family_updated": "2/29/26",
+      "metric_expression": "5.406+",
+      "metric_symbol": "s",
+      "metric_value": 5.406,
+      "reference_text": "s = 5.406+ | Found by Joah Frenzley | in April 2026.",
+      "source_image": "tt26.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt26.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
+      "title": "Triangles in Triangles"
+    },
+    "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/triintri/",
+    "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": -7.500259235878409e-09
+    },
+    {
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+    {
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+      "x": -1.1483323587849912,
+      "y": 0.3332561094092902
+    }
+  ],
+  "problem": "26 equal items for Triangles in Triangles",
+  "setup": "triintri",
+  "source_image": "https://erich-friedman.github.io/packing/triintri/tt26.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_027_f1c2be61e829f1e2.json b/data/solutions/generated/triintri_027_f1c2be61e829f1e2.json
new file mode 100644
index 0000000000000000000000000000000000000000..d9be1b5bcbd3e45d828f8a2b49fcf9acd8cdd8fe
--- /dev/null
+++ b/data/solutions/generated/triintri_027_f1c2be61e829f1e2.json
@@ -0,0 +1,224 @@
+{
+  "case": "triintri@27",
+  "container": {
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+    "orientation_radians": 0.0,
+    "side_length": 5.500192155493054,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triintri@27",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "2/29/26",
+    "metric_expression": "11/2 = 5.500",
+    "metric_symbol": "s",
+    "metric_value": 5.5,
+    "reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.",
+    "source_image": "tt28.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
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+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triintri@27",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "2/29/26",
+      "metric_expression": "11/2 = 5.500",
+      "metric_symbol": "s",
+      "metric_value": 5.5,
+      "reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.",
+      "source_image": "tt28.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
+      "title": "Triangles in Triangles"
+    },
+    "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/triintri/",
+    "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": 23,
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+    {
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+    {
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+    {
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+    {
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+      "x": -1.2990860970291063,
+      "y": -2.2500848999157412
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+  ],
+  "problem": "27 equal items for Triangles in Triangles",
+  "setup": "triintri",
+  "source_image": "https://erich-friedman.github.io/packing/triintri/tt28.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_028_9562d7d6e075a347.json b/data/solutions/generated/triintri_028_9562d7d6e075a347.json
new file mode 100644
index 0000000000000000000000000000000000000000..6d91424dafd6b87a36ce4e117601e2c8c9c14f54
--- /dev/null
+++ b/data/solutions/generated/triintri_028_9562d7d6e075a347.json
@@ -0,0 +1,230 @@
+{
+  "case": "triintri@28",
+  "container": {
+    "circumradius": 3.175523634890182,
+    "orientation_radians": 0.0,
+    "side_length": 5.500168276265596,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triintri@28",
+    "credit": "Erich Friedman",
+    "date": "1997",
+    "family_updated": "2/29/26",
+    "metric_expression": "11/2 = 5.500",
+    "metric_symbol": "s",
+    "metric_value": 5.5,
+    "reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.",
+    "source_image": "tt28.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triintri@28",
+      "credit": "Erich Friedman",
+      "date": "1997",
+      "family_updated": "2/29/26",
+      "metric_expression": "11/2 = 5.500",
+      "metric_symbol": "s",
+      "metric_value": 5.5,
+      "reference_text": "s = 11/2 = 5.500 | Found by Erich Friedman | in 1997.",
+      "source_image": "tt28.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt28.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
+      "title": "Triangles in Triangles"
+    },
+    "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/triintri/",
+    "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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+    {
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+      "x": -1.2990785253239168,
+      "y": 2.2500713843273457
+    },
+    {
+      "id": 23,
+      "rotation_radians": -3.1415818576827457,
+      "x": 1.154736529587972,
+      "y": -0.5000169378527385
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+    {
+      "id": 24,
+      "rotation_radians": 8.763585979686832e-06,
+      "x": 1.732104258918298,
+      "y": -0.5000169436704749
+    },
+    {
+      "id": 25,
+      "rotation_radians": -3.141581954097244,
+      "x": -0.14433947205272424,
+      "y": 1.2500388832162375
+    },
+    {
+      "id": 26,
+      "rotation_radians": 7.579213112610313e-06,
+      "x": -0.43302227584468417,
+      "y": 1.7500533444599347
+    },
+    {
+      "id": 27,
+      "rotation_radians": -2.1550190193066363e-06,
+      "x": -1.2990783250927131,
+      "y": -2.2500728964714147
+    },
+    {
+      "id": 28,
+      "rotation_radians": 3.735710263860949e-06,
+      "x": 2.598158901215976,
+      "y": -8.710915779338132e-07
+    }
+  ],
+  "problem": "28 equal items for Triangles in Triangles",
+  "setup": "triintri",
+  "source_image": "https://erich-friedman.github.io/packing/triintri/tt28.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_029_1e26d810ba567eb4.json b/data/solutions/generated/triintri_029_1e26d810ba567eb4.json
new file mode 100644
index 0000000000000000000000000000000000000000..0a45636cb5c829859a2a6a586f9538741ee1eb26
--- /dev/null
+++ b/data/solutions/generated/triintri_029_1e26d810ba567eb4.json
@@ -0,0 +1,236 @@
+{
+  "case": "triintri@29",
+  "container": {
+    "circumradius": 3.426199144438565,
+    "orientation_radians": 0.0,
+    "side_length": 5.9343509950166125,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triintri@29",
+    "credit": "David W",
+    "date": "July 2007",
+    "family_updated": "2/29/26",
+    "metric_expression": "17/3 = 5.666+",
+    "metric_symbol": "s",
+    "metric_value": 5.666,
+    "reference_text": "s = 17/3 = 5.666+ | Found by David W. Cantrell | in July 2007.",
+    "source_image": "tt29.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt29.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triintri@29",
+      "credit": "David W",
+      "date": "July 2007",
+      "family_updated": "2/29/26",
+      "metric_expression": "17/3 = 5.666+",
+      "metric_symbol": "s",
+      "metric_value": 5.666,
+      "reference_text": "s = 17/3 = 5.666+ | Found by David W. Cantrell | in July 2007.",
+      "source_image": "tt29.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt29.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
+      "title": "Triangles in Triangles"
+    },
+    "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/triintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "y": -1.9132441575608266
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+    {
+      "id": 18,
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+      "x": 2.2466600316261007,
+      "y": 0.014396748755630087
+    },
+    {
+      "id": 19,
+      "rotation_radians": -0.01712147968171313,
+      "x": 1.9487887956740755,
+      "y": 0.5094786630753254
+    },
+    {
+      "id": 20,
+      "rotation_radians": -3.1460735676825085,
+      "x": -1.1357401712652677,
+      "y": -0.9288865044654412
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.022910182412551383,
+      "x": -1.413035675883102,
+      "y": -1.459489634779813
+    },
+    {
+      "id": 22,
+      "rotation_radians": -1.3702749565408005e-06,
+      "x": -1.4243547203869007,
+      "y": 2.4670536120844466
+    },
+    {
+      "id": 23,
+      "rotation_radians": -3.185687540017272,
+      "x": 1.3820292102922778,
+      "y": -0.5141768632623858
+    },
+    {
+      "id": 24,
+      "rotation_radians": -0.017225911940517515,
+      "x": 1.973645420470798,
+      "y": -0.49530228281750777
+    },
+    {
+      "id": 25,
+      "rotation_radians": -2.8755640329191245,
+      "x": -0.13111017117466242,
+      "y": 1.4105620190316457
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.06666729093150213,
+      "x": -0.560164954255608,
+      "y": 1.930410724284226
+    },
+    {
+      "id": 27,
+      "rotation_radians": -0.007598303057121794,
+      "x": -1.4009141734953012,
+      "y": -2.4491696487750696
+    },
+    {
+      "id": 28,
+      "rotation_radians": -0.004192913653787636,
+      "x": 2.8304872883062653,
+      "y": 0.008070451983530428
+    },
+    {
+      "id": 29,
+      "rotation_radians": -3.1371915261215535,
+      "x": -1.1357048758130828,
+      "y": 0.06860300067740176
+    }
+  ],
+  "problem": "29 equal items for Triangles in Triangles",
+  "setup": "triintri",
+  "source_image": "https://erich-friedman.github.io/packing/triintri/tt29.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_030_1ace87e09c5f6fc8.json b/data/solutions/generated/triintri_030_1ace87e09c5f6fc8.json
new file mode 100644
index 0000000000000000000000000000000000000000..6a2362513c70f348dee4c3744aa491e769c2f04e
--- /dev/null
+++ b/data/solutions/generated/triintri_030_1ace87e09c5f6fc8.json
@@ -0,0 +1,242 @@
+{
+  "case": "triintri@30",
+  "container": {
+    "circumradius": 3.385039888444194,
+    "orientation_radians": 0.0,
+    "side_length": 5.863061072432628,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triintri@30",
+    "credit": "Maurizio Morandi",
+    "date": "May 2008",
+    "family_updated": "2/29/26",
+    "metric_expression": "23/4 = 5.75",
+    "metric_symbol": "s",
+    "metric_value": 5.75,
+    "reference_text": "s = 23/4 = 5.75 | Found by Maurizio Morandi | in May 2008.",
+    "source_image": "tt30.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt30.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triintri@30",
+      "credit": "Maurizio Morandi",
+      "date": "May 2008",
+      "family_updated": "2/29/26",
+      "metric_expression": "23/4 = 5.75",
+      "metric_symbol": "s",
+      "metric_value": 5.75,
+      "reference_text": "s = 23/4 = 5.75 | Found by Maurizio Morandi | in May 2008.",
+      "source_image": "tt30.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt30.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
+      "title": "Triangles in Triangles"
+    },
+    "generator": "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/triintri/",
+    "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": 2.228563002576475,
+      "y": -0.00099465753444093
+    },
+    {
+      "id": 19,
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+      "x": 1.940574199430399,
+      "y": 0.499445608529456
+    },
+    {
+      "id": 20,
+      "rotation_radians": -3.152459550684218,
+      "x": -1.1151749185969324,
+      "y": -0.9202173652516796
+    },
+    {
+      "id": 21,
+      "rotation_radians": -0.002787670788031332,
+      "x": -1.4023948356558726,
+      "y": -1.4268533729616797
+    },
+    {
+      "id": 22,
+      "rotation_radians": 6.305861203922947e-07,
+      "x": -1.4038134125121906,
+      "y": 2.425912133311592
+    },
+    {
+      "id": 23,
+      "rotation_radians": -3.13938591286586,
+      "x": 1.3612959261289472,
+      "y": -0.5017254735505068
+    },
+    {
+      "id": 24,
+      "rotation_radians": 0.002169035422815537,
+      "x": 1.9386968254048949,
+      "y": -0.500448620086004
+    },
+    {
+      "id": 25,
+      "rotation_radians": -2.625876487035642,
+      "x": 0.03644988386249646,
+      "y": 1.3533198027972884
+    },
+    {
+      "id": 26,
+      "rotation_radians": 2.74436385669055e-06,
+      "x": -0.5377315181867781,
+      "y": 1.931435569752772
+    },
+    {
+      "id": 27,
+      "rotation_radians": 4.2782761204968766e-05,
+      "x": -1.4035883668619658,
+      "y": -2.431289606785198
+    },
+    {
+      "id": 28,
+      "rotation_radians": 0.00036796750907112724,
+      "x": 2.8071131567848537,
+      "y": 6.161892937853694e-05
+    },
+    {
+      "id": 29,
+      "rotation_radians": -3.2658153064674647,
+      "x": -1.119595546364335,
+      "y": 0.34360241570983546
+    },
+    {
+      "id": 30,
+      "rotation_radians": -0.005692315935521574,
+      "x": -1.388916212744204,
+      "y": -0.2632375343347301
+    }
+  ],
+  "problem": "30 equal items for Triangles in Triangles",
+  "setup": "triintri",
+  "source_image": "https://erich-friedman.github.io/packing/triintri/tt30.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_031_e94aa7c2fc600373.json b/data/solutions/generated/triintri_031_e94aa7c2fc600373.json
new file mode 100644
index 0000000000000000000000000000000000000000..f1a4298fa965a9cc276f549aaf8bcc7d5e04e196
--- /dev/null
+++ b/data/solutions/generated/triintri_031_e94aa7c2fc600373.json
@@ -0,0 +1,248 @@
+{
+  "case": "triintri@31",
+  "container": {
+    "circumradius": 3.4552664201656547,
+    "orientation_radians": 0.0,
+    "side_length": 5.984696993413546,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triintri@31",
+    "credit": "Emerson Connelly",
+    "date": "April 2026",
+    "family_updated": "2/29/26",
+    "metric_expression": "5.912+",
+    "metric_symbol": "s",
+    "metric_value": 5.912,
+    "reference_text": "s = 5.912+ | Found by Emerson Connelly | in April 2026.",
+    "source_image": "tt31.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt31.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000700021000353,
+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triintri@31",
+      "credit": "Emerson Connelly",
+      "date": "April 2026",
+      "family_updated": "2/29/26",
+      "metric_expression": "5.912+",
+      "metric_symbol": "s",
+      "metric_value": 5.912,
+      "reference_text": "s = 5.912+ | Found by Emerson Connelly | in April 2026.",
+      "source_image": "tt31.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt31.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
+      "title": "Triangles in Triangles"
+    },
+    "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/triintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
+      "rotation_radians": 2.0886499761420567,
+      "x": 0.2812020383319575,
+      "y": 0.46387920394800314
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+    },
+    {
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+    },
+    {
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+    },
+    {
+      "id": 21,
+      "rotation_radians": 2.0943911609749235,
+      "x": 2.8778836831854147,
+      "y": -1.0620042248207255e-11
+    },
+    {
+      "id": 22,
+      "rotation_radians": 1.0428783366268315,
+      "x": 2.298344144611439,
+      "y": -1.744122344414036e-05
+    },
+    {
+      "id": 23,
+      "rotation_radians": -1.2197715703786823e-06,
+      "x": -1.4389408003062725,
+      "y": 2.492316634066301
+    },
+    {
+      "id": 24,
+      "rotation_radians": 1.0557427091983265,
+      "x": -1.141722311571437,
+      "y": -1.9873883823192633
+    },
+    {
+      "id": 25,
+      "rotation_radians": 2.1695724749280085,
+      "x": -1.4022189696372827,
+      "y": 0.5151207444042699
+    },
+    {
+      "id": 26,
+      "rotation_radians": 0.8870400399576205,
+      "x": 0.44371972416739364,
+      "y": -0.9611198960517189
+    },
+    {
+      "id": 27,
+      "rotation_radians": 1.04272538733824,
+      "x": 0.5631910003313485,
+      "y": 0.9803751875686811
+    },
+    {
+      "id": 28,
+      "rotation_radians": 1.0414635707991915,
+      "x": 1.4304508847155428,
+      "y": -0.5023383988884602
+    },
+    {
+      "id": 29,
+      "rotation_radians": 0.00838615563373402,
+      "x": -1.4347600539544323,
+      "y": -2.485077403259616
+    },
+    {
+      "id": 30,
+      "rotation_radians": 1.0491498969790045,
+      "x": -0.3038544828921732,
+      "y": 1.4797621293552434
+    },
+    {
+      "id": 31,
+      "rotation_radians": 1.0427235210798669,
+      "x": 1.4311242503632788,
+      "y": 0.5013754065179874
+    }
+  ],
+  "problem": "31 equal items for Triangles in Triangles",
+  "setup": "triintri",
+  "source_image": "https://erich-friedman.github.io/packing/triintri/tt31.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_032_ea3eb3c434a6db88.json b/data/solutions/generated/triintri_032_ea3eb3c434a6db88.json
new file mode 100644
index 0000000000000000000000000000000000000000..d3327c6c39acad2d87d035730c63a1d24fdfe2a9
--- /dev/null
+++ b/data/solutions/generated/triintri_032_ea3eb3c434a6db88.json
@@ -0,0 +1,254 @@
+{
+  "case": "triintri@32",
+  "container": {
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+    "orientation_radians": 0.0,
+    "side_length": 6.000179653895976,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": false,
+    "case": "triintri@32",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "2/29/26",
+    "metric_expression": "5.951+",
+    "metric_symbol": "s",
+    "metric_value": 5.951,
+    "reference_text": "s = 5.951+ | Found by Ian Watson | in April 2026.",
+    "source_image": "tt32.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt32.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
+  },
+  "item": {
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+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
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+    "friedman_reference": {
+      "analytical_or_proved": false,
+      "case": "triintri@32",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "2/29/26",
+      "metric_expression": "5.951+",
+      "metric_symbol": "s",
+      "metric_value": 5.951,
+      "reference_text": "s = 5.951+ | Found by Ian Watson | in April 2026.",
+      "source_image": "tt32.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt32.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
+      "title": "Triangles in Triangles"
+    },
+    "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/triintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
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+  ],
+  "problem": "32 equal items for Triangles in Triangles",
+  "setup": "triintri",
+  "source_image": "https://erich-friedman.github.io/packing/triintri/tt32.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_033_5e7c3bf3ddd6ef7e.json b/data/solutions/generated/triintri_033_5e7c3bf3ddd6ef7e.json
new file mode 100644
index 0000000000000000000000000000000000000000..bc44aec9ec5f58edcf93c75739e2e2341ed95b6b
--- /dev/null
+++ b/data/solutions/generated/triintri_033_5e7c3bf3ddd6ef7e.json
@@ -0,0 +1,260 @@
+{
+  "case": "triintri@33",
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+    "orientation_radians": 0.0,
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+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triintri@33",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "2/29/26",
+    "metric_expression": "6",
+    "metric_symbol": "s",
+    "metric_value": 6.0,
+    "reference_text": "s = 6 | Trivial. |",
+    "source_image": "tt36.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
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+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triintri@33",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "2/29/26",
+      "metric_expression": "6",
+      "metric_symbol": "s",
+      "metric_value": 6.0,
+      "reference_text": "s = 6 | Trivial. |",
+      "source_image": "tt36.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
+      "title": "Triangles in Triangles"
+    },
+    "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/triintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
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+      "x": -1.1547444662495034,
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+  ],
+  "problem": "33 equal items for Triangles in Triangles",
+  "setup": "triintri",
+  "source_image": "https://erich-friedman.github.io/packing/triintri/tt36.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_034_ec0928eb613cde82.json b/data/solutions/generated/triintri_034_ec0928eb613cde82.json
new file mode 100644
index 0000000000000000000000000000000000000000..a8dbc2f7b96980768d6c0eb418ea2708545d20c1
--- /dev/null
+++ b/data/solutions/generated/triintri_034_ec0928eb613cde82.json
@@ -0,0 +1,266 @@
+{
+  "case": "triintri@34",
+  "container": {
+    "circumradius": 3.4642816665434033,
+    "orientation_radians": 0.0,
+    "side_length": 6.000311858182558,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triintri@34",
+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "2/29/26",
+    "metric_expression": "6",
+    "metric_symbol": "s",
+    "metric_value": 6.0,
+    "reference_text": "s = 6 | Trivial. |",
+    "source_image": "tt36.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000600015000203,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triintri@34",
+      "credit": "Trivial",
+      "date": "",
+      "family_updated": "2/29/26",
+      "metric_expression": "6",
+      "metric_symbol": "s",
+      "metric_value": 6.0,
+      "reference_text": "s = 6 | Trivial. |",
+      "source_image": "tt36.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt36.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
+      "title": "Triangles in Triangles"
+    },
+    "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/triintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
+  },
+  "placements": [
+    {
+      "id": 1,
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+  "problem": "34 equal items for Triangles in Triangles",
+  "setup": "triintri",
+  "source_image": "https://erich-friedman.github.io/packing/triintri/tt36.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_035_e1b770e700ac967a.json b/data/solutions/generated/triintri_035_e1b770e700ac967a.json
new file mode 100644
index 0000000000000000000000000000000000000000..efd46a9c27c6af081e6413648940ea2d4b47f8ea
--- /dev/null
+++ b/data/solutions/generated/triintri_035_e1b770e700ac967a.json
@@ -0,0 +1,272 @@
+{
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+    "family_updated": "2/29/26",
+    "metric_expression": "6",
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+    "reference_text": "s = 6 | Trivial. |",
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+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
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+      "reference_text": "s = 6 | Trivial. |",
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+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
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+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_036_8e7fac2536d01e26.json b/data/solutions/generated/triintri_036_8e7fac2536d01e26.json
new file mode 100644
index 0000000000000000000000000000000000000000..83d42e50733d5967403349545f04e9f1e37949e9
--- /dev/null
+++ b/data/solutions/generated/triintri_036_8e7fac2536d01e26.json
@@ -0,0 +1,278 @@
+{
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+    "credit": "Trivial",
+    "date": "",
+    "family_updated": "2/29/26",
+    "metric_expression": "6",
+    "metric_symbol": "s",
+    "metric_value": 6.0,
+    "reference_text": "s = 6 | Trivial. |",
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+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
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+      "metric_expression": "6",
+      "metric_symbol": "s",
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+      "reference_text": "s = 6 | Trivial. |",
+      "source_image": "tt36.gif",
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+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
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+    "source_url": "https://erich-friedman.github.io/packing/triintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
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+    {
+      "id": 31,
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+      "y": 1.000024443046137
+    },
+    {
+      "id": 32,
+      "rotation_radians": 3.1415861853844795,
+      "x": -0.2886810141217273,
+      "y": 0.5000113586187306
+    },
+    {
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+      "rotation_radians": 3.1415876581285205,
+      "x": -1.1547288548023176,
+      "y": -1.4200009764746755e-06
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+    {
+      "id": 34,
+      "rotation_radians": 3.1415886532271506,
+      "x": -0.2886831537863115,
+      "y": 1.5000352573515516
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+    {
+      "id": 35,
+      "rotation_radians": 3.1415886740816075,
+      "x": -1.154727225361355,
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+    {
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+      "rotation_radians": 3.1415907532542917,
+      "x": -1.1547288469156163,
+      "y": 2.0000457517317813
+    }
+  ],
+  "problem": "36 equal items for Triangles in Triangles",
+  "setup": "triintri",
+  "source_image": "https://erich-friedman.github.io/packing/triintri/tt36.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_037_a824891b660555f5.json b/data/solutions/generated/triintri_037_a824891b660555f5.json
new file mode 100644
index 0000000000000000000000000000000000000000..c26a39e9377bde1556c0a34422e8b53d9db2fe20
--- /dev/null
+++ b/data/solutions/generated/triintri_037_a824891b660555f5.json
@@ -0,0 +1,284 @@
+{
+  "case": "triintri@37",
+  "container": {
+    "circumradius": 3.6566795617553987,
+    "orientation_radians": 0.0,
+    "side_length": 6.333554787959046,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triintri@37",
+    "credit": "Ian Watson",
+    "date": "April 2026",
+    "family_updated": "2/29/26",
+    "metric_expression": "19/3 = 6.333+",
+    "metric_symbol": "s",
+    "metric_value": 6.333,
+    "reference_text": "s = 19/3 = 6.333+ | Found by Ian Watson | in April 2026.",
+    "source_image": "tt37.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt37.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.000040000600004,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triintri@37",
+      "credit": "Ian Watson",
+      "date": "April 2026",
+      "family_updated": "2/29/26",
+      "metric_expression": "19/3 = 6.333+",
+      "metric_symbol": "s",
+      "metric_value": 6.333,
+      "reference_text": "s = 19/3 = 6.333+ | Found by Ian Watson | in April 2026.",
+      "source_image": "tt37.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt37.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
+      "title": "Triangles in Triangles"
+    },
+    "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/triintri/",
+    "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": 33,
+      "rotation_radians": 1.0472033262256921,
+      "x": -1.2509652155565953,
+      "y": -1.1667035346211863
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+    {
+      "id": 34,
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+      "x": -1.2509654169187077,
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+    },
+    {
+      "id": 35,
+      "rotation_radians": 1.0472050204903673,
+      "x": -1.2509681603891591,
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+    {
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+    },
+    {
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+      "x": 0.769792564923053,
+      "y": 1.3334081346620628
+    }
+  ],
+  "problem": "37 equal items for Triangles in Triangles",
+  "setup": "triintri",
+  "source_image": "https://erich-friedman.github.io/packing/triintri/tt37.gif",
+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_039_5ff069bd30790b7f.json b/data/solutions/generated/triintri_039_5ff069bd30790b7f.json
new file mode 100644
index 0000000000000000000000000000000000000000..a1aace4aca73343c2e276aeac5cd324cc8a2c5af
--- /dev/null
+++ b/data/solutions/generated/triintri_039_5ff069bd30790b7f.json
@@ -0,0 +1,296 @@
+{
+  "case": "triintri@39",
+  "container": {
+    "circumradius": 3.7529414734985855,
+    "orientation_radians": 0.0,
+    "side_length": 6.500285309931957,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triintri@39",
+    "credit": "Erich Friedman",
+    "date": "April 2026",
+    "family_updated": "2/29/26",
+    "metric_expression": "13/2 = 6.500",
+    "metric_symbol": "s",
+    "metric_value": 6.5,
+    "reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.",
+    "source_image": "tt40.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
+  },
+  "item": {
+    "circumradius": 0.5773502691896258,
+    "side_length": 1.0,
+    "sides": 3,
+    "type": "regular_polygon"
+  },
+  "metadata": {
+    "certification_slack": 1.0000500010000102,
+    "friedman_reference": {
+      "analytical_or_proved": true,
+      "case": "triintri@39",
+      "credit": "Erich Friedman",
+      "date": "April 2026",
+      "family_updated": "2/29/26",
+      "metric_expression": "13/2 = 6.500",
+      "metric_symbol": "s",
+      "metric_value": 6.5,
+      "reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.",
+      "source_image": "tt40.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
+      "title": "Triangles in Triangles"
+    },
+    "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/triintri/",
+    "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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+  "problem": "39 equal items for Triangles in Triangles",
+  "setup": "triintri",
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+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
+}
diff --git a/data/solutions/generated/triintri_040_7890a1da940c9143.json b/data/solutions/generated/triintri_040_7890a1da940c9143.json
new file mode 100644
index 0000000000000000000000000000000000000000..ea308d246d81bf7a4eca8badbe28ad4bbdf5be38
--- /dev/null
+++ b/data/solutions/generated/triintri_040_7890a1da940c9143.json
@@ -0,0 +1,302 @@
+{
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+  "friedman_reference": {
+    "analytical_or_proved": true,
+    "case": "triintri@40",
+    "credit": "Erich Friedman",
+    "date": "April 2026",
+    "family_updated": "2/29/26",
+    "metric_expression": "13/2 = 6.500",
+    "metric_symbol": "s",
+    "metric_value": 6.5,
+    "reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.",
+    "source_image": "tt40.gif",
+    "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif",
+    "source_page": "https://erich-friedman.github.io/packing/triintri/",
+    "title": "Triangles in Triangles"
+  },
+  "item": {
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+      "case": "triintri@40",
+      "credit": "Erich Friedman",
+      "date": "April 2026",
+      "family_updated": "2/29/26",
+      "metric_expression": "13/2 = 6.500",
+      "metric_symbol": "s",
+      "metric_value": 6.5,
+      "reference_text": "s = 13/2 = 6.500 | Found by Erich Friedman | in April 2026.",
+      "source_image": "tt40.gif",
+      "source_image_url": "https://erich-friedman.github.io/packing/triintri/tt40.gif",
+      "source_page": "https://erich-friedman.github.io/packing/triintri/",
+      "title": "Triangles in Triangles"
+    },
+    "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/triintri/",
+    "submitted_at": "2026-05-01T01:47:21+00:00",
+    "submitted_by": "polygon-packer-c seed"
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+  "source_page": "https://erich-friedman.github.io/packing/triintri/"
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diff --git a/data/svg/003a713177cb171c.svg b/data/svg/003a713177cb171c.svg
new file mode 100644
index 0000000000000000000000000000000000000000..ece37058a009de75c105793d32ccae0b9cf491db
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+    <circle cx="0" cy="-0" r="3.53691632129" fill="none" stroke-width="0.0707383264257"/>
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+</svg>
diff --git a/data/svg/fe395a0426baa674.svg b/data/svg/fe395a0426baa674.svg
index 68516257357a4ff390a90e6224cb1c172f9a56ab..33d7c3971b7ece97851e1604838caba921ab8c90 100644
--- a/data/svg/fe395a0426baa674.svg
+++ b/data/svg/fe395a0426baa674.svg
@@ -18,6 +18,6 @@
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-    <polygon points="-5.19628164135,2.59814082067 5.19628164135,2.59814082067 5.19628164135,-2.59814082067 -5.19628164135,-2.59814082067" fill="none" stroke-width="0.139899890344"/>
+    <polygon points="-5.19628164135,2.59814082067 5.19628164135,2.59814082067 5.19628164135,-2.59814082067 -5.19628164135,-2.59814082067" fill="none" stroke-width="0.103925632827"/>
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diff --git a/data/svg/fe93ba87f23c6c01.svg b/data/svg/fe93ba87f23c6c01.svg
index 0b2fc90552aabfe40cced8d8bb53f29dafc5bd86..f87f9797909f642deb9c8dcde74aab435c527c2b 100644
--- a/data/svg/fe93ba87f23c6c01.svg
+++ b/data/svg/fe93ba87f23c6c01.svg
@@ -7,6 +7,6 @@
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-    <circle cx="0" cy="-0" r="1.00001796174" fill="none" stroke-width="0.0269235605084"/>
+    <circle cx="0" cy="-0" r="1.00001796174" fill="none" stroke-width="0.0200003592348"/>
   </g>
 </svg>
diff --git a/data/svg/fe973ff9a23dc34c.svg b/data/svg/fe973ff9a23dc34c.svg
index 8b138a2bbb20bff9a559ed353bd7803ab5f6eee9..7041592d492cd2bc423fe576496146b105d86c8b 100644
--- a/data/svg/fe973ff9a23dc34c.svg
+++ b/data/svg/fe973ff9a23dc34c.svg
@@ -4,6 +4,6 @@
     <circle cx="-0.816532270362" cy="0.816532270362" r="1" fill="#cdf7d6" stroke-width="0.0165751013722"/>
     <circle cx="1.11540736073" cy="0.298870909648" r="1" fill="#cdf7d6" stroke-width="0.0165751013722"/>
     <circle cx="-0.298870909648" cy="-1.11540736073" r="1" fill="#cdf7d6" stroke-width="0.0165751013722"/>
-    <circle cx="0" cy="-0" r="2.15476317839" fill="none" stroke-width="0.0580128548027"/>
+    <circle cx="0" cy="-0" r="2.15476317839" fill="none" stroke-width="0.0430952635677"/>
   </g>
 </svg>
diff --git a/data/svg/ff43d04cda84c856.svg b/data/svg/ff43d04cda84c856.svg
index 4e3d56820aeacc61558d312c150a350f4836a7f2..730e0ba0bdcd8739334adaad322908584d619d7b 100644
--- a/data/svg/ff43d04cda84c856.svg
+++ b/data/svg/ff43d04cda84c856.svg
@@ -3,6 +3,6 @@
   <g stroke="black" stroke-linejoin="round">
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-    <polygon points="2.23210575749,-0 1.36677058564e-16,-2.23210575749 -2.23210575749,-2.73354117127e-16 -4.10031175691e-16,2.23210575749" fill="none" stroke-width="0.0600951550094"/>
+    <polygon points="2.23210575749,-0 1.36677058564e-16,-2.23210575749 -2.23210575749,-2.73354117127e-16 -4.10031175691e-16,2.23210575749" fill="none" stroke-width="0.0446421151498"/>
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diff --git a/data/svg/ffb43ba6e2cd5818.svg b/data/svg/ffb43ba6e2cd5818.svg
new file mode 100644
index 0000000000000000000000000000000000000000..1fb0b27a33df6ecfbbcb0685a4cff33d39af1cd7
--- /dev/null
+++ b/data/svg/ffb43ba6e2cd5818.svg
@@ -0,0 +1,32 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-3.87075686194 -3.39931769149 7.74151372387 6.79863538298" width="900" height="900">
+  <title>squinhex@26</title>
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+</svg>
diff --git a/data/svg/ffc152ae79167d33.svg b/data/svg/ffc152ae79167d33.svg
index f1d3a37b6c6534c855f487fca0a53da112f0f85f..33f27ad191ef23d5f4d833bd1482bacb102363b0 100644
--- a/data/svg/ffc152ae79167d33.svg
+++ b/data/svg/ffc152ae79167d33.svg
@@ -15,6 +15,6 @@
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-    <polygon points="3.7321625744,-0 -1.8660812872,-3.23214760048 -1.8660812872,3.23214760048" fill="none" stroke-width="0.0870193584746"/>
+    <polygon points="3.7321625744,-0 -1.8660812872,-3.23214760048 -1.8660812872,3.23214760048" fill="none" stroke-width="0.0646429520097"/>
   </g>
 </svg>
diff --git a/packing_benchmark/renderer.py b/packing_benchmark/renderer.py
index 646c2bac358cdb299f28487a867bbef854d985fb..52a40fd1746f583958dce484c8744b08a72f8e26 100644
--- a/packing_benchmark/renderer.py
+++ b/packing_benchmark/renderer.py
@@ -161,9 +161,9 @@ def svg_markup(solution: dict[str, Any], size: int = 900) -> str:
     if container["kind"] == "circle":
         cx, cy = container["center"]
         body.append(
-            f'    <circle cx="{cx:.12g}" cy="{-cy:.12g}" r="{container["radius"]:.12g}" fill="none" stroke-width="{3.5 * stroke:.12g}"/>'
+            f'    <circle cx="{cx:.12g}" cy="{-cy:.12g}" r="{container["radius"]:.12g}" fill="none" stroke-width="{2.6 * stroke:.12g}"/>'
         )
     else:
-        body.append(f'    <polygon points="{pts(container["vertices"])}" fill="none" stroke-width="{3.5 * stroke:.12g}"/>')
+        body.append(f'    <polygon points="{pts(container["vertices"])}" fill="none" stroke-width="{2.6 * stroke:.12g}"/>')
     body.extend(["  </g>", "</svg>"])
     return "\n".join(body) + "\n"