From 07adc46931af22160239f507e6d4706a576095b1 Mon Sep 17 00:00:00 2001
From: openresearch <bot@openresearch.sh>
Date: Sat, 4 Jul 2026 08:47:32 +0000
Subject: [PATCH] fix(hn): fix Golomb graph construction + EVAL NoneType
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1. Golomb graph: scale pentagon to side=1 (radius=1/(2*sin(π/5)))
   Previous construction had 0 edges (vertices not at unit distance)
2. Fix f-string NoneType crash in EVAL writer when welch_wynn is None
---
 scripts/hn_spectral_database.py | 30 ++++++++++++++++--------------
 1 file changed, 16 insertions(+), 14 deletions(-)

diff --git a/scripts/hn_spectral_database.py b/scripts/hn_spectral_database.py
index adeb7caf..9be9bd64 100644
--- a/scripts/hn_spectral_database.py
+++ b/scripts/hn_spectral_database.py
@@ -47,26 +47,26 @@ def moser_spindle():
     return adj, pts, "Moser spindle", 4
 
 def golomb_graph():
-    """Golomb graph: 10 vertices, χ=4, unit-distance graph.
+    """Golomb graph: 10 vertices, unit-distance graph.
     
-    Constructed from two 5-cycles sharing a vertex, with unit distances.
-    Based on Golomb's construction (1970).
+    Two regular pentagons with side length 1, sharing one vertex.
+    Pentagon side = 1 → radius = 1/(2*sin(π/5)).
     """
-    # Golomb's 10-vertex graph: two pentagons connected at one vertex
-    # Each pentagon has side length 1 (unit distance)
+    r = 1.0 / (2 * math.sin(math.pi / 5))  # circumradius for side=1
     pts = []
-    # First pentagon centered at origin
+    # First pentagon, vertex 0 at origin
     for i in range(5):
         angle = 2 * math.pi * i / 5
-        pts.append((math.cos(angle), math.sin(angle)))
-    # Second pentagon, rotated and translated
-    # The connection vertex is at (1, 0) — shared
-    # Second pentagon centered at (2, 0), rotated by π/5
-    cx, cy = 2.0, 0.0
+        pts.append((r * math.cos(angle) - r, r * math.sin(angle)))
+    # Second pentagon, sharing vertex 0, rotated by π/5
     for i in range(5):
         angle = 2 * math.pi * i / 5 + math.pi / 5
-        pts.append((cx + math.cos(angle), cy + math.sin(angle)))
+        # Shift so vertex 0 aligns with first pentagon's vertex 0
+        dx = r * math.cos(math.pi / 5) - r
+        dy = r * math.sin(math.pi / 5)
+        pts.append((r * math.cos(angle) - r - dx, r * math.sin(angle) - dy))
     
+    pts = hn.remove_duplicates(pts)
     adj = hn.build_adjacency(pts)
     n_v = len(pts)
     n_e = sum(len(a) for a in adj) // 2
@@ -357,11 +357,13 @@ def write_eval(results):
         "|-------|---|---|-------|------|---------|--------|------------|------|---------|-----|",
     ]
     for g in results["graphs"]:
+        ww = g['welch_wynn']
+        ww_str = f"{ww:.4f}" if ww is not None else "N/A"
         lines.append(
             f"| {g['description']} | {g['n_vertices']} | {g['n_edges']} | "
             f"{g['lambda_max']:.4f} | {g['lambda_min']:.4f} | "
-            f"{g['hoffman_bound']:.4f} | {g['chi_hoffman']} | "
-            f"{g['welch_wynn']:.4f if g['welch_wynn'] else 'N/A'} | "
+            f"{g['hoffman_bound']:.4f} if g['hoffman_bound'] is not None else 'inf' | "
+            f"{g['chi_hoffman']} | {ww_str} | "
             f"{g['chi_welch_wynn']} | {g['chi_known']} | {g['gap']} |"
         )