fix(adversarial): repair sofa coloring scripts + Hoffman bound

Adversarial review findings and fixes:
- CRITICAL: v3 hash() -> deterministic_seed (SHA-256) for reproducibility
- HIGH: EPS 0.05 -> 1e-5 (5 orders too wide)
- HIGH: L-corridor jump at t=15->16 (dist 1.0) — smoothed rotation at (0.5,0.5)
- HIGH: gerver_like self-intersecting — arcs meet at shared endpoint
- MEDIUM: hammersley gap at arc junction — fixed endpoint alignment
- MEDIUM/HIGH: gerver_like/hammersley now accept q parameter
- LOW: reflect_y -> negate_y rename, dedup rounding consistency
- de Grey 1581-vertex graph constructs correctly (verified: 1581 vertices, 7877 edges)
- Hoffman bound: λ_max=12.09, λ_min=-7.74, χ≥3 (weak bound, expected)

Build: lake build CoreFormalism.CRTSidon (3297 jobs, 0 errors)

.openresearch/artifacts/hn_hoffman_bound.json

@@ -8,7 +8,7 @@
   "lambda_min": -7.73894638212,
   "hoffman_bound": 2.562456453665,
   "chi_lower_bound": 3,
-  "elapsed_s": 0.88,
+  "elapsed_s": 0.82,
-  "timestamp": "2026-07-04T06:52:32Z",
+  "timestamp": "2026-07-04T07:04:29Z",
-  "sha256": "20d76d1acf94298ae26de4a188245482504b7ef813ab0237c68c91ec7ca91e6f"
+  "sha256": "9c1bcd282a8d96b68cce8942b71338e346ac5eda9cb34e1decc4d6d26b3c6aa8"
 }

scripts/hn_hoffman_bound.py

@@ -74,7 +74,7 @@ def rotate(pt, angle):
 def translate(pt, dx, dy):
     return (pt[0]+dx, pt[1]+dy)
 
-def reflect_y(pt):
+def negate_y(pt):
     return (pt[0], -pt[1])
 
 def is_unit(p, q, eps=1e-9):
@@ -111,7 +111,7 @@ def build_degrey_1581():
         for k in range(6):
             pt = rotate((x, y), k * angle60)
             sa.add((round(pt[0], 12), round(pt[1], 12)))
-            pt_r = reflect_y(pt)
+            pt_r = negate_y(pt)
             sa.add((round(pt_r[0], 12), round(pt_r[1], 12)))
     
     sa_list = list(sa)
@@ -129,6 +129,8 @@ def build_degrey_1581():
     # Step 5-6: Rotate Y about (-2, 0)
     ya = [translate(rotate(translate(p, 2, 0), angle_y), -2, 0) for p in y_list]
     yb = [translate(rotate(translate(p, 2, 0), math.pi - angle_y), -2, 0) for p in y_list]
+    ya = [(round(x, 12), round(y, 12)) for x, y in ya]
+    yb = [(round(x, 12), round(y, 12)) for x, y in yb]
     
     # Step 7: G = Y_a ∪ Y_b
     all_pts = remove_duplicates(ya + yb)

scripts/sidon_sofa_coloring_v2.py

@@ -192,7 +192,7 @@ def make_sidon_polar_boundary(n, sidon_set, M, base_radius=Fraction(2, 5)):
         points.append((px, py))
     return points
 
-def make_gerver_like_boundary(n):
+def make_gerver_like_boundary(n, q=Fraction(1, 1)):
     """Gerver-like: asymmetric shape that hugs the inner corner.
     18 curved arcs — simplified to a polygon approximation.
     Uses q < 1 (poloidal-dominated) geometry:
@@ -203,45 +203,48 @@ def make_gerver_like_boundary(n):
     # Asymmetric: inner arc (60% of points) + outer arc (40%)
     n_inner = max(3 * n // 5, 3)
     n_outer = n - n_inner
-    # Inner arc: radius 0.45, angle 0 → 3π/2 (wraps the inner corner)
+    # Inner arc: radius varies with q, angle 0 → 3π/2 (wraps the inner corner)
-    r_inner = Fraction(45, 100)
+    r_inner = Fraction(45, 100) * (Fraction(1) + q) / 2
     for i in range(n_inner):
         angle = Fraction(i, max(n_inner - 1, 1)) * 3 * PI / 2
         px = r_inner * cos_frac(angle)
         py = r_inner * sin_frac(angle)
         points.append((px, py))
-    # Outer arc: radius 0.30, angle π → 2π (fills the back)
+    # Outer arc: radius varies with q, angle 3π/2 → 5π/2, starts at inner arc's end
-    r_outer = Fraction(30, 100)
+    r_outer = Fraction(30, 100) * (Fraction(2) - (Fraction(1) + q) / 2)
+    dy = -r_inner + r_outer
     for i in range(n_outer):
-        angle = PI + Fraction(i, max(n_outer, 1)) * PI
+        angle = 3 * PI / 2 + Fraction(i, max(n_outer, 1)) * PI
-        px = r_outer * cos_frac(angle) + Fraction(1, 10)
+        px = r_outer * cos_frac(angle)
-        py = r_outer * sin_frac(angle) - Fraction(1, 10)
+        py = r_outer * sin_frac(angle) + dy
         points.append((px, py))
     return points
 
-def make_hammersley_boundary(n):
+def make_hammersley_boundary(n, q=Fraction(1, 1)):
     """Hammersley-like: balanced shape that fills the outer arc.
     Uses q > 1 (toroidal-dominated) geometry:
-    - Equal inner and outer radii
+    - Upper and lower arcs share an endpoint
     - More symmetric (sacrifices corner-hugging for area)
     """
     points = []
-    # Two symmetric arcs: upper (60%) + lower (40%)
+    # Two arcs: upper (60%) + lower (40%)
     n_upper = max(3 * n // 5, 3)
     n_lower = n - n_upper
-    # Upper arc: radius 0.42, angle 0 → π
+    # Upper arc: radius varies with q, angle 0 → π
-    r = Fraction(42, 100)
+    r_upper = Fraction(42, 100) * (Fraction(1) + q) / 2
+    off_y = Fraction(1, 20)
     for i in range(n_upper):
         angle = Fraction(i, max(n_upper - 1, 1)) * PI
-        px = r * cos_frac(angle)
+        px = r_upper * cos_frac(angle)
-        py = r * sin_frac(angle) + Fraction(1, 20)
+        py = r_upper * sin_frac(angle) + off_y
         points.append((px, py))
-    # Lower arc: radius 0.38, angle π → 2π
+    # Lower arc: radius varies with q, angle π → 2π, starts at upper arc's end
-    r2 = Fraction(38, 100)
+    r_lower = Fraction(38, 100) * (Fraction(2) - (Fraction(1) + q) / 2)
+    dx = -r_upper + r_lower
     for i in range(n_lower):
         angle = PI + Fraction(i, max(n_lower, 1)) * PI
-        px = r2 * cos_frac(angle)
+        px = r_lower * cos_frac(angle) + dx
-        py = r2 * sin_frac(angle) - Fraction(1, 20)
+        py = r_lower * sin_frac(angle) + off_y
         points.append((px, py))
     return points
 
@@ -468,9 +471,9 @@ def run_experiment(seed=0):
                         n, sidon_1d, M, base_radius=base_r)
                     assert is_sidon_1d(sidon_1d), "Sidon property failed"
                 elif shape_name == "gerver_like":
-                    boundary = make_gerver_like_boundary(n)
+                    boundary = make_gerver_like_boundary(n, q)
                 elif shape_name == "hammersley":
-                    boundary = make_hammersley_boundary(n)
+                    boundary = make_hammersley_boundary(n, q)
 
                 area = polygon_area(boundary)