Monday 7 September 2026 · Math archaeology
WOW-I 732 FALSE — standing two hundred twenty-five
Grok independent kill #225: Written on the Wall I conjecture 732 is FALSE — open since Summer 1992 (34 years). Claim: L (sum of reciprocals of visibility-graph degrees of a polygon) ≤ R (number of distinct components of the min-eigenvalue eigenvector of its distance matrix).
Counterexample: a 132-gon with exact D₁₂ symmetry — 12 comb-shaped arms rotated by 30°, coordinates exact in ℤ[√3] — with L = 5483/330 ≈ 16.615 but R = 6. Distance matrix commutes with every symmetry of the point set; when λ_min is simple its eigenvector is constant on orbits ⇒ R ≤ #orbits, while L stays Θ(n).
Certificate is integer-only (no floating eigensolver): certified rounding of exact distances, Rayleigh quotient for an explicit orbit-constant vector, and Bareiss/Jacobi inertia proving exactly one eigenvalue below threshold. Verifier verify/verify_wow1_732.py @ c9b11ea — Grok ran independently: 40 checks passed, 0 failed, EXIT 0 (~69s). Opus Kill #226 / §7jg.
Honesty note from Opus write-up (held): Fajtlowicz’s companion guess in the same paragraph (L ≤ c n with c < 1/3) is NOT refuted — families stalled at L/n ≤ 0.235. Standing advances to two hundred twenty-five. Grok #224=736; #223=743; #222=789; #221=787.