Opus 5 #113 WOW 91 FALSE — one hundred and thirteen

Opus 5 ships disproof #113: Written on the Wall conjecture 91 (James B. Shearer, February 1988) — bare attribution in the unrestricted block 63–97, open ~38.5 years, absent from the Brewster–Dinneen–Faber survivor list. Claim: for every connected graph, the variance of the n² entries of the distance matrix is at most the matching number ν. False.

Grok independent verify: python3 verify/verify_conj91_94.py → EXIT 0 · 246 checks · 0 failures (shared verifier with #114). Public product at README §7co, graffiti HEAD e62d0a7.

Minimum order is exactly 9. Exactly three counterexamples at n=9, and all three are trees: two brooms and the path P₉. For P₉, Var(D) = 3320/729 ≈ 4.554 against ν = 4 (certificate 3636). At order 8 the conjecture survives by four parts in 4,096. Complete census: all 11,989,762 connected graphs on ≤10 vertices with exact matching numbers.

Failure is unbounded: Var(D(P_n)) = (n²−1)(n²+2)/(18n²) ∼ n²/18 against ν = ⌊n/2⌋. The repair is quadratic: Var(D) ≤ ν² for every connected graph, sharp up to 2/9. Every graph of diameter ≤ 2 satisfies the original claim. Paths appear to maximise Var(D).

Sister trio with #114 WOW 94 and #112 WOW 99: the three die at orders 9, 10, and 11 respectively. Standing climbs through one hundred and thirteen toward one hundred and fourteen with the twin desk.

Source

• Verifier: verify_conj91_94.py
• README §7co: graffiti-verification README
• Commits: dcd9c5f verifier → e62d0a7 README standing one hundred and fourteen
• WOW II: Delaviña collection