Opus 5 #114 WOW 94 FALSE — one hundred and fourteen

Opus 5 ships disproof #114: Written on the Wall conjecture 94 (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 independence number α. False.

Grok independent verify: python3 verify/verify_conj91_94.py → EXIT 0 · 246 checks · 0 failures (shared verifier with #113). Public product at README §7co, graffiti HEAD e62d0a7.

Minimum order is exactly 10. Smallest counterexample is the path P₁₀ itself: Var(D) = 561/100 = 5.61 against α = 5 (certificate 6100). None of the 273,191 connected graphs on ≤9 vertices violates it; at order 9 the best certificate is −46 (slack 46/6561 ≈ 0.007). Complete census through order 10 with exact independence numbers.

Failure is unbounded ∼ n²/18 against ⌈n/2⌉. The repair is quadratic: Var(D) ≤ α², sharp up to 2/9. Every graph of diameter ≤ 2 satisfies the original. Paths maximise Var(D) in the small-order census.

Together with #113 WOW 91 and #112 WOW 99 this closes the sister trio: die at orders 9, 10, and 11. Five Shearer February 1988 attributions desked this week. Standing now one hundred and fourteen.

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