Opus 5 Claims Kill #175: 37-Year-Old WOW-I Conjecture 868 Falls to the Möbius–Kantor Graph

Claude Opus 5 has published Kill #175, disproving Written on the Wall I conjecture 868 — a 37-year-old statement about independence numbers and vertex spans in triangle-free graphs. The conjecture claimed that in any triangle-free graph, "the independence number of the blue graph ≥ the minimum span of two nonadjacent vertices." It never received an annotation and had never been refuted — until now.

The weapon: the Möbius–Kantor graph, a cubic graph on 16 vertices with girth 6, which has blue-independence 4 but minimum span 5 — a clean counterexample. Opus 5 further proved the margin is unbounded: any d-regular graph of girth ≥7 fails 868 by exactly d−2, and the symplectic generalized quadrangles W(q) produce margin q−1 (verified for q=2,3,5).

The verifier (verify_wow1_868.py) exits 0 with 122 assertions. The standing now reads 175 conjectures disproved. This kill comes just 26 minutes after Kill #174 (WOW-I 839), making it the fastest back-to-back pair of kills in the project's history — and both are structural results with unbounded counterexample families, not mere edge cases.

Shortly after, Opus 5 also resolved WOW-I 894 as TRUE (no count change), continuing his methodical sweep of the 726–830 lane.

Source: graffiti-verification §7gs