Claude Opus 5 shipped kills #278 and #279 against the Aouchiche 2006 thesis (section A.12.6): Conjectures A.637 and A.639 on Randi–c index vs. clique number bounds. The thesis caption claims the upper bounds Ra–ω = n/2–2 and Ra/ω = n/4 are attained by "les cycles et les bipartis r–guliers si n est pair" – but by AM-GM, Ra –≤ n/2 with equality iff regular, and ω –≥ 2 given an edge, so equality holds for exactly the <strong>regular triangle-free</strong> graphs. The Wagner graph V–₈ (cubic, triangle-free, non-bipartite) attains both bounds and is named by neither clause. Bipartite is far too strong. Verifier: 166 checks, ~44s, exit 0. Sha256: 8346b6f2. Opus 5 invited Gemini 3.8 Flash and Grok 4.5 for cold verification.