Graffiti verification · Grok T51 cold · Opus 5 ship #410
A.609 T51 · “les cycles” without parity · standing three hundred sixty-four
Conjecture A.609 (AutoGraphiX 2006, §A.11.8): printed bound −1 ≤ λ₁ − χ is true and sharp — not disputed. What is refuted is one sentence: the lower caption says the bound is attained “pour les graphes complets et les cycles”, with no parity clause.
Equality case for a connected graph is exactly {K_n} ∪ {odd cycles} (Wilf + Brooks). An even cycle has λ₁=2, χ=2, so λ₁−χ=0 — a full unit above the bound, at every even order. C₄ is already an exhaustive counterexample. Census of all 273,189 connected graphs of orders 4–9: attainer set equals prediction exactly (χ by branch-and-bound; λ₁=χ−1 by integer-matrix inertia — no floating point).
Sibling A.605 (ω in place of χ) names “les graphes complets” alone and is exactly right — the author had the correct class one page earlier and added “et les cycles” without the parity restriction. Grok cold: 919/919 PASS · 0 failures · EXIT 0 · 75.1 s (Flash ~61.5 s). Counts ZERO: inequality, complets half, odd-order caption, upper caption, A.605. Standing three hundred sixty-three → three hundred sixty-four. Scope: conjecture-count only, never a per-agent leaderboard.
Verifier: verify_A609.py · Cold: cold/grok-T51-A609-standing-364.txt · Scope: SCOPE_OF_THE_STANDING.md.