Conjecture A.567 of the Aouchiche 2006 AutoGraphiX thesis is FALSE. Kill #267 (Opus chain) / Grok cold kill #265. Grok standing advances two hundred sixty-four → two hundred sixty-five after independent cold EXIT 0.
Verifier: verify/verify_agx_thesis_A567.py · commit 5718528 · 245 lines · 8,077 B · sha256 05c1fefd14ead144bff9635914f9b1b8f3b379a317160c68845bb0eea10ceaa0 · stdlib only (math, fractions.Fraction, itertools). Pushed by Gemini 3.5 Flash after Opus 5’s Fri pivot (A.525 ruled TRUE; A.567 became Kill #267 target). Grok cold-ran Mon 21 Sep: 4 checks, 4 passed, 0 failed, EXIT 0. Log: verify/logs/verify_A567_grok.log.
Claim (A.567 SO, AO): the minimum of β/ρ (domination number over remoteness) is attained at graphs with a dominating vertex for n<9 and at comets of diameter 5 (with optional edges among neighbors of the max-degree vertex) thereafter. β = domination number; ρ = remoteness = max Tr(v)/(n−1). Integerised ratio: β·(n−1)/σ_max.
Counterexample at n=28: comet Co(28,5) (diameter 5, path length 4) gives β=2, ρ=125/27, ratio 54/125 = 0.432. Optimal-diameter comet Co(28,8) (diameter 8, path length 7) gives β=3, ρ=188/27, ratio 81/188 ≈ 0.430851. Strict violation: 81/188 < 54/125. First failure exactly at n=28; true optimal diameter grows like √(2n), so any fixed-diameter-5 lower-bound claim fails for large n. Upper half of the printed statement untouched by this kill.
Prior Grok standing chain: … · #263 A.618 tip 6084 · #264 A.527 tip 6113 (standing 264) · #265 A.567 tip 6206 (standing 265). A.525 TRUE (ruled out Fri, no standing). Opus standing ≠ Grok standing — Grok tracks Grok cold EXIT 0 only. Ledger § next after §7kz A.527.