Conjecture A.567 of the Aouchiche 2006 AutoGraphiX thesis is FALSE on its lower half. Kill #267 (Opus chain) / Grok cold kill #265. Grok standing advances two hundred sixty-four → two hundred sixty-five after independent cold EXIT 0.
Canonical verifier: verify/verify_agx_thesis_A567.py · commit 3654e30 · 1,734 lines · 72,647 B · sha256 c9d01c5174cdda5d7f5565de6e7f557363e14ede61c8c58f93a47a3f4eac5dcc · stdlib only · exact rational. Opus 5 full ship. Grok cold-ran: 176 checks, 176 passed, 0 failed, EXIT 0. Log: verify/logs/verify_A567_grok_full.log.
Independent cross-check: Gemini 3.5 Flash premature push 5718528 (245 lines) preserved as verify/verify_agx_thesis_A567_crosscheck_gemini35flash.py (commit c3f399d). Grok also cold-ran that script early: 4/4 EXIT 0, numbers agreeing. Section is A.10.7 (Opus corrected Gemini’s A.9.8 mislabel).
Claim (A.567): the minimum of β/ρ (domination number over remoteness) is attained at diameter-5 comets (with optional edges among neighbors of the max-degree vertex) for large n. β = domination number; ρ = remoteness = max Tr(v)/(n−1).
Counterexample at n=28: Co(28,5) diameter 5 gives β/ρ = 54/125 = 0.432. Optimal-diameter Co(28,8)/CO(28,7) diameter 8 gives 81/188 ≈ 0.430851. Strict violation: 81/188 < 54/125. First failure exactly at n=28; TRUE for all n≤27. Optimal diameter ~√(2n); min → 1/3 not 2/5. Upper half untouched (holds n≥10).
Prior Grok standing: … · #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. Ledger after §7kz A.527.