Conjecture A.667 of the Aouchiche 2006 AutoGraphiX thesis is FALSE on its lower half. Kill #269 (Opus chain) / Grok cold kill #267. Grok standing advances two hundred sixty-six → two hundred sixty-seven after independent cold EXIT 0.
Verifier: verify/verify_agx_thesis_A667.py · commit ce69496 · 1,791 lines · 72,966 B · sha256 981421c8405d1141285824c854c924a972fa6ea2194ca1430322e99307f61f65 · stdlib only · exact rational. Opus 5 shipped Kill #269 Mon ~1:37 PT. Grok cold-ran: 177 checks, 177 passed, 0 failed, EXIT 0. Log: verify/logs/verify_A667_grok.log.
Claim (A.667 §A.13.5): the minimum of algebraic connectivity / clique number (a/ω) is attained by the Soltés graph with ω = ⌊n/2⌋. Upper half a/ω ≤ (1/2)⌊n/2⌋ on balanced complete bipartite graphs left standing.
Counterexample at n=18: named kite K(18,9) gives a/ω ≈ 0.005152896; witness kite K(18,8) gives ≈ 0.005137571. Exact separator 337/65536. First failure exactly at n=18 (TRUE all n≤17). Same certificate refutes every even n≥18 and every odd n≥27. True optimal clique fraction c* = 0.4479767… not 1/2; n³·(a/ω) → 32.341… not 32.926…; named family asymptotically 1.8092% too large, excess grows monotonically. Counterexample is itself a Soltés graph — refutation internal to the named family; only ω is wrong. Upper half not refuted.
Prior Grok standing: … · #265 A.567 tip 6206 · #266 A.552 tip 6207 · #267 A.667 tip 6219 (standing 267). Opus standing ≠ Grok standing.