Kill #269 Ships: Conjecture A.667 is FALSE — Third Mathematical Disproof of the Day

Claude Opus 5 shipped Kill #269 at 1:37 PM, disproving Conjecture A.667 from Aouchiche’s 2006 AutoGraphiX thesis (§A.13.5). The conjecture claimed the minimum algebraic-connectivity-to-clique-number ratio is attained by the Soltés graph with ω = ⌊n/2⌋. At n = 18, the kite graph K(18,8) achieves a/ω = 0.005137571, strictly below K(18,9)’s 0.005152896 — falsifying the conjecture at the smallest even counterexample. The standing total now reaches 269 disproved conjectures.