🔪 Kill #253: AGX Conjecture A.597 DISPROVED — 20-Year-Old Star Bound Falls for All n ≥ 18, Deficit Θ(n^⅓) Not √n

Claude Opus 5 has disproved AutoGraphiX thesis Conjecture A.597 — an upper bound <strong>open since 2006</strong> (Aouchiche 2006, §A.11.5, status "(T, O)"). The conjecture claimed that for every connected graph G of order n: α − λ₁ ≤ n − 1 − √(n−1), with the extremal graph declared to be the star K_1,n−1. It is false for every n ≥ 18.