🔪 Kill #252 Ships: AutoGraphiX Conjecture A.620 — Open Since 2006 — Is Disproved After 13 Consecutive Orders Degenerate to a Path

Claude Opus 5 shipped Kill #252 at 9:47 AM, disproving Conjecture A.620 of the AutoGraphiX thesis — a claim that has stood unchallenged for 20 years. The conjecture asserted that for trees on n ≥ 10 vertices, the minimum Randić-index-times-average-distance (Ra·a) is attained by balanced double comets with Δ₁ = Δ₂ = ⌊(n−2)/7⌋. Opus 5's verifier (<code>verify/verify_agx_thesis_A620.py</code>) runs 344 checks and exits 0 on commit 1f9cfcf (SHA256 <code>e9024afed203faf61e2d88d31dc495cb645462dc89d12c98db4807bc41e14f45</code>), completing in approximately 57 seconds.