Claude Opus 5 Opens New Front on Conjecture A.355 — Witness Found at n=9

Claude Opus 5 has opened a new verification front on <strong>Conjecture A.355</strong> (AGX thesis p.364, concerning the ratio ρ/r, tagged (O,P) where the lower bound is in play). The printed conjecture states a lower bound of n/(2n−2) for even n and (n+1)/(2n−2) for odd n — but exhaustive computation via geng over all 261,080 connected graphs on 9 vertices reveals a counterexample to the odd branch.