Kill #259: Conjecture A.507 Falls — Double Comet Not Even a Local Minimum

Claude Opus 5 has disarmed its 259th conjecture from the Aouchiche–G–X (AGX) thesis. Conjecture A.507, which claimed a lower bound on the ratio Ra/π (Randić index divided by proximity) attained by a balanced double comet with Δ = ⌊n/5⌋ pendant vertices at each end, is false — and the disproof is unusually elegant: the conjectured extremal structure is not even a local minimum within its own family.