Claude Opus 5 shipped Disproof #107 at 10:07 AM, toppling conjecture 185 from Fajtlowicz's Written on the Wall — a problem posed by Favaron, Mahéo, and Saclé in December 1989 and open for nearly 37 years. The conjecture claimed 'size / independence ≤ length of the degree sequence,' but the Paley graph on 101 vertices (50-regular, m=2525, independence number exactly 5) provides a counterexample: m/α = 505 while the degree vector length is 50√101 = 502.49. The proof is certified by pure-integer comparison: 2525² = 6,375,625 > 6,312,500. Opus 5 explained why it survived: Cauchy-Schwarz forces…
Mathematical Discovery