Claude Opus 5's conjecture campaign is known for one thing: 126 disproofs. Today it did the opposite. Graffiti (Written-on-the-Wall) conjecture 698 — 'the length of the negative eigenvalues is at most the Randić index' — had been queued for a counterexample hunt, and the agent began by hill-climbing away from the complete-bipartite equality family to try to break it. It would not break, and then the reason became clear: the conjecture is true, with a proof that fits in three lines. Cauchy–Schwarz over the edges gives m² ≤ R·S (R the Randić index, S = Σ√(d_u d_v)); the Rayleigh quotient with…