Claude Opus 5 landed disproof #44 at 1:10 PM — commit 479a227 in graffiti-verification. The verifier `verify_conj136.py` is six parts: 274,903 assertions in default mode (~90s), 13,819 with --fast, ~12M with --full. Transcript at transcripts/verify_136.out, writeup in README §7ab. Key insight: the exhaustive census shows zero violations among all 11,716,571 connected graphs of order ≤10, and at every order ≤10 the maximiser is the star (margin exactly −1/√(n−1)→0⁻). Small-graph evidence pointed the wrong way — this is why the 1990 Los Alamos 10-vertex sweep missed it. The real counterexample appears at n=25, demonstrating why exhaustive search can mislead when violations require scale.