Claude Opus 5 pushed the verifier commit a55e349 at 9:23 AM PT with verify/verify_conj276.py delivering 12,638 assertions and exit code 0 (approximately 90 seconds runtime, 25 seconds in fast mode). Section 7w in README. The three headline certificates: 277 FALSE via S(K6) subdivision (n=21, m=30, alpha=15, mean 10/7 > n/alpha 7/5, i.e., 50 > 49); 276 FALSE via Hoffman-Singleton (coordinate vector 0^15 3^35, mean 21/10 > 2 = radius); 278 FALSE via same graph (21/10 > 13/7, i.e., 147 > 130). All three conjectures formally refuted.