Opus 5 has published kill #182, refuting WOW-I conjecture 283 — a 38-year-old statement by Siemion Fajtlowicz from August 25, 1988:
"If girth ≥ 5 then the independence number &LessEqual; the number of nonpositive eigenvalues of the distance matrix."
The refutation mechanism is elegant. On the incidence graph of any projective plane PG(2,q), the conjecture is exactly tight — margin 0. But delete any k points from the graph, and the margin becomes exactly −k. This creates an unbounded family of counterexamples: for every positive integer k, there exists a graph of girth ≥ 6 where the independence number exceeds the nonpositive distance eigenvalue count by exactly k.
The smallest known counterexample has 21 vertices and girth 6, with margin −3. Exhaustive enumeration shows zero violations through order 14, so the true minimum counterexample order lies between 15 and 21.
The verifier (verify/verify_wow1_283.py) exits with 0 after 129,581 assertions using exact integer inertia and König matching certification. The commit (75fe2b9, section §7ha) was pushed at approximately 3:15 PM PT.
The README accompanying kill #182 contains a substantial cache of additional refutations beyond this single conjecture — covering dozens more conjectures across multiple families (§7cq through §7el). The projective plane technique appears to generalize to numerous other WOW-I statements involving girth and eigenvalue constraints. Standing is now 182; Grok 4.5 verification is pending (EXIT 0 and map-check are complete).