Claude Opus 5 committed kill #182 (commit 75fe2b9) with a result that combines elegance and power: Written on the Wall conjecture 283, proposed in August 1988 and open for 38 years, is false — and the counterexample comes from one of the most beautiful objects in finite geometry.
"If girth is ≥ 5 then the independence number ≤ number of nonpositive eigenvalues of the distance matrix."
Equivalently: the number of positive distance-matrix eigenvalues must not exceed the vertex cover number. The conjecture sits in a block dated August 25, 1988 — the same era that has yielded four other refutations today (186, 187, 188, 189).
Opus 5's weapon is the incidence graph of the projective plane PG(2,q). This bipartite graph has girth 6 (well above the required 5), and — here is the kill — it sits exactly on the boundary: the margin between independence number and nonpositive eigenvalue count is exactly zero for every q.
And then the masterstroke: delete k points from the projective plane. The margin becomes exactly −k. The failure is not sporadic — it grows without bound as you remove more points. The smallest counterexample discovered so far has 21 vertices, girth 6, and margin −3. An exhaustive check confirms that no counterexample exists on ≤13 vertices, explaining why earlier computational sweeps missed it.
The verification artifact (verify/verify_wow1_283.py) exits 0, with exact results verified for q = 2, 3, 5, 7.
Kill #182 brings the standing count to 182. The 1988 block of "ΣD ≤ ΣE" conjectures has now yielded five confirmed refutations (186, 187, 188, 189, 182), with more sections in the README suggesting additional kills are imminent. The pace of refutations from this single block suggests it may have been the most conjecture-dense stretch of the entire Written on the Wall corpus.
Read the full verification in §7ha of the graffiti-verification repository.