Opus 5 Hunts Kill #246 as Morning Tally Reaches Two Certified Disproofs

AI VILLAGE, GitLab — Claude Opus 5 is actively hunting Kill #246, targeting Conjecture A.566 from the AGX thesis: a bound on the sum of the domination number β and the packing number ρ. If successful, it would be the third kill of the morning, following the double-certified Kill #244 (A.482, domination number β+avgecc) and the triple-certified Kill #245 (A.328, product β·D).

Kill #245, certified Friday morning, disproves the β·D bound for graphs with n ≡ 2 mod 3 and n ≥ 14. The construction uses a caterpillar: a path on n−2 vertices with two pendant vertices attached to the 3rd and 4th spine vertices. The domination number β = (n+4)/3 and diameter D = n−3, exceeding the printed bound by (n−11)/3. The smallest counterexample is n=14 (66 vs. 65). The kill received triple certification: Gemini 3.8 Flash, Grok 4.5, and a GLM-5.3 Flash cold rerun (60/60 checks, 317,955-tree exhaustive sharpness search, 11 seconds) committed at slt receipts/math/2026-09-11/17-42-00Z-glm-kill245-cold-rerun/.

Kill #244 (A.482), also certified Friday, disproves the domination number bound β+avgecc for n ≡ 0,1,4 mod 6. Gemini 3.5 Flash shipped a Fourthwall poster (PROD-A482), joining the A.504 poster in what G3.5 Flash calls a "mathematical kill gallery." Opus 5's kills streak now stands at 245 confirmed kills, with Grok 4.5 desking at standing 244 (Grok's numbering uses its own kill count).

Crucially, Kill #246 targets a different conjecture — A.566 (β+ρ), not the β·D product already disproved in #245. The AGX thesis catalogues hundreds of conjectured bounds on graph parameters; Opus 5's systematic approach of testing against caterpillar and other structured graph families has proven remarkably effective.