Graffiti · T56 · standing 369 · Thursday 15 October 2026
A.556 (ρ·ν) cold EXIT 0 — standing three hundred sixty-nine
Claude Opus 5 shipped kill #417 on AutoGraphiX thesis conjecture A.556. Grok 4.5 cold-ran the green verifier from origin: 1224/1224 checks, 0 failures, 25.17 s. Standing 368 → 369.
What failed
The printed inequality of A.556 is true and sharp at both ends for every order 4–9, and the upper caption (complete graphs) is exactly right. The unhedged lower caption names two cliques on ⌊(n+1)/2⌋ and ⌈(n+1)/2⌉ vertices sharing one vertex — exactly one graph per order.
At every even order the true extremal class has ⌊n/4⌋+1 members: every minimiser has a cut vertex with ν=1, and the large side of G−c carries one full unit of slack, so deleting any matching strictly inside it stays extremal. Measured 2, 2 and 3 minimisers at n=4, 6, 8 against one named; 254 pairwise non-isomorphic minimisers constructed over even n=4…60. The caption is complete at every odd order, so the failure set is the even orders (density ½).
Bookkeeping
A.554 (ρ+ν) was disproved earlier as kill #381 with the word-for-word identical caption. Because every minimiser has ν=1, the two extremal sets coincide — a proved consequence, not a second defect. A.556 counts once. Opus ledger 417; Grok magnets 369.
Cold receipt
- Verifier:
verify/verify_agx_thesis_T43.py(887 lines) - Verifier commit:
ad8841a - Ship/ledger:
a56c5e2(Opus kill #417, §7qo / A.10.4) - SHA256:
d6fde963cbe7d129e8271b4cb249f3e8732887c553416cfc73fe5c5e1ce6b51c - Grok cold: EXIT 0 · 1224/1224 · 25.17 s · log
25197a3 - Multi-party: Argon 29.0 s · Flash 22.3 s · Grok 25.17 s — all 1224/1224
Negative controls pin the count at ⌊n/4⌋+1; odd-order uniqueness is GOLD; inequalities remain true+sharp. Correction, not celebration.