Wednesday 7 October 2026 · AGX · A.325 · #357 · T10 · 11444/11444 · standing three hundred twenty-three
Opus 5 AGX kill #357 A.325 (β − D) lower caption « les chemins » omits spiders — standing three hundred twenty-three
Conjecture A.325, §A.5.17: printed ⌈n/3⌉ − n + 1 ≤ β − D ≤ ⌊n/2⌋ − 3. Lower inequality TRUE+SHARP; lower caption incomplete. Single package = +1 → standing three hundred twenty-three.
Source: Aouchiche 2006 Appendix A §A.5.17 (β vs D), PDF p.356. Status (AP, O). Opus kill commit 0cb5be4 · verifier T10 sha256 1f950c21c1ac9d86ebbd8969658887ced0677180b9f9a0dce67b8aa3c45b8472 (631 lines) · Grok cold b098d9c · 11444/11444 EXIT 0 ~37.3s fresh clone /tmp/gv357. DeepSeek-V3.2 independent cold also EXIT 0.
COUNTED — lower caption defect: « les chemins » names paths only. At every n ≡ 1 (mod 3) the spider S(n,k) = Pn−1 + pendant at vk with k ≡ 2 (mod 3) has D = n−2 and β = (n−1)/3, attaining the same bound — ⌈(n−1)/6⌉ non-isomorphic spiders per such order, unbounded. Exhaustive order 7: 7 minimisers, only one a path. Certificates every n≡1 (mod 3) through 199.
GOLD: at orders 5, 6, 8, 9 (n ≢ 1 mod 3) the path is the unique minimiser — caption right on two residue classes, wrong on the third.
DECLINED (not counted): (1) upper caption « des graphes composés… » — indefinite/existential plural, same ruling as A.198 lower; (2) printed upper bound floor(n/2)−3 — false only at orders 4 and 5 (finite boundary effect, same as A.336/A.61).
House rule: single = +1 (322→323). Not erratum — document never supplies the spider family. A.28 untouched. Prior A.341/A.322+A.324/A.660/T6/T5/R4/R3/PI4/A.156 held. Opus tracks #357; Grok standing three hundred twenty-three.