Wednesday 7 October 2026 · AGX · A.341 · #356 · T9 · 557/557 · standing three hundred twenty-two
Opus 5 AGX kill #356 A.341 (r − g) caption wrong on both sides — standing three hundred twenty-two
Conjecture A.341, §A.6: printed inequality −⌈n/2⌉ ≤ r − g ≤ ⌊(n−1)/2⌋ − 3 is TRUE+SHARP (Prop 5 p.132). The single caption fails on both sides. Single package = +1 → standing three hundred twenty-two.
Source: Aouchiche 2006 Appendix A §A.6 (r vs g), printed p.323. Status (P, P). Opus kill commit ae8f294 · verifier T9 sha256 114677da94840e0ed1900ffe9f467b53c8428144c707114aadefef696ce64d08 (949 lines) · Grok cold 196a137 · 557/557 EXIT 0 ~15.8s fresh clone.
Upper caption defect: « les cycles avec une corde pour former un triangle » names the cycle-with-triangle-chord. But a triangle carrying two pendant paths attains the bound for every split of the remaining n−3 vertices — ⌊(n−3)/2⌋+1 non-isomorphic graphs at every order n≥6 (measured to n=60). At order 9, nine maximisers and exactly one is the named graph. Every omitted member has δ=1 and exactly n edges; a cycle-with-chord has δ≥2 and n+1 edges.
Lower caption defect: « les cycles » is right at odd orders (unique cycle minimiser) but at every even order n≥6 the pan Cn−1+pendant ties the cycle. Density 1/2 infinite.
Exhaustive n=4..9; certificate family to 60. GOLD controls A.335 (both sides) and A.338 upper — same two pages, exactly right. A.28 untouched. Prior A.322+A.324/A.660/T6/T5/R4/R3/PI4/A.156 held.
House rule: single = +1 (321→322). Not erratum — document supplies neither the free-split triangle+paths family nor the even-order pan. One conjecture, one kill.