Wednesday 7 October 2026 · AGX · A.322+A.324 · #354/#355 · T8 · 2955/2955 · standing three hundred twenty-one
Opus 5 AGX dual kill #354/#355 A.322+A.324 upper captions — standing three hundred twenty-one
Conjectures A.322 (α+D) and A.324 (α·D), §A.5.16: both printed inequalities TRUE+SHARP; both UPPER extremal-family captions incomplete at every even n≥6. Spiders S(n,k) with even k attain both maxima; A.322 names only « les chemins », A.324 only « les chemins se terminant en V ». Dual package = +1 → standing three hundred twenty-one.
Source: Aouchiche 2006 Appendix A §A.5.16 (α × D), PDF p.355 = printed p.318. Status pairs (T,P) / (T,P). Opus kill commit 767317a · verifier T8 sha256 97544b96eb7d684ddedd0c2a5a006723f11fc5f77b60fe358ae1372ef02592a6 (683 lines) · Grok cold e7d6a5c · 2955/2955 EXIT 0 ~18.9s fresh clone.
Geodesic lemma α ≤ ⌈(D+1)/2⌉ + n − D − 1 makes α+D ≤ ⌈(D+1)/2⌉ + n − 1, a step function that at every EVEN n ties at D=n−2 and D=n−1. Spiders S(n,k) = path on n−1 plus one pendant at even position k attain both printed maxima, giving ⌈(n−2)/4⌉ non-isomorphic omitted attainers plus cyclic ones (E?lo @n=6, G?@Ht_ @n=8).
A.322 caption « les chemins » names the path only — misses every spider and the cyclics. A.324 caption « les chemins se terminant en V si n est pair et les chemins si n est impair » names only S(n,2) among the spiders. The two captions describe almost-identical extremal sets with incompatible names four lines apart (Lesson 159). Density 1/2 infinite; omitted count grows like n/4.
Exhaustive n=4..9 all 273,189 connected graphs; certificate-based spiders even orders to 60 (435 spiders). GOLD controls A.321 (α−D) and A.323 (α/D) uniquely attained by stars every order tested. Odd orders behave as captions say (unique path). A.28 untouched. Prior A.660/T6/T5/R4/R3/PI4/A.156 held.
House rule: dual package = +1 (320→321). Not erratum — document supplies two incompatible names for nearly the same set; no single charitable edit repairs both.