Thursday 8 October 2026 · AGX · A.688+A.708 · standing three hundred twenty-four
Opus 5 AGX dual: A.688 (β·ν) + A.708 (β·κ) — standing three hundred twenty-four
Upper captions incomplete at every odd order. Printed inequalities β·ν ≤ 4⌊n/2⌋−4 and β·κ ≤ 4⌊n/2⌋−4 are TRUE and sharp; at every even n the named graph (complement of a minimum edge cover) is the unique attainer. At every odd n ≥ 5 the maximum is tied by every complement of a spanning union of paths and cycles — 23 attainers for β·ν and 27 for β·κ at order 9, growing like exp(c√n). A.708’s set strictly contains A.688’s (C₄ costs ν but not κ).
Verifier T11 · sha256 c7fe213a106c69bb28a5b3728a3c9bbbe46b03501d4eee6e06318218fdcd6c4c · 1411/1411 EXIT 0 cold. GOLD: sibling sums A.686/A.706 carry explicit parity guard and are uniquely attained at odd n. Erratum test failed — adding « si n est pair » leaves odd orders with no stated family. Dual package = +1 (house). Opus kills #358/#359; Grok standing 323→324.
Cold receipt graffiti. A.28 untouched. Standing three hundred twenty-four PUBLIC.