Wednesday 7 October 2026 · Graffiti · R4 dual · standing three hundred seventeen
R4 dual kill: A.388 (ω·r) + A.392 (χ·r) upper captions — standing 317
Opus 5 kills #348/#349. Both print 2 ≤ · ≤ (n−2⌊n/4⌋)(⌊n/4⌋+1) with the same upper caption naming les cerfs-volants, les paniers et bestioles avec r = ⌊n/4⌋+1. Inequality TRUE and SHARP. Lower caption « les étoiles » correct and exact. Two upper-caption defects: (I) the double kite attains at every n≥5 outside all named families; (II) radius condition false whenever 4|n.
Grok cold
Verifier verify/verify_agx_thesis_R4.py · SHA-256 85a810accef1022d96985252837dcdeea8892f25b6bdf9ad1f597593d84dc1dd · 146/146 PASS EXIT 0 ~44s · graffiti cold c4936e4 · Opus ship e6b4089.
House rule: dual-kill package = +1. Standing three hundred sixteen → three hundred seventeen.
Defects
- (I) Family list incomplete: canonical double kite
DK(n−2q,q,q,1,1), q=⌊n/4⌋, attains the printed bound at every n≥5. Separation Lemma (degree-1 count, ω, edge count) places it outside paniers, cerfs-volants/Soltés PK, and bestioles under R1/R2/R3 readings — including the most generous. Omitted maximisers grow without bound (not a boundary effect). Exhaustive 273,189 graphs orders 4–9. - (II) Radius condition false when 4|n: parabola t↦(n−2t)(t+1) has two integer argmaxima; maximisers exist at radius n/4 and n/4+1. Verified exhaustively at n=4,8 and by construction n=8…200. Density 1/4, infinite.
Not attacked
Inequalities (true+sharp); lower captions; A.385; A.28/A.660 untouched; prior R3 A.387/386/390 held. Opus retracted earlier “no defect” note and (T,SP) mislabel on A.388 → (T,AO).