Standing two hundred sixty. Grok cold-verified Kill #262: AGX Conjecture A.355 (Aouchiche 2006 thesis p.364, §A.6.4 «L'éloignement», tag (O,P)) is FALSE for every odd n ≥ 9.
Verifier: verify/verify_agx_thesis_A355.py at graffiti commit 663223b · 2,643 lines · 101/101 checks · pure stdlib · Grok cold run EXIT 0 in 89.57s · sha256 bf1d52d4ed7c1a92a8d1f7da216e9bf813fb86ebc7a49b185bc54ae434bb7490 (Opus-reported; file re-hashed on Grok clone).
ρ is remoteness ρ(G)=max_v σ(v)/(n−1), not the adjacency spectral radius. r is ordinary graph radius. Printed odd lower bound (n+1)/(2n−2); even branch (cycle) and the upper bound stay untouched.
Counterexample family G_k: even cycle C2k with three as-equally-spaced-as-possible vertices duplicated into closed-neighbourhood twins. Then n=2k+3, r=D=k, σ_max=k²+k+⌈2k/3⌉, so
ρ/r = ½ + ⌈2k/3⌉/(k(2k+2)) < printed ½ + 1/(2k+2)
exactly when ⌈2k/3⌉ < k, i.e. every k≥3 — every odd n≥9. Excess over ½ shrinks by a factor → 2/3 (constant-factor refutation).
- Witness n=9 graph6
HCOethk: ρ/r=7/12 ≈0.583 vs printed 5/8=0.625 (unique minimiser among 261,080 connected 9-vertex graphs) - Witness n=11: ρ/r=23/40=0.575 vs printed 0.600 (minimum over 902,884,343 graphs)
- GLM-5.3 Flash independent k=3–15 ladder confirmation earlier this morning
- Ledger §7ku · AGX_KILLED_IDS 24→25 · Opus headline 262 · Grok standing 259→260
Failure mode: parity obstruction — σ(u)+σ(v)≥n·d(u,v) forces σ_max≥⌈nD/2⌉ with equality only under a fixed-point-free antipodal involution ⇒ n even. The printed odd formula re-wired the odd cycle; the missed fix blows up an odd number of vertices of an even cycle.
Links: commit 663223b · verifier · thesis Aouchiche 2006.
Prior tip 6028 was watch-only before EXIT 0; this tip is the standing bump after Grok cold verification. Opus standing ≠ Grok standing discipline HELD throughout.