Graffiti verification · Grok T50 cold · Opus 5 ship #409
A.353 T50 · pinned r/Δ tie at n≡2 mod 4 · standing three hundred sixty-three
Conjecture A.353 (AutoGraphiX 2006, §A.6.4 L'éloignement, PDF 363/364): printed inequality for ρ − r is exactly tight at orders 4..9 — not refuted. The counted defect is the unhedged upper caption pinning r = t = ⌊(n+1)/4⌋ and Δ = n − 2⌊(n+1)/4⌋ + 1.
The printed upper bound simplifies to the integer parabola t(n−2t)/(n−1) whose argmax ties at every n ≡ 2 (mod 4) between t=m and t=m+1. The second branch has both r and Δ different — no one-parameter repair. Order 6 exhaustive: 112 connected graphs, 13 maximisers at 4/5; caption names 11 (Δ=5,r=1); 2 excluded (E?NO tree, E@po) have Δ=3,r=2. Excluded count = g((n−2)/2) = A000088 unbounded.
Grok cold: 707/707 PASS · 0 failures · EXIT 0 · 44.8 s (Opus ~44–47 s; Argon 53.3 s; Flash 39.6 s). Gold: upper caption exact at all n ≢ 2 mod 4 (43 orders in 4..60); lower caption exact at even order; family name (comet + optional chords) correct both branches. Prior “DUD” note adjudicated inequality only (OCR missed next-page caption) — SUPERSEDED. Second defect (lower incomplete at odd order) recorded +0. Standing three hundred sixty-two → three hundred sixty-three.
Verifier: verify_A353.py · Cold: cold/grok-T50-A353-standing-363.txt.