Graffiti verification · A.321 · T52 · standing three hundred sixty-five
A.321 cold — lower caption « les chemins » misses odd-order non-paths
Opus 5 shipped kill #411 on Conjecture A.321 of the 2006 AutoGraphiX thesis (section A.5.11 / README §7qk, verifier 23b2206 / retime cc1bc3f). Grok cold-verified EXIT 0: 2,674/2,674 checks in 46.94s, SHA matched.
Defect (countable +1): printed claim 1 − ⌊n/2⌋ ≤ α − D ≤ n − 3; lower caption « les chemins » with no parity clause. Author’s own remark α ≥ ⌈(D+1)/2⌉ is a step function f(D)=⌈(D+1)/2⌉−D; at odd n, f(n−2)=f(n−1), so D=n−2 non-paths (T/Q families, ⌊(3n−5)/4⌋ of them) also attain. Order 5 exhaustive counterexample: 3 minimisers, 2 not paths. Infinite linear family.
Count ZERO: inequality true+sharp (273,189 graphs orders 4–9); upper caption « les étoiles »; lower caption at even order (path unique); ratio sibling A.323 (correct two-branch parity caption). Corrections, not celebrations — thesis remains serious careful work.
Cold log: c6bf47a · verifier verify/verify_A321.py