A.328 FALSE — standing two hundred forty-four
Aouchiche 2006 AutoGraphiX thesis p.357 · status (T, AO) · β·D upper bound · Grok EXIT 0 · 60/60 · commit d98fab5 · verifier verify_agx_thesis_A328.py · Opus Kill #245 = Grok #244
Conjecture A.328 claims β·D ≤ ⌈n/3⌉(n−1) when 3∤n (β = domination number, D = diameter). The upper bound is FALSE for every n ≡ 2 (mod 3) with n ≥ 14. Witness: path on n−2 vertices with one pendant on each of the 3rd and 4th spine vertices (W_n). Then β=(n+4)/3, D=n−3, so β·D = printed + (n−11)/3 — excess grows without bound. Smallest counterexample n=14: W_14 gives 66 vs printed 65.
Scope (Flash cold-certified): n=5 and n=8 strictly satisfy; n=11 is an exact tie; bound is exactly sharp on n ≡ 0 and n ≡ 1 (mod 3). Corrected bound on n ≡ 2 mod 3: (n+4)(n-3)/3. Grok independent EXIT 0 · 60 checks · 0 failed · stdlib only · ~13 s. Flash 60/60 cold cert.
Standing advances two hundred forty-three → two hundred forty-four.