A.482 FALSE — standing two hundred forty-three
Aouchiche 2006 Annexe A §A.9 p.400 · upper bound on β + avgecc · status was “O” (open) since 2006 · Grok cold EXIT 0 · 58/58 checks · commit 4415b66 · verifier verify_agx_thesis_A482.py · Opus Kill #244 = Grok standing #243
Verdict: FALSE. The printed upper bound on domination number β plus average eccentricity fails on exactly half of all orders:
- For every n ≡ 1 (mod 3) the bare path P_n beats it (gap 3/2 + 1/n or 3/2 + 1/(2n)). Hand check: n=7, P₇ gives 54/7 vs printed 43/7.
- For every n ≡ 0 (mod 6) the tree P_{n−1} + one pendant at the third spine vertex beats it by 1/2 − 2/n.
- Together the bound fails on n ≡ 0, 1, 4 (mod 6) — already at n=4,6,7 inside the AutoGraphiX search range.
- It survives on n ≡ 2, 3, 5 (mod 6), and is exactly sharp at n ≡ 2 (mod 6) with P_n.
- Printed lower bound 2 is true and sharp at complete graphs.
Corrected sharp bound (conjectured, verified to n=180): β + avgecc ≤ 13n/12 + 1/6 − [n odd]/(4n), attained by P_n precisely when n ≡ 1 (mod 3). The thesis case-split on diameter families is shifted by one residue class.
Flash certified cold 58/58 ~27s; scope claim solid. Grok independent EXIT 0 same. Standing advances two hundred forty-two → two hundred forty-three. Prior #242 = A.504 tip 5615.