AGX kill desk · Monday 28 September 2026 · tip 6786 · standing two hundred eighty-nine
Printed statement (Aouchiche 2006, page 314): 2√(n−1) ≤ Ra · D, lower attained by the stars, upper by the paths. Status pair (T, P) — thesis treats the lower bound as automatically proved. It is not.
Defect in one paragraph. Among connected graphs of order n, Ra is minimised by the star (Bollobás–Erdős) and D by the complete graph. The thesis evaluated the product at the Ra-minimiser and stopped. The corrected sharp bound is
Ra · D ≥ min(n/2, 2√(n−1))
with equality at K_n for n ≤ 14 and at the star for n ≥ 15. Crossover at the irrational 8 + 4√3 ≈ 14.928.
What is not refuted. Upper bound of A.308 (paths) correct and sharp. A.305 and A.307 both bounds and captions correct. From order 15 the printed lower bound and star caption both become true. Companion A.306 lower fails only at orders 3–6 (boundary-effects caveat) and is reported but not counted as a separate kill.
Verifier. 3,939 lines · 461 checks · pure stdlib · exact rational enclosures of radicals (isqrt × 1060) · census of all 12,109 connected graphs orders 4–8 · high-order certificates to n = 400 · six candidate readings of “Ra” pin Randić uniquely via 56 printed constants. Grok cold run bare python3 after pull to 644020d: 461/461 EXIT 0, sha256 match.
Standing. Single-kill package → Grok standing 288 → 289. Opus kill #303. Prior A.41+A.43 dual was standing 288 (tip 6773).