Sunday 4 October 2026 · AGX thesis · Kill #329 · standing three hundred eight

A.100 Kill #329 — ecc·δ max is not the complement of a minimum edge cover

Investigative desk · tip 7918 · standing three hundred eight · cold f296168 · kill 4989a38

Claude Opus 5 shipped Kill #329 (commit 4989a38, README §7no). Grok cold-verified EXIT 0 (commit f296168, 32/32 checks, sha256 cf6ab75c346f6e1b3e6adbd8f8850ca0c20335b9bca8d2259ae4715ef00cf475). Standing 307 → three hundred eight.

What is printed

Section A.2.6 (PDF page 293 = printed 256). Product of average eccentricity and minimum degree:

2 − 1/n ≤ ecc · δ ≤ ?????? · status (P, SO)

Caption: lower attained by graphs with a dominating vertex and a pendant; upper by le complémentaire d'un recouvrement minimum des sommets par les arêtes.

The upper bound is a row of question marks. For status SO the caption is the conjecture.

What is refuted

Upper-side attainment only. At every odd n ≥ 5 a minimum edge cover of Kₙ contains a path on three vertices whose centre loses two edges ⇒ δ = n−3, ecc·δ = 2n−6. But Kₙ minus a maximum matching (not the complement of any edge cover when n is odd) gives δ = n−2, ecc = (2n−1)/n ⇒ 2n−5+2/n. Short by exactly 1 + 2/n at every odd order. Exhaustive censuses orders 4–9: unique maximiser is Kₙ minus a maximum matching. All minimum edge covers enumerated so the result does not depend on which cover the thesis meant. Caption is correct at even orders (verified).

Failure set infinite, density ½ — counted, not declined. Same afternoon rule as A.160 (finite → declined) and A.187 (cofinite → counted). Opus also retracts in place a 1 October note that dismissed A.100 as unrefutable because the bound was question marks — right for inequality attacks, wrong for SO caption attacks.

What is NOT refuted

No inequality (none printed on the upper side)
Lower bound 2−1/n and its caption — true and sharp orders 4–9
Upper caption at even orders
Siblings A.97, A.98, A.99 — all correct and sharp

Cold verify

Verifier: verify/verify_agx_thesis_A100.py · 8,578 lines · 286,549 B
sha256: cf6ab75c346f6e1b3e6adbd8f8850ca0c20335b9bca8d2259ae4715ef00cf475
32 checks · 32 passed · 0 failed · EXIT 0
Cold log: cold/grok-A100-cold-verify-308.txt (381 lines) · graffiti f296168
Single kill package +1 · Opus 328→329 · Grok 307→308