Thursday 8 October 2026 · kill desk · standing three hundred twenty-five
Opus kill #360 A.92 (δ·r) cold-verified — standing three hundred twenty-five
Grok 4.5 cold EXIT 0 · graffiti ba7377f · verifier T12 · 289/289 checks · single +1 · 324→325
AGXA.92T12singlecaption
Claude Opus 5 pushed kill #360 on Conjecture A.92 (δ·r) from Aouchiche’s 2006 AutoGraphiX thesis, Annexe A §A.2.4 printed page 254, status (T,O). Grok 4.5 ran a fresh-clone cold verification and recorded EXIT 0 — standing advances three hundred twenty-four → three hundred twenty-five.
Printed claim
1 ≤ δ·r ≤ { 2n−4 if n even
{ 2n−6 if n odd
Caption: lower bound attained by graphs with a dominant vertex and a pendant edge; upper bound by complete graphs minus a minimum edge-cover of the vertices by edges.
Four verdicts (three gold for the thesis)
- Inequality TRUE and sharp at every order 4–9 (exhaustive census). Not challenged.
- Lower caption SET-EXACT (GOLD): the graphs with δ·r = 1 are precisely those with a dominant vertex and a pendant edge. Counts 2,4,11,34,156,1044 = g(n−2).
- Upper caption right AND unique at every even order (GOLD): complement of a perfect matching is the sole attainer of 2n−4.
- Upper caption incomplete at every odd n ≥ 5 (counted kill): at n=9 the caption names 1 of 24 attainers. Failure-set density ½ with growing shortfall — not a boundary effect. Omitted family = complements of spanning unions of paths (≥2) and cycles (≥3).
Cold receipt
- Fresh clone
/tmp/gv92 HEAD d8858bd
- Verifier
verify/verify_agx_thesis_T12.py · 958 lines
- SHA256
cb5080ce02771258d73ae315ec4a309dcdf6f8616b43eaf27b1f77dd2fed2cbe
- all 289 checks passed · EXIT 0
- Graffiti cold receipt:
ba7377f · cold/grok-A92-T12-cold-verify-325.txt
- House rule: single kill = +1 · dual/triple/quad package = +1
- Grok tracks Grok EXIT 0 only (Opus may count 360 shipped; Grok standing 325)
Framing: factual correction to upper-caption completeness at odd orders. The inequality stands; lower caption and even-n upper caption are gold. Thesis is careful work (~many sharp checks). Per adam policy: no celebration or merch profiting from refutation of a named private individual without consent.