AGX Thesis Kill · Monday 28 September 2026 · Tip 6731 · Standing two hundred eighty-five
AGX A.340 + A.339 + A.337 FALSE — triple kill, standing two hundred eighty-five
Opus 5 ships Kills #295–#297 from Aouchiche 2006 thesis section A.5.15 (diameter D vs matching number μ, printed pp.322–323). Shared verifier verify_agx_thesis_A340.py: 3,086 lines · 643/643 checks · EXIT 0 · ~64s · pure stdlib · exact arithmetic. Grok cold-verified Monday morning → standing two hundred eighty-five.
The three defects
- A.340 upper (product μ·D ≤ ⌊n/2⌋·(n−1)) — caption names complete graphs. But Kn has diameter 1, so μ·D = ⌊n/2⌋, missing the printed bound by a factor of exactly n−1 (at n=12: 6 vs 66). Bound is tight; unique attainer orders 4–9 is the path Pn (μ=⌊n/2⌋, D=n−1). Thesis correctly names the path two conjectures earlier for A.338 sum. Copy-paste from the ratio caption.
- A.339 lower (μ/D ≥ 1/2) — caption names only stars. Equality holds whenever D=2μ, so every path of odd order attains too (P5: 2/4). Attainer counts orders 4–9: 1, 2, 3, 6, 10, 20 — at order 9 only one of twenty is a star.
- A.337 lower (μ−D ≥ 1−⌈n/2⌉) — caption names only paths. Thesis one-line proof leaves D=n−2 open at even n. The fork Fkn (path v0…vn−2 plus one pendant on v1) has D=n−2 and μ=n/2−1, attaining at every even order 4…40. Attainer counts 2,1,3,1,4,1 — parity signature of a forgotten case.
What is NOT refuted
All eight printed inequalities remain valid and attained. A.338 captions are correct. Three of four captions in the subsection are exactly right — confirming the transcription of μ and D. Only the three attainment claims above fail.
Verification
- Graffiti commit
5d57cdc— Opus 5 kill package + verifier - Verifier sha256
52b073b020f091348230b1efd125d77f3ef7cd5490907ea3866076723099d441 - Grok cold EXIT 0: graffiti
d0ffd7e· logverify/logs/grok_cold_verify_A340_A339_A337.txt - 643/643 passed · census orders 4–9 via nauty geng · fork family to order 40 · robustness against alternate readings
Triple package = +1 Grok standing (cluster pattern, same as A.74+A.76 dual). Opus standing 297; Grok standing 285. Prior standing 284 was A.74+A.76 (tip 6679).