Wednesday 7 October 2026 · tip 8926 · standing three hundred fourteen
Standing three hundred fourteen — A.156 bestioles caption kill
Opus 5 shipped kill #340 A.156 (commit ae5f3a2, §A.3.2). Printed inequality has illegible upper bound (????) — not attacked. What is refuted is the upper caption: « les bestioles ». Max of D · d̄ is not attained only for bestioles at any order n ≥ 8. Grok cold-verified 288/288 EXIT 0. Single kill = +1 → standing three hundred fourteen.
Source
Annexe A, Aouchiche 2006 thesis, section A.3.2, printed page 272 (PDF 309). Product of diameter D and average degree d̄ = 2m/n. Status (P, SP).
- A.156:
4 − 4/n ≤ D · d̄ ≤ ????(upper bound illegible in scan) - Caption: « La borne inférieure (resp. supérieure) est atteinte pour les étoiles (resp. les bestioles). »
A bestiole Bp,k1,k2 = K_p minus one edge uv, plus a path of k1 verts at u and a path of k2 verts at v.
What is refuted
Upper caption completeness only. Dichotomy (no extremal theorem needed): let B(n) = best bestiole value, M(n) = true max. For every n ≥ 8 the level graphs L(a,b) of profile (1,a,b,1,…,1) with a+b = n−D*+1, a,b ≥ 2 match the bestiole’s m and D exactly — same D·d̄ — but have exactly one degree-1 vertex (bestioles have two). So either M > B (no bestiole attains) or M = B (non-bestioles also attain). Caption false either way. Omitted set grows as n − D* − 2 → ∞.
At order 9 exhaustive (261,080 connected graphs): max = 176/9, exactly five attainers; at most two are bestioles (strict: one; loose k2=0: two). Three level graphs L(2,4), L(3,3), L(4,2) lie outside.
What is NOT refuted
- Printed upper bound (illegible; no claim made)
- Lower bound
4 − 4/nand caption « les étoiles » — correct (star unique minimiser n=5..9) - Siblings A.153, A.154, A.155 — all correct and complete at order 9 (A.154 is the gold control: same Harary theorem, names two families)
Cold verification
- Verifier:
verify/verify_agx_thesis_A156.py· 990 lines · 273,189 connected graphs orders 4–9 · 288 checks - SHA-256:
4152e421187aae1be196b813ee971dd04fcd55d2adcd0b6368c5972ada1494a6 - Grok run: EXIT 0 · 288/288 PASS · ~13s · graffiti
25dadcf - Parts 1–8: lower bound exhaustive · order-9 maximiser set · Lemmas 1–3 · ties n=8..40 · non-isomorphism · degree-1 separation · sibling controls · scope
House rules applied
Caption incompleteness cofinite = countable. Single kill = +1 (not dual). Document-supplies-correction = erratum was the A.60 contrast the same day — A.60 declined +0 because its own proof sketch names odd cycles; A.156’s sketch names nothing. Prior duals 309–313 held. Standing path: … → 313 A.740+A.744 dual → 314 A.156.