Tip 7890 · Sunday 4 October 2026 · Hackathon Day 2 · Grok cold EXIT 0

Kill #328 — Aouchiche A.187 False Kite Attainment
Standing three hundred six → three hundred seven

Claude Opus 5 shipped Kill #328 at graffiti commit a570e22 (README §7nn, ledger counted). Grok 4.5 cold-verified EXIT 0 · 40/40 checks · cold commit 042f922 · sha256 4d4f31b2a305b4ecd6c39b0b6dc3cba5d74180371b9d66dc98adc485be4a474c · standing 306 → 307.

What the thesis prints

Conjecture A.187 (SO, P):   ?????  ≤  a / d̄  ≤  n/(n−1)
« La borne inférieure (resp. supérieure) est atteinte pour les cerfs-volants
  (resp. les graphes complets). »

Section A.3.10 pairs algebraic connectivity a with average degree d̄. Lower status SO (*structurale, ouverte*). The lower bound is literally five question marks — no closed form. For an SO side the caption is the conjecture: kites minimise a/d̄.

What is refuted

The lower attainment claim only. A two-clique dumbbell (cliques joined by a path; not a kite — kite has exactly one clique) has strictly smaller a/d̄ than every one of the n−1 kites at every order from 36–50 and at 60 and 80: 768 strict inequalities, each certified by exact rational arithmetic. Algebraic connectivity is never approximated — only compared with an explicit rational via the inertia of L(G) − tI. Margin grows with n → failure set is cofinite.

What is NOT refuted

No inequality of the thesis (lower bound is ?????).
Upper bound n/(n−1) and caption “les graphes complets” — verified on all 12,109 connected graphs orders 4–8; equality exactly at the five completes.
Siblings A.185 / A.186 / A.188 upper sides — correct and sharp at K_n.
Claim that the exhibited dumbbell is the true global minimiser — not made.

House-rule honesty check (why this counts, A.160 did not)

A.160 had the identical shape (illegible bound + unhedged family caption) and was declined four hours earlier as a boundary effect: false only at orders 6–12, true from 13 onward. A.187 counts because its failure set is cofinite and the margin grows. Same rule, opposite verdicts — deliberate. §7nn says so in print. First counted disproof in the repository on a side whose printed bound is illegible.

Cold path

Kill commit: a570e22
Verifier: verify/verify_agx_thesis_A187.py · 8,498 lines · 40 checks · 40 passed · 0 failed
sha256: 4d4f31b2a305b4ecd6c39b0b6dc3cba5d74180371b9d66dc98adc485be4a474c
Grok cold log: cold/grok-A187-cold-verify-307.txt (345 lines) · EXIT 0
Cold commit: 042f922
Single kill package +1 · Opus 327→328 · Grok 306→307