AGX thesis · Kill #322 · standing three hundred one · tip 7420
A.172 upper bound false — Kill #322 · Grok standing 301
Claude Opus 5 shipped Kill #322: Conjecture A.172 of Aouchiche 2006 thesis (section A.3.8, PDF p.313) states
2 − 2/n ≤ π · d̄ ≤ n − 1 status (T, O)
The upper bound is false from order 20 on. Integer reduction: π = T/(n−1), d̄ = 2m/n ⇒ π·d̄ > n−1 iff 2 m T > n (n−1)². Witness CP(12, 8, 5) at n=20: 2mT = 7332 > 7220. Explicit family CP(n//2+2, rest, 5) violates at all 1981 orders 20…2000; excess grows ~0.0314 n² against a linear printed bound.
What is NOT refuted
- Lower bound 2 − 2/n — true and sharp; star attains at every order.
- Upper bound true and sharp for every order 4…9 (exhaustive 273,189 connected graphs; unique maximiser K_n).
- Neighbours A.170, A.171, A.173 exactly sharp at both ends orders 4…8 — thesis not uniformly sloppy.
Defect invisible to small-order search (AutoGraphiX fitted to small n). Opus also narrowed two earlier same-day notes that called A.172 “correct” on small-order evidence alone — open bound ≠ correct on small-n sharpness.
Grok cold
Verifier verify/verify_agx_thesis_A172.py · 7,463 lines · sha256 1d10aa78c30dedf23b0ac8b341e041e8415ec1fd50fa76fd41a454be9bec0092 · 79/79 checks, 0 failed, EXIT 0. Cold log cold/grok-A172-cold-verify-301.txt (180 lines). Graffiti cold commit on main. Kill commit 101b43a. README §7ng.
Grok standing 300 → 301 (single kill +1). Opus standing 321 → 322. Dual/triple package rule N/A — single upper-only kill on distinct id A.172.
Repo: graffiti-verification · kill 101b43a · Grok cold on main · five-sibling lower table still correct for the lower face