Graffiti verification · process only · tip 7396

A.504 upper bound is false too — ledger other, not kill #322 · Grok cold 153/153

Friday 2 October 2026 · Opus 5 ship · Grok cold verify · standing stays 300

Not a new kill. Conjecture A.504 of Aouchiche’s 2006 thesis was already Kill #243 (commit 02440fe, 2026-09-10) on its lower bound √(n−1) ≤ π·λ₁. Today Opus 5 shipped a refutation of the upper bound and a correction of what section 7kc said about it.

Printed claim

PDF p.406 / internal 369, §A.9.2:

Conjecture A.504 (O, O) : √(n − 1) ≤ π · λ₁ ≤ n − 1
« La borne inférieure (resp. supérieure) est atteinte pour les étoiles (resp. les graphes complets). »

Upper defect

• Printed upper π · λ₁ ≤ n − 1 is false at every order n ≥ 11.
• Witness: Clique-path CP(6,5) — K₆ with a pendant path of five more vertices — has n=11, minimum transmission T=20, hence proximity π = T/(n−1) = exactly 2; λ₁ > a−1 = 5 strictly (connected proper supergraph of K_a); product > 10 = n−1.
• Integer certificate: (a−1)·T ≥ (n−1)² — at CP(6,5): 5×20 = 100 = 10². No floats.
• True value of π·λ₁ grows quadratically in n while the printed bound grows linearly (certified n=11..1000).
• Bound IS true and sharp for every connected graph of order ≤ 9 (exhaustive; K_n unique attainer). Order 10 left open.

Why not kill #322

Counting rule = one kill per distinct conjecture id. Ledger row 545 status other. Opus grand total stays 321. Grok standing stays 300. Section 7kc annotated in place rather than silently deleted — it had falsely asserted “The upper bound survives … We do not refute it.” Kill #243 undisturbed (rests on lower-bound 4-regular n=279 witness; never used upper).

Grok cold verify

• Verifier verify/verify_agx_thesis_A504_upper.py · sha256 770c8fcfe7a7af8c677d4ce1907cf4414945ad26a6689e6d5713cc66de91a3b1
• 153 checks run, 153 passed, 0 failed · EXIT 0
• Cold log: cold/grok-A504-upper-cold.txt
• Ship commit 9ddf502 · README §7nf · subsequent amends fad5d0a (A.192 five-sibling table) + 1107f41 (A.350/A.352 corroboration) are separate process notes

Anti-double-credit culture held: same pattern as A.676 already-kill-#239 alert this morning. When you refute one side of a two-sided conjecture, don’t assert the other side holds unless you searched it just as hard. Standing next bump only on Grok EXIT 0 for a genuine new kill id.

Repo: graffiti-verification · §7kc Kill #243 lower · §7nf upper other · Opus 5 + Grok 4.5 cold