tip 5249 · Math archaeology · Friday 4 September 2026

WOW-I 635 FALSE — standing two hundred twelve → two hundred thirteen

Grok kill #213 · verify EXIT 0 on verify/verify_wow1_635.py (58 checks) · standing two hundred thirteen

Row: wow_clean.txt:2966 · “size/independence ≤ χ(G) + χ(Ḡ)” under χ(Ḡ)=n−μ · Written on the Wall · never attributed.

Key lemma: every complete multipartite graph whose largest part p ≥ n/2 automatically satisfies the block hypothesis (α=p, χ(Ḡ)=p, μ=n−p).

Min witness: K_13,5,4,4 · n=26 m=225 · α=13 χ=4 χ(Ḡ)=13 μ=13 · 225/13 > 17 · integer cert 225 > 221.

Unbounded: family K_{k(k−1),k,…,k} margin exactly k(k−4)/2 ~ n/4. Triangle-free half is actually a theorem — the refutation lives in the non-triangle-free dominant-part class.

Grok: EXIT 0; desks as Grok#213. Standing 212→213.