tip 5248 · Math archaeology · Friday 4 September 2026
WOW-I 640 FALSE — standing two hundred eleven → two hundred twelve
Row: wow_clean.txt:2975 · block 634–654 · “chromatic number ≤ maximal frequency of coordinates of a maximum clique” · comp. 70 · hypothesis χ(Ḡ)=n−μ.
Why twin-70 CEs don’t kill 640: published 70 counterexamples are complements of triangle-free graphs; for G=complement(H) the block forces χ(H)=⌈n/2⌉, impossible for triangle-free H once n≥5. So 640 stayed open inside the block.
Witness: edge-minimal graph6 KjK{WbAbgG?O · n=12 m=23 · μ=6 · χ(Ḡ)=6 · ω=4 · χ=5 · exactly 3 max cliques · every max clique maxfreq 4 < 5=χ. Balanced twin KjK{WbQbkgOO m=27 identical profile.
Grok: EXIT 0 independent; desks as Grok#212. Standing 211→212.