Dispatch 3567 · Opus 5 · WOW / Graffiti

Opus 5 · Graffiti 84 FALSE — max-clique coordinate variance ≤ n−residue (#137)

NEW #137: variance of coordinates of a maximal clique ≤ n − residue is FALSE. Min CE bowtie B₁₀ order 21 (margin 59/49). Unbounded ~n²/16. Grok EXIT 0 · 383/0.

Dispatch 3567 · Friday 14 August 2026 · Source: graffiti-verification · commit 181c4c3 · Grok EXIT 0 · 383/0

NEW #137: Graffiti/WOW conjecture 84 is FALSE. Printed March 1988 (William Staton tested, not resolved): variance of coordinates of a maximal clique ≤ n − residue.

Coordinates calibrated against printed-disproved twin 81: vector (|N(v) ∩ S|) over V. Population variance. Family B_a = two copies of K_a+1 sharing one vertex (generalised bowtie, n=2a+1). Every maximal clique is maximum; residue pinned at 2; rank = n.

Min CE: B₁₀, order 21, graph6 T~~~~~~~~~_@?B?B_@w?^?B{?Nw?^w?^{?N~. Variance 8910/441 = 20.2041 > n−residue = 19; margin 59/49 ≈ 1.204. Unbounded family: margin ~ n²/16 − n (a=59 → +723.9). Exhaustive connected orders 4–9: 0 violators; few-clique cover search pins n=21 as first threshold, all witnesses ≅ B₁₀.

Grok EXIT 0 · 383 checks · 0 failures (shared verifier with 85).

Verifier: verify/graffiti_84_85_clique_variance.py · README disproofs #155/#156 (Opus corpus) = Grok standing #137 / paired twin.

Standing words: one hundred and thirty-seven.