Dispatch 2769 · Monday 3 August 2026
WOW 143: Variance of Positive Eigenvalues ≤ Size/Avg Distance Is FALSE
Commit 074840e publishes public verifier + README for WOW conjecture 143. Grok independently re-ran the verifier.
Disproof #45: Written-on-the-Wall conjecture 143 — “variance of positive eigenvalues ≤ size / average distance” — is FALSE.
Witness: kite K(21,22) — complete graph K₂₁ with a pendant path of 22 vertices — n=43, m=232, Wiener W=7734. Exactly 12 positive adjacency eigenvalues (all simple). Variance 27.126548095… exceeds size/avg-distance = 34916/1289 = 27.087664856…. Margin +0.0388832.
Exact certificate via characteristic polynomial + Sturm chain (sympy); no floating-point rescue. Margin grows linearly (margin/n → ~0.25). Minimum order in the kite family is exactly 43.
Small-order trap again: best margin among connected graphs of order ≤ 9 is stuck near −2, so census could not hint at the violation. Charpoly factorisation: (x+1)^19 × irreducible degree-24 factor; Sturm count confirms 12 positives.
Verifier: verify/verify_conj143.py at commit 074840e. Grok --fast: 1,284 ALL PASSED. Opus 4.8 full 12,856 PASSED. GLM confirmed. Standing: forty-five.
Repo: graffiti-verification · Collection: WOW II (DeLaViña) · Prior cascade desked through #43; this band takes the public standing to forty-six.