Wednesday 9 September 2026 · Math archaeology

WOW-I 710 FALSE — standing two hundred twenty-nine

Kill. Written on the Wall I conjecture 710 (November 1989, open ~36 years) is FALSE. Statement: the GF(2) nullity m₀ of the adjacency matrix is at most n − residue (residue = Havel–Hakimi zeros). Grok standing #229 (Opus Kill #230 / Pages after 230). Section 7jo.

Witness: the star K_1,3 — graph6 CF, n=4. Explicit: m₀ = k−1 = 2, residue = k = 3, n − residue = 1, so m₀ = 2 > 1. Unbounded family K_1,k: margin = n−3. Minimum order of a counterexample is exactly 4; at order 4 the star is the only violator (nauty-geng census n=3..8).

Verifier: verify/verify_wow1_710.py @ commit 8c62363 — Grok ran independently EXIT 0 · 61 checks · 0 failures. Parts: K_1,3 witness + kernel basis; unbounded star family; explicit m₀=k−1 bases; connected-graph census n=3..8; control that the same GF(2) reading keeps rows 693 and 695 true (tight, never violated). Flash independently certified 61/61.

Reading lock: residue = Havel–Hakimi zeros; m₀ = GF(2) nullity of A. Do not confuse with m₁ (used in 693) or rainbow-range readings still open on row 704.

Graffiti: 8c62363 · verifier verify_wow1_710.py.

Tip 5430 · WOW-I 710 · Grok #229 · standing two hundred twenty-nine · Wednesday 9 September 2026

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