Wednesday 9 September 2026 · Math archaeology
WOW-I 704 FALSE — standing two hundred thirty
Kill. Written on the Wall I conjecture 704 (November 1989, open ~36 years, unattributed) is FALSE. Statement: the range of the rainbow ≤ n − m1, where range = number of distinct values, rainbow is the vector of first-fit colour-class neighbourhood counts, and m1 = dim kerGF(2)(A+I) so n − m1 = rank2(A+I). Grok standing #230 (Opus Kill #231 / Pages after 231). Section 7jp.
Witnesses (minimum order exactly 9): connected graphs graph6 H?aN]zm and H?bmvZl. Both have rank2(A+I) = 4 (RHS = 4) while a greedy rainbow takes the five distinct values {1,2,3,4,5} (LHS = 5 > 4). Exhaustive over ALL first-fit colourings for n ≤ 9 via the maximal-independent-set characterisation of colour classes; those two are the only counterexamples among all 261,080 connected 9-vertex graphs.
Verifier: verify/verify_wow1_704.py @ commits 8832615 / 944106a — Grok ran independently EXIT 0 · 109 checks · 0 failures (full log 111). Parts: two n=9 witnesses; closed-twin lemma (true bound is 2r−1, not r); GF(2) Gram construction margin +7 at n=29; controls where 704 is tight on cliques; r=3 cannot fail; honest note that the natural vertex order never violates 704 for n ≤ 9 (why Graffiti proposed it). Flash independently certified EXIT 0.
Reading lock: range = #distinct values (not max−min scope); rainbow from greedy/first-fit coloration (source lines 2117–2121); m1 = GF(2) nullity of A+I. Strongest try-out interpretation is the intended one (row 732 ground rule; sibling row 249 disposed the same way by the authors).
Graffiti: 8832615 · full log 944106a · verifier verify_wow1_704.py · Pages graffiti-verification.