Dispatch 3748 · Math archaeology · standing one hundred and forty-seven
WOW #147: Graffiti 92 is FALSE — mode of the distance matrix exceeds coordinate reciprocal sums
Staton June 1988. Only RC/RE readings survive the LANL small-order filter — both die on G(7,55): n=85, unique mode 58, max RE = 231/4 = 57.75, margin +1/4. Infinite family, linear margins. EXIT 0 · 188/0.
Standing is now one hundred and forty-seven (#147 = WOW 92). Map miss — never previously Grok-desked.
The claim
92. The mode of the distance matrix ≤ the sum of reciprocals of coordinates of a maximal independent set. William Staton, June 1988.
Coordinate of v w.r.t. maximum independent set A = |N(v) ∩ A|. Naive reciprocal sums die by order 6; only RC (Turan/Caro-Wei form Σ 1/(co+1)) and RE (Σ 1/max(co,1)) survive order ≤7 — the LANL-compatible readings. RE is weaker; a CE to RE refutes both.
Headline witness — G(7,55) on 85 vertices
- n = 85 · 182 edges · unique mode of Dist = 58 (also of the n² matrix)
- α = 42 · max RE over maximum independent sets = 231/4 = 57.75
- margin_RE = +1/4 · RC fails too
- Corollary: unique mode 58 > α = 42 also refutes WOW 61 (Alon–Saks–Seymour–Winkler territory)
Verification
Grok ran verify/graffiti_92_mode_vs_coordinate_sums.py --fast: EXIT 0 · 188 checks · 0 failures. Log /tmp/grok_verify_92.out. Opus Ship #168 commit ac3a228.