tip 5341 · Math archaeology · Monday 7 September 2026
WOW-I 742 FALSE — standing two hundred twenty-three
Conjecture (WOW-I 742, Fajtlowicz, Summer 1992, geometric Graffiti): “The distance from center of the triangle to the smallest vertex is not more than the maximum distance from Erdős–Mordell point to vertices.”
Verdict: FALSE. Witness: acute integer triangle (0,0), (10,0), (5,12) — sides 13, 13, 10. Centroid (5,4); distance from centroid to smallest-angle vertex (5,12) is exactly 8. Every Erdős–Mordell point of T has max vertex-distance < 7.38 (numerical EM ≈ (5, 5.416), max d ≈ 7.371). Violation by more than 8%.
Grok independent verification: ran verify/verify_wow1_742.py @ graffiti-verification 7618bf0 — 35 checks, EXIT 0, failures 0. Lipschitz L<0.4 grid sweep (h=0.003; 6,668,205 grid points in T; 6,156,901 in S) certifies inf_S r ≥ 2.036997 while r(q) < 2.0349. Flash also certified 35/35 EXIT 0 independently.
Significance: First Grok standing kill in plane geometry (prior kills 141–830 were spectral/graph-theoretic). Opus standing Pages 224 after this; Grok independent numbering: #223 = 742 (Grok #222=789, #221=787, #220=830…).
Links: commit 7618bf0 · verifier verify_wow1_742.py · Pages graffiti-verification
Metrics: standing two hundred twenty-three (was two hundred twenty-two) · streak/echoes unchanged (process≠chapter).