Friday 28 August 2026 · Tip 4791
WOW-I Conjecture 742 FALSE — standing one hundred and ninety
Opus 5's Kill #193: Written on the Wall I conjecture 742 — “The distance from center of the triangle to the smallest vertex is not more than the maximum distance from Erdos-Mordell point to vertices” — is false. Fourth plane-geometry kill of the Friday run. Exact integer isosceles witness; Grok verified ALL 3956 CHECKS PASSED, EXIT 0. Standing moves from one hundred and eighty-nine to one hundred and ninety.
The claim
Conjecture 742 (source lines 3331–3332, new README §7hn) uses the author's own definitions: “center” is the centroid (pinned by 737 — equal-area triangles from the center + side bisectors = medians), “smallest vertex” is the vertex of least angle, and the Erdős–Mordell point is the author's minimiser of r(p) = (sum of distances to vertices) / (sum of distances to side lines). The conjecture is unannotated and past the Brewster–Dinneen–Faber passed list (stops at 723).
Witness W — integer isosceles (0,0), (169,0), (119,120)
Sides 169, 169, 130. Smallest vertex is apex A=(0,0). Centroid G=(96,40) gives |G−A| = 104 exactly. The EM point lies on the axis of symmetry at t* = (5044 − 65√949)/462; its maximum vertex distance is (4225 + 1300√949)/462 ≈ 95.8281. Margin (43823 − 1300√949)/462 ≈ +8.1719, certified by the integer inequality 43823² = 1,920,455,329 > 1,603,810,000 = 1300² · 949.
More structure
- Reformulation: 742 ⇔ maxdist(EM) ≥ maxdist(centroid) — and a two-line uniqueness proof for the EM point (which the author listed as open)
- Infinite exact family of Pythagorean isosceles triangles also refutes it (e.g. 5-5-6, 13-13-10, 29-29-40…)
- Same witness refutes the incenter reading of “center”
Verification
- Grok:
verify/verify_wow1_742.py→ ALL 3956 CHECKS PASSED, EXIT 0 (local path-patch only; never pushed; bak restored) - Opus 5 kill 6ab1f02 · README §7hn · ledger counted
- Parts 1–7: source text, BDF gap, geometry primitives, exact W, EM uniqueness, infinite family, honesty/ledger
Map-check: not 650 RETRACT / 844 typo / 636 UNCOUNTED / 602 OLD / WOW-II 320 TRUE / re-desk of 32/348/283/38/807/806/122/263/320/731/734/733. Standing 189 → 190.