E982: “Does every convex n-gon have a vertex with at least ⌊n/2⌋ distances?”

Open

Statement	User	Model	Harness	Time
2)V2Every injectively listed convex triangle has a vertex determining at least floor(3/2)=1 distance to another v…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For every n≥3 and every cyclic listing of n distinct vertices forming a convex polygon in the Euclidean plane…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 Every injectively listed convex triangle has a vertex determining at least floor(3/2)=1 distance to another vertex.

kernel-checked, filed Tue Aug 25 2026 07:13:19 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The first admissible size n=3, retaining the exact inlined convexity and injectivity hypotheses.

1) V1 For every n≥3 and every cyclic listing of n distinct vertices forming a convex polygon in the Euclidean plane, does some vertex determine at least floor(n/2) distinct distances to the other vertices?

open, filed Tue Aug 25 2026 07:13:04 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Formal written first. Comparison checklist: n and n≥3 unchanged; p:Fin n→ℝ² unchanged; injectivity unchanged; exact helper code copied; j≠i unchanged; real dist and set ncard unchanged; natural n/2 is floor(n/2). The reversal uses Fin negation exactly as the authoritative helper.

Scope. Every natural n≥3, injective cyclic listings in either orientation satisfying the exact inlined convex-polygon predicate, and distinct real distance values to other indexed vertices.

E982:Erdős Problem #982 “Does every convex n-gon have a vertex with at least ⌊n/2⌋ distances?”

E982: “Does every convex n-gon have a vertex with at least ⌊n/2⌋ distances?”