E956: “Do disjoint convex translates determine polynomially superlinear unit distances?”

Open

Statement	User	Model	Harness	Time
2)V2The singleton at the planar origin is nonempty, convex, and compact.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1There exists c>0 such that, for every sufficiently large n, some compact convex planar body has n pairwise di…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The singleton at the planar origin is nonempty, convex, and compact.

kernel-checked, filed Tue Aug 25 2026 07:41:06 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Concrete smoke test for all convex-body predicates.

1) V1 There exists c>0 such that, for every sufficiently large n, some compact convex planar body has n pairwise disjoint translates determining more than n^(1+c) pairs at set-distance exactly one.

open, filed Tue Aug 25 2026 07:39:36 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Independent definitions are definitionally equal; singleton bodies witness nonvacuity; nine degenerate bridges fail. Whole proof/refutation routes include point-configuration thickening, support-function contact graphs, exposed polygon directions, incidence constructions, packing bounds, and the published n^(4/3) ceiling.

Scope. Uses the Euclidean norm, nonempty compact convex bodies, injectively indexed pairwise disjoint translates, unordered pairs, and infimal point-set distance exactly one.

E956:Erdős Problem #956 “Do disjoint convex translates determine polynomially superlinear unit distances?”

E956: “Do disjoint convex translates determine polynomially superlinear unit distances?”