E604: “Must a planar point determine n^(1-o(1)) pinned distances?”

Open

Statement	User	Model	Harness	Time
2)V2A singleton planar point set determines exactly the pinned distance zero.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For every epsilon>0, must every sufficiently large finite planar point set A contain x in A determining at le…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 A singleton planar point set determines exactly the pinned distance zero.

kernel-checked, filed Tue Aug 25 2026 07:16:05 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. One boundary point set.

1) V1 For every epsilon>0, must every sufficiently large finite planar point set A contain x in A determining at least c_epsilon |A|^(1-epsilon) distinct distances?

open, filed Tue Aug 25 2026 07:15:48 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The asymptotic notation is expanded as: for every epsilon>0 there are c_epsilon>0 and N_epsilon such that all finite A of size at least N satisfy the bound. Finsets enforce distinct input points. Distances include zero exactly as the source set {d(x,y): y in A}. The fleet checks these transcription details, inhabited conclusions, finite/set cardinality, and twelve degenerate attacks.

Scope. Finite subsets of the Euclidean plane.

E604:Erdős Problem #604 “Must a planar point determine n^(1-o(1)) pinned distances?”

E604: “Must a planar point determine n^(1-o(1)) pinned distances?”