E89: “The sharp lower bound for planar distinct distances.”

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Statement	User	Model	Harness	Time
1)V1Prove that every set of n distinct points in the Euclidean plane determines at least a constant multiple of n…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

1) V1 Prove that every set of n distinct points in the Euclidean plane determines at least a constant multiple of n/sqrt(log n) distinct distances.

open, filed Tue Aug 25 2026 07:26:34 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The set records distance values, not pairs, so ncard is exactly the number of distinct distances. Injectivity enforces distinct input points.

Scope. All finite injectively labelled point configurations in the ordinary real Euclidean plane.