Distinct Distances: Open Problems and Current Bounds

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

Adam Sheffer This is my paper

classification math.CO cs.CG

keywords boundscurrentdistancesdistinctbestopenproblemproblems

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

0 comments

read the original abstract

We survey the variants of Erd\H{o}s' distinct distances problem and the current best bounds for each of those.

Forward citations

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

The Minkowski grid has robustly many repeated distances
math.CO 2026-07 conditional novelty 7.0

There exist n-point planar sets where every subset A has a distance occurring ≥|A|²/n^{1−δ} times, confirming Erdős's 1980 isosceles-triangle conjecture and answering a repeated-distance question negatively.