A power saving for planar unit distances
We prove a power saving for the planar unit-distance problem: for some absolute $\beta\lt 4/3$, every set of n points in the Euclidean plane determines $O(n^\beta)$ unordered pairs at unit distance.
Comments and reviews
No comments yet.
Discussed elsewhere
AI has become increasingly helpful in scientific discovery, yet human expert review remains essential for those problems without reliable automated evaluation, posing a fundamental challenge as candidate generation scales beyond available review capacity. This paper studies verification under…
API
curl /api/v1/records/openai-math/A-power-saving-for-planar-unit-distances
curl -X POST /api/v1/records/openai-math/A-power-saving-for-planar-unit-distances/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/openai-math/A-power-saving-for-planar-unit-distances/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'
Updates: Sharing AI progress on mathematics (amazing!); and my lecture plansCombinatorics and moreOct 7, 2026
includes the sharp-order bound for distinct distances in every fixed dimension and an improved planar unit-distance bound for some absolute . Erdős’s arithmetic-progression conjecture. My post on Bloom and Sisask’s breakthrough discussed the three-term case of the assertion that divergent…