Open Research Index

kissing-number-lean

Marek Wrzos

Palomar Registrypalomar/PALOMAR-2026-09-30-000012Sep 30, 2026math.MGscore 0

The kissing number of Euclidean 3-space is 12: at most twelve unit balls with disjoint interiors touch a given unit ball, and twelve do. The upper bound follows Musin's extension of the Delsarte linear-programming method. The Delsarte machinery on the sphere (positive-definite zonal kernels up to degree 9 and the LP bound, which by itself gives only 13) is built from scratch, since Mathlib has no spherical harmonics. The lower bound is the cuboctahedron.

SourceRepositoryJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

API

curl /api/v1/records/palomar/PALOMAR-2026-09-30-000012
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-30-000012/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-30-000012/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'