Kissing number in dimension 19

12,276≤ value ≤24,417lower boundupper bound

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Nov 7, 2024lower bound 11,692by Henry Cohn and Anqi Liarxiv.org
Mar 11, 2026lower bound 11,948by Boon Suan Hoarxiv.org
Oct 10, 2026lower bound 12,276by Kevin Ligithub.com
Oct 12, 2026Last checked

Lower bound · published · Oct 10, 2026

Exact value : 12276

Li : 12276 en dimension 19 (délétion et ajout de points signés pondérés) · github.com

by Kevin Li

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DiscoverIA. Kissing number in dimension 19 [Frontier, checked on Oct 12, 2026]. DiscoverIA registry. https://discoveria.ai/en/frontieres/kissing-d19/

The exact value lies somewhere in between, within a factor of ×1.99. The lower bound has moved 3 times since 1967, most recently on Oct 10, 2026. The upper bound has not moved since 2022.

The maximum number of unit spheres with disjoint interiors that can touch a central unit sphere in R^19. A valid configuration of N spheres gives the lower bound N; a linear or semidefinite programming bound gives an upper bound.

Exact value unknown: gap 12276 versus 24417 (ratio 1.990 on Cohn's table consulted 2026-10-13). Lower bounds are explicit constructions (the recent ones announce an exact-arithmetic program check); no named third-party review appears in the sources read. The sources read declare AI use for these lower bounds: GPT-6-Astra Pro, Claude Opus 5.5 (12276, 2026-10-10). The latest (12276, Kevin Li, 2026-10-10) has AI use declared by its source. The upper bound (24417) is a semidefinite programming bound (Cohn's table, credited to Leijenhorst-de Laat); no source read attributes it to an AI.

Every step, as a table : Lower bound (4 points)

Best known configuration (constructions), from the Leech, Kallal-Kan-Wang or Cohn-Li records to the AI-assisted constructions of 2025-2026.

Points : Lower bound
Date	Exact value	Nature	Authors	Source
Oct 10, 2026	`12276` Current record	published	Kevin Li	github.com
Mar 11, 2026	`11948` Current record	published	Boon Suan Ho	arxiv.org
Nov 7, 2024	`11692` Current record	published	Henry Cohn, Anqi Li	arxiv.org
1967	`10668` Current record	published	John Leech	doi.org

Every step, as a table : Upper bound (1 points)

Best known upper bound (three-point semidefinite programming).

Points : Upper bound
Date	Exact value	Nature	Authors	Source
Feb 24, 2022	`24417` Current record	published	David de Laat, Nando Leijenhorst	arxiv.org

Kissing number (21)

Kissing number in dimension 19

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