Kissing number in dimension 39
Lower bound: the records, digit by digit
- Sep 28, 2026763,668+0.999%by Shuxing Yang and 15 others
- Aug 30, 2026756,116first recordby Alexander Kravatskiy
Coloured and underlined: the digits that changed since the previous record. No chart: since the first published record, neither bound has moved by more than 5% of the gap between them.
Cite this frontier
DiscoverIA. Kissing number in dimension 39 [Frontier, checked on Oct 12, 2026]. DiscoverIA registry. https://discoveria.ai/en/frontieres/kissing-d39/
The exact value lies somewhere in between, within a factor of ×49.53. The lower bound has moved once since 2026, on Sep 28, 2026. The upper bound has not moved since 2024.
The maximum number of unit spheres with disjoint interiors that can touch a central unit sphere in R^39. 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 763668 versus 37826766 (ratio 49.54 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: Qiushi Engine (763668, 2026-09-28). The latest (763668, Shuxing Yang, Rui Zhao, Junyao Wu et al., 2026-09-28) has AI use declared by its source. The upper bound (37826766) 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 (2 points)
Best known configuration (constructions), from the Leech, Kallal-Kan-Wang or Cohn-Li records to the AI-assisted constructions of 2025-2026.
| Date | Exact value | Nature | Authors | Source |
|---|---|---|---|---|
| Sep 28, 2026 | 763668 Current record | published | Shuxing Yang, Rui Zhao, Junyao Wu, Yize Wang, Fujia Chen, Kaihao Zhu, Wenhao Li, Zichen Li, Yaqi Li, Shenzhan Hong, Yuang Pan, Junjie Yang, Taowen Deng, Jincheng Mi, Hongsheng Chen, Yihao Yang | arxiv.org |
| Aug 30, 2026 | 756116 Current record | published | Alexander Kravatskiy | github.com |
Every step, as a table : Upper bound (1 points)
Best known upper bound (three-point semidefinite programming).
| Date | Exact value | Nature | Authors | Source |
|---|---|---|---|---|
| 2024 | 37826766 Current record | published | David de Laat, Nando Leijenhorst | cohn.mit.edu |
Kissing number (21)
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