Kissing number in dimension 27
Lower bound: the records, digit by digit
- Oct 5, 2026201,589+0.011%by Rustem Takhanov and Stanislav Yun
- Sep 28, 2026201,567+5.0×10−4%by Shuxing Yang and 15 others
- Sep 22, 2026201,566+0.761%by Ben Lindow
- Nov 17, 2025200,044+0.034%by Chengdong Ma and 8 others
- 2017199,976first recordby Kenz Kallal and 2 others
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 27 [Frontier, checked on Oct 12, 2026]. DiscoverIA registry. https://discoveria.ai/en/frontieres/kissing-d27/
The exact value lies somewhere in between, within a factor of ×2.59. The lower bound has moved 4 times since 2017, most recently on Oct 5, 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^27. 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 201589 versus 522212 (ratio 2.591 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: PackingStar (200044, 2025-11-17); Qiushi Engine (201567, 2026-09-28); Claude Code (Claude Opus 5.5), GPT-6 Astra (201589, 2026-10-05). The latest (201589, Rustem Takhanov, Stanislav Yun, 2026-10-05) has AI use declared by its source. The upper bound (522212) 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 (6 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 |
|---|---|---|---|---|
| Oct 5, 2026 | 201589 Current record | published | Rustem Takhanov, Stanislav Yun | github.com |
| Sep 28, 2026 | 201567 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 |
| Sep 23, 2026 | 200046 | published | Rustem Takhanov, Stanislav Yun | arxiv.org |
| Sep 22, 2026 | 201566 Current record | published | Ben Lindow | github.com |
| Nov 17, 2025 | 200044 Current record | published | Chengdong Ma, Théo Tao Zhaowei, Pengyu Li, Minghao Liu, Haojun Chen, Zihao Mao, Yuan Cheng, Yuan Qi, Yaodong Yang | arxiv.org |
| 2017 | 199976 Current record | published | Kenz Kallal, Tomoka Kan, Eric Wang | doi.org |
Every step, as a table : Upper bound (1 points)
Best known upper bound (three-point semidefinite programming).
| Date | Exact value | Nature | Authors | Source |
|---|---|---|---|---|
| 2024 | 522212 Current record | published | David de Laat, Nando Leijenhorst | cohn.mit.edu |
Kissing number (21)
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