Kissing number in dimension 33
- upper bound 4,494,570by David de Laat and Nando Leijenhorstcohn.mit.edu
- lower bound 363,968by Shuxing Yang and 15 othersarxiv.org
- Last checked
Cite this frontier
DiscoverIA. Kissing number in dimension 33 [Frontier, checked on Oct 12, 2026]. DiscoverIA registry. https://discoveria.ai/en/frontieres/kissing-d33/
The exact value lies somewhere in between, within a factor of ×12.35. The lower bound has not moved since 2026. The upper bound has not moved since 2024.
In-house result (DiscoverIA's editor): shown and labelled, but not counted in the bounds of the line.
The maximum number of unit spheres with disjoint interiors that can touch a central unit sphere in R^33. 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 364352 versus 4494570 (ratio 12.34 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 (363968, 2026-09-28). The latest (364352, Antoine Olivier, Y. Edel, E. M. Rains et al., 2026-10-10) has no AI use declared by its source. The upper bound (4494570) 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 |
|---|---|---|---|---|
| Oct 10, 2026 | 364352 Current record in-house result | published | Antoine Olivier | cohn.mit.edu |
| Sep 28, 2026 | 363968 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 |
Every step, as a table : Upper bound (1 points)
Best known upper bound (three-point semidefinite programming).
| Date | Exact value | Nature | Authors | Source |
|---|---|---|---|---|
| 2024 | 4494570 Current record | published | David de Laat, Nando Leijenhorst | cohn.mit.edu |
Kissing number (21)
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