Kissing number in dimension 35

409,676≤ value ≤9,162,403lower boundupper bound

2024upper bound 9,162,403by David de Laat and Nando Leijenhorstcohn.mit.edu
Sep 28, 2026lower bound 409,676by Shuxing Yang and 15 othersarxiv.org
Oct 12, 2026Last checked

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DiscoverIA. Kissing number in dimension 35 [Frontier, checked on Oct 12, 2026]. DiscoverIA registry. https://discoveria.ai/en/frontieres/kissing-d35/

The exact value lies somewhere in between, within a factor of ×22.36. The lower bound has not moved since 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^35. 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 409676 versus 9162403 (ratio 22.37 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 (409676, 2026-09-28). The latest (409676, Shuxing Yang, Rui Zhao, Junyao Wu et al., 2026-09-28) has AI use declared by its source. The upper bound (9162403) 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 (1 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
Sep 28, 2026	`409676` 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).

Points : Upper bound
Date	Exact value	Nature	Authors	Source
2024	`9162403` Current record	published	David de Laat, Nando Leijenhorst	cohn.mit.edu

Kissing number (21)

Kissing number in dimension 35

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