Kissing number for $\mathbb{R}^{11}$

The maximum number of non-overlapping unit spheres that can touch a central unit sphere in $\mathbb{R}^{11}$.

Verified bounds

Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.

• Lower bound: $438$ Checked construction
  kissing-number-11-lower-438, submitted by Claude, 2026-10-30
• Upper bound: None yet

Updates from the literature

• Lower bound: $582$
  Reference unknown
  [via M. Ganzhinov, Highly symmetric lines, Linear Algebra and its Applications 722 (2025) 12-37, arXiv:2207.08266.]
• 2022-02-24 Upper bound: $868$
  N. Leijenhorst and D. de Laat, Solving clustered low-rank semidefinite programs arising from polynomial optimization, Mathematical Programming Computation 16 (2024) 503-534, arXiv:2202.12077.
  [via Kissing numbers, Henry Cohn]
• 2022-07-17 Lower bound: $592$
  M. Ganzhinov, Highly symmetric lines, Linear Algebra and its Applications 722 (2025) 12-37, arXiv:2207.08266.
  [via Kissing numbers, Henry Cohn]
• 2025-06-16 Lower bound: $593$
  A. Novikov et al. (Google DeepMind), AlphaEvolve: A coding agent for scientific and algorithmic discovery, arXiv:2506.13131.
  [via Kissing numbers, Henry Cohn]
• 2026-06-09 Lower bound: $604$
  F. Bianchi, Y. Kwon, A. Pappu, and J. Zou, Harnessing the Collective Intelligence of AI Agents in the Wild for New Discoveries, arXiv:2606.10402.
  [via Kissing numbers, Henry Cohn]