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Kissing number in dimension 11

604≤ value ≤868lower boundupper bound
600800198020002020updated on Oct 12, 2026Lower bound 582, 1988, J. H. Conway and N. J. A. Sloane, publishedLower bound 592, Jul 17, 2022, Mikhail Ganzhinov, publishedLower bound 593, May 14, 2025, Google DeepMind, publishedLower bound 594, Apr 10, 2026, an agent, publishedLower bound 604, Apr 13, 2026, published604Upper bound 915, Mar 1979, A. M. Odlyzko and N. J. A. Sloane, publishedUpper bound 870, Jun 26, 2009, Hans D. Mittelmann and Frank Vallentin, publishedUpper bound 869, Sep 16, 2016, Fabrício Caluza Machado and Fernando Mário de Oliveira Filho, publishedUpper bound 868, Feb 24, 2022, David de Laat and Nando Leijenhorst, published868lowerupper60080019801990200020102020updated on Oct 12, 2026Lower bound 582, 1988, J. H. Conway and N. J. A. Sloane, publishedLower bound 592, Jul 17, 2022, Mikhail Ganzhinov, publishedLower bound 593, May 14, 2025, Google DeepMind, publishedLower bound 594, Apr 10, 2026, an agent, publishedLower bound 604, Apr 13, 2026, published604Upper bound 915, Mar 1979, A. M. Odlyzko and N. J. A. Sloane, publishedUpper bound 870, Jun 26, 2009, Hans D. Mittelmann and Frank Vallentin, publishedUpper bound 869, Sep 16, 2016, Fabrício Caluza Machado and Fernando Mário de Oliveira Filho, publishedUpper bound 868, Feb 24, 2022, David de Laat and Nando Leijenhorst, published868lower boundupper bound
Hover over the points or move through them with the keyboard; a click opens the PR, the commit or the source page.Tap a point to read its source; tap it again to open the PR or the page.What is a bound?
  1. lower bound 593by Google DeepMinddeepmind.google
  2. lower bound 594by an agenteinsteinarena.com
  3. lower bound 604together.ai
  4. Last checked
Lower bound · published · Apr 13, 2026
Exact value : 604
EinsteinArena : 604 sphères en dimension 11 (ancienne borne 593) · together.ai
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Cite this frontier

DiscoverIA. Kissing number in dimension 11 [Frontier, checked on Oct 12, 2026]. DiscoverIA registry. https://discoveria.ai/frontiers/kissing-d11

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The exact value lies somewhere in between, within a factor of ×1.44. The lower bound has moved 4 times since 1988, most recently on Apr 13, 2026. The upper bound has moved 3 times since 1979, most recently on Feb 24, 2022.

The maximum number of unit spheres with disjoint interiors that can touch a central unit sphere in R^11. 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 604 versus 868 (ratio 1.438 on Cohn's table). Lower bounds are explicit, checkable constructions; the latest (604) was found by AI agents on EinsteinArena, checked in exact integer arithmetic, and not reviewed by a named third party. Integer upper bounds are floors of three-point semidefinite programming optima (degree 14, 16, 20); the latest was not rigorously verified by its authors.

Analogy

Take a marble and surround it with identical marbles that all touch it without overlapping: how many can you fit? Flat on a table, with coins around a coin, a few tries give the answer. In space, with marbles, there is room for them to shift, and it took centuries to prove that no extra one can be squeezed in. The kissing number asks the same question in spaces with more than three dimensions.

Where the picture stops

Beyond three dimensions there are no marbles to move around: a marble becomes a list of numbers, "touching" becomes a distance to compute, and the exact answer is known in only a handful of dimensions.

In the glossary : Kissing number

Linked announcements in the registry

Every step, as a table : Lower bound (5 points)

Best known configuration (constructions), from the Conway-Sloane table to EinsteinArena.

Points : Lower bound
DateExact valueNatureAuthorsSource
Apr 13, 2026604 Current recordpublished—together.ai
Apr 10, 2026594 Current recordpublishedan agenteinsteinarena.com
May 14, 2025593 Current recordpublishedGoogle DeepMinddeepmind.google
Jul 17, 2022592 Current recordpublishedMikhail Ganzhinovarxiv.org
1988582 Current recordpublishedJ. H. Conway, N. J. A. Sloanearxiv.org
Every step, as a table : Upper bound (4 points)

Best known upper bound (linear then semidefinite programming).

Points : Upper bound
DateExact valueNatureAuthorsSource
Feb 24, 2022868 Current recordpublishedDavid de Laat, Nando Leijenhorstarxiv.org
Sep 16, 2016869 Current recordpublishedFabrício Caluza Machado, Fernando Mário de Oliveira Filhoarxiv.org
Jun 26, 2009870 Current recordpublishedHans D. Mittelmann, Frank Vallentinarxiv.org
Mar 1979915 Current recordpublishedA. M. Odlyzko, N. J. A. Sloanedoi.org
Kissing number (21)

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