Discrete geometry·kissing:dimension-11
Kissing number in dimension 11
No formal proof attached. Any claim here rests on a write-up or a report.
Fidelity F0: Absent. No formal statement is attached to the result.
The largest number of non-overlapping unit spheres that can touch a central unit sphere in 11 dimensions. The exact value is unknown; the record is the largest known configuration, and the best upper bound is 868.
Record history
5 steps·spheres, higher is betterLeech and Sloane's constructions from codes gave 566 in 1971, and Zinoviev and Ericson reached 582 in 1999. Ganzhinov found 592 in 2022 from highly symmetric line systems. AlphaEvolve reported 593 in 2025, and agents working on the EinsteinArena platform moved the bound to 604 by May 2026 through a sequence of submissions and public discussion. Henry Cohn's table of kissing numbers, whose references the older steps follow, lists 604 against an upper bound of 868.
Reached by May 2026 through a sequence of agent submissions, public discussion and verifier refinement, as the paper describes.
Reported in the AlphaEvolve white paper; the EinsteinArena paper states 593 as the bound it improved.
Highly symmetric line systems; published in Linear Algebra and its Applications in 2025.
New lower bounds for contact numbers in small dimensions, as referenced in Cohn's table.
Sphere packings and error-correcting codes, as referenced in Cohn's table.
AI activity
How grades workA configuration of 593 spheres in dimension 11, improving 592.
Reasoning and sources
Autonomy
An evolutionary coding agent searching against an evaluator written by people, who also chose the problem.
A configuration of 604 spheres in dimension 11, improving 593.
Reasoning and sources
Autonomy
Agents searched and discussed against verifiers the platform's builders wrote; the paper says the advance came from a sequence of agent submissions and agent-to-agent borrowing of ideas.
Details
platform: EinsteinArena
Fidelity
How fidelity is gradedF0 no formal statement. Absent. No formal statement is attached to the result.
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qed.bot, “Kissing number in dimension 11”, https://qed.bot/t/kissing-dimension-11, as of 30 Sep 2026.