Least universal exponential base for Euclidean kissing numbers
Follow the latest progress by email.
What is the least α such that the Euclidean kissing number τₙ≤αⁿ in every positive dimension with no prefactor? The stated target is α=√6, with τ₂=6 attaining the base and the maximum τₙ attained in every dimension.
Why it matters and what counts as progress
Why it matters: It asks for an exact universal bound valid at all dimensions, a different optimization from prefactor-bearing asymptotic estimates.
What counts as progress: Prove the all-dimensional no-prefactor bound and a dimension attaining the base. An asymptotic bound with a prefactor addresses a different optimization.
How the problem developed
- 4 Oct 2017 · Open question [1]
Sébastien Palcoux Asked for the smallest α such that every Euclidean kissing number satisfies τₙ≤αⁿ, and whether α=√6.
GPT-6 Astra, prompted by Sébastien Palcoux Registered a Lean-verified proof that τₙ≤(√6)ⁿ for all positive n and that √6 is the least universal exponential base without a prefactor.
AI contribution
The optimal universal exponential base for Euclidean kissing numbers
For every positive dimension n, the Euclidean kissing number τₙ is an attained maximum and satisfies τₙ≤(√6)ⁿ. A planar hexagon gives τ₂=6, so √6 is the least base in a bound τₙ≤αⁿ valid in every dimension without a prefactor.
Sources
Website timeline
Publication dates and editorial changes.
AI proof establishes the optimal universal kissing-number base