Autonomous system finds improved solutions to kissing number problem
Large-Scale Autonomous Discovery of Kissing Number Constructions
Information Theory
Summary
The kissing number problem asks how many non-overlapping spheres can touch another sphere of the same size, a puzzle solved exactly in only a few dimensions. The authors used an autonomous AI-based system named Qiushi Engine to discover new, improved solutions for this problem in higher dimensions. These new solutions come with detailed mathematical constructions and proofs that make the findings rigorous. Their approach shows how AI can help uncover complex geometric arrangements and mathematical relationships beyond straightforward optimization.
What this means in practice
- •For communication engineers: Develop more efficient signal constellation designs for high-dimensional data transmission using new kissing number bounds.
- •For cryptographic system designers: Use improved sphere packing configurations for constructing stronger high-dimensional codes that resist errors and attacks.
Authors
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
Abstract
The kissing-number problem is a classical problem in discrete geometry whose exact solution is known in only a few dimensions. Recent artificial-intelligence approaches have begun to discover improved configurations through large-scale numerical and combinatorial search, but converting such searches into general mathematical constructions and rigorous proofs remains challenging. Here we use Qiushi Engine, an autonomous multi-agent research system, to investigate kissing numbers and obtain new lower bounds in nineteen dimensions: $25$, $27$, $32$--$39$, $43$, $45$, and $49$--$55$. The resulting constructions arise from distinct structural mechanisms, including coordinated motions of contact layers, labelled direction reuse, joint support exchanges, signed-code replacements, cross-shell lattice constructions, low-overlap lattice isometries, and spherical-design moment certificates. They yield sharp capacities for parameterized signed-code models, deterministic image-union guarantees, and exact section and projection counts controlled by embedded root systems and anchor-graph statistics. These methods yield, among others, $K(25)\ge197580$, $K(27)\ge201567$, $K(38)\ge591900$, $K(43)\ge2553792$, $K(45)\ge7380090$, and $K(55)\ge53301140$. The autonomous system carried out the construction searches, mathematical analysis and computational verification, while each final result was reduced to explicit mathematical arguments and independently checkable finite certificates. Our results illustrate how autonomous research systems can move beyond optimization within fixed formulations to discover new mathematical representations and constructions at scale.