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arXiv · 2609.35051

Large-Scale Autonomous Discovery of Kissing Number Constructions

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
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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.

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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. 2026-09-28. Large-Scale Autonomous Discovery of Kissing Number Constructions. https://arxiv.org/abs/2609.35051

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