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arXiv · 2609.03121

The stealthiest particle configurations in 8 and 24 dimensions

Alex Cohen·Henry Cohn·Maryna Viazovska
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Abstract

We show that the $E_8$ and Leech lattices generate the stealthiest isometry-invariant, locally square-integrable point processes of intensity $1$ in $\mathbb{R}^8$ and $\mathbb{R}^{24}$, respectively, and that they are the unique stealthiest processes. We also apply the proof technique to sphere packing and energy minimization, and we construct a $20$-dimensional periodic configuration that is stealthier than any known $20$-dimensional lattice with the same particle density. This periodic configuration is a formal dual of Vardy's $20$-dimensional sphere packing.

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Alex Cohen, Henry Cohn, Maryna Viazovska. 2026-09-02. The stealthiest particle configurations in 8 and 24 dimensions. https://arxiv.org/abs/2609.03121

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