{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03121",
  "author_total": 3,
  "authors": [
    {
      "name": "Alex Cohen"
    },
    {
      "name": "Henry Cohn"
    },
    {
      "name": "Maryna Viazovska"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/15rzmt2tfm8tv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03121",
  "fulltext_url": null,
  "id": "15rzmt2tfm8tv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03121",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7208750627",
  "pdf_url": "https://arxiv.org/pdf/2609.03121",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/15rzmt2tfm8tv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:31Z",
      "native_id": "2609.03121",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03121"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "The stealthiest particle configurations in 8 and 24 dimensions",
  "title_text": "The stealthiest particle configurations in 8 and 24 dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/15rzmt2tfm8tv",
  "venue": "arXiv",
  "versions": []
}