{
  "abstract": "We improve the best known sphere packings in every dimension from $38$ to $43$. Our packings in dimensions $38$ to $42$ come from one chain of cross-sections of the extremal even unimodular lattice $P_{48p}$, $\\sqrt3E_6 \\subset \\sqrt3E_7 \\subset \\sqrt3E_8 \\subset K_9 \\subset K_{10}$, whose first three members are cut from the fixed lattice $\\sqrt3(E_8 \\perp E_8)$ of an order-three automorphism; their orthogonal complements are lattice packings and set the records in dimensions $42$ down to $38$. Each successive section is a determinant-minimal extension of its predecessor. Our $43$-dimensional packing is an antipode packing: six translates of the complement of a $5$-dimensional section. We also improve some kissing numbers. Conway and Sloane's twelve $1982$ cross-section packings appear never to have had theirs computed; we compute them and find that, in dimensions $42$ to $47$, they exceed the previously tabulated lower bounds. Our chain does better in dimensions $40$, $41$ and $42$, and a further antipode packing beats the record in dimension $45$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.20359",
  "author_total": 3,
  "authors": [
    {
      "name": "Ivan Dorofeev"
    },
    {
      "name": "Xiaoming Sun"
    },
    {
      "name": "Chengu Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1j9vkb0x3nbrs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.20359",
  "fulltext_url": null,
  "id": "1j9vkb0x3nbrs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.20359",
  "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",
      "math.MG"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7170191363",
  "pdf_url": "https://arxiv.org/pdf/2607.20359",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1j9vkb0x3nbrs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2607.20359",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.20359"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Optimal Extensions of Cross-Sections: Sphere Packings in Dimensions 38 to 43",
  "title_text": "Optimal Extensions of Cross-Sections: Sphere Packings in Dimensions 38 to 43",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/1j9vkb0x3nbrs",
  "venue": "arXiv",
  "versions": []
}