{
  "abstract": "We formalize the Hamilton--Perelman Ricci-flow proof of Thurston's geometrization conjecture. The public Lean declaration is reproduced in this paper. Its geometric interpretation follows, and verification is recorded in 4.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13897",
  "author_total": 10,
  "authors": [
    {
      "name": "Yuan Liao"
    },
    {
      "name": "Ziyang Qin"
    },
    {
      "name": "Jui-Hui Chung"
    },
    {
      "name": "Ayush Khaitan"
    },
    {
      "name": "Zhengyang Zhang"
    },
    {
      "name": "Hongzhou Lin"
    },
    {
      "name": "Zijian Zhang"
    },
    {
      "name": "Ligeng Zhu"
    },
    {
      "name": "Peng Lu"
    },
    {
      "name": "Bennett Chow"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/avh2tv3zvp85k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13897",
  "fulltext_url": null,
  "id": "avh2tv3zvp85k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13897",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7221511735",
  "pdf_url": "https://arxiv.org/pdf/2610.13897",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/avh2tv3zvp85k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13897",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13897"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Lean Formalization of the Hamilton--Perelman Proof of Thurston's Geometrization Conjecture",
  "title_text": "A Lean Formalization of the Hamilton--Perelman Proof of Thurston's Geometrization Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/avh2tv3zvp85k",
  "venue": "arXiv",
  "versions": []
}