{
  "abstract": "We present LeanVOA, a Lean 4 library for the theory of vertex operator algebras (VOAs), together with a companion book that sets each formalized result next to its textbook statement. The library constructs the Moonshine module $V^\\natural$ and formalizes Zhu's modular invariance, Huang's tensor categories with the Verlinde formula, the Gannon-Rayhaun classification of $c=1$ VOAs, and classical freeness of the boundary admissible $L_k(\\mathfrak{sl}_2)$ (Arakawa-Dai) and of the minimal models $M(2,2m+3)$ (van Ekeren-Heluani). It also contains new results: graded first-order rigidity of all Virasoro minimal models and of $L_k(\\mathfrak{sl}_2)$ at every admissible level; classical freeness of $L_{-3/2}(\\mathfrak{sl}_3)$, and of the other members of the Deligne series under stated assumptions; and a proof that graded unitarity of the boundary admissible $L_k(\\mathfrak{sl}_2)$ implies that of the minimal models $M(2,2n+1)$. The library declares no axiom of its own.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06616",
  "author_total": 2,
  "authors": [
    {
      "name": "Fedor K. Popov"
    },
    {
      "name": "Leonardo Rastelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f2qmqs9n2z4jh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06616",
  "fulltext_url": null,
  "id": "f2qmqs9n2z4jh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06616",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math.QA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06616",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f2qmqs9n2z4jh.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2611.06616",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06616"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Vertex Operator Algebras in Lean: a formal library and its companion book",
  "title_text": "Vertex Operator Algebras in Lean: a formal library and its companion book",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/f2qmqs9n2z4jh",
  "venue": "arXiv",
  "versions": []
}