{
  "abstract": "We classify the Classifying Grothendieck rings of pivotal fusion categories of rank four over the complex field. There are exactly fifteen, each admitting a unitary categorification. Central induction and Frobenius-Schur indicators give a uniform Frobenius-Perron dimension bound of 3600. The finite classification combines new arithmetic and twist obstructions with an exhaustive census and exact exclusion certificates.",
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  "article_type": null,
  "arxiv": "2609.33272",
  "author_total": 3,
  "authors": [
    {
      "name": "Jingcheng Dong"
    },
    {
      "name": "Sebastien Palcoux"
    },
    {
      "name": "Arnaud Plessis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ftd4pnsy1qk23.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33272",
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  "id": "ftd4pnsy1qk23",
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  "landing_url": "https://arxiv.org/abs/2609.33272",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "arxiv",
      "math.CT"
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      "arxiv",
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      "arxiv",
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      "openalex",
      "2608|Algebraic structures and combinatorial models"
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  "openalex": "W7214804429",
  "pdf_url": "https://arxiv.org/pdf/2609.33272",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ftd4pnsy1qk23.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.33272",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33272"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Classifying Grothendieck rings of pivotal fusion categories of rank four",
  "title_text": "Classifying Grothendieck rings of pivotal fusion categories of rank four",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/ftd4pnsy1qk23",
  "venue": "arXiv",
  "versions": []
}