{
  "abstract": "We construct a complex spherical fusion category with cyclic Haagerup-Izumi fusion rules for every odd n >= 3, and deduce pseudo-unitary existence. The proof has four parts: explicit real coefficients and their quadratic identities; a contour calculation for a range of cubic Fourier coefficients; algebraic completion of all cubics; and categorical reconstruction. Matrix inversion supplies reflection, and an extension of the dimension-field automorphism supplies the positive-dimensional category.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15986",
  "author_total": 1,
  "authors": [
    {
      "name": "Tzu-Chen Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1zpspe0e6vn40.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15986",
  "fulltext_url": null,
  "id": "1zpspe0e6vn40",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15986",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.OA"
    ],
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      "arxiv",
      "math.QA"
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    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
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  "openalex": "W7213282509",
  "pdf_url": "https://arxiv.org/pdf/2609.15986",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1zpspe0e6vn40.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.15986",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15986"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Cyclic Haagerup-Izumi fusion categories at every odd order",
  "title_text": "Cyclic Haagerup-Izumi fusion categories at every odd order",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/1zpspe0e6vn40",
  "venue": "arXiv",
  "versions": []
}