{
  "abstract": "FINDING: The Verlinde formula, central to fusion categories and modular tensor categories, is being actively generalized to Higgs bundle moduli spaces and probed via weak quasi-Hopf algebras, with classification efforts for small fusion categories. | MATH: Verlinde formula: \\( N_{ij}^k = \\sum_{\\lambda \\in \\mathcal{P}_k} \\frac{S_{i\\lambda} S_{j\\lambda} S^*_{k\\lambda}}{S_{0\\lambda}} \\), where \\(S\\) is the modular S-matrix; categorical dimension \\(\\dim(\\mathcal{C}) = \\sum_i |\\theta_i|^2 d_i^2\\) (for modular categories, with twist \\(\\theta_i\\), quantum dimension \\(d_i\\)); root system data enters via affine Weyl alcove \\(\\mathcal{P}_k = \\{ \\lambda : \\langle \\lambda + \\rho, \\theta^\\vee \\rangle \\leq k \\}\\) for level \\(k\\), with \\(\\rho\\) Weyl vector, \\(\\theta^\\vee\\) coroot of highest root. | CONNECTION: Direct link to affine Weyl alcoves — the summation domain is a simplex whose geometry encodes crystallographic root systems (e.g., \\(A_n, D_n, E_6, E_7, E_8\\)). Quantum dimensions \\(d_i\\) are o\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/85bbbhwba4ghj.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635163",
  "fulltext_url": null,
  "id": "85bbbhwba4ghj",
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  "landing_url": "https://zenodo.org/records/23635163",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
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  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/85bbbhwba4ghj.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:58Z",
      "native_id": "23635163",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23635163"
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  ],
  "subjects": [],
  "title": "Generalizing Verlinde Formulas to Higgs Bundles via Quasi-Hopf Algebras — E8 Intelligence Research",
  "title_text": "Generalizing Verlinde Formulas to Higgs Bundles via Quasi-Hopf Algebras — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:58Z",
  "url": "https://research.draconitic.com/paper/85bbbhwba4ghj",
  "venue": "Zenodo",
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}