{
  "abstract": "FINDING: The quantum geometric Langlands program centers on a categorical equivalence between derived categories of sheaves on moduli stacks of G-bundles and those on dual Langlands group ^G-bundles, with the \"fundamental local equivalence\" as the core new structural result (2024–2026 talks by Gaitsgory, Dhillon, Hayash). | MATH: The equivalence is conjecturally of the form: \\( \\mathrm{QCoh}(\\mathrm{LocSys}_{^G G}(X)) \\cong \\mathrm{IndCoh}(\\mathrm{Bun}_G(X)) \\) twisted by a quantum parameter \\(\\hbar\\). The \"fundamental local equivalence\" refines this to a local statement: for a formal disk \\(D\\), the category of factorization modules over the affine Grassmannian \\(\\mathrm{Gr}_G\\) with level \\(\\hbar\\) is equivalent to that for \\(^G G\\) with level \\(1/\\hbar\\) — i.e., \\(\\mathrm{FactMod}_{\\hbar}(\\mathrm{Gr}_G) \\simeq \\mathrm{FactMod}_{1/\\hbar}(\\mathrm{Gr}_{^G G})\\). This is a categorical Fourier–Mukai transform, with the duality parameter \\(\\hbar \\leftrightarrow 1/\\hbar\\) mirroring \\(q \\le\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/7tmkjcpe0znmb.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23526294",
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  "id": "7tmkjcpe0znmb",
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  "landing_url": "https://zenodo.org/records/23526294",
  "language": "eng",
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  "licence_label": "CC BY 4.0",
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  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7tmkjcpe0znmb.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:21:49Z",
      "native_id": "23526294",
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      "url": "https://zenodo.org/records/23526294"
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  "subjects": [],
  "title": "Quantum Geometric Langlands: A Categorical Equivalence via Fundamental Local Duality — E8 Intelligence Research",
  "title_text": "Quantum Geometric Langlands: A Categorical Equivalence via Fundamental Local Duality — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-04T12:21:49Z",
  "url": "https://research.draconitic.com/paper/7tmkjcpe0znmb",
  "venue": "Zenodo",
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}