{
  "abstract": "FINDING: Gaitsgory–Lurie's \"fundamental local equivalence\" replaces Satake equivalence in quantum geometric Langlands, proven for most cases by Dhillon et al. (arXiv:1907.03204), extending to affine flag varieties.\n\nMATH: - Core object: categorical equivalence between factorization modules (or D-modules on loop groups) and representations of the quantum group / Kac-Moody algebra at critical level. - Key structure: **quantum parameter** \\( \\psi \\) (level) — the equivalence holds for generic \\( \\psi \\), degenerating at roots of unity where quantum groups become finite-dimensional. - The classical Satake equivalence: \\( \\text{Rep}(\\check{G}) \\cong \\text{Perv}(\\text{Gr}_G) \\) — replaced by a **local equivalence** involving **factorization algebras** and **affine flag varieties** (not just Grassmannians). - No explicit numerical constants appear in the abstract; the mathematics is categorical (∞-categories, ind-coherent sheaves, chiral algebras).\n\nCONNECTION: - **Root systems*\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/0103cdc4s7m3h.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23526427",
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  "id": "0103cdc4s7m3h",
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  "landing_url": "https://zenodo.org/records/23526427",
  "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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  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0103cdc4s7m3h.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:21:48Z",
      "native_id": "23526427",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23526427"
    }
  ],
  "subjects": [],
  "title": "Quantum Geometric Langlands via Fundamental Local Equivalence — E8 Intelligence Research",
  "title_text": "Quantum Geometric Langlands via Fundamental Local Equivalence — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-04T12:21:48Z",
  "url": "https://research.draconitic.com/paper/0103cdc4s7m3h",
  "venue": "Zenodo",
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}