{
  "abstract": "FINDING: Recent proof of the geometric Langlands conjecture (2024, by Gaitsgory et al.) completes a central pillar of the Langlands program, linking Galois representations to automorphic forms via sheaves on moduli stacks. | MATH: Core duality: \\( \\text{Gal}(\\bar{\\mathbb{Q}}/\\mathbb{Q}) \\leftrightarrow \\text{Automorphic forms} \\); geometric version: \\( \\text{LocSys}_G \\leftrightarrow \\text{D-modules on Bun}_G \\); key objects: \\( \\text{Bun}_G \\) (moduli of principal \\(G\\)-bundles), \\( \\text{LocSys}_G \\) (local systems), categorical equivalence via derived categories \\( D^b(\\text{QCoh}(\\text{LocSys}_G)) \\cong D^b(\\text{D-mod}(\\text{Bun}_G)) \\). | CONNECTION: The geometric Langlands correspondence is built on **root systems** (Dynkin diagrams) and **affine Kac-Moody algebras** — crystallographic symmetry groups (Weyl groups) are intrinsic. The moduli spaces \\( \\text{Bun}_G \\) carry **Hecke eigensheaves** whose eigenvalues are local systems — this mirrors the **harmonic ratio structure** 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"
    }
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  "bibtex": "https://research.draconitic.com/paper/9cj3zvx6ge3gh.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23465400",
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  "id": "9cj3zvx6ge3gh",
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  "landing_url": "https://zenodo.org/records/23465400",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9cj3zvx6ge3gh.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:44Z",
      "native_id": "23465400",
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  "subjects": [],
  "title": "Geometric Langlands Conjecture Proved: Galois-Automorphic Duality via Sheaves — E8 Intelligence Research",
  "title_text": "Geometric Langlands Conjecture Proved: Galois-Automorphic Duality via Sheaves — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-02T12:21:44Z",
  "url": "https://research.draconitic.com/paper/9cj3zvx6ge3gh",
  "venue": "Zenodo",
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}