{
  "abstract": "FINDING: Non-abelian Hodge theory provides a triple equivalence (Dolbeault/de Rham/Betti) that underpins Geometric Langlands, with Hitchin's system as the integrable core, and Donagi's work extends this to direct images via harmonic bundles and twistor D-modules. | MATH: The central object is the **Hitchin fibration** \\( h: \\mathcal{M}_H \\to \\mathcal{A} \\), where \\(\\mathcal{M}_H\\) is the moduli of stable Higgs bundles \\((E,\\phi)\\) on a curve \\(C\\), \\(\\phi \\in H^0(C, \\text{End}(E)\\otimes K_C)\\). The **non-abelian Hodge correspondence** is the homeomorphism (not holomorphic) between: - **Dolbeault**: \\( \\mathcal{M}_{\\text{Dol}} = \\{(E,\\phi)\\}/\\text{equivalence} \\) - **de Rham**: \\( \\mathcal{M}_{\\text{dR}} = \\{\\text{flat connections } \\nabla\\} \\) - **Betti**: \\( \\mathcal{M}_{\\text{B}} = \\text{Hom}(\\pi_1(C), G)/G \\) (character variety) The **Hitchin system** is a completely integrable system: \\(\\dim \\mathcal{M}_H = 2d\\), with \\(d = \\dim \\mathcal{A} = \\frac{1}{2}\\dim \\mathcal{M}_H =\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/1tq7cgz55vw0t.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23430932",
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  "id": "1tq7cgz55vw0t",
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  "landing_url": "https://zenodo.org/records/23430932",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
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  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1tq7cgz55vw0t.ris",
  "sources": [
    {
      "first_seen": "2026-10-31T12:22:09Z",
      "native_id": "23430932",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23430932"
    }
  ],
  "subjects": [],
  "title": "Non-abelian Hodge Theory, Hitchin Fibrations, and Geometric Langlands — E8 Intelligence Research",
  "title_text": "Non-abelian Hodge Theory, Hitchin Fibrations, and Geometric Langlands — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-31T12:22:09Z",
  "url": "https://research.draconitic.com/paper/1tq7cgz55vw0t",
  "venue": "Zenodo",
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}