{
  "abstract": "FINDING: Categorification of the Jones polynomial via Khovanov homology yields a bigraded chain complex whose graded Euler characteristic recovers the polynomial, with gauge-theoretic and immersed-surface extensions revealing deeper topological invariants. | MATH: Jones polynomial \\(V_L(q)\\) satisfies skein relation \\(q^{-1}V_{L_+} - qV_{L_-} = (q^{1/2} - q^{-1/2})V_{L_0}\\). Khovanov homology: bigraded abelian groups \\(H^{i,j}(L)\\) with \\(\\chi_q(H^{*,*}(L)) = V_L(q)\\) (graded Euler characteristic). Categorification replaces polynomial coefficients (integers) with homology groups (vector spaces), lifting multiplication to tensor products and direct sums. Witten's gauge-theoretic approach: Khovanov homology arises from Floer homology of a 3-manifold with link complement, using \\(SU(2)\\) or \\(U(1)\\) gauge fields; immersed surface cobordisms in \\(\\mathbb{R}^4\\) with double points induce functorial maps between homology groups (arXiv:2510.14760v2). | CONNECTION: The graded Euler characteris\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
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  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
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  "author_total": 1,
  "authors": [
    {
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        0
      ],
      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/7ns7st64qh65y.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23447069",
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  "published": "2026-10-18",
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  "ris": "https://research.draconitic.com/paper/7ns7st64qh65y.ris",
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      "first_seen": "2026-11-01T12:21:48Z",
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  "title": "Khovanov Homology and Gauge-Theoretic Extensions of the Jones Polynomial — E8 Intelligence Research",
  "title_text": "Khovanov Homology and Gauge-Theoretic Extensions of the Jones Polynomial — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:48Z",
  "url": "https://research.draconitic.com/paper/7ns7st64qh65y",
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