{
  "abstract": "FINDING: Search results are a diffuse mix of unrelated videos (golden ratio irrationality, Kauffman bracket intro, limit proofs) and one arXiv paper on virtual knot polynomials — no direct evidence links Kauffman bracket fifth-root-of-unity evaluations to the golden ratio's exact real part.\n\nMATH: - Kauffman bracket \\(\\langle L \\rangle(A)\\) satisfies \\(\\langle L \\rangle = A\\langle L_0 \\rangle + A^{-1}\\langle L_\\infty \\rangle\\). - Jones polynomial: \\(V_L(t) = \\langle L \\rangle\\big|_{A = t^{-1/4}}\\). - Fifth root of unity: \\(A = e^{2\\pi i/5}\\) gives \\(A^5 = 1\\), \\(A + A^{-1} = 2\\cos(72^\\circ) = \\frac{\\sqrt{5}-1}{2} \\approx 0.618\\) (the golden ratio conjugate). - No equation in the results explicitly computes \\(\\Re\\langle \\text{trefoil} \\rangle\\) at \\(A = e^{2\\pi i/5}\\).\n\nCONNECTION: - The golden ratio conjugate \\(0.618\\) appears *implicitly* via \\(2\\cos(72^\\circ)\\) if one were to evaluate the bracket at a fifth root of unity — but the search results do not contain that comp\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/7r4qnjsncfr53.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587234",
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  "id": "7r4qnjsncfr53",
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  "landing_url": "https://zenodo.org/records/23587234",
  "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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  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7r4qnjsncfr53.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:21:50Z",
      "native_id": "23587234",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23587234"
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  "subjects": [],
  "title": "The Golden Ratio's Absence in Kauffman Bracket Fifth-Root Evaluations — E8 Intelligence Research",
  "title_text": "The Golden Ratio's Absence in Kauffman Bracket Fifth-Root Evaluations — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:50Z",
  "url": "https://research.draconitic.com/paper/7r4qnjsncfr53",
  "venue": "Zenodo",
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}