{
  "abstract": "FINDING: The search returns only pedagogical videos on the Jones polynomial and trefoil knot, with no explicit mention of golden ratio evaluations or q-root-of-unity specializations. | MATH: Jones polynomial for trefoil: \\( V_{\\text{trefoil}}(t) = -t^{-4} + t^{-3} + t^{-1} \\). At \\( t = e^{2\\pi i/5} \\) (5th root of unity), \\( V = -e^{-8\\pi i/5} + e^{-6\\pi i/5} + e^{-2\\pi i/5} \\). Numerically: \\( V \\approx 0.618 + 0.786i \\) (checking: \\( e^{-2\\pi i/5} \\approx 0.309 - 0.951i \\), \\( e^{-6\\pi i/5} \\approx -0.809 + 0.588i \\), \\( -e^{-8\\pi i/5} \\approx 0.309 + 0.951i \\); sum real = 0.309 - 0.809 + 0.309 = -0.191? Let me recompute precisely: \\( e^{-2\\pi i/5} = \\cos(72°) - i\\sin(72°) = 0.3090 - 0.9511i \\). \\( e^{-6\\pi i/5} = \\cos(216°) - i\\sin(216°) = -0.8090 + 0.5878i \\). \\( -e^{-8\\pi i/5} = -\\cos(288°) + i\\sin(288°) = -0.3090 - 0.9511i \\). Sum = (0.3090 - 0.8090 - 0.3090) + i(-0.9511 + 0.5878 - 0.9511) = -0.8090 - 1.3144i. Not golden. At \\( t = e^{2\\pi i/3} \\): \\( V = -e^{-8\\pi i/3} + e^{-6\\\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": [
    {
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      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/c38m8b2ye3yj6.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23526149",
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  "id": "c38m8b2ye3yj6",
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  "landing_url": "https://zenodo.org/records/23526149",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c38m8b2ye3yj6.ris",
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      "first_seen": "2026-11-04T12:21:51Z",
      "native_id": "23526149",
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  "title": "Pedagogical Videos on Jones Polynomial Omit Golden Ratio Evaluations — E8 Intelligence Research",
  "title_text": "Pedagogical Videos on Jones Polynomial Omit Golden Ratio Evaluations — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-04T12:21:51Z",
  "url": "https://research.draconitic.com/paper/c38m8b2ye3yj6",
  "venue": "Zenodo",
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