{
  "abstract": "FINDING: Nested radical \\(2\\cos(2\\pi/7)\\) encodes the heptagon's cubic field via Chebyshev \\(T_7\\), linking a 7×7 determinant to \\(\\cos(7\\theta)\\) and enabling periodic nested radical solutions of certain polynomials. | MATH: Chebyshev identity: \\(T_7(x) = 64x^7 - 112x^5 + 56x^3 - 7x = \\cos(7\\arccos x)\\). For \\(x = 2\\cos(2\\pi/7)\\), \\(T_7(x/2) = \\cos(2\\pi) = 1\\) → \\(x\\) satisfies \\(x^3 - x^2 - 2x + 1 = 0\\) (minimal polynomial, degree 3, discriminant 49). Nested radical: \\(2\\cos(2\\pi/7) = \\sqrt[3]{\\frac{7 + 21\\sqrt{-3}}{2}} + \\sqrt[3]{\\frac{7 - 21\\sqrt{-3}}{2}}\\) (Cardano form). Ramanujan nested radical: \\(\\sqrt[3]{\\frac{7}{2} + \\frac{3}{2}\\sqrt{-3}} + \\sqrt[3]{\\frac{7}{2} - \\frac{3}{2}\\sqrt{-3}}\\). The 7×7 determinant: \\(\\det(I - 2x A)\\) where \\(A\\) is adjacency of cycle \\(C_7\\) yields \\(T_7(x/2) - 1\\), linking to Chebyshev. | CONNECTION: Heptagon central angle \\(2\\pi/7\\) → \\(2\\cos(2\\pi/7) \\approx 1.24698\\). Golden ratio cousin: \\(2\\cos(\\pi/7) \\approx 1.80194\\), \\(2\\cos(3\\pi/7) \\approx\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/bbash0emmhpwr.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23431335",
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  "id": "bbash0emmhpwr",
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  "landing_url": "https://zenodo.org/records/23431335",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "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/bbash0emmhpwr.ris",
  "sources": [
    {
      "first_seen": "2026-10-31T12:22:00Z",
      "native_id": "23431335",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23431335"
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  "subjects": [],
  "title": "Heptagonal Nested Radicals via Chebyshev T7 and Cubic Field Link — E8 Intelligence Research",
  "title_text": "Heptagonal Nested Radicals via Chebyshev T7 and Cubic Field Link — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-31T12:22:00Z",
  "url": "https://research.draconitic.com/paper/bbash0emmhpwr",
  "venue": "Zenodo",
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