{
  "abstract": "FINDING: Alexander polynomials of twisted torus knots admit explicit closed-form formulas via knot group presentations, with Fibonacci numbers emerging as determinant sequences in special torus-knot cases. MATH: - Alexander polynomial Δ(t) for torus knot T(p,q): Δ(t) = ((t^{pq}−1)(t−1)) / ((t^p−1)(t^q−1)). - For T(2,n): Δ(t) = (t^n+1)/(t+1) = 1 − t + t² − … + t^{n−1} (alternating sum). - Determinant |Δ(−1)| for T(2,n) = n (odd) — but for Fibonacci-type braid closures, determinants follow F_{k+1} (Fibonacci numbers) when Seifert matrix has characteristic polynomial t²−t−1. - Twisted torus knot formula (arXiv:2411.13003): Δ(t) expressed as product of cyclotomic-like factors with exponents determined by twist parameters (full twists m on adjacent strands). - Fibonacci matrix Q = [[1,1],[1,0]] has det(Q) = −1, trace = 1, eigenvalues φ = (1+√5)/2 and ψ = (1−√5)/2. Q^n yields F_{n+1}, F_n. CONNECTION: - Golden ratio φ = 1.618 appears as spectral radius of the Fibonacci matrix\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/bqn8f4rt9wmat.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23409900",
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  "id": "bqn8f4rt9wmat",
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  "landing_url": "https://zenodo.org/records/23409900",
  "language": "eng",
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  "licence_label": "CC BY 4.0",
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  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bqn8f4rt9wmat.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:24Z",
      "native_id": "23409900",
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  "subjects": [],
  "title": "Twisted Torus Knots: Closed-Form Alexander Polynomials and Fibonacci Determinants — E8 Intelligence Research",
  "title_text": "Twisted Torus Knots: Closed-Form Alexander Polynomials and Fibonacci Determinants — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:21Z",
  "url": "https://research.draconitic.com/paper/bqn8f4rt9wmat",
  "venue": "Zenodo",
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}