{
  "abstract": "FINDING: Cyclotomic Aperiodic Substitution Tilings (CAST) — substitution matrices over ℤ[ζ₂ₙ] yield algebraic integer inflation multipliers whose eigenvalues encode rotational symmetries and self-similarity. | MATH: Let ζ₂ₙ = e^{2πi/2n}. CAST vertices lie in ℤ[ζ₂ₙ]. Substitution matrix M has Perron–Frobenius eigenvalue λ (inflation multiplier). λ is an algebraic integer in ℤ[ζ₂ₙ] (or its real subfield ℤ[ζ₂ₙ + ζ₂ₙ⁻¹]). Minimal polynomial of λ divides the characteristic polynomial of M. For n=5 (decagonal), λ often satisfies λ² − φλ − 1 = 0 or λ² − (φ+1)λ + φ = 0, where φ = (1+√5)/2 = 1.618…, and φ⁻¹ = 0.618…, φ⁻² = 0.382… . For n=7 (tetradecagonal), λ may be root of λ³ − (2cos(π/7))λ² − … = 0, with 2cos(π/7) ≈ 1.8019, 2cos(2π/7) ≈ 1.24698, 2cos(3π/7) ≈ 0.44504. | CONNECTION: Direct. The real subfield of ℤ[ζ₂ₙ] contains 2cos(2πk/2n). For n=5, 2cos(2π/5) = φ⁻¹ = 0.618, 2cos(π/5) = φ = 1.618, 2cos(4π/5) = −φ⁻¹, 2cos(3π/5) = −φ. For n=6 (dodecagonal), 2cos(π/6) = √3 ≈ 1.732, 2cos(π/3) = 1,\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/darrrc2654413.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23465018",
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  "id": "darrrc2654413",
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  "landing_url": "https://zenodo.org/records/23465018",
  "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": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/darrrc2654413.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:49Z",
      "native_id": "23465018",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23465018"
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  "subjects": [],
  "title": "Cyclotomic Aperiodic Substitution Tilings: Algebraic Integer Inflation Multipliers Encoding Rotational Symmetry — E8 Intelligence Research",
  "title_text": "Cyclotomic Aperiodic Substitution Tilings: Algebraic Integer Inflation Multipliers Encoding Rotational Symmetry — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-02T12:21:49Z",
  "url": "https://research.draconitic.com/paper/darrrc2654413",
  "venue": "Zenodo",
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}