{
  "abstract": "FINDING: Penrose tiling and quasicrystals are governed by golden-ratio inflation/deflation rules, with topological invariants classified via K-theory; a 5D projection model generates aperiodic order. | MATH: Golden ratio φ = (1+√5)/2 ≈ 1.618; reciprocal φ⁻¹ = φ−1 ≈ 0.618; φ² = φ+1 ≈ 2.618. Penrose tiling uses two rhombi with acute angles 36° and 72° (π/5 and 2π/5), enforcing fivefold rotational symmetry (C₅, crystallographically forbidden in periodic lattices). Inflation rule: substitution matrix [[2,1],[1,1]] has eigenvalues φ² and φ⁻². K-theory: topological invariants for quasicrystals live in K₀(C*-algebra of the hull), with gap labels in ℤ[φ] — a rank-2 abelian group. 5D projection: quasicrystal points = intersection of 5D hypercubic lattice ℤ⁵ with a 2D (or 3D) irrational plane, slope components in ℚ(√5). | CONNECTION: Direct — φ, φ⁻¹, φ² appear as scaling factors in inflation; 0.618 = 1/φ is the ratio of tile areas (fat:thin = φ:1). Fivefold symmetry relates to icosahedral root s\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"
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  ],
  "bibtex": "https://research.draconitic.com/paper/c05eyec43z3f2.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23446959",
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  "id": "c05eyec43z3f2",
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  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c05eyec43z3f2.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T12:21:49Z",
      "native_id": "23446959",
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  "subjects": [],
  "title": "Golden Ratio Inflation and K-Theory in Aperiodic Penrose Quasicrystals — E8 Intelligence Research",
  "title_text": "Golden Ratio Inflation and K-Theory in Aperiodic Penrose Quasicrystals — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:49Z",
  "url": "https://research.draconitic.com/paper/c05eyec43z3f2",
  "venue": "Zenodo",
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