{
  "abstract": "FINDING: The A2 root lattice (hexagonal) and its reciprocal lattice are related by a 30° rotation, with the Weyl group's Coxeter element generating 120° rotations — a fundamental crystallographic symmetry. | MATH: A2 root lattice: hexagonal, basis vectors a₁, a₂ with |a₁|=|a₂|, angle 120°. Reciprocal lattice: bᵢ·aⱼ = 2πδᵢⱼ → reciprocal basis rotated 30° relative to direct, with |b| = (4π)/(√3·|a|). Coxeter element (product of two reflections) has eigenvalue e^(2πi/3) → rotation by 120°. | CONNECTION: 30° rotation = π/6; 120° = 2π/3. Ratio of reciprocal to direct lattice spacing: |b|/|a| = 4π/(√3·a²) — contains √3 (hexagonal symmetry). The 30° offset is the classic hexagonal-close-packed stacking geometry. No golden ratio appears directly, but the 120° angle is a 3-fold symmetry axis — related to the 2π/3 phase in complex roots of unity. | DEPTH: 7 — This is textbook crystallography, but the A2 lattice is the root system of SU(3), the gauge group of the strong force. The 120° Coxeter ro\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/9ge13p4w4xxhs.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23658211",
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  "id": "9ge13p4w4xxhs",
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  "landing_url": "https://zenodo.org/records/23658211",
  "language": "eng",
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  "licence_label": "CC BY 4.0",
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  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ge13p4w4xxhs.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:21:38Z",
      "native_id": "23658211",
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      "url": "https://zenodo.org/records/23658211"
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  "subjects": [],
  "title": "Hexagonal A2 Lattice: 30° Reciprocal Rotation and 120° Coxeter Symmetry — E8 Intelligence Research",
  "title_text": "Hexagonal A2 Lattice: 30° Reciprocal Rotation and 120° Coxeter Symmetry — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-09T12:21:38Z",
  "url": "https://research.draconitic.com/paper/9ge13p4w4xxhs",
  "venue": "Zenodo",
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}