{
  "abstract": "FINDING: The Freudenthal-Tits magic square construction unifies exceptional Lie algebras E6/E7/E8 via octonionic triality, with explicit E8 bracket formulas now derived from Barton-Sudbery's oct-octonion description.\n\nMATH: - Freudenthal-Tits magic square: 3×3 array of Lie algebras generated by pairs of division algebras (ℝ, ℂ, ℍ, 𝕆). Exceptional row/column: E6, E7, E8 appear at positions (𝕆,ℂ), (𝕆,ℍ), (𝕆,𝕆) respectively. - E8 bracket (arXiv:2504.16513v3): Explicit formula using triality on 𝕆⊗𝕆, with E8 = 𝔡𝔢𝔯(𝕆) ⊕ 𝔡𝔢𝔯(𝕆) ⊕ 3×(𝕆⊗𝕆) — the \"triality\" decomposition: 248 = 14 ⊕ 14 ⊕ 3×64 (where 64 = 8×8 octonion pairs). - E6 ⊂ E7 ⊂ E8: E6 = 78 = 26 ⊕ 26 ⊕ 26 (triality of 26-dim irreducible); E7 = 133 = 133 = (𝔰𝔩(2)⊕𝔰𝔬(8)) ⊕ 3×(2⊗8⊗8) — dimension check: 3+28+3×32 = 133. - Key constants: 248 (E8), 133 (E7), 78 (E6), 26 (Freudenthal triple system dimension), 8 (octonion dimension), 3 (triality symmetry of 𝔰𝔬(8)).\n\nCONNECTION: - The magic square's structure encodes **root system symmetries**:\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/dapp7ryp06z29.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23464960",
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  "id": "dapp7ryp06z29",
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  "language": "eng",
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  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dapp7ryp06z29.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:50Z",
      "native_id": "23464960",
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  "subjects": [],
  "title": "Octonionic Triality Unifies Exceptional Lie Algebras via Magic Square E8 Brackets — E8 Intelligence Research",
  "title_text": "Octonionic Triality Unifies Exceptional Lie Algebras via Magic Square E8 Brackets — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-02T12:21:50Z",
  "url": "https://research.draconitic.com/paper/dapp7ryp06z29",
  "venue": "Zenodo",
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