{
  "abstract": "FINDING: The Freudenthal–Tits magic square construction of exceptional Lie algebras E6/E7/E8 is explicitly realized via triality and octo‑octonions, with an explicit bracket formula for E8 and its E6/E7 subalgebras. | MATH: The magic square is a 3×3 (or 4×4) array of Lie algebras built from division algebras (R, C, H, O) and their Jordan algebras. For E8: the Barton–Sudbery decomposition gives \\(\\mathfrak{e}_8 = \\mathfrak{so}(8) \\oplus \\mathfrak{so}(8) \\oplus 8_v \\otimes 8_s \\oplus 8_v \\otimes 8_c \\oplus 8_s \\otimes 8_c\\) (triality triple of 8‑dimensional representations). The explicit bracket uses the octonionic structure constants \\(c_{ijk}\\) (totally antisymmetric, satisfying \\(c_{ijm}c_{klm} = \\delta_{ik}\\delta_{jl} - \\delta_{il}\\delta_{jk} + \\epsilon_{ijkl}\\) with \\(\\epsilon\\) the 4‑form). E7 arises as \\(\\mathfrak{e}_7 = \\mathfrak{so}(12) \\oplus \\mathfrak{su}(2) \\oplus 32\\) (spinor), E6 as \\(\\mathfrak{e}_6 = \\mathfrak{so}(10) \\oplus \\mathfrak{u}(1) \\oplus 16 \\oplus \\overline{16}\\)\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/94ggaxfwq65by.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23464950",
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  "id": "94ggaxfwq65by",
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  "landing_url": "https://zenodo.org/records/23464950",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/94ggaxfwq65by.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:50Z",
      "native_id": "23464950",
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      "url": "https://zenodo.org/records/23464950"
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  "subjects": [],
  "title": "Octo-Octonion Triality Realizes E8 via Explicit Freudenthal–Tits Brackets — E8 Intelligence Research",
  "title_text": "Octo-Octonion Triality Realizes E8 via Explicit Freudenthal–Tits Brackets — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-02T12:21:50Z",
  "url": "https://research.draconitic.com/paper/94ggaxfwq65by",
  "venue": "Zenodo",
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}