{
  "abstract": "FINDING: Babylonian sexagesimal quadratic methods prefigure Vieta jumping's root-pair symmetry, which itself mirrors Weyl group reflections in root systems. | MATH: Babylonian normal form \\(x^2 - bx + c = 0\\) with base-60 arithmetic; solution via \\(x = \\frac{b}{2} \\pm \\sqrt{(\\frac{b}{2})^2 - c}\\) (equivalent to modern quadratic formula). Vieta jumping: for integer solutions \\((a,b)\\) to \\(a^2 + b^2 = k(ab+1)\\), the transformation \\((a,b) \\mapsto (a, ka - b)\\) preserves the equation — this is a reflection in the root lattice of type \\(A_2\\) (or \\(A_1 \\times A_1\\) for the IMO 1988 case). The invariant \\(k\\) is fixed; the jump is a Weyl group action on the solution set. | CONNECTION: The ratio \\(k\\) in Vieta jumping is constrained to perfect squares (IMO 1988: \\(k = q^2\\)). For \\(q=1\\), the golden ratio emerges: \\(a/b \\to \\phi = 1.618...\\) as solutions grow. The base-60 system yields exact fractions with denominators \\(2^a 3^b 5^c\\) — the same primes generating the crystallographic 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"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9z79pnrcw73hk.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23410063",
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  "id": "9z79pnrcw73hk",
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  "landing_url": "https://zenodo.org/records/23410063",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
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  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9z79pnrcw73hk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "23410063",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23410063"
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  "subjects": [],
  "title": "Babylonian Roots to Weyl Reflections: A Unified Symmetry — E8 Intelligence Research",
  "title_text": "Babylonian Roots to Weyl Reflections: A Unified Symmetry — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:19Z",
  "url": "https://research.draconitic.com/paper/9z79pnrcw73hk",
  "venue": "Zenodo",
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