{
  "abstract": "FINDING: Plimpton 322 encodes Pythagorean triples via a sexagesimal algorithm equivalent to rational parametrization of the unit circle, with a proposed new generative rule \\(b = M \\cdot Q_M\\). MATH: - Standard reconstruction: For coprime \\(p > q > 0\\), triples \\((a, b, d)\\) satisfy \\(a = p^2 - q^2\\), \\(b = 2pq\\), \\(d = p^2 + q^2\\) (or swapped). - Rational parametrization: \\(x = \\frac{2t}{1+t^2}\\), \\(y = \\frac{1-t^2}{1+t^2}\\) for \\(t = q/p\\) (or reciprocal), mapping \\(t \\in \\mathbb{Q}\\) to points on \\(x^2 + y^2 = 1\\). - New algorithm (arXiv 2001.11141): \\(b = M \\cdot Q_M\\), with \\(M, Q_M \\in \\mathbb{Z}^+\\), generating the tablet's rows — data‑driven, not assuming the standard \\(p,q\\) form. - Sexagesimal base‑60 appears in column headers (squares of sides, diagonals) — e.g., values like 1;59, 2;49, etc., implying use of reciprocal pairs and regular numbers (smooth in base 60). CONNECTION: - The parametrization \\(t = \\tan(\\theta/2)\\) yields ratios: for \\(t = 1/\\sqrt{3}\\) →\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/9zmgxhtyqcjeg.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23553644",
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  "id": "9zmgxhtyqcjeg",
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  "landing_url": "https://zenodo.org/records/23553644",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
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  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9zmgxhtyqcjeg.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T12:21:20Z",
      "native_id": "23553644",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23553644"
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  "subjects": [],
  "title": "Plimpton 322's Sexagesimal Algorithm as Rational Circle Parametrization — E8 Intelligence Research",
  "title_text": "Plimpton 322's Sexagesimal Algorithm as Rational Circle Parametrization — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-05T12:21:20Z",
  "url": "https://research.draconitic.com/paper/9zmgxhtyqcjeg",
  "venue": "Zenodo",
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}