{
  "abstract": "FINDING: Babylonian geometry tablets contain implicit proto-proofs of √2 irrationality via reciprocal-pair algorithms, not formal Greek-style proof. | MATH: √2 ≈ 1;24,51,10 (sexagesimal) = 1 + 24/60 + 51/3600 + 10/216000 = 1.41421296… (error < 2×10⁻⁷). Tablet YBC 7289 shows diagonal of unit square as 1;24,51,10 with side 30 (0;30). Reciprocal pairs (x, 1/x) in base-60 generate approximations: e.g., 1;25 and 0;42,21 form product 1;00,00,00 (exact in sexagesimal). The algorithm iterates xₙ₊₁ = (xₙ + 2/xₙ)/2 (Heron's method) — but tablets show only final values, not proof of non-termination. | CONNECTION: √2 irrationality implies no finite sexagesimal expansion — the diagonal/side ratio (1.4142…) is incommensurable, a geometric root of the 1-1-√2 triangle (crystallographic point group D₄, square lattice symmetry). The reciprocal-pair structure mirrors the golden ratio conjugate pair (φ, 1/φ) = (1.618, 0.618) — both satisfy x = 1/x + integer (φ: x = 1/x + 1; √2: x = 1/x + 2/x? No — but √2\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
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  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
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      ],
      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/0y5b2k7awkj1t.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635307",
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  "published": "2026-10-25",
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  "ris": "https://research.draconitic.com/paper/0y5b2k7awkj1t.ris",
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      "first_seen": "2026-11-08T12:21:56Z",
      "native_id": "23635307",
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  "title": "Babylonian Tablets Reveal Proto-Proofs of √2 Irrationality via Reciprocal Algorithms — E8 Intelligence Research",
  "title_text": "Babylonian Tablets Reveal Proto-Proofs of √2 Irrationality via Reciprocal Algorithms — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:56Z",
  "url": "https://research.draconitic.com/paper/0y5b2k7awkj1t",
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