{
  "abstract": "FINDING: Babylonian reciprocal tables were constructed via an algorithmic sieve over regular numbers (2^a·3^b·5^c·…), not brute force; the arxiv paper (1401.0065) details how large tables were generated by iterative multiplication by 2, 3, 5 — the prime factors of 60. | MATH: Regular number n = 2^a·3^b·5^c (a,b,c ≥ 0). Reciprocal 1/n has finite sexagesimal expansion iff n divides 60^k for some k. Table construction: start with 1, repeatedly multiply by {2,3,5}, sort, truncate at a bound (e.g., n ≤ 60^m). Reciprocal pairs (n, 1/n) satisfy n·(1/n) = 1 exactly in base-60. No closed-form for 1/223 or 1/239 — these are *irregular* (223, 239 are primes > 5), so they do NOT appear in standard tables; their reciprocals are infinite repeating sexagesimals. | CONNECTION: The set of regular numbers forms a multiplicative lattice in ℤ³ (exponents a,b,c). The ratio structure mirrors the 3D root lattice A₃ (fcc) — the fundamental parallelepiped has volume log(2)·log(3)·log(5). The density of regular\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/1z40bx0wr72st.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23447156",
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  "id": "1z40bx0wr72st",
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  "landing_url": "https://zenodo.org/records/23447156",
  "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": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1z40bx0wr72st.ris",
  "sources": [
    {
      "first_seen": "2026-11-01T12:21:45Z",
      "native_id": "23447156",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23447156"
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  "subjects": [],
  "title": "Babylonian Sieve Algorithm for Constructing Sexagesimal Reciprocal Tables — E8 Intelligence Research",
  "title_text": "Babylonian Sieve Algorithm for Constructing Sexagesimal Reciprocal Tables — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:45Z",
  "url": "https://research.draconitic.com/paper/1z40bx0wr72st",
  "venue": "Zenodo",
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}