{
  "abstract": "FINDING: The Stern-Brocot tree and Farey sequences form a complete, ordered enumeration of rationals via mediants, with deep links to continued fractions and uniform distribution under ergodic weighting. MATH: - Mediant operation: (a/b) ⊕ (c/d) = (a+c)/(b+d) — generates all reduced fractions exactly once in Stern-Brocot tree. - Farey sequence F_n: all reduced fractions between 0 and 1 with denominator ≤ n, ordered; adjacent fractions satisfy bc − ad = 1 (determinant condition). - Continued fraction map: rationals ↔ finite CFs; Stern-Brocot path encodes CF digits (L/R moves). - Uniform distribution result (arXiv:1009.1823): even Stern-Brocot and Farey sequences are uniformly distributed mod 1 under canonical weightings; asymptotic for Lebesgue measure of CF sum-level sets derived. CONNECTION: - The determinant condition bc − ad = 1 is the symplectic/lattice unimodular condition — directly links to SL(2,Z) and modular group, whose fundamental domain tessellates the hyperbol\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/efpqn0wnxkcqb.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635623",
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  "id": "efpqn0wnxkcqb",
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  "landing_url": "https://zenodo.org/records/23635623",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/efpqn0wnxkcqb.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:52Z",
      "native_id": "23635623",
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      "url": "https://zenodo.org/records/23635623"
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  "subjects": [],
  "title": "Mediant Trees, Farey Sequences, and Rational Enumeration via Continued Fractions — E8 Intelligence Research",
  "title_text": "Mediant Trees, Farey Sequences, and Rational Enumeration via Continued Fractions — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:52Z",
  "url": "https://research.draconitic.com/paper/efpqn0wnxkcqb",
  "venue": "Zenodo",
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}