{
  "abstract": "FINDING: The Stern-Brocot tree, Farey sequences, and the Farey tessellation form a single combinatorial-geometric object whose symmetry group is PSL(2,Z), connecting rational approximation to hyperbolic tiling. | MATH: Stern-Brocot tree = binary tree of mediants (a/b ⊕ c/d = (a+c)/(b+d)); Farey sequence F_n = sorted reduced fractions in [0,1] with denominator ≤ n; Farey tessellation = ideal triangles in upper half-plane with vertices at rationals ∪ {∞}; PSL(2,Z) acts transitively on oriented edges of this tessellation; the tree is the Cayley graph of PSL(2,Z) modulo its congruence subgroup Γ(2); key invariant: the modular group's fundamental domain has area π/3; continued fraction map T(x) = {1/x} is the shift on the Stern-Brocot tree's boundary (the real line). | CONNECTION: The Farey tessellation's edge lengths in hyperbolic metric correspond to the golden ratio φ = (1+√5)/2 when considering the orbit of the ideal triangle (0,1,∞) under the generator S: z→-1/z; the cusp width 1 and t\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/b8pt5qkv4tya4.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23464952",
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  "id": "b8pt5qkv4tya4",
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  "landing_url": "https://zenodo.org/records/23464952",
  "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": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b8pt5qkv4tya4.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:50Z",
      "native_id": "23464952",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23464952"
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  ],
  "subjects": [],
  "title": "Unifying Stern-Brocot, Farey Sequences, and Tessellation via PSL(2,Z) — E8 Intelligence Research",
  "title_text": "Unifying Stern-Brocot, Farey Sequences, and Tessellation via PSL(2,Z) — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-02T12:21:50Z",
  "url": "https://research.draconitic.com/paper/b8pt5qkv4tya4",
  "venue": "Zenodo",
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}