{
  "abstract": "FINDING: A claimed proof of the Collatz conjecture via automorphic Cayley colour graphs, where the $3n+1$ map is encoded as a group action on a rooted tree, making the conjecture equivalent to a decidability statement about $an+b$ generalizations. | MATH: Collatz map $T(n) = n/2$ if $n$ even, $T(n) = 3n+1$ if $n$ odd; the \"trivial cycle\" $4 \\to 2 \\to 1 \\to 4$; the paper (arXiv:2008.13643v8) constructs a Cayley graph whose automorphism group encodes $T$; the conjecture becomes: every vertex has a path to the cycle containing $c=4$. The $an+b$ conjecture generalizes $3n+1$ to $an+b$ with $a,b$ coprime, $a>1$. | CONNECTION: The Cayley graph structure is a lattice/root-system-like object — the branching at odd numbers (multiplying by 3) and halving at even numbers creates a binary tree with a single cycle. The ratio of odd-to-even steps in the Collatz trajectory statistically approaches $\\log_2 3 \\approx 1.585$, which is *not* a golden-ratio harmonic, but the *automorphism group* of the Ca\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": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ffe5ggc5n4m7z.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635465",
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  "id": "ffe5ggc5n4m7z",
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  "language": "eng",
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  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ffe5ggc5n4m7z.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:54Z",
      "native_id": "23635465",
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      "url": "https://zenodo.org/records/23635465"
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  "subjects": [],
  "title": "Collatz Conjecture via Automorphic Cayley Graphs and Decidability — E8 Intelligence Research",
  "title_text": "Collatz Conjecture via Automorphic Cayley Graphs and Decidability — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:54Z",
  "url": "https://research.draconitic.com/paper/ffe5ggc5n4m7z",
  "venue": "Zenodo",
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