{
  "abstract": "FINDING: Collatz remains unsolved; recent work explores automorphic Cayley graph structures and symbolic digit patterns, with no breakthrough proof. | MATH: Collatz map T(n) = n/2 if even, (3n+1) if odd; trivial cycle 4→2→1→4; arXiv:2008.13643v8 claims proof via Cayley colour graphs and decidability of an+b conjectures, but unverified. | CONNECTION: The trivial cycle 4→2→1 has ratio 1:2:4 (powers of 2, base-2 symmetry); branching at c=4 suggests a binary tree structure — but no explicit golden ratio, 0.618, 0.786, or base-60 link appears in the findings. The automorphic graph approach hints at lattice/root-system analogies (Cayley graphs of groups), but no crystallographic symmetry is explicitly stated. | DEPTH: 3 — The findings are meta-commentary (YouTube videos, a Lean kernel vulnerability hoax) plus one unverified preprint. No new verified equations, constants, or geometric harmonies emerge. The Collatz structure (2-adic dynamics) has deep ties to 2-adic integers and ergodic theory\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/b8mn2yqeeetyb.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23553688",
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  "id": "b8mn2yqeeetyb",
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  "language": "eng",
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  "licence_label": "CC BY 4.0",
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  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b8mn2yqeeetyb.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T12:21:19Z",
      "native_id": "23553688",
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  "subjects": [],
  "title": "Collatz Conjecture: Unresolved Despite Cayley Graph and Digit Pattern Approaches — E8 Intelligence Research",
  "title_text": "Collatz Conjecture: Unresolved Despite Cayley Graph and Digit Pattern Approaches — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-05T12:21:19Z",
  "url": "https://research.draconitic.com/paper/b8mn2yqeeetyb",
  "venue": "Zenodo",
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