{
  "abstract": "FINDING: Collatz research clusters around modular-prime frameworks, automorphic Cayley graphs, and an \"Information-Loss Cascade\" — none yet yield a proof, but the structure is being recast as a discrete dynamical system on a rooted tree with modular periodicity.\n\nMATH: - Core map: \\( T(n) = \\begin{cases} n/2 & n \\equiv 0 \\pmod{2} \\\\ 3n+1 & n \\equiv 1 \\pmod{2} \\end{cases} \\) - Modular approach: choose prime \\( P \\) with \\( 2 \\) as primitive root → the map acts as a permutation on residues mod \\( P \\), forcing cycles of length \\( \\text{ord}_P(2) \\) — this is the key structural constraint. - Cayley graph formulation: Collatz function as automorphism on a colour graph; the trivial cycle \\( 4 \\to 2 \\to 1 \\to 4 \\) is the root. The arXiv paper claims decidability of \\( an+b \\) conjectures via this graph. - Information-Loss Cascade: a proposed measure of how many binary digits are irreversibly lost per iteration — likely tied to \\( \\log_2(3) \\approx 1.585 \\) for odd steps (since \\( 3\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/9hbh02j5wbrwb.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635274",
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  "id": "9hbh02j5wbrwb",
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  "landing_url": "https://zenodo.org/records/23635274",
  "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/9hbh02j5wbrwb.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:56Z",
      "native_id": "23635274",
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      "url": "https://zenodo.org/records/23635274"
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  "subjects": [],
  "title": "Collatz Conjecture Recast as Modular Tree Dynamics — E8 Intelligence Research",
  "title_text": "Collatz Conjecture Recast as Modular Tree Dynamics — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:56Z",
  "url": "https://research.draconitic.com/paper/9hbh02j5wbrwb",
  "venue": "Zenodo",
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}