{
  "abstract": "FINDING: Collatz conjecture analyzed via modular arithmetic (prime moduli with primitive root 2), automorphic Cayley graphs, and an \"Information-Loss Cascade\" framework; a claimed proof exists via Cayley colour graph decidability. MATH: - Collatz map: \\( T(n) = n/2 \\) if \\( n \\) even; \\( T(n) = 3n+1 \\) if \\( n \\) odd. - Modular reduction: \\( T(n) \\bmod p \\) for prime \\( p \\) where 2 is a primitive root — ensures full cycle of residues under doubling, linking to multiplicative order \\( \\text{ord}_p(2) = p-1 \\). - Trivial cycle: \\( 4 \\to 2 \\to 1 \\to 4 \\). - Cayley graph formulation: Collatz function as automorphism on a directed graph with vertices \\( \\mathbb{Z}^+ \\), edges \\( n \\to T(n) \\); root path to \\( c=4 \\). - arXiv claim (2008.13643v8): proof of \\( 3n+1 \\) via decidability of \\( an+b \\) conjectures in this graph. CONNECTION: - **Primitive root 2** implies the multiplicative group \\( (\\mathbb{Z}/p\\mathbb{Z})^\\times \\) is cyclic of order \\( p-1 \\) — a **cyclic symme\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/0c06chw9rd3r4.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23616333",
  "fulltext_url": null,
  "id": "0c06chw9rd3r4",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23616333",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0c06chw9rd3r4.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T12:20:53Z",
      "native_id": "23616333",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23616333"
    }
  ],
  "subjects": [],
  "title": "Modular Automorphic Proof of the Collatz Conjecture via Information-Loss Cascades — E8 Intelligence Research",
  "title_text": "Modular Automorphic Proof of the Collatz Conjecture via Information-Loss Cascades — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-07T12:20:53Z",
  "url": "https://research.draconitic.com/paper/0c06chw9rd3r4",
  "venue": "Zenodo",
  "versions": []
}