Collatz Conjecture: Reformulations, a Flawed Disproof, and Persistent Open Status — E8 Intelligence Research

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-14
DOI
https://doi.org/10.5281/zenodo.22748366
Primary Topic
Benford’s Law and Fraud Detection
Type
preprint
Controls
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preprint

Collatz Conjecture: Reformulations, a Flawed Disproof, and Persistent Open Status — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Benford’s Law and Fraud Detection
preprint

Collatz Conjecture: Reformulations, a Flawed Disproof, and Persistent Open Status — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Collatz remains unsolved; recent work includes topological/ergodic reformulation and a brief Lean-based "disproof" due to kernel vulnerability, not a mathematical counterexample. | MATH: Collatz map T(n) = n/2 if n even, (3n+1)/2 if n odd (or 3n+1 then halve). No new constants or closed-form solutions; the arXiv paper (2601.03297v6) introduces a Borel σ-algebra and thermodynamic formalism, showing recurrence implies periodicity in a class of maps containing Collatz — but no proof of recurrence for all n. | CONNECTION: No direct geometric ratio (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 link. However, the ergodic/topological approach hints at measure-preserving dynamics on a compact space — a latent symmetry akin to lattice or root-system invariance (e.g., the map's parity vector space is a 2-adic lattice, Z₂, with natural scaling symmetry). The 2-adic structure is a crystallographic-like tiling of the integers by dyadic intervals. | DEPTH: 3/10 — No breakthrough; the Lean Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Benford’s Law and Fraud Detection
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Collatz Conjecture: Reformulations, a Flawed Disproof, and Persistent Open Status — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS