Automorphic Cayley Walks and the Unproven Collatz Conjecture — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Collatz conjecture remains unproven; recent work frames it as automorphic Cayley graph walks, with a notable Lean formalization vulnerability incident. | MATH: Core map: \(T(n) = n/2\) if \(n\) even, \(T(n) = 3n+1\) if \(n\) odd. Trivial cycle: \(4 \to 2 \to 1 \to 4\). arXiv:2008.13643v8 claims proof via Cayley colour graphs and decidability of \(an+b\) conjectures — but this is not peer-validated. No new constants or ratios emerge. | CONNECTION: The Cayley graph framing hints at group-theoretic structure, but no explicit link to golden ratio, base-60, or crystallographic symmetries is present in the provided findings. The trivial cycle \(4\to2\to1\) is a 3-cycle — a symmetry of order 3, but not a harmonic ratio. | DEPTH: 4/10 — The conjecture is profound in its simplicity and resistance, but the findings here are either popular expositions, a claimed proof of dubious status, or a formalization incident (a bug in Lean, not a mathematical breakthrough). No new mathematical esse Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204537192
Cites:
Cited by:
Related to: