Collatz Conjecture Unproven; Cayley Graph Model Offers No New Solution — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Collatz conjecture remains unproven; recent work frames it as automorphic Cayley colour graphs, with no new closed-form solution or harmonic constant emerging from the provided sources. | MATH: Collatz map: \(T(n) = n/2\) if \(n\) even, \(T(n) = 3n+1\) if \(n\) odd. Conjecture: \(\forall n \in \mathbb{N}, \exists k: T^k(n) = 1\). The arXiv paper (2008.13643v8) models the iteration as walks on a Cayley graph with root cycle \(4 \to 2 \to 1 \to 4\). No new constants or ratios appear in the search results — only the structural claim of decidability for generalized \(an+b\) maps. | CONNECTION: No direct geometric harmony (0.382, 0.618, 0.786, 1.618, 2.618) or base-60 link is present. The Cayley graph framing touches on lattice/root-system adjacency (graph automorphisms), but no crystallographic symmetry or golden-ratio scaling is evidenced. The trivial cycle \(4 \to 2 \to 1\) has ratio 2:1, a binary doubling/halving symmetry, not a golden-ratio one. | DEPTH: 3 — The findings are m 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: W7212427363
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