Unverified Claim of Collatz Proof Using Automorphic Cayley Graphs — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: No proof of Collatz conjecture found; a single paper claims a proof using automorphic Cayley colour graphs, but the claim is unverified and likely flawed. | MATH: Collatz map: \( f(n) = \begin{cases} 3n+1 & n \text{ odd} \\ n/2 & n \text{ even} \end{cases} \). Conjecture: for all positive integers \( n \), iterating \( f \) eventually reaches the cycle \( 4 \to 2 \to 1 \to 4 \). The paper (arXiv:2008.13643v8) attempts to model the dynamics as walks on a Cayley graph with automorphic structure, claiming decidability of \( an+b \) conjectures and a proof of the \( 3n+1 \) case. | CONNECTION: None. No geometric constants (0.382, 0.618, 0.786, 1.618, 2.618), base-60, or crystallographic symmetries appear in the standard formulation or in the cited paper's abstract. The graph-theoretic approach uses group actions but not harmonic ratios. | DEPTH: 1 — The finding is a negative result (no verified proof) and the claimed proof is not accepted by the mathematical community. No new equa Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203889948
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