Unverified Claim of Collatz Proof Using Automorphic Cayley Graphs — E8 Intelligence Research

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: \( f(n) = {cases} 3n+1 & n odd \\ n/2 & n even {cases} \). Conjecture: for all positive integers \( n \), iterating \( f \) eventually reaches the cycle \( 4 → 2 → 1 → 4 \). 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