Collatz Conjecture Unproven: Key Source Is Unvalidated arXiv Preprint — E8 Intelligence Research

Abstract

FINDING: Collatz conjecture remains unproven; most cited sources are popular expositions or claimed proofs without peer-reviewed validation. The only substantive mathematical work is an arXiv preprint (2008.13643v8) framing Collatz as an automorphic Cayley colour graph, claiming decidability of generalized $an+b$ conjectures and a proof of $3n+1$. | 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 preprint's core structure: Collatz graph as a Cayley graph with automorphism group acting on colour classes; root cycle $4 \to 2 \to 1 \to 4$; branching number $c=4$. No explicit new constants or ratios extracted from the abstract. | CONNECTION: The Cayley graph framing suggests a lattice/root-system structure — the Collatz graph's branching at odd numbers (multiplying by 3, adding 1) and halving at evens creates a directed tree with self-similar scaling. The trivial cycle $4 \to 2 \to 1$ has ratio $2$ (h Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com