Unverified Proof Claims Collatz Conjecture Decidable via Cayley Colour Graph — E8 Intelligence Research

FINDING: Collatz conjecture remains unproven; a claimed proof exists but is not peer-reviewed; one paper models the function as an automorphic Cayley colour graph, claiming decidability of \(an+b\) conjectures and a proof of the \(3n+1\) case. MATH: - Collatz map: \( f(n) = \begin{cases} n/2 & \text{if } n \equiv 0 \pmod{2} \\ 3n+1 & \text{if } n \equiv 1 \pmod{2} \end{cases} \) - Conjecture: \(\forall n \in \mathbb{N}^+, \exists k: f^k(n) = 1\) (the trivial cycle \(4 \to 2 \to 1 \to 4\)). - Paper (arXiv:2008.13643v8) claims: - Collatz graph is a connected automorphic Cayley colour graph. - Decidability of all \(an+b\) conjectures (generalized Collatz). - Proof that \(3n+1\) conjecture holds. - No new constants, ratios, or numerical invariants are reported in the provided summaries. CONNECTION: - The automorphic Cayley colour graph approach may implicitly involve group symmetries, but no explicit link to geometric harmony ratios (0.382, 0.618, 0.786, 1.618, 2.61 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com