Collatz Conjecture: Automorphic Cayley Graphs, Lean Flaw, and Symbolic Reinterpretation — E8 Intelligence Research

FINDING: Collatz remains unproven; recent work frames it as automorphic Cayley colour graphs, with a notable false-disproof via Lean kernel vulnerability (July 2024), and a symbolic-digit reinterpretation claim. | MATH: Collatz map: T(n) = n/2 if n even; T(n) = 3n+1 if n odd. Conjecture: ∀n∈ℕ, ∃k: T^k(n)=1. The arXiv paper (2008.13643v8) models Collatz as walks on a Cayley graph with root cycle 4→2→1→4; claims decidability of an+b conjectures and a proof of 3n+1 via automorphic colouring. No new constants or ratios appear in the search results. | CONNECTION: The Cayley graph structure hints at lattice/root-system analogies (e.g., affine A1 or binary tree embeddings), but no explicit golden ratio, 0.618, 0.786, or base-60 link is stated. The trivial cycle 4→2→1 has ratio 2:1, not φ. The automorphic colouring suggests group-theoretic symmetry, but not crystallographic in the classical sense. | DEPTH: 3 — The findings are mostly meta-commentary (videos, a false disproof) plus one serious Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com