Collatz Conjecture: Unresolved Despite Cayley Graph and Digit Pattern Approaches — E8 Intelligence Research

FINDING: Collatz remains unsolved; recent work explores automorphic Cayley graph structures and symbolic digit patterns, with no breakthrough proof. | MATH: Collatz map T(n) = n/2 if even, (3n+1) if odd; trivial cycle 4→2→1→4; arXiv:2008.13643v8 claims proof via Cayley colour graphs and decidability of an+b conjectures, but unverified. | CONNECTION: The trivial cycle 4→2→1 has ratio 1:2:4 (powers of 2, base-2 symmetry); branching at c=4 suggests a binary tree structure — but no explicit golden ratio, 0.618, 0.786, or base-60 link appears in the findings. The automorphic graph approach hints at lattice/root-system analogies (Cayley graphs of groups), but no crystallographic symmetry is explicitly stated. | DEPTH: 3 — The findings are meta-commentary (YouTube videos, a Lean kernel vulnerability hoax) plus one unverified preprint. No new verified equations, constants, or geometric harmonies emerge. The Collatz structure (2-adic dynamics) has deep ties to 2-adic integers and ergodic theory Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com