Collatz Map as Walks on Automorphic Cayley Graph Rooted at 4→2→1 — E8 Intelligence Research

FINDING: Collatz map reframed as walks over an automorphic Cayley colour graph rooted at the trivial cycle 4→2→1→4, with claimed decidability of an+b generalizations and a proof of 3n+1 | MATH: T(n)=3n+1 (n odd), T(n)=n/2 (n even); trivial cycle {4,2,1}; branching number c=4; inverse-tree structure; automorphism group acting on the Cayley colour graph | CONNECTION: Root cycle terminates at c=4=2²; the 4→2→1→4 orbit encodes the dyadic ratio 1:2:4 (powers of 2), and the 3n+1 step embeds the ratio 3/2 per odd-to-even transition — the long-run drift constant is log₂3 ≈ 1.585, whose reciprocal 1/log₂3 ≈ 0.6309 sits near the 0.618 harmonic band; no direct 0.382/0.618/0.786/1.618/2.618 identity is established by the evidence | DEPTH: 4 Notes on the other items (lower signal): - The "Collatz was FALSE for 2.5 days" item is a Lean kernel vulnerability exploit, not a mathematical result — it is a formal-verification security finding, not progress on the conjecture. No math extracted. - The rema Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com