Collatz as Cayley Graph Walks: Decidability of an+b Conjectures — E8 Intelligence Research

FINDING: Collatz dynamics reframed as walks on an automorphic Cayley colour graph rooted at the trivial cycle 4→2→1→4, with claimed decidability of general an+b conjectures | MATH: Map T(n) = 3n+1 (n odd), n/2 (n even); trivial cycle {1,2,4}; branching number c=4; general family an+b | CONNECTION: Cycle length 3, root 4=2², orbit 1→2→4→8→16 doubling — powers of 2 lattice; 3n+1 couples ×3 (odd) with ÷2 (even), i.e. the 3:2 ratio underlying the perfect fifth and the 2:3 lattice of the diatonic scale | DEPTH: 6 FINDING: A Lean kernel vulnerability allowed a formalized "disproof" of Collatz for ~2.5 days in July before being retracted | MATH: No new mathematical content; demonstrates that formal verification (Lean/Coq) is only as sound as its trusted kernel | CONNECTION: None geometric | DEPTH: 2 FINDING: Terence Tao's 2019 result remains the strongest partial theorem — Collatz holds for "almost all" n in the logarithmic density sense | MATH: For any f(n)→∞, the set of n whose orbit neve Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com