Deterministic Resolution of Generalized and Extended Collatz Dynamics: Arithmetic Chiral Topology and the Δ' Oracle

The Collatz conjecture (3x+1) resists absolute proof due to pointwise intractability, necessitating innovative methods beyond probabilistic heuristics to preclude measure-zero anomalies. This paper introduces the Arithmetic Chiral Topology (ACT) framework—a pure deterministic resolution of generalized Collatz dynamics via topological invariants. Through ACT, we transition the analysis from discrete path-finding to macroscopic ergodic geometry. First, we unconditionally prove the absolute converg