Collatz Dynamics as a Ze-System

This paper constructs a formal framework for analyzing the Collatz conjecture using the principles of Ze-theory, a novel approach to dynamical systems introduced in previous work. On the set of positive integers, we define a Ze-system Z=(X,F,v,) induced by the Collatz map. The Ze-velocity v(n) and Ze-complexity (n) are given explicit closed-form expressions. We prove theorems regarding their ranges and asymptotic behavior. The central dynamical claim — that trajectories exhibit a logarithmic drift toward 1 — is presented as a formal conjecture, derived from heuristic parity assumptions. Unlike previous versions, this paper includes numerical verification of the conjecture and a consistent, non-contradictory definition of (n). The work does not claim to prove the Collatz conjecture but offers a new structured language for its analysis, including generalizations to an+b problems and a novel argument about cycles via the irrationality of log23.