Modular Closure and Internal 2-adic Structure in Collatz Dynamics

We present a structural analysis of Collatz dynamics based on an early modular closure and on the study of the 2-adic valuation of odd terms. We prove that, after the first odd term, trajectories permanently avoid multiples of 3 and become confined to a rigid modular cycle modulo 9. Within this framework, the dynamics reduces to the analysis of the factors 3n+1 and their 2-adic valuation. A systematic decomposition of trajectories into odd segments and even tails is introduced, showing that the global structural organization of the orbit —though not its exact length— is determined from the initial value. The balance between episodes of odd growth and divisions by 2 is interpreted as a structural constraint of the dynamics, without recourse to probabilistic hypotheses or heuristic arguments.