2-adic Structure of Tails and Survival Sets in the Collatz Dynamics

This paper studies the 2-adic structure of the compressed Collatz dynamics from a purely arithmetic perspective. We prove that each tail level corresponds to a unique modular class and that the dynamics acts affinely within each of them. From this classification, the existence of non-trivial cycles in the classes with valuation at least two is ruled out, and restricted survival sets are introduced, which parametrize exactly the initial conditions compatible with avoiding descent for an arbitrary number of steps. The necessity of the defining restriction is established, and a deterministic upper bound for the measure of these sets is proved without additional hypotheses. The equivalence between the emptiness of the infinite survival set and the Collatz conjecture on the corresponding class is also established. The analysis does not rely on probabilistic models and precisely delimits the only remaining structural obstruction: the possible existence of global arithmetic dependencies in the iteration with variable scale.