2-adic structure and rigid regime in Collatz dynamics

This article develops a structural framework for the study of the Collatz dynamics based on its 2-adic structure. The approach introduces cylindrical constraints on the initial parameter, a binary budget describing the irreversible consumption of bits along dynamical excursions, and an autonomous return map governing the rigid regime. It is shown that any infinite orbit must eventually enter this regime, reducing the Collatz problem to a regularity condition on the parametrization of the entry map. The paper consolidates and reorganizes several results previously developed by the author in a series of related works into a single self-contained exposition.

Spanish version:  https://doi.org/10.5281/zenodo.18874277