Structural Reduction of the Collatz Conjecture to the Dynamics of an Induced Function

This work develops a structural reformulation of the Collatz conjecture based on the decomposition of trajectories into maximal odd segments and the introduction of an induced map acting on their segment-starts. The conjecture is shown to be equivalent to an eventual descent property for this induced function. Odd integers of the form 4n+1 are identified as structural critical points (“portals”) where binary information is reorganized. The analysis isolates the core difficulty of the problem, reducing it to a precise arithmetic question concerning the distribution of 2-adic valuations of certain exponential expressions.

This is the English version of the paper originally written in Spanish.

Note of version 1.2: This is a revised version of the paper originally deposited as v1.0. The main changes are: a table of contents has been added at the beginning of the document, which was absent in the first version, and several passages have been expanded and clarified throughout the text. The mathematical results and their proofs remain unchanged.