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.
Miguel Cerdá Bennassar (Wed,) studied this question.