William Betancourt Reyes

A Modular Structure for the Collatz Dynamics: Upper Bound and Uniqueness of the 4–2–1 Cycle

This work introduces a modular mechanism for controlling Collatz orbits through two operators: the projection function S(n) and the elevator E(n)=n·64^k. The function S(n) is defined through a complete classification of residues modulo 18 and maps every natural number directly in...

A Modular Structure for the Collatz Dynamics: Upper Bound and Uniqueness of the 4–2–1 Cycle

This work introduces a modular mechanism for controlling Collatz orbits through two operators: the projection function S(n) and the elevator E(n)=n·64^k. The function S(n) is defined through a complete classification of residues modulo 18 and maps every natural number directly in...