This work complements and extends the results of the author's previous manuscript, where a modular structure was introduced to analyze the dynamics of the Collatz function through a modular transformation \ (S (n) \) and a roof function \ (T (n) \). In this continuation, we show that the dynamics of roofs are governed by a closed modular system consisting only of the classes \ (4, 16, 22, 34 36\). After the first cycle, odd numbers congruent to \ (3 6\) disappear from the orbit, eliminating the classes \ (10\) and \ (28 36\). A complete classification according to \ (n 6\), \ (n 9\), and \ (n 4\) shows that stable roofs arise exclusively from odd numbers \ (5 6\), and that all roofs satisfy \ (T (n) 1636\). This closed modular system explains why every chain of roofs inevitably descends to the minimal roof \ (16\), reducing the global Collatz dynamics to a discrete process defined solely on roofs. The modular elevation operator introduced in the appendix shows that every unstable roof can be promoted to a stable one without altering the orbit, providing a theoretical explanation for the modular rigidity observed in the previous work.
William Betancourt Reyes (Mon,) studied this question.