Collatz Conjecture Dynamics via the Sum of Prime Factors (sopfr) and Absorbing State Transitions

In this paper, the behavior of sequences generated by the Collatz conjecture (3n+1 problem) is analyzed through the sum-of-prime-factors function with repetition, denoted as sopfr(n), rather than relying solely on standard numerical values. We investigate structural conservation, fluctuation bands of sopfr(n) values across iteration steps, and critical breaking dynamics during transitions into absorbing states of the form 2^k, where sopfr(2^k) = 2k.