Resolution of Generalized Collatz Functions

The Collatz Conjecture and its generalized class of parity-driven recurrence relations are
shown to obey recursive compression symmetries governed by parity, modular class, and log-
arithmic descent. In this paper, we extend the proof structure established for the classical
3n + 1 problem to the full family of parity-based functions, demonstrating that conver-
gence arises naturally from recursive reduction over modular orbits. These functions are
not chaotic, but structurally harmonic when understood through the lens of information
compression and resolution limits.