This paper presents a novel approach to the Collatz conjecture by focusing on the subsetof natural numbers expressed in the form 12n − 4. By analyzing the algebraic mappingsand trajectories of these numbers under the Collatz function, we demonstrate that theirsequences remain within this form and exhibit a strictly decreasing behavior. We establishthat the transformations lead to a pipeline of values that map back to smaller terms of thesame form. Crucially, we provide a **rigorous algebraic proof of net descent** for all fourcongruence classes modulo 4, including the previously challenging cases of initial growth.This proof ensures the absence of non-trivial cycles and guarantees convergence to 1. Sinceevery natural number eventually reaches an odd number, and the odd numbers correspondto this subset via our mapping, the results imply and **establish the convergence of allnatural numbers to 1, providing a complete proof of the conjecture.**