Inverse Structure and Formal Validation of the Collatz Conjecture_corrected_version

This work constructs a rigorous algebraic framework modeling the behavior of natural numbers under the Collatz function. By defining critical structural elements, namely solution points and ramification points, and developing a controlled inverse expansion strategy, we demonstrate a systematic method to cover all natural numbers. We address the major challenges hindering a complete proof of the Collatz Conjecture, notably the potential existence of infinite divergent trajectories. Our approach leverages modular structures and density arguments, yielding a coherent inverse tree whose completeness suggests the resolution of the conjecture.