The Global Odd Tower: A Finite-Depth Structural Coordinate System for Odd Integers with an Application to Odd Perfect Numbers

This preprint introduces the Global Odd Tower (GOT), a finite-depth structural coordinate system for odd integers based on parity and 2-adic valuation patterns. The framework does not assume convergence of Collatz orbits and treats Collatz-type maps purely as structural reading devices. As a critical test case, the paper examines odd perfect numbers and shows that the structural cell corresponding to odd perfect numbers is empty within the GOT. The argument is purely structural and does not rely on analytic bounds, computational verification, or unproven conjectures. This work is intended as a structural contribution to number theory and as a reference framework for future developments.