Channel-Indexed Static Aggregation in Dimensional-Structural Describability

In this paper, we formally establish and rigorously prove the Axiom of Topological Degrees ofFreedom. The axiom asserts that intrinsic structural complexity in a topological configurationadmits a stable and well-defined weighted aggregation of local scaling exponents.We construct a precise functional framework in which this principle is formulated explicitlyas an axiom. Within this setting, we demonstrate that the weighted effective dimension ismathematically well-defined, bounded, continuous, and stable under perturbations.This establishes the internal consistency and functional realizability of the axiom, providinga rigorous foundation for the concept of topological degrees of freedom as an intrinsic invariant.