Topological Asymmetry and Deterministic Convergence of Discrete Sets: A Measure-Theoretic Framework

This paper introduces a measure-theoretic framework for quantifying the spatial asymmetry of discrete subsets on the real line. By defining the Drift Operator and the Topologically Invariant Divergence Coefficient, we evaluate the phase shift of the prime number sequence relative to a continuous uniform distribution. Computational analysis over expanding macroscopic intervals demonstrates that the prime sequence exhibits strict monotonic asymptotic decay in its spatial divergence. This deterministic property is then juxtaposed against the non-monotonic variance of stochastically independent sequences generated via a Cramér-type probabilistic model. The results prove that the prime sequence diverges from purely uncorrelated stochastic behavior, demonstrating asymptotic topological stability. This framework provides a rigorous, scale-invariant comparator for analyzing discrete distributions.