Systematic Resolution of Infinite Subdivision Problems via Srinivas Bounded Mathematics: Applications Across Mathematics and Physics

This paper demonstrates the systematic resolution of diverse mathematical and physical problems through a single unifying principle: the prohibition of infinite subdivision established by Srinivas Bounded Mathematics (SBM). We show that seemingly unrelated problems—including division by zero (0÷0 = 1), classical paradoxes (Gabriel's Horn, Zeno's Dichotomy, Banach-Tarski), limit processes, two Clay Millennium Prize Problems (Navier-Stokes existence and smoothness, Yang-Mills mass gap), black hole singularities, quantum field theory ultraviolet divergences, and thermodynamic infinities—share a common mathematical structure arising from the implicit assumption that quantities may be subdivided without bound. By axiomatically prohibiting infinite subdivision through Axiom 1 of SBM (r ≥ εAR > 0), we demonstrate systematic resolution of these problems as direct implications of bounded subdivision. The paper also discusses the relationship to Hilbert's Axiom of Continuity and offers conjectures regarding axiomatic independence for future investigation.