We present a revolutionary mathematical framework, Structural Cosmic Mathematics, that addresses the fundamental limitations of applying local field-theoretic mathematics to the cosmic space. By extracting the mechanical nuclei hidden within General Relativity and Quantum Field Theory, we construct a purely structural, algebraic-combinatorial mathematics that operates in the cosmic domains P2 and P3 while reducing Einsteinian mathematics to its proper local domain P1. This framework provides a unified, non-perturbative description of dark energy and dark matter without invoking new fields or particles, predicts a z-dependent equation of state w(z) = -1, and generates a distinct gravitationalwave background in the pulsar timing array band. We demonstrate that this is not merely an alternative model but the only mathematically consistent framework that respects the organizational necessity of cosmic structure, thereby redefining the very notion of ”cosmic mathematics” and relegating conventional theories to their local validity domains.