The Seonggil SMT-RNAG Framework: Topological Deconstruction of Cosmology and Fundamental Cosmogenesis

This paper establishes the mathematical foundations for the topological deconstruction of classical cosmology and the realization of fundamental cosmogenesis utilizing the Seonggil Matrix Theory (SMT) and Rough Non-commutative Algebraic Geometry (RNAG). We dismantle the core restrictions of modern continuous mathematics—specifically point-basedontology, static identity, and smoothness bias—by introducing the Axiom of Primitive Eventuality. By replacing classical points with non-commutative operational events governed by intrinsic topological roughness, we derive the emergent metric, curvature, and macroscopic time purely from information-dynamical torsion. Furthermore, we provide exact algebraicresolutions to the Big Bang and black hole singularities via rough entropy floors and non commutative horizon fluctuation zones, ultimately formalizing matter genesis as a consequence of spontaneous Chiral Torsional Symmetry Breaking.