Universal Phase Transition of Cosmology: A Comprehensive Framework Unifying General Relativity, Quantum Fields, and String Theory via the Seonggil Operator

This paper presents a comprehensive theoretical framework that establishes a unified, non-commutative cosmological model, aiming to subsume Einstein’s General Relativity, Quantum Field Theory (QFT), and String Theory into a single algebraic paradigm. By utilizing Rough Operator Algebra (ROA) and the Seonggil Matrix Theory (SMT), we propose an alternative topological perspective where the smooth macroscopic spacetime manifold is viewed as a low-energy commutative state emerging from a topological phase transition of a purely algebraic space. This transition is governed by the roughness index α. We address the10¹20 vacuum energy discrepancy through a non-linear ROA filter and derive the arithmetic cosmological constant Λarith from first principles. Furthermore, we redefine strings as one dimensional topological defects inherent in the Operator of Beginning Aα. We also model the black hole event horizon as an (N −1) -dimensional algebraic boundary membrane where quantum entanglement entropy is conserved via the Connes cocycle derivative. Finally, we explore the topological regularization of wormhole throats via golden-ratio resonance with out exotic matter, and mathematically define the continuous topological information state of an observer to ensure causal consistency within a cobordism of dual manifolds.