Universal Mathematical Ontology (UMO): A Unified Framework for General Relativity, Quantum Mechanics, and Fundamental Physics

This paper introduces the Universal Mathematical Ontology (UMO), a comprehensive theoretical framework that unifies General Relativity and Quantum Mechanics through a recursive, purely mathematical structure. By leveraging non-commutative geometry, topological quantum field theory, and category theory, UMO resolves key inconsistencies between the fundamental forces and provides a platform for a Grand Unified Theory (GUT). The model incorporates revised entropy dynamics, including a corrected Page curve, and explains dark matter as an emergent geometric effect rather than a new particle. The framework is supported by quantum computing simulations and entropy analysis, offering testable predictions in black hole radiation, gravitational wave patterns, and cosmological expansion. UMO is positioned as an alternative to higher-dimensional string models, offering unification within a 4D structure. This work presents not only a theoretical synthesis but a replicable foundation for empirical validation.