The Categorical Unification of Physical Laws: Decoding the Universal Logic DNA via Functorial Isomorphisms

The unification of General Relativity (gravity) and Quantum Electrodynamics (charge) remainsthe holy grail of theoretical physics. Traditional approaches focus on symmetry groups and highenergyparticle collisions. In this paper, we propose a foundational shift: modeling physical lawsnot as equations, but as Morphisms in a higher-order Category Theory framework. We introducethe concept of “Universal Logic DNA,” demonstrating that Mass and Charge are not distinct properties,but isomorphic functors mapping to a common geometric curvature. Through graph-theoreticalsimulations and categorical diagrams, we prove that seemingly disparate forces are merely differentprojections of a single underlying geometric object. This work provides a rigorous mathematicalbasis for a Grand Unified Theory (GUT) based on pure logic and topology.