Information Geometry Unification Principle: Complete Derivations with Fiber Bundles, Gauge Fields, and Yang–Mills Unification

This paper presents the complete, fully extended formulation of the Information Geometry Unification Principle (IGUP), unifying quantum mechanics, statistical thermodynamics, general relativity, and all fundamental gauge interactions within a single information-theoretic ontology. We establish quantum information as the primary physical substrate, endow the space of density matrices with the Bures–Fisher–Rao metric, and construct the universal information action. Full variational derivations yield the unified field equations that govern information geometry and its evolution. We then incorporate principal fiber bundles and associated vector bundles to describe internal symmetries, identifying gauge potentials as connections on information bundles and field strengths as bundle curvatures. The framework naturally incorporates Yang–Mills theory, electroweak unification, and quantum chromodynamics, showing that all forces arise from geometric structures on the information manifold. We recover Schrödinger–Dirac theory, equilibrium and nonequilibrium thermodynamics, Einstein gravity, and the Standard Model in appropriate limits. The theory resolves the black hole information paradox, the measurement problem, and the arrow of time, while providing ten testable predictions. This work constitutes a self-contained, mathematically complete theory of everything based on the identity: Geometry = Information.