Information Geometry Unification Principle (IGUP) I

This paper presents the full, step-by-step construction of the Information Geometry Unification Principle. We start with three rigorous axioms defining quantum information as the fundamental ontology. We derive classical Fisher information geometry, quantum Bures geometry, Levi-Civita connection, Riemann curvature, Ricci tensor, and scalar curvature in full detail. We construct the universal information action and perform complete variational calculus with respect to the quantum state ρ and the information metric gμν. Every algebraic step is explicitly shown. We recover Schrödinger mechanics, statistical mechanics, and Einstein gravity as limiting cases. This paper is self-contained and requires no external reference to follow the derivations.