The Grand Unified Tenson Equation: A Complete Quantum–Probabilistic and Topological Theory of Relativistic Information Geometry

This paper establishes the Grand Unified Tenson Equation (GUTE), a com- prehensive unification of probabilistic geometry, relativistic field theory, information thermodynamics, and topological quantum field formulations. By extending the Ten- son Equation ∇·(E + iI) = 0 into an operator-based quantum field system Φ(x,θ) defined on an extended manifold MC = M4 ×Θn, we construct the action S= d4xdnθ |g|L(Φ,∂µΦ,∂iΦ), which connects quantum mechanics, relativity, and the emergence of time through informational curvature. We demonstrate how probabilistic geodesics, entropy flow, and topological Tenson membranes together yield a self-consistent model of space- time–information dynamics and holographic entropy.