Tenson Geometry: The Temporalization of Euclid and the Living Structure of Space

This paper presents a rigorous mathematical foundation for Tenson Geometry, a temporal generalization of Euclidean space. By introducing an intrinsic time variable τ into geometric structure, Euclidean geometry is reinterpreted as a living tensor field where geometric quantities evolve continuously. Using tensor calculus, Cauchy–Riemann-type conditions, and variational symmetry, we derive the Tenson Equation ∇·(E+ iI) = 0, expressing the equilibrium between energetic (E) and informational (I) components of space. The theory unifies geometric deformation, analytic continuation, and dy- namic information balance within a single differential framework, providing a new formal bridge between classical geometry, field theory, and information thermody- namics.