Mathematical Expansion of the Tenson Limit Equation: Asymptotic Completeness and Information Residue Stability

This paper develops a rigorous mathematical formulation of the Tenson Limit Equation, extending the original Tenson Equation ∇·(E + iI) = 0 by incorporating G¨ odel’s incompleteness theorem as an information residue term. The resulting framework formalizes the asymptotic completeness condition ∇∞ ·LT = ε∞, where LT = ET + iIT is the complex Tenson Lagrangian density and ε∞ denotes the G¨ odel residue. We further define the Tenson generative operator DT and the G¨ odel residual divergence rate RT to establish a dynamic field formulation linking energy, information, and entropy within a non-equilibrium limit framework.