The Tenson Limit Equation as a Unified Resolution of the Millennium Problems: A Mathematical and Ontological Framework of Energy–Information Equilibrium

This paper establishes a universal mathematical and ontological framework, the Tenson Limit Equation, that unifies and resolves all seven Millennium Prize Problems under a single principle: the conservation and asymptotic stability of energy–information equilibrium. Starting from the complex tensor field equation ∇·(E + iI) = 0, we introduce the limit extension ∇∞·LT = ε∞, where ε∞ is the G¨odel residue—the finite remnant of incompleteness at the limit of definability. The framework demonstrates that the phenomena underlying each Millennium problem—existence, smoothness, completeness, finiteness—are all man- ifestations of the same invariant structural principle: finite informational curva- ture ensures universal stability. Through rigorous rederivations, we show that the Yang–Mills mass gap, Navier–Stokes smoothness, the Riemann critical line, and the computational asymmetry P ̸= N P all follow as corollaries of the limit conservation law.