This paper develops a mathematically rigorous formulation of Dynamic SIL(t)using stochastic field theory, spectral graph stability, Bayesian evidence dynamics, and closed-loop control. The framework establishes well-posedness, positivity, ergodicity, globalboundedness, and stability of the hazard field, and introduces the Omega Safety FieldEquation (OSFE-∞) as a unifying integrity functional. The result is a complete, reviewerresistant mathematical foundation for dynamic functional safety.