This paper presents a rigorous mathematical derivation for upgrading geometric regularization frameworks in deep neural networks. We address the generalization gap by replacing the global Rademacher complexity with a tighter Local Rademacher Generalization Bound, and introducing a dynamic, data-dependent Lipschitz constant based on the feature space supremum. To resolve the critical mathematical discrepancy between average-case input space expectations and worst-case feature space limits, we introduce an 'Adversarial Layer-wise Lipschitz Regularizer'. Furthermore, we establish a computable 'Jacobian Pullback' bridge via the chain rule, providing a closed-loop, adversarial proxy for the non-computable supremum. This framework is mathematically closed-loop and ready for engineering implementation in advanced model regularization.