One-Shot Control Theorem

We introduce the One-Shot Control Theorem, a formal framework for model improvement via localized, single-step functional updates. Let a base model operate over an input space under a measurable risk functional. Instead of iterative optimization, we consider a one-shot update defined as a bounded transformation applied over a restricted support region. Under mild assumptions, locality, integrability, guaranteed correctness gain on the update region, and no collateral effect outside it, we prove that the expected risk of the updated model is non-increasing, with strict improvement when the update region has nonzero measure.