Irreversible Actions Require Pre-Admissible Execution: An Impossibility Theorem for Asynchronous Systems with Hidden External Predicates

We study computation in environments where actions have irreversible external consequences and must satisfy admissibility constraints defined by independent authorities. Working within an asynchronous distributed computational model, we show that post-validation architectures cannot guarantee safety. We derive—rather than assume—that the unique maximal safe admissibility operator is set intersection, and prove a collapse result: any safe post-validation architecture is observationally equivalent to pre-admissible execution. We establish an impossibility theorem for the safety–liveness frontier using bivalence arguments adapted to the admissibility-commit boundary. Further results include information lower bounds, anti-equivocation necessity, epoch normal form, a compositionality theorem, a finality phase transition, and a separating example. The paper situates these results within the landscape of impossibility theorems in distributed computation, showing that pre-admissible execution is a structural requirement implicit in prior constructions.