This preprint introduces admissibility as a minimal, pre-parametric constraint on functional systems. A system is admissible if, after perturbation, it can re-enter a bounded region of functional equivalence within a finite coherence window sufficient to preserve functional identity. The framework does not propose a mechanism, metric, or optimization principle. Instead, it specifies a necessary condition that must hold before parameterization, selection, or efficiency analysis becomes meaningful. Importantly, increased speed, energy, or optimization may hasten functional collapse by reducing coherence time rather than restoring function. Admissibility is presented as a falsifiable structural hypothesis applicable across physical, biological, informational, and cognitive domains whenever function depends on timely reintegration under perturbation.