Admissibility Constraints as a General Stability Theorem

This work formalizes admissibility as a structural mechanism for stabilizing dynamical evolutions without modifying the underlying dynamics. Rather than introducing regulators, counterterms, or additional degrees of freedom, admissibility constrains the space of allowable trajectories via invariant sets and non-expansive projections. Under mild and explicit conditions, the induced admissible evolution becomes contractive, guaranteeing boundedness, uniqueness of fixed points, and computable convergence rates. The paper establishes: A general admissibility-induced contraction theorem on complete metric spaces Necessary vs. sufficient conditions for admissibility-based stabilization A sharp distinction between structural (non-degenerate) admissibility and degenerate cases equivalent to parameter tuning Explicit failure modes and falsifiability criteria Two concrete, non-physics examples (projected optimization and control safety envelopes) illustrate how admissibility produces invariant, contractive domains in familiar settings. No assumptions are made regarding microscopic completion, physical ontology, or privileged dynamics. The results are domain-agnostic and apply equally to iterative algorithms, control updates, and abstract flows. This paper is intended as a foundational stability result. Concrete instantiations of admissibility in renormalization-group–like settings are developed separately.