On the Impossibility of A Priori Criteria for Dynamical Admissibility

Translator A recurring assumption in fundamental physics is that physically admissible processes can be characterized a priori by specifying an allowed class of dynamics (e.g. Hamiltonian systems, field equations, variational principles). This paper shows that no non-trivial, complete, and representation-independent criterion can exist that determines, prior to interaction, whether a given operational process admits stable closure under composition. The result is not empirical and does not depend on any specific physical formalism. It follows from structural limitations rooted in computability theory, fixed-point theory, and semantic closure: any global admissibility criterion would entail solving decision problems known to be undecidable. Apparent counterexamples arise only through silent restriction to pre-stabilized mathematical domains, a strategy that historically shaped classical physics without making the restriction explicit. The paper clarifies that admissibility cannot be a property of processes in isolation. Instead, closure is a joint property of (process × resolution × inference language), rendering purely process-internal admissibility ill-posed. While global a priori criteria are impossible, the analysis identifies what can be recovered instead: necessary structural filters, families of architectures likely to support stabilization, and early-stage operational diagnostics that enable progressive, non-arbitrary inquiry. The results explain why stabilization must be conditional and retrospective in finite-resolution frameworks, and why any taxonomy of admissible regimes can only apply after stabilization has been demonstrated. The paper serves as a foundational clarification of the epistemological limits and possibilities of physical law formation, without altering or presupposing specific dynamical models.