Persistence Under Change: The β-Registry as an Architecture of Structural Resistance

A persistent physical structure must remain identifiable while its physical conditions change. This paper asks what that requirement entails before inertia, force, or a particular dynamical law is assumed. A local persistence-compensation theorem is established: if a change threatens the diagnostics defining a persistent role, preservation of that role requires a compensating physical re-realization. The independently derived primitive response registry β∈\{4,9,16,27\} is then examined as a candidate classification of the complete primitive modes by which such preservation debt can be discharged. This yields a proposed interpretation of the registry as an architecture of structural resistance: not resistance as opposition to change, but as the structured response required for identity to persist through change. Constitutive response, realized response, and finite-rate tracking defect are kept distinct, allowing equilibrium burden to be separated from memory and relaxation effects. Inertia provides the principal test case. A non-circular factorization criterion is formulated under which inertial response could emerge as a macroscopic projection of the primitive response architecture, with finite-rate corrections appearing beyond the adiabatic limit. The interpretation remains explicitly conditional: its significance depends on deriving the persistence–response bridge and observable coefficients without importing the physical laws they are intended to explain. The result is a precise programme for testing whether familiar dynamical resistance is fundamental or instead the observable consequence of a deeper requirement: persistent structure must be physically re-realized when the conditions of its persistence change.