Physics without Primitives

This work establishes a constructive closure of physical mechanics under an explicit admissibility criterion: a regime qualifies as physical only if it provides (i) a governing equation, (ii) numerical calibration, and (iii) a directly testable observable. Under this equation–number–observable constraint, exactly five admissible regimes arise: propagation (light), ordering (time), localization (matter), coupling (gravity), and global drift (cosmology). The central result is that these regimes are not independent constructions but controlled limits of a single ordering-covariant Hamilton–Jacobi master constraint for the principal phase of a substrate excitation. The master constraint contains only three induced scalars: an ordering distortion potential, a localization gap, and a global drift term. In distinct limits, it yields null propagation with invariant speed, gapped dispersion with inertial mass, gravitational time dilation and weak-field coupling, and cosmological redshift as ordering drift. No additional primitive structures or unfixed constants are introduced. All coefficients are fixed by calibration. Under the stated admissibility hypothesis, the five regimes exhaust the predictive expressions of the substrate, yielding a closed mechanical framework conditional on constructive physical determination.