Emergence and Persistence Inheritance - Physical higher-level wholes, autonomous reduction and sustained identity

A collective variable can obey a closed equation while concealing differences in what physical whole it represents. Conversely, many different microscopic realizations can constitute one higher whole without producing multiple constitution classes. This paper derives when a higher-level description constitutes autonomous physical emergence and when that higher whole inherits persistent identity. The derivation joins higher-level role formation, admissible reduction and sustained persistence within the full LP architecture. La Profilée is the structure of determinate reality; physical systems realize its Frame, Module and Coupling roles. Constitution identifies the complete higher bearer before Transformation evaluates its continuation and Coexistence evaluates relations between bearers. For exact autonomous reduction, a joint descent theorem requires the reduction fibers to preserve the independently certified higher constitution, the relevant higher-level verdicts and the projected future. In finite Markov systems, these requirements generate a coarsest admissible partition by refining constitution and verdict distinctions together with transition probabilities. A coupled-oscillator construction supplies a complete model-level collective bearer, separates its constitution from that of its supporting assembly and proves that unrestricted exact closure of the mean coordinate requires an affine onsite force. A quartic interaction provides an explicit failure witness and a quantitative finite-horizon alternative. The resulting certificate distinguishes physical emergence from a convenient compression, constitution multiplicity from multiple realization, and constitution formation from sustained persistence. It combines the earlier emergence and multi-level results with the system-cut and coarse-graining criteria without introducing a new fundamental force.