Emergence as Persistence Inheritance: When a higher level is a persister — and the reduction condition that unifies the series

A higher-level object — a quasiparticle, a phase, a fluid, an organism — is usually accepted when a coarse variable behaves autonomously enough to model. This paper fixes when that autonomy is real. It imports the domain machinery unchanged — the projection-operator (Mori–Zwanzig) account of reduced dynamics with memory, effective field theory, and Wilsonian universality classes — and adds a derivation. La Profilée fixes, from a pre-physical root, which distinctions are constitutive for the candidate higher-level persister, and on that basis a macro-persister emerges exactly when a non-injective realization map carries the microdynamics to a representative-independent macrodynamics, ; the roles and the identity verdict are unique on each realization fiber; the macro level has its own continuation-admissibility; and at least two micro-distinct configurations carry the same macro-history. Those six conditions are necessary and jointly sufficient — a complete emergence certificate. The reach of the result is that its central condition is not new: is the general form of the criteria proved for the quantum system cut (the dynamic congruence of LP-PHY-05) and for classical coarse-graining (the strong lumpability of LP-PHY-08). Those two are instances of one reduction structure, and this paper states it abstractly, so the recurrence that the universality claim asserts becomes, at the level of reduction, a theorem. The paper further proves the sectoral form of role inheritance , a universality theorem identifying when several micro-theories are dynamically and persistence-equivalent on a named macro-description, together with the additional conditions under which that equivalence strengthens to sameness of physics, and an effective-theory validity criterion — an effective theory is correct for a target persister over a horizon when its error stays below the persistence margin there, , the general form of the robust-verdict test of LP-PHY-05. What is not delivered is stated throughout: the exact certificate is the memoryless case, and controlling Mori–Zwanzig memory terms, constructing the realization in each field, and the quantitative thresholds for quasiparticles, phases, biological systems, and emergent spacetime remain the domain’s.