A Persistence Witness for Classicality: Separating decoherence, objectivity, and the re-identifiability of a record

When is a record classical — and does “classical” mean the same thing at one instant and across time? The literature runs together three properties: decoherence, the suppression of interference that einselects a stable pointer basis; objectivity, the redundant broadcasting of a record into many environment fragments (Quantum Darwinism, and its exact form, Spectrum Broadcast Structure); and the persistence of the record as the same record under later dynamics. This paper separates them. It imports the domain machinery unchanged — the pointer/record algebra, state discrimination, channel distances, and the objectivity criteria — and adds a persistence measure derived from the identity architecture. La Profilée requires identity to be checked on the correct quotient, the maximal record class; on that quotient the persistence defect is the worst-case error with which a record class is re-identified as the same class after real continuation. Technically it is an operational channel witness, not a single Hermitian observable. Four explicit finite-dimensional models then prove that the three properties are pairwise independent: decoherence without persistence, persistence without decoherence, perfect redundancy with no later persistence, and persistence with no redundancy; and a separate theorem shows that Spectrum Broadcast Structure delivers perfect momentary readability but neither temporal identity nor exclusive actuality. The persistence defect composes additively over quotient steps, and the qualitative claim that coherence-loss and classical identity are different thresholds becomes a proved fact. What is not delivered is stated throughout: the pointer basis and its dynamics are domain input, the numerical thresholds and -complete decoders are realization physics, and actuality is supplied by neither decoherence nor redundancy.