Admissible Spectral Comparison Across Configurations — Analytic continuation as an admissibility rule

Minimal Consistency Requirements for Transport Persistence under composed variation requires that comparisons remain representative-independent when local evaluations are recombined. Local equivalence of descriptions suffices for single comparisons but fails under recomposition once loss is path-dependent. Consistency then forces the existence of a transport rule relating equivalence classes across variation. Transport is derived here as a structural necessity of persistence bookkeeping, introduced prior to and independent of time, dynamics, geometry, or symmetry principles.