Relational Redshift as an Operational Kinematic Limit: Conditional Equivalence, Local UCRP Matching, and Parent-Dynamics Tests in ECSM

We examine a conditional operational construction of cosmological redshift in the Emergent Condensate Superfluid Medium (ECSM) framework. Under specified homogeneous coherent-transport assumptions in ordinary three-dimensional substrate coordinates, constitutive clock and ruler factors yield a redshift endpoint relation and the familiar time-dilation, temperature, distance-duality, brightness and redshift-drift identities. The corresponding homogeneous formulae are exactly those of spatially flat FLRW background optics when the operational scale factor is identified with the material clock/ruler scale. This correspondence does not establish a physically non-expanding Universe and does not claim priority for general conformal-frame equivalence. Restricted no-go results apply to smooth static endpoint redshift explanations; matching to the separately proposed Universal Coherent Response Principle is explicitly conditional. Additional ray and wave-transport checks identify conditions under which evolving inhomogeneous burden and common electromagnetic constitutive response can invalidate endpoint-only or spectrum-preserving assumptions. An unfixed parent inertia/potential cannot predict a unique cosmological expansion history. The paper sets out specific parent-level and empirical requirements for a future falsifiable ECSM alternative, without claiming a parameter-free cosmological model or quantitative replacement of Lambda-CDM.