Cosmological Completion of FCLET: Operational FLRW Geometry, Dynamical Closure, and the Field-Theoretic Derivation of {\boldsymbol{q}}_{\mathbf{FCLET}}

This article embeds the FCLET latency field in FLRW cosmology. Matter, clocks and rulers couple to , and the local geometrical transport factor is . Consequently, , and . The background field equation determines once the expansion, source dynamics and initial data are specified. A self-consistent background additionally requires the capacity-sector evolution and stress tensor. In a controlled adiabatic equilibrium, The constant branch gives the stated geometrical co-transport relations for expansion rates, matched distances and rulers. The registered-growth relation , and hence , is a separate reciprocal-response closure assumption. It is not a conformal transformation law for the dimensionless matter contrast. The article distinguishes the derived geometrical field state from this additional observable-response model. Under their stated source, calibration and branch assumptions, they provide a common framework for the proposed cosmological tests.