We complete the microphysical branch of the finite-capacity latency–erasure acoustic program by deriving the constitutive origin of the effective scalar operator discovered in the companion perturbation paper. The background transport paper established that FCLET contracts the sound horizon through a burdened acoustic transport law implemented in CLASS with exact CDM limit recovery. The companion discovery paper then showed that this contracted ruler does not automatically propagate into an observable TT peak displacement and identified the missing perturbative carrier as a split scalar acoustic operator with distinct phase and source continuation channels. The unresolved question is therefore exact: what radiative medium produces that operator? The answer developed here is that the early photon sector must be treated, in FCLET, as a causal finite-capacity radiative medium with retarded response. Present radiative stress is not determined by a strictly memoryless ideal-fluid law. It is generated by burden-weighted response kernels acting on radiative drivers. We construct the corresponding covariant response structure, show that it separates into propagation and source channels, and reduce it to the FRW scalar sector. In the short-memory regime relevant to the acoustic hierarchy, the required continuation coefficients become kernel moments, with the physically admissible ordering We further show that the exact photon momentum-side normalization is fixed by relativistic photon enthalpy, so that the effective phase-carrier replacement discovered previously, is the correct enthalpy-normalized scalar reduction of the propagation response. The constitutive program is then closed by introducing the canonical microphysical kernel family. Under the postulate of Poissonian memory overwrite with channel-dependent constant hazard, the propagation and source kernels take the exponential form and admit an exact Markovian auxiliary-field representation. The locked implementation values are thereby reinterpreted as the first stable kernel-moment realization of the finite-capacity radiative medium rather than ad hoc fitting constants. This paper therefore completes the constitutive origin of the FCLET scalar acoustic operator by deriving it from a causal finite-capacity radiative medium with retarded response and canonical kernel moments.
Ali Caner Yücel (Sat,) studied this question.