Linearized Latency Dynamics in the Saturated Core of FCLET Compact Objects

We derive the inner latency boundary condition of the finite-capacity latency–erasure theory directly from the linearized saturated-core dynamics and thereby remove the last non-derived closure standing between the minimal shell branch and the full finite-thickness shell program. Earlier FCLET work established the shell background, fixed the shell-onset threshold, derived the shell location and echo-delay scale, constructed the odd-parity shell perturbation sector, and then derived the axial shell-kernel coefficients from the quadratic metric–latency action. What remained open was the core-side closure problem: once the shell is treated as a finite-thickness layer and the latency perturbation becomes dynamical in the coupled sector, what inner condition does the saturated core impose on ? This paper answers that question from the action itself. We linearize the latency equation in the saturated-core regime around and derive the effective core perturbation operator in terms of the shell-center kinetic normalization and the local potential curvature . We show that the inner latency behavior is controlled by two distinct FCLET quenching channels. In the first, the kinetic sector degenerates at saturation, , and the perturbation loses propagating support. In the second, the core remains kinetically regular but the potential curvature is large and positive, forcing the latency perturbation into a massive quenching regime. In both cases the dynamically admissible core solution is a decaying, non-growing branch rather than a freely oscillatory inner latency cavity. The result is decisive. The inner latency condition is no longer introduced as a physically motivated anchoring ansatz. It is derived as the regular quenching branch of the saturated-core perturbation equation. This closes the methodological gap identified at the end of the axial shell-kernel program and prepares the next strong-field step: finite-thickness shell matching with fully coupled metric–latency perturbations.