Finite-Thickness Shell Dynamics and Coupled Metric–Latency Matching in FCLET Compact Objects

We develop the finite-thickness shell dynamics of the finite-capacity latency–erasure theory and derive the first coupled metric–latency matching problem of the compact-object sector. Earlier FCLET work established the shell-onset threshold , derived the shell location and echo-delay scale, obtained the minimal odd-parity thin-shell reflectivity law, determined the axial shell coupling and kernel coefficients from the quadratic action, and derived the inner latency closure of the saturated core as a regular quenching branch. Those results completed the minimal branch of the strong-field program and revealed its decisive limitation: the odd-parity thin-shell shell is too rigid, yielding near-perfect infrared reflection throughout the observational band. The present paper moves beyond that limit. We no longer compress the shell into a delta-supported interaction. We resolve it as a finite-thickness transition layer and retain the coupled perturbation dynamics of the metric and latency sectors inside the shell. Starting from the quadratic FCLET action on a shell background, we derive the coupled perturbation system for the polar master gravitational variable and the latency perturbation , identify the shell-supported mixing operators, and formulate the full shell matching problem across the outer shell face, the shell interior, and the saturated core. The exterior sector is matched to the shell layer by continuity of the master variables and their canonical radial momenta, while the core side is closed not by ansatz but by the previously derived regular quenching branch, This produces the first fully derived finite-thickness shell transfer problem of FCLET compact objects. The strong-field consequence is immediate. The physical shell response is no longer governed by the rigid one-channel thin-shell law alone. It is softened by finite-width propagation, shell-internal metric–latency coupling, and shell-layer mode conversion. The shell reflectivity sector therefore ceases to be maximally infrared-rigid and becomes a genuine spectroscopic response problem. The compact-object branch of FCLET thus advances from minimal shell perturbation theory to physical shell spectroscopy