We derive the axial shell-coupling coefficient of the finite-capacity latency–erasure theory directly from the strong-field shell background and thereby convert the previously derived reflectivity law into a numerically evaluable strong-field prediction. Earlier FCLET work established the shell background, fixed the shell-onset threshold , derived the shell location, obtained the echo-delay scale, and then derived the first action-based shell reflectivity law in the odd-parity thin-shell sector. What remained open was the background-to-response bridge: the shell reflectivity law was known analytically, but its coupling scale had not yet been evaluated from the shell burden profile itself. The present paper closes that gap. We begin from the FCLET strong-field background with static shell profile and derive the shell contribution to the odd-parity master operator by linearizing the metric-latency system in the axial sector. This yields an explicit shell kernel , constructed from the shell-dressed background geometry, the radial gradient structure of , and the shell-support sector of the effective stress tensor. In the strict thin-shell limit, the integrated axial shell coupling is then We evaluate this expression for a Schwarzschild-like FCLET shell background and obtain the first numerical estimate of , and therefore the first numerical axial reflectivity profile in the observationally relevant low-frequency regime. This converts the shell-response sector from a formally derived law into a numerically testable strong-field prediction. The result completes the first closed derivational sequence of the FCLET compact-object program: shell onset, shell location, echo timing, shell perturbation law, and shell-response scale now form a single calculable chain. The strong-field sector of the theory no longer states only where a shell forms and how it scatters in principle. It now begins to determine how strongly that shell responds in practice.
Ali Caner Yücel (Wed,) studied this question.