Kerr FCLET Spectroscopy and Injection–Recovery Protocol

We construct the detector-facing spectroscopy and injection–recovery program of the finite-capacity latency–erasure theory on rotating compact-remnant backgrounds. Article 83 established the Kerr-sector shell theory in a mathematically controlled form and provided the first stabilized numerical benchmark of the Schwarzschild FCLET shell spectrum, anchoring the dominant real-sector shift at approximately and the support anchor at approximately in the zero-spin limit. The covariant saturation surface was defined, the stationary axisymmetric latency closure was derived, the Teukolsky/Generalized Sasaki–Nakamura projection was constructed, the admissible rotating-shell branch was isolated, and the principal detector-facing observables , , , and were obtained. What remained open was the decisive detector-level question. A rotating shell theory does not become scientifically relevant merely because its perturbation sector exists. It becomes relevant only when its signal family is recoverable, distinguishable, and non-mimickable under realistic inference conditions. In this paper we build that recovery framework. We construct the first Kerr FCLET waveform family for post-merger spectroscopy by combining four structures inherited from the admissible branch of the rotating shell theory: spin-dependent quasi-normal frequency deformation, shell-induced damping modification, excitation-branch hierarchy, and delayed shell-response structure. The resulting waveform family is not an ad hoc echo toy model. It is a shell-informed rotating strong-field template family derived from the detector-facing outputs of the Kerr FCLET perturbation program. We then develop a full injection–recovery protocol over a benchmark atlas spanning weak-shell, moderate-shell, strong-but-admissible shell, and near-instability rotating branches. Synthetic FCLET signals are injected across controlled noise realizations and are recovered using three competing model families: standard Kerr ringdown, Kerr ringdown with overtone enrichment, and the Kerr FCLET shell model. The central purpose of the analysis is identifiability. We determine which regions of admissible FCLET parameter space are absorbed by standard Kerr freedom, which remain ambiguous under realistic recovery, and which form decisive-island regions in which the delayed phase structure, excitation hierarchy, or mode-branch deformation cannot be reproduced by non-FCLET templates. To make this distinction sharp, we define a mimicry map from FCLET effective parameters to their best false-Kerr counterparts and construct an identifiability corridor over theory space. We also quantify false alarm, false FCLET identification, and FCLET suppression by Kerr overfitting, thereby separating mere detectability from actual model-level discrimination. The main outputs are a detector-facing Kerr FCLET waveform family, a benchmark injection atlas, a recovery protocol, a parameter-degeneracy map, a mimicry/exclusion classification, and a decisive-island search strategy for event-level confrontation. These results do not yet constitute direct confrontation with specific LVK events. They perform the indispensable prior task: they determine where the admissible Kerr FCLET branch is recoverable, where it is indistinguishable from standard Kerr spectroscopy, and where it becomes a falsifiable detector-level target. Article 85 will use this infrastructure for direct confrontation with real merger data. The benchmark atlas is therefore no longer qualitative only. It is numerically anchored by the stabilized Schwarzschild shell result of Article 83, so that the detector-facing recovery problem is organized around explicit spectral-departure scales with a calibrated zero-spin reference point.