Photon-Sphere Deformation, Critical Impact Parameter Shift, and Black-Hole Shadow Geometry in the Finite-Capacity Latency–Erasure Theory

We construct the first shadow-geometry interface of the finite-capacity latency–erasure theory by deriving the black-hole photon-sphere structure, critical impact parameter, and apparent shadow deformation generated by the FCLET-modified strong-field exterior. Earlier stages of the program established the rotating shell benchmark, detector-facing ringdown confrontation architecture, the shell–cosmology bridge, the microstate completion of the finite-capacity burden–latency hierarchy, the multi-messenger observational constitution, the first global-survival geometry linking strong-field and cosmological sectors, and the Hubble-sector background-and-transport closure. What remained absent was a direct derivation of how the FCLET strong-field structure modifies null geodesics and therefore the observable shadow geometry of compact objects. The present article provides that derivation. The analysis proceeds in four stages. First, we construct the effective FCLET-modified exterior metric relevant to null propagation in the strong-field regime by embedding the benchmark shell sector into a Kerr-like stationary axisymmetric geometry with finite-capacity corrections. Second, we derive the modified null-geodesic equations and obtain the FCLET photon-sphere and critical impact-parameter conditions. Third, we translate these into observable shadow quantities: shadow radius, photon-ring shift, and leading deformation parameters relative to the standard Kerr benchmark. Fourth, we identify the parameter region in which FCLET predicts either an observationally negligible shadow correction, a potentially resolvable next-generation correction, or an overdriven branch incompatible with the previously established strong-field confrontation corridor. The result is not a loose phenomenological estimate. It is the first metric-derived shadow prediction of the FCLET program. The paper distinguishes sharply between three levels of shadow outcome: null-like recovery, corridor-safe weak deformation, and genuinely measurable photon-ring displacement. This distinction is decisive because the theory need not predict a large present-day Event Horizon Telescope anomaly in order to remain scientifically strong. A small but definite shadow correction is already a nontrivial prediction if it is derived from the same strong-field shell architecture that governs ringdown confrontation. The outcome of the article is therefore a quantitative FCLET mapping together with exact criteria for whether the shadow branch is negligible, next-generation relevant, or incompatible with the established strong-field corridor. The paper therefore does not merely say that FCLET may influence black-hole imaging. It derives the first explicit shadow-sector interface of the theory. In this sense, Article 91 is the first EHT/ngEHT geometry paper of the FCLET program.