Corridor Width as a Diagnostic Calibration Scale

This work introduces corridor width as a diagnostic observable for determining when structure revealed by a projection, reconstruction, or inversion is physically meaningful rather than representation-induced. Corridor width is defined as the smallest tolerance of a system’s governing operator to perturbation before its qualitative observable structure changes, and is operationally identified with the least stable mode of a relevant linearized operator (e.g., minimum singular value, smallest eigenvalue, or response pole). We demonstrate the utility of this diagnostic through a proof-of-concept analysis in gravitational lensing, where corridor width—computed from the lensing Jacobian—predicts image multiplicity, distinguishes rings from arcs, and explains resolution-dependent instabilities. We further show that corridor width provides a principled resolution-calibration criterion: under-resolution suppresses narrow structural corridors, while over-resolution amplifies noise-induced spurious degeneracies. Motivated by this result, we interpret operator degeneracy, normal modes, and response-function poles in holographic systems as manifestations of vanishing corridor width, framing phase transitions and marginal modes as boundary-driven observability phenomena. Throughout, degeneracy is treated not as a numerical pathology but as a diagnostic signal indicating the limits of reliable observability. This framework unifies conditioning, stability, and resolution selection across inverse problems, numerical physics, and constrained systems, offering a general method for distinguishing intrinsic structure from projection artifacts without introducing new dynamics.