Hidden Record Routing Limits Quantum Measurement Reversibility

Continuous quantum measurements are calibrated by detector-side parameters---measurement rate $k$ and efficiency $\eta_D$---but these do not determine measurement reversibility. We prove that recoverable visibility is ceilinged by the Uhlmann fidelity of inaccessible record degrees of freedom (Theorem 1}). In an explicit routing model, this ceiling depends exponentially on a hidden irrecoverable routing rate $\kappa_L$ that can vary at fixed $(k,\eta_D)$. We further prove that detector-only statistics cannot identify this rate or the ceiling without additional physical assumptions (Theorem 2}). To break this impasse, we introduce \emph{reversibility spectroscopy}: a direct interference-recovery protocol that extracts $\kappa_L$ as a measurable calibration primitive, transforming hidden routing from an uncontrolled uncertainty into an operationally quantified parameter.