From Recoverability to Functional Use: Certifying Temporal Reports in Time-Series Forecasting

Models increasingly accompany time-series forecasts with temporal reports---delays, leading indicators, or selected history---yet a correct report need not describe the computation that produced the forecast. We formalize this as a three-stage certification problem: \emph{recoverability} of the target from the realized trajectory, \emph{correctness} of the model's report, and \emph{functional use} of the reported history. For Gaussian point delays, we derive an exact finite-sample recovery--substitutability identity: the same realized shift geometry yields structural evidence at scale $nη_n$ but normalized proxy-prediction cost at scale $η_n$. Thus a delay can be decisively identifiable while a correlated alternative remains near-oracle. We then audit intentionally unconstrained TCN and N-HiTS forecasters only on trajectories that are recoverable, correctly reported, and near-oracle. Even there, Jacobian and in-distribution conditional-replacement response peaks lie $9.3$--$13.5$ time steps from the reported delay. Finally, a report-conditioned no-bypass factorization provides a sufficient access certificate; architecture-matched post-hoc routing and gate-destruction controls show that the alignment change is attributable to report-coordinate access. The framework distinguishes evidence that a temporal statement is identifiable and correct from evidence that the forecast computation actually depends on it.