Observationally Equivalent, Interventionally Different: Identifiability of Multiscale World Models

A world model can predict every observed coarse trajectory correctly while giving the wrong answer to an intervention on a hidden fast mechanism. We formalize this gap through observational fibers: an intervention target is identifiable exactly when it is constant over all models with the same observational law. This yields a two-point minimax lower bound and a general gauge certificate for non-identifiability. For a slow diffusion driven by a fast Ornstein–Uhlenbeck mechanism, we construct a continuum of microscopic models with the same complete averaged slow-path law but different responses to replacement of the fast conditional mean. We then characterize the missing cross-scale information. Frozen conditional means or a calibrated stationary variance identify the intervention response; one positive-lag covariance together with the variance separates the fast mixing rate from its diffusion scale. A perturbation bound quantifies the instability of intervention transport when the fast mean response is weak. The results distinguish observational prediction, microscopic parameter recovery, and target-specific intervention identification. They also show why architectural clock factorization alone cannot resolve an informational ambiguity in a coarse world model.