Reset-Window Limits for Latent World-Model Interfaces

We study the data interface that underlies a class of latent world models: a homogeneous two-state controlled process observed through binary emissions. Given only $N$ independent reset triples, how much post-training control loss is unavoidable over a fresh $H$-step episode? For binary actions and observations, a known uniform reset, and reward $(1+X)/2$, we characterize the boundary-uniform loss for $H\ge 8$ and $N\ge 1$ as $\min \{H,H^{3/2}{N}^{-1/4},H^3{N}^{-1/2}\}$ up to absolute constants. The lower bound permits adaptive training and useful deployment-time inference; the upper bound uses thirteen intervention moments, a one-dimensional legal-model fit, and a finite belief controller. A disclosed two-model construction shows how the reset window changes the information available at equal observation count. The result is an interface theorem for controlled latent processes, not a neural representation-learning benchmark.