arXiv:2611.08505v1 Announce Type: new Abstract: We introduce structure-aware optimal transport diagnostics for assessing whether empirical time-series dynamics are compatible with a prescribed predictable-drift class. Our approach translates a pathwise property of stochastic processes into a finite-dimensional projection problem over empirical transition laws, encoding admissibility as row-wise moment constraints on local couplings and quantifying deviations via a Kullback--Leibler projection gap $G_{\lambda,k}$. This yields both a principled diagnostic and a scalable Bregman--Dykstra algorithm that retains the efficiency of Sinkhorn-type methods while incorporating structural constraints. Calibrated against a Brownian reference null, $G_{\lambda,k}$ separates process classes that are indistinguishable by second-order statistics alone---including fractional Brownian motion and BSS processes sharing identical Hurst indices---without asymptotic resampling or continuous-time recovery. This positions the method as a general tool for structure-aware model validation of sequential data.