Temporally aligned sensory history restores Markov-blanket function in delayed sensorimotor systems

Biological sensorimotor interactions involve finite delays, raising the question of whether an instantaneous Markov blanket contains the temporally relevant information required to separate internal from external dynamics. We examined this problem in a minimal stochastic sensorimotor system with an explicit sensory-to-internal delay and compared instantaneous, generalized-coordinate, history-extended, oracle-delay, random-history, and shuffled-history recognition models. Boundary function was evaluated using cross-fitted residual internal-external dependence together with current-state reconstruction, delay-aligned sensory reconstruction, and future-state prediction. Instantaneous recognition left substantial residual dependence under delay, whereas temporally aligned sensory history strongly reduced this dependence and improved reconstruction and prediction. Generalized coordinates provided partial compensation, while direct access to the true delayed sensory state was optimal for delay-specific reconstruction but not for all functional criteria. Temporally disrupted history failed to reproduce the history advantage. The residual-screening result was preserved across regularization strengths, nonparametric mutual-information estimation, an alternative temporal-disruption control, and multivariate parameter variation. These findings show that under delayed coupling, the functional sufficiency of a Markov-blanket representation depends not only on which variables constitute the boundary but also on whether the representation contains the temporally relevant information mediating system-environment interactions.