Process Memory Beyond Prediction: Auditing Algebraic Structure in Learned Dynamics

Does accurate prediction imply recovery of the process that generates the observations? We study this question in a controlled physical-representation benchmark with eight latent states and six primitive operations whose closure forms a 104-element transformation semigroup. The states are rendered as high-dimensional spatial fields under controlled carrier variation, letting us measure physical-state recoverability, predictive generalization, and process-structure recovery separately. The physical states are highly recoverable from observation, with a frozen diagnostic decoder reaching 98.31% mean validation accuracy, and learned models consistently outperform persistence across sealed distribution shifts. Yet the predictively trained Operation Channel Model (OCM), despite an explicit eight-state categorical representation and operation-specific transition channels, reaches only 15.72% state alignment and 13.89% sealed state-path accuracy against a 12.5% chance reference. It exactly recovers only 1 of 104 transformations and none of the nine held-out transformations, and it does not outperform the validation-selected B4 baseline in the frozen primary joint-OOD comparison. An earlier simpler observation regime provides a positive control in which OCM recovers the full finite transformation structure at low-to-moderate noise, showing that the broader process-memory analysis can register exact structural recovery under less demanding conditions. In Tier-C-v4, state recoverability and predictive learnability therefore do not, by themselves, guarantee recovery of the intended process algebra in the structured model tested here. When mechanistic or compositional structure is a modeling objective, process memory should be evaluated directly rather than inferred from forecasting accuracy.