Open-system versus unitary density-matrix predictors on long-horizon predictive error: a pre-registered comparison against an exact Bayes reference

Technical report; not peer reviewed (internal review only). On synthetic partially observed Markov processes with an exact Bayes reference and about 10³ parameters, we compare unitary and open-system (GKSL, Kraus-channel, contraction-only) density-matrix belief predictors, trained on horizons 1–50 and evaluated to 200, by excess predictive error against the Bayes predictor. Pre-registered, over ten seeds under the registered learning-rate selection, a unitary predictor whose blind rollout does not marginalise its observation instrument carried 0.0237 nats more extrapolation-window error than the GKSL predictor on the simple task, meeting the 0.02-nat threshold; on the metastable task the excess was 0.0189 nats, below the threshold. In these near-stationary configurations, contraction towards a stationary state removed most of the excess; the general GKSL generator added nothing beyond it in the registered windows, and neither a recurrence mechanism nor a dose–response in the environment dimension was established. Post hoc, applying the instrument's non-selective channel at each blind step removed nearly all of the excess. In a matched-parameter comparison, density-matrix sequence models did not meet the pre-registered margin over flexible classical recurrent networks on any arm or budget, and that comparison's registered conclusion is not accepted because its positive control failed. In a pre-registered follow-up, a moment-matching warm start let the true-order density-matrix model capture at least 90% of the predictable information on 10 of 10 fresh seeds of one HQMM-generated process, with a recipe developed on exploratory seeds of that process, and on 0 of 10 for a weaker-signal instance. Neither the limitation nor the remedy is new. Licences: report, text and own data CC BY 4.0; supplement code Apache-2.0; third-party data keep their own licences.