Closing the Loop: Auditable Half-Life Prediction with Open-Space Retrieval and Capacity-Aware Scheduling

Spaced repetition requires accurate memory-state prediction and effective scheduling under limited review capacity. We present a closed-loop framework that couples Open-Space Retrieval for Half-Life Regression (OSR-HLR) with the OSR Adaptive Calibration-Regret Index (OSR-ACRI). OSR-HLR combines relative half-life estimation with open-space retrieval, which transfers deterministic, source-traceable residual evidence from recurring and related historical memory states, while OSR-ACRI converts half-life estimates into capacity-aware review decisions using online calibration, marginal delay cost, and queue age. Across MaiMemo, Anki, and EdNet-Recall, under source-only protocols that keep every Test outcome out of training and retrieval, OSR-HLR achieves the lowest H-SMAPE among 27 baselines in all 15 dataset-protocol settings. It reduces H-SMAPE by 17.40%, 2.59%, and 42.46%, respectively, under the Row protocol, and by 11.36% on held-out Anki users. Under a fixed scheduler, improved predictions reduce 365-day regret by 8.7%-15.8%. With the predictor fixed and workload matched, OSR-ACRI improves retention AUC by 11.1%, reduces time below target by 7.5%, and improves final recall by 19.8%. Together, the two components provide an auditable prediction-to-scheduling loop for efficient spaced repetition.