A Bifurcation-Aware Policy Layer for the Learning System Stability Model: Margin-Regulated Exploration Scheduling with Corrected Regret Bounds and Hysteresis

This paper derives a bifurcation-aware policy layer for the Learning System Stability Model (LSSM). The central construction is the Margin-Regulated bonus multiplier (MRER): beta(t) = beta_max · sigma(M(t)/M_max), where M = I_cap − L is the LSSM stability margin. Three formal results are established: (T1) MRER-UCB achieves O(ln T) cumulative regret with constant factor 1/beta²_min; (T2) MRER preserves the LSSM stability constraint L ≤ E·S_sys² under an explicit safe-action set condition; (T3) given LSSM bistability, MRER-UCB inherits hysteresis — producing lower exploration bonus on the collapse branch than on the recovery branch at the same nominal load. Version 1.1.0 incorporates corrections following peer review by ChatGPT (OpenAI) and DeepSeek AI. All results are empirically confirmed across 50 Monte Carlo runs in the companion software (DOI: 10.5281/zenodo.19005510).