A Five-Variable Coupled Dynamical Extension of the Learning System Stability Model

This paper derives a five-variable coupled continuous-time dynamical extension of the Learning System Stability Model (LSSM). The system tracks labile traces (T), prior knowledge (E), relevance (r), synaptic consolidation (S_syn), and systems consolidation (S_sys). Eight structural corrections are incorporated, including mass conservation, logistic knowledge growth bounded by capacity ceiling E_max, normalised selection function sigma in [0,1], and saturated relevance dynamics. The corrected system is well-posed, admits bistability consistent with the original LSSM saddle-node structure, and preserves the stability constraint L ≤ E·S_sys² as a slow-timescale condition. Reference Python implementation provided separately.