From STT Memory Kernels to Hysteresis Models: A Computational Comparative Bridge Between Critical Memory Zones and Path-Dependent Dynamics

This technical note presents the fourth study in the computational sequence associated with Selector-Time Theory (STT). After the construction of minimal irreversibility-memory kernels, parametric sweeps, robustness tests, and cross-drive prediction, the present work introduces Listing 08, a computational script designed to build a methodological bridge between memory regimes observed in STT-inspired toy models and operational metrics associated with memory systems, hysteresis, path dependence, loss of invertibility, and lock-like behavior. The purpose of the study is not to physically validate STT, nor to claim equivalence between the STT-inspired computational kernel and established physical models of hysteresis such as Preisach or Jiles-Atherton. The proposal is more restricted and methodologically cautious: to define reproducible computational metrics through which operational signatures of the toy model can be compared, at a structural level, with typical features of path-dependent systems. The main execution tested six drive profiles, four noise levels, fifty-one memory-weight values, eight repetitions per configuration, and 420 steps per simulation, totaling 9, 792 executions. The results show growth of residual memory, formation of hysteresis-like loops, increasing path asymmetry, drive-dependent variation of invertibility loss, and growth of a lock-like indicator at high memory. The observed global maximum, memoryweight = 0. 4900, is interpreted as the peak of the composite hysteresis-bridge metric, not as a replacement for the residual critical zone refined in previous studies. The classification of computational regimes is presented as heuristic and exploratory, not as a physical phase diagram. This record includes the article PDF and a supplementary package containing the Python script, generated CSV files, metadata, execution log, figures, READMEs, and requirements file.