The Dynamics of Learning Accessibility: Phase Space, Attractors, Transitions, and Regime Change

If learning accessibility is treated as a situated, time-dependent relation rather than a stable learner property, the central methodological problem is not whether learning can be described dynamically. Educational state-space models, knowledge tracing, control-theoretic and continuous-time differential-equation learner models, recurrence analysis, bifurcation accounts, and regime-switching methods already establish that it can. The narrower problem is how to decide which dynamical claims are warranted for a configuration-scoped construct when observations are finite, noisy, irregular, and partly generated by interventions. This paper develops a falsification-oriented identification protocol for the Dynamic Map of Learning Accessibility (MDAA), which conceptualizes learning accessibility not as a stable property of the learner but as a situated and time-dependent relation among subject, learning object, and conditions. We distinguish latent process state x(t), observation y(t), conditions c(t), deliberate intervention u(t), and, only when empirically justified, a latent regime q(t). The protocol comprises four interpretation gates (observability, structural and practical identifiability, and semantic validity), explicit null tests for nonlinear structure, a differential diagnosis of recurrence, regime change, and bifurcation, and a predeclared model lattice in which nonlinearity, regime switching, memory, and stochasticity are separately testable and reversible axes rather than rungs of a ladder. Because the protocol precedes data, we also specify a simulation-based recovery study that must be completed before empirical fitting. Direct precedents constrain the novelty claim, from Self (1977) to recent control-theoretic and fractional learner models; the candidate contribution is the integrated protocol and its explicit criteria for reducing the model when added structure fails to earn support. Preprint. Methodological manuscript, not peer reviewed. No human data were collected. Section 9.1 reports two preregistered simulation recovery grids (1,280 runs each); the bench, preregistrations and full outputs are archived at https://doi.org/10.5281/zenodo.22728835