Human learning is a dissipative dynamical process: mastery accumulates through practice, decays through forgetting, and propagates across interdependent concepts. We model it as a nonlinear dissipative system of ordinary differential equations whose parameters are mechanistically meaningful (a transfer-of-practice matrix, per-concept forgetting rates, and a saturating practice-response gain), and we study when those parameters can actually be recovered from data. For two concepts, we prove a constructive structural identifiability theorem for the associated inverse problem under explicit excitation conditions, together with monotonicity, robustness and L-stability results. We derive an implicit L-stable scheme and a batched solver numerically equivalent to the per-trajectory formulation (bit-exact predictions, gradients to $10^{-10}$) yet two orders of magnitude faster, making estimation feasible on cohorts of $2.5\times10^4$ learners. The empirical study is two-sided. Under the theorem's excitation conditions, synthetic recovery is exact: parameters to machine precision, coupling structure at $F_1 = 1.0$. On large observational benchmarks it is not. An apparently strong recovery, with forgetting rates correlating with topic error rates at Spearman $ρ= 0.83$, is refuted by four controls: it survives destroying the temporal order of the data, is matched by a classical Bayesian baseline, and is unaffected by removing real timestamps. We trace this to the stationary structure of the model and show that it is consistent with the degeneration anticipated by the theory in the absence of designed excitation. The result delineates a boundary between identifiable and unidentifiable regimes and motivates controls for interpretability claims.

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