Abstract
<p>Adaptive systems recover their capacities in reproducible orders. Predicting it has meant fitting a dynamical model to each system and reading the order off its trajectories, an output of the fit, not of structure. Here we show that recovery order follows from dependency structure: which capacities must be in place before which others recover. From four axioms we prove that where prerequisite gates vanish at baseline no capacity begins to recover before its prerequisites, whatever the rate constants, and that under a common deficit-closing rule with rates non-increasing along dependencies the admissible orders are exactly the linear extensions of the graph: a chain gives a unique sequence, a branch a partial order. We map where steep heterogeneity adds further orders. The graph is an input, realized in probabilistic models as identifiability structure. We instantiate it in catatonia, post-injury motor recovery and curriculum learning, the last without a probabilistic model.</p>