Catatonia recovery separates two intervention axes that constrain electroconvulsive therapy

A treatment can start a recovery or carry one further, and outcomes alone do not say whether these are actions on the same quantity. We ask this of a model motivated by catatonia, in which twenty-five inpatients recovered through five capacities in one fixed order and whose two effective treatments have no known dynamical representation. The model is an evidence-coupled bistable cascade on a dependency chain: each capacity is bistable, the threshold falls as evidence consolidates, and recovery propagates from a root by diffusive coupling. Two quantities are taken as intervention coordinates, an excursion applied to the root and the coupling between adjacent capacities, with the evidence coordinate closed to input by assumption; we show that they act on disjoint regions of state space. While every capacity is below threshold, a maximum principle forbids any non-negative diffusive coupling, on any graph and in either direction, from crossing the switching surface, so an acute conversion requires an excursion. With the root restored and the downstream chain collapsed, propagation is governed by one exact criterion, the prevailing threshold squared over four, because the first-stage equilibrium condition factorises; the weakest coupling sets where recovery stops, the same discriminant gives the first-stage eigenvalue and the inverse-square-root passage time through the fold, and the coupling is identifiable from the resting first stage. Eight falsifiable predictions are separated into consequences of the theorems, predictions needing an added clinical correspondence, and predictions needing a latent quantity measured; exploratory comparisons with published data bear on two of them.