Terminal Failure Is Not Computational Failure: A Pre-Collapse Readout Regime in Nonlinear Dynamical Learners

Reservoirs, equilibrium models, neural ODEs, and recurrent test-time compute all perform inference by running a state trajectory. Standard practice collapses that trajectory to a terminal readout, implicitly assuming that the final state is the right summary of the computation. We show that this assumption can fail: in supercritical nonlinear dynamics, terminal representations can degrade while earlier trajectory prefixes still support accurate prediction. We formalise the usable prefix as an accuracy-defined grace period and compare fixed early-window readout, norm-ratio stopping, and GRACE (Growth-Regulated Adaptive State Extraction). In complex modReLU reservoirs, non-terminal readouts preserve near-stable MNIST accuracy across an unstable spectral sweep while terminal readout collapses. The best decoder is nonlinearity-dependent: GRACE is strongest in fixed unbounded dynamics and under injected dynamical noise, while simple early-window readout is strongest in trained LeakyReLU and LSTM checks. The same endpoint-vs.-trajectory gap appears on CIFAR-10, including a frozen-feature variant where it survives translation to an 85%-accuracy substrate, and cross-system comparisons show that the regime is severe in unbounded nonlinear dynamics, milder in bounded tanh systems, and absent in linear systems. Terminal failure, therefore, is not necessarily computational failure; it can be a failure of when we choose to read the system out.