An Unfalsifiable Inverse Problem: Latent-Source Identifiability from Non-Stationary Timeseries

Latent-source identifiability theorems for nonlinear ICA and causal representation learning promise that, under stated assumptions, the sources generating an observed signal are recoverable up to trivial indeterminacies. We argue that when these methods are applied to purely observational scalp-level EEG and MEG, the identifiability claim is not falsifiable in the Popperian sense: the scalp inverse problem is many-to-one, and no recording channel, source-reconstruction method, or behavioural readout gives a method-independent reference against which recovery could be checked. We make the argument empirical on a synthetic testbed with ground truth by construction, and show that the methods that claim nonlinear identifiability break precisely on the stress axes that characterise real scalp EEG.