Spectral Accessibility: Probing What EEG Foundation Models Preserve

Downstream accuracy measures task utility, but does not reveal how broadly a frozen EEG representation exposes signal structure. We introduce spectral accessibility, a label-independent audit of a declared second-order state built from multiresolution complex cross-spectral matrices. A subject-disjoint fit selects and whitens 64 reliable state directions. Their recoverability defines an accessibility spectrum; SPA-20 tests broad coverage by averaging its weakest 20% under the worst declared input environment. We distinguish the unrestricted population operator, its best-linear counterpart, and the finite cross-fitted ridge estimate. Population theory gives data processing inequalities and task-error bounds, including bounds restricted to accessible subspaces. Across five masked-reconstruction or masked prediction EEG foundation models, seven datasets, and four input conditions, all 140 estimated linear lower tails reach zero. Strong split-taper controls on four datasets show that the same pipeline can recover the target’s weak directions, although pooling, subject transfer, and probe estimation remain possible bottlenecks. Non-zero access is concentrated in upper subspaces. We report their exploratory environmental profiles and conditional uncertainty. In this regime, SPA-20 is a diagnostic stress test; the full spectrum, null floor, and split-taper reference carry the comparative information.