A selected signal space gives finite posterior EEG ratio limits in all 88 ds004504 v1.0.9 records under an alpha power cap

We tested whether a joint theta-alpha signal space gives finite reference ratio limits when the full alpha matrix is nearly singular. We used all 88 processed eyes-closed EEG records in OpenNeuro ds004504 v1.0.9. A fixed 1e-8 joint power threshold gave finite posterior theta-to-alpha ratio limits under an alpha mean power cap in all records. The full alpha matrix check admitted 36 records. The direct median upper-to-lower factor was 9.86. The planned median log10 width was 0.993. Source powers agreed with the saved endpoint weights within 3.01e-11 in relative terms. A 1e-6 threshold changed eight spaces and changed one endpoint by 60.4%. The proof permits singular alpha matrices when their null space is also null for theta. The empirical limits apply to reference weights in the selected space. Small removed power does not prove limits for unrestricted source weights. The package preserves inputs, code, proof, all results, hashes, source replay checks, and reproduction instructions. No disease effect was tested.

EEG · signal processing · reference choice · signal space · theta-to-alpha ratio · spectral power · generalized eigenvalues · numerical rank