Block conjugation gave an exact reference test for regularized EEG GIM under joint block symmetry

We derived a finite block conjugation reference for the established global interaction measure (GIM). Conjugation keeps real cross-density and sensor metric ridge weights fixed. A block Gram matrix gives every score, its exact reference mean, and its exact variance. The upper tail is a conservative test p value under joint block conjugation symmetry. That assumption is stronger than zero expected imaginary density. We tested three six-sensor Gaussian models with 2,000 records each. With a shared component inside independent windows, segment signs rejected 89.3% of zero-lag records at 0.05. Window signs rejected 4.1%. With a shared component across a record, window signs rejected 96.1%. We also analyzed all 88 processed EEG records in OpenNeuro ds004504 v1.0.9. The main setting used the first 200 accepted seconds at 10 Hz, 20 window sign units, and ridge alpha 0.1. We evaluated all 524,288 distinct sign patterns for squared scores per person. Mean observed GIM was 0.553264. Mean reference GIM was 0.266852. Mean signed excess was 0.286411, with a 95% person bootstrap interval of 0.249321 to 0.324672. The reference mean was 48.23% of the observed mean. Subtraction reversed 747 of 3,828 person score pairs. These EEG results describe a finite reference. Block symmetry was not established in the data. The package has the proof, full Fourier input, source hashes, retrieval code, model results, scores, resamples, and repeat instructions. Direct formula checks, a fresh source replay, fresh snapshot checks, and a separate offline repeat passed.

EEG · global interaction measure · complex conjugation · block symmetry · finite reference · sensor metric ridge · signal processing