Longitudinal persistence of EEG brain fingerprints: phase and complex coherency geometry across sessions and functional states

Sensor-level EEG coherency can distinguish individuals, although its phase and magnitude patterns may reflect neural activity, source mixing, and recording geometry. We evaluated two geometric representations of complex coherency - unit phasors and full complex coherency - alongside triangle holonomies and magnitude-only descriptors. Using direct enrollment-probe matching without a trained identity classifier, we analyzed three independent longitudinal cohorts: RestCog (N = 60; approximately one month), L-FAME (N = 44; six weeks), and Dortmund (N = 206; approximately five years). In eyes-closed rest-to-rest matching, alpha phasors identified 81.67% of participants in RestCog (AUC 0.9473) and 79.55% in L-FAME (AUC 0.9735); full complex coherency identified 78.33% and 84.09%, respectively. After five years in Dortmund, fixed row-standardized alpha-beta fusion yielded 77.67% rank-1 identification (AUC 0.9744) for phasors and 70.39% (AUC 0.9527) for full coherency. Changes in functional state exposed different strengths: full coherency preserved higher rank-1 accuracy in some monthly RestCog rest-to-task comparisons, whereas alpha phasors retained higher verification AUC. Switching between eyes-closed and eyes-open recordings in Dortmund substantially weakened identification with both representations. Triangle holonomies also retained individual information across visits. An exact factorization of complex cosine shows how magnitude-pattern alignment and magnitude-weighted phase agreement contribute to full-coherency matching. Together, the results establish longitudinally discriminative structure in measured scalp EEG coherency over weeks to years, while distinguishing persistence across visits from robustness to changes in recording state.