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

EEG connectivity can distinguish individuals, but the persistence of its phase and magnitude structure across visits and functional states remains incompletely understood. We examined 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 reveal persistent individual structure in both phase and complex coherency over weeks to years, while distinguishing temporal persistence from robustness across functional states.