Abstract

Negative Space Encoding (NSE) proposes that information in neural systems is encoded not only in patterns of activity, but in structured absences -- topological constraints on the trajectories a brain can realize in its state space. These forbidden regions are constitutive of individual neural identity: each brain has a characteristic negative space that defines what it cannot do.

We tested two core NSE predictions on 60 subjects x 3 sessions x 5 cognitive states from the OpenNeuro ds004148 dataset, using persistent homology (Vietoris-Rips, H1) applied to delay-embedded EEG phase spaces. T1 predicts that the topology of each subject's EEG attractor is individually characteristic and reproducible across sessions. O3 predicts that forbidden regions of phase space are subject-specific across all cognitive states.

Both predictions were fully confirmed, and confirmed by three independent statistical methods. T1 was confirmed in alpha (Mann-Whitney p<0.0001, permutation p<0.001, classifier accuracy 9.4% vs chance 1.7%) and beta bands. O3 was confirmed for all five cognitive tasks. Theta showed no robust subject-specificity, consistent with the theoretical prediction that theta implements universal temporal segmentation. Subject identification from alpha-band topological fingerprints alone achieves 9.4% accuracy (5.7x chance) across 60 subjects and 3 sessions, a result with strong implications for neural individuality.