Negative Space Encoding: A Multi-Dataset Empirical Validation - Topological Signatures of Cognitive Constraints Across Four EEG Datasets

Abstract We report a comprehensive empirical validation of Negative Space Encoding (NSE) theory using persistent homology applied to four independent EEG datasets (total N = 122 subjects, 486 recordings). NSE proposes that neural information is encoded in the topological structure of constrained absence: long-lived H₁ cycles in neural phase space, termed C-scars, that encode computational boundaries established through learning and experience. Across four paradigms — propofol sedation, five-task cognitive battery, anagram insight, and probabilistic reversal learning — we find convergent evidence for three core NSE predictions: • C-scars collapse selectively under propofol sedation (1.4–1.7× reduction, p < 0.001, ds005620, N=20), while short-lived cycles persist, demonstrating that topological complexity is not a simple correlate of arousal. • C-scar 2D position (birth, death) in the persistence diagram constitutes a subject-specific neural fingerprint, stable across three sessions and five cognitive tasks (alpha Betti d=+1.214, p<0.001, ds004148, N=60). • A time-resolved sliding-window analysis reveals the birth of a new C-scar approximately 390–600 ms following reversal learning events (baseline vs post-reversal: d=+1.277, p<0.0001, ds004295, N=22), providing the first direct temporal observation of C-scar formation. Extended surrogate testing and Betti number analysis reveal that while large portions of the persistence effect co-vary with theta-band power, directed Betti number analysis using Granger causality-based flag complexes shows a significant increase in directed H₁ cycles at reversal (p=0.014, d=+0.477), an effect that is by definition independent of signal amplitude. A hierarchical organisation of C-scars by frequency band emerges across datasets: theta (4–8 Hz) encodes transient rule-level constraints (reversal learning), alpha (8–13 Hz) encodes lifelong perceptual fingerprints (cross-session r=0.847), and beta (13–30 Hz) encodes intermediate conceptual restructuring (insight). We interpret this hierarchy as evidence that C-scars operate across multiple timescales of constraint learning, from minutes to years. These findings are discussed in relation to RDRT (Refusal-Driven Dimensionality Reduction Theory), IIT, and Global Workspace Theory, and concrete directions for future work including directed persistent homology, intracranial recordings, and longitudinal fingerprint tracking are proposed.