Spatiotemporal Geometry Integration Theory: Temporal Relational Closure as a Reproducible Higher-Order Signature of Conscious Neural Dynamics

Abstract

Spatiotemporal Geometry Integration Theory: Temporal Relational Closure as a Reproducible Higher-Order Signature of Conscious Neural Dynamics This manuscript introduces Spatiotemporal Geometry Integration Theory (SGIT), a mathematical and computational framework for investigating higher-order spatiotemporal organization of distributed neural activity associated with conscious processing. SGIT represents oriented relationships between EEG signals using discrete Hodge geometry, separating gradient and curl components of neural relational dynamics. Temporal dependencies across three successive analysis windows are described by third-order tensors. Their permutation-symmetry decomposition provides quantitative measures of higher-order organization, while Temporal Relational Closure (TRC) evaluates this organization against pair-preserving permutation-based null models. The manuscript presents experimental evidence from visual conscious-detection datasets, cross-cohort analyses, tactile perception, propofol-modulated brain states, and no-report perceptual paradigms. The findings indicate that higher-order relational neural dynamics contain reproducible information associated with conscious processing across several experimental conditions. The strength and specificity of the evidence vary across datasets, and some proposed mechanistic interpretations remain open to further testing. The framework provides explicit mathematical definitions, computational procedures, experimental protocols, statistical analyses, and falsifiable hypotheses for future research into the neural organization of consciousness. Software and reproducibility: The accompanying version-independent SGIT–TRC research repository contains reference implementations, frozen configurations, selected experimental results, and mathematical verification tools. GitHub: https://github.com/miroslavsvitek/SGIT-Theory-TRC Archived software (v1.0.1): https://doi.org/10.5281/zenodo.23287648 Document type: Scientific preprint. Author: Miroslav Svítek, Czech Technical University in Prague, Czech Republic. Status: Manuscript prepared for submission to Network Neuroscience.