Topological Theory of Cognitive States: Spectral Signatures of Information Processing Regimes

We propose a formal theoretical framework where cognitive states are defined not by their semantic content, but by the topological regime of the underlying dynamic network. Building on the Information Saturation Postulate (Iflow ≤ Cmax), we demonstrate that phenomenology is a direct consequence of spectral topology. We identify distinct spectral signatures for healthy criticality, entropic trapping (anxiety), and modular fragmentation (dissociation). The quantitative description of cognitive states remains an open problem in complex systems science. While neuroscience has successfully mapped local functions, the global dynamical regimes lack a unified mathematical definition. We propose a shift from semantic description to topological characterization. Key Findings & Spectral Signatures: We employ Spectral Graph Theory to analyze the system (eigenvalues of the Laplacian). Our computational toy models confirm distinct physical signatures for proposed biotypes: Healthy State (Criticality): High connectivity (λ2 ~ 0.36), Broad/Small-World spectral profile. Anxiety (Entropic Trap): Low connectivity (λ2 ~ 0.12), Compressed/Red noise profile. Maintains global connectivity but traps energy in local loops. Dissociation (Fragmentation): λ2 ~ 0, Disconnected Peaks. Fragmentation of the giant component. Mania (Hypersynchrony): Very High λ2 (> 1.0), White Noise profile. Signal diffuses too fast to form structure. Dementia (Decay): Modeled as random edge pruning leading to topological phase transition. Conclusion: The Topological Theory of Cognitive States provides a falsifiable, physics-based framework for psychiatry. It suggests that treatment must target the geometry of the mind (e.g., Energy Injection for Traps, Damping for Mania) rather than just its chemistry.