The Flow–Constraint Theory of Consciousness: A Mathematical Framework for Optimal System Organization

This record introduces the Flow–Constraint Theory of Consciousness (FCTC), a mathematical and systems-theoretic framework that models consciousness as an emergent regime of optimal system organization, rather than as a by-product of activity, complexity, or information alone.

The theory proposes that conscious states arise when a system maintains a stable balance between energy or information flow (F) and structural constraint (L), operating near a critical “visibility peak.” Consciousness is formalized via a composite C-index:

C = Φ × V(F/L) × P(σ²)

where Φ represents system integration, V captures visibility arising from flow–constraint balance, and P represents robustness via homeostatic persistence around an optimal variance regime.

Using computational simulations, the framework demonstrates that biologically structured networks exhibit markedly higher C-index values and substantially greater resilience to perturbation than random networks under matched conditions. Distinct conscious and unconscious brain states (e.g., flow, dreamless sleep, anesthesia, seizure, psychedelic states) are interpreted as different failure modes or success regimes of the same underlying viability principle.

The theory reframes the traditional “hard problem” of consciousness by proposing that subjective feeling corresponds to the internal experience of successful stability navigation—the lived signal of a system actively maintaining itself within a narrow viable region of informational space.

This Zenodo record contains:

A formal technical paper detailing the theoretical framework, equations, simulations, and falsifiable predictions

A comprehensive appendix specifying implementation details, pseudocode, parameter sensitivity analyses, and reproducibility guidelines

The framework is intended as a viability and organization index, not as a standalone detector of moral status or subjective experience, and is designed to be testable, modular, and extensible across biological, artificial, and other complex systems.