The Structural Operational Closure Framework: A Substrate-Independent Topological Approach to Consciousness

Abstract

The explanatory gap between physical neural processes and subjective experience remains a primary hurdle in consciousness science. Here, we present the Structural Operational Closure Framework, a topological and information-theoretic account proposing that this gap is an observational artifact rather than an ontological divide. We formalize operational closure on a topologically non-factorable manifold M through three core axioms: dynamical attractor closure within neural networks, temporal scale decoupling (tau_int << tau_ext) characteristic of recurrent cortico-thalamic circuits, and bounded entropic self-representation. Mathematically, we demonstrate that first-person interiority is a necessary structural requirement for self-referential closed dynamics, rendering functionally identical non-conscious systems (philosophical zombies) physically impossible under these dynamics. We map core phenomenological properties directly to geometric features: perceptual unity corresponds to manifold non-factorability, while qualia privacy reflects operational boundary stability under external driving. Furthermore, we show that non-invasive third-person neural measurements inherent to external observer frames (Pi_O) project dynamics onto a lower-dimensional subspace, systematically destroying global phase coherence and generating an artificial observation gap (Delta_gap > 0). Finally, we define the Operational Closure Index Omega(S), providing a quantitative metric that accounts for why feedforward architectures lack subjective experience while establishing testable constraints for consciousness in both biological neural systems and synthetic architectures.