From neural propagation to conscious experience: A geometro-diffusion theory of consciousness.

Theories of consciousness frequently emphasize integration, differentiation, recurrent processing, or global availability, but the mathematical organization connecting neural propagation with subjective experience remains unclear. We introduce the Geometro-Diffusion Theory (GDT), in which diffusion-like dynamics on a structured substrate induces an intrinsic relational geometry. We introduce the Diffusion-Based Machine (DBM) as an operational model designed to distinguish information obtained from a single realized activity pattern from invariant information encoded across the family of possible dynamical responses. We show that independent diffusion realizations generate a Euclidean embedding whose Gram matrix is the diffusion kernel. This construction reveals metric relations, equivalence classes, symmetries, and globally organized routes that may remain inaccessible from an individual realization. To quantify this distinction, we define a partition gap comparing observational and geometric classifications and a normalized signature difference measuring their respective temporal differentiation. The central hypothesis is that conscious experience requires an intrinsic mechanism capable of accessing, integrating, and recursively using invariants of a sufficiently rich diffusion-induced geometry. Diffusion or geometry alone is therefore insufficient. We discuss how recurrent neural interactions, continuous activity, population integration, feedback, and plasticity could implement the required geometric access without explicit mathematical computation. The framework is summarized by six principles specifying the substrate, propagation dynamics, emergence and timescale of geometry, intrinsic decoding, and recursive integration. GDT provides operational quantities that can be examined using perturbational neural data across wakefulness, sleep, anesthesia, and disorders of consciousness.