The Geometric Control Manifold Hypothesis: A Framework Induced by Informational Dynamics

We propose that functional coherence can be modeled as a geometric structure—a “Geometric Control Manifold” (GCM, denoted Ψ)—whose shape is determined by neural information dynamics. Points in Ψ represent distinct representational states, and distances reflect geometric similarity. The geometry emerges from three neural properties: information integration (I), large-scale coherence (Γ), and differentiation (∆). We provide: (1) formal mathematical definitions with theoretical justification for the neural-geometric projection, (2) operational methods to reconstruct Ψ from brain data with rigorous validation protocols, (3) predictions differing from existing theories (IIT, GNWT, Predictive Processing), and (4) concrete falsification criteria. This framework offers testable, quantitative hypotheses about structural organization without making ontological claims.