Multilayer Informational Geometry of Mind: An Expansion of Recursive Informational Curvature

We propose a multilayer geometric model of consciousness based on Recursive Informational Curvature (RIC), in which awareness emerges from curvature dynamics across nested informational manifolds. The model comprises three principal layers: (i) a Fisher layer, encoding unconscious probabilistic inference; (ii) a Finsler layer, capturing direction-sensitive effort and goal-directed cognition; and (iii) a Hermitian layer, modeling recursive symbolic modulation and introspective phase dynamics. Each layer is formalized through a distinct metric and curvature function, and their coupling governs the informational evolution of conscious states.We derive a unifying scalar field, K(t)=α λ(t)-β ∇S(t), where λ(t) represents recursive gain and ∇S(t) the symbolic entropy gradient. Conscious access is predicted to emerge when K(t) exceeds a critical threshold, whereas collapse into unconscious or unstable states occurs when curvature falls below this bifurcation point. Simulations across all three layers reveal the geometric structure of attention, effort, and symbolic cycling, visualizing cognitive dynamics as phase trajectories over recursive curvature fields.We further present an illustrative case study of moral decision-making under cognitive conflict, demonstrating the model’s interpretive capacity. To test empirical feasibility, Appendix B implements a minimal simulation using synthetic EEG-like signals under low- and high-noise regimes. Results confirm that positive curvature corresponds to semantic closure and awareness, while negative curvature indicates collapse into unstable symbolic states. Together, these results suggest that RIC provides a coherent, mathematically grounded framework for unifying cognitive geometry, symbolic dynamics, and informational collapse.