Geometric Control Manifolds for Hyperbolic Self-Organizing Intelligence

We present an architectural specification resolving the Geometric Capacity Bottle-neck through precise geometric alignment between computational substrate and informationstructure. Neural dynamics within a Lorentzian hyperbolic manifold (Ln ) leverage constantnegative curvature for exponential volume growth (V ∝ eζr ). The Geometric ControlManifold (GCM) is defined as a differentiable manifold induced on the system’s statespace, characterized by joint optimization of Integration, Coherence, and Differentiation.The computational substrate consists of H-NCA on pentagrid tessellations coupled withH-AKOrN for temporal binding. Differentiable proxies (Persistence Landscapes) enableclosed-loop topological regularization.