Networked Information Manifolds, Entropic Transport Curvature, and Spectral Phase Transitions in the Information Manifold Model

We extend the Information Manifold Model (IMM) from single-manifold projection dynamics to networks of coupled information manifolds. Projection-induced entropy is generalized to a vector-valued structure derived from a global operator decomposition theorem. We define entropic transport curvature on manifold networks and show that structural phase transitions correspond to changes in the spectral inertia of the signed Laplacian. Analytical examples and curvature-coupled spectral evolution demonstrate entropy-driven topological bifurcation under bounded dynamics. Under small-divergence symmetry conditions, IMM curvature converges to Ollivier–Ricci curvature, establishing compatibility with discrete geometric frameworks.