Informational Holonomy Curvature and Its Discrete–to–Continuous Convergence

We introduce an informational holonomy curvature associated with a state bundle over a Riemannian manifold and a family of channels acting on the fibres. In the continuous setting, we define an informational holonomy defect by transporting a reference state around small geodesic loops and measuring the deviation via an informational divergence, and we show that the resulting sectional-type curvature is determined by the curvature of the connection on the state bundle. On quasi-uniform sampling graphs endowed with discrete fibres, divergences and channels, we define a discrete informational holonomy curvature and prove a discrete-to-continuous convergence theorem under explicit sampling and consistency assumptions. In geometric Fisher-type models, the limit reduces, on spaces of constant curvature, to a constant multiple of the classical sectional curvature.