Informational Curvature: A Geometric Framework for Structured Information

This paper introduces a geometric framework for structured information using tools from information geometry and differential geometry. Informational states are represented as points on a statistical manifold induced by the Fisher information metric, and curvature on this manifold serves as a diagnostic of informational constraint, coherence, and regime transitions. A robust curvature proxy is introduced to avoid fragile higher-order derivative estimates, and conceptual visualizations illustrate how structured regions emerge in information space. The framework provides a mathematical foundation for analyzing structure in cognitive systems, neural signals, and artificial intelligence representations.This paper is the first in a five-paper series. The geometric framework introduced here is formalized in Paper 3 (Reflexivity: A Geometric Framework for Self-Referential Dynamics) where the self-consistency condition uniquely determines the manifold geometry and phase transition at τ* = √(3/2).