Informational Stability: A Geometric Framework for Structured Information Over Time

This paper introduces Informational Stability, a geometric framework for measuring structured information in dynamical systems by comparing how nearby trajectories contract or expand over time. Building on prior work that defined informational curvature as a diagnostic of structure in observation space, this paper extends the framework to time-evolving systems. Local and global stability measures are defined over different temporal horizons, and a comparative scalar is introduced to distinguish persistent structure from short-term sensitivity. The framework applies to both continuous and discrete systems and provides implementable diagnostics for artificial intelligence, biological signals, and other complex dynamical processes.This is the second paper in a five-paper series. The stability scalar D(t) is analytically connected to the reflexive Fisher manifold in Paper 3 (Reflexivity: A Geometric Framework for Self-Referential Dynamics), where it is proven to be an exact projection of the manifold eigenvalue structure.