Informational Constraint Framework: A Riemannian Geometry of Constrained Informational States, Activation Thresholds, and Relaxation Dynamics

This paper introduces the Informational Constraint Framework (ICF), a differential‑geometric formalism for modeling constrained informational systems with activation thresholds, saturation boundaries, and relaxation dynamics. The ICF treats the space of admissible informational states as a constrained Riemannian manifold equipped with an induced metric, a constraint potential, and a relaxation vector field. Five governing equations define the evolution, activation, saturation, and geometric structure of the system. Ten geometric constructions visualize the topology and dynamics of the constraint manifold, including the constraint surface, activation ladder, cross‑sections, saturation boundary, relaxation pathway, rank‑6 horizon, induced metric, ΛFC map, and global relaxation manifold. Numerical integration of the relaxation flow and saturation boundary condition yields a three‑phase diagram distinguishing sub‑threshold, active, and saturated regimes.This record is the primary research article and is supplemented by a companion data paper containing all executable Python code used to generate the figures and numerical results.10.5281/zenodo.20634077