Admissibility Curvature A Structural Measure of Stability Shape in Constraint Space

This paper introduces Admissibility Curvature within the Paton System as a structural measure of how stability changes across constraint space. Building on the Admissibility Field and Viability Gradient the framework defines curvature as a second order structural property capturing how directional change in admissibility evolves across system states. This enables classification of stabilising basin regions neutral transition zones and destabilising ridge or collapse regions. The approach provides a domain independent geometric interpretation of system behaviour extending stability analysis beyond first order measures without modifying underlying governing equations.