K=1 as a Structural Entropy Attractor: Curvature-Based Stability and Predictive Theory

This paper redefines entropy dynamics by characterizing K = 1 as a structural attractor within a negative curvature plateau. We derive a curvature-based predictive model for the entropy-maximizing exponent Kmax(ǫ) under kernel perturbations, replacing empirical fits. Key findings include: K = 1 lies in a robust negative curvature plateau in finite-support log2 entropy; Plateau width collapses under asymmetric perturbations; A curvature-based model eliminates empirical parameters; The curvature surface ∂3H ∂K∂ǫ2 generalizes maxima to stable entropy basins. This curvature-driven approach reframes entropy modeling for robust prediction in AI, neu- ral dynamics, and complex systems.