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

This paper redefines entropy dynamics by characterizing K = 1 as a struc-tural attractor within a negative curvature plateau. We derive a curvature-basedpredictive model for the entropy-maximizing exponent Kmax(ϵ) under kernel per-turbations, replacing empirical fits. Key findings include:• K = 1 lies in a robust negative curvature plateau under ideal symmetrickernels;• However, this plateau collapses rapidly under asymmetric or sufficiently strongsymmetric perturbations;• A curvature-based model predicts attractor drift Kmax(ϵ) beyond K = 1;• The third-order curvature surface ∂3H∂K∂ϵ2 generalizes local maxima into movingentropy basins.This curvature-driven approach reframes entropy modeling for robust prediction inAI, neural dynamics, and complex systems.