The Scale-Kinetic Hierarchical Transfer Function (SKHTF): A Geometrically Normalized Stability Architecture for Nonlinear Systems

This paper presents the Scale-Kinetic Hierarchical Transfer Function (SKHTF), a geometrically normalized prognostic architecture for nonlinear systems. The framework enforces dimensional invariance by embedding normalized stress and historical accumulation variables into a bounded semicircular domain termed the Semicircle Kinetic Phase Space ($\mathbf{KPS}_{\frac{1}{2}}$). Within this geometry, a symmetric angular partition $\theta_c = \pi/8$ emerges as a topology-preserving stability envelope. By strictly separating feature extraction, geometric constraint, and kinetic time-scale estimation (via the $R^*$ decoupling framework), the SKHTF transitions prognostic modeling from empirical thresholding toward a structured geometric stability architecture. This version (V2) formalizes the Lyapunov-consistent stability conditions and establishes the $\pi/8$ boundary as a geometric invariant of the normalized embedding.