GAP-3 Operationalization: Structural Inertia and Inertial Shadowing in Information-Dynamic Theory

This work operationalizes the structural inertia framework of Information-Dynamic Theory (IDT) and provides a computational program for testing the GAP-3 hypothesis. The paper introduces a matrix formulation based on the generalized eigenvalue problem Hv = λGv where H is the Hessian of the information potential and G is the Fisher–Rao metric. The resulting structural inertia measure M(ω) is shown to generate inertial shadowing effects, where relaxation time ratios τslow / τfast are controlled by the spectral structure of the operator G⁻¹H. A series of 25 model experiments (2D and 3D parameter spaces) demonstrates the stability of inertial shadowing and the emergence of large structural inertia values. The results provide a concrete operational framework for testing Information-Dynamic Theory in physical systems such as spin-torque nano-oscillators and magnonic structures.