Structural Inertia and Relaxation Geometry in Information-Dynamic Theory

We introduce structural inertia m_IDT(u) = (uᵀGu)/(uᵀHu) for stable regimes of the Information-Dynamic Theory (IDT) gradient flow dω/dτ = −G⁻¹∇Φ. We prove that structural inertia equals the inverse relaxation time along eigenmodes of the linearized dynamics. The resulting spectrum characterizes the relaxation geometry of regimes on Fisher-metric manifolds. An explicit Gaussian example demonstrates how non-flat Fisher geometry modifies the relaxation spectrum relative to standard Hessian analysis. Structural inertia is proposed as a geometric invariant describing regime stability in the IDT framework.