Fixed Points III: Disturbance–Damping Balance and Stability

Corrected fourth edition. This paper develops disturbance-damping estimates on the joint noncoherent modal spectrum inherited from Fixed Points I-II. It separates deterministic forcing amplitude from stochastic noise power, proves input-to-state and second-moment floors under positive modal damping, restricts Gaussian invariant-law claims to exact Ornstein-Uhlenbeck dynamics, and states the enhanced invariance-principle and rough-path hypotheses required for deterministic homogenization. Scope boundary. The estimates concern the noncoherent Q sector unless coherent forcing is supplied separately. Nonlinear invariant laws, physical stochastic interpretation, and homogenized dynamics beyond the declared functional-CLT data are not derived.