AbstractWe introduce a computable stability framework for nonlinearcontrolled systems of the formdx/dt = f(x) − k(x)∇ζ(x).The central contribution is a dimensionless LUKIN INDEX (Q)that quantifies the balance between nonlinear amplificationand linear contraction margin. A sharp critical threshold Q_c= 1 is established, separating guaranteed contraction fromloss of Lyapunov decrease. This yields an explicit contractionradiusr_c = 2ρ_k / (L_f + kL_ζ).Unlike classical contraction theory, which providesqualitative convergence conditions, the present frameworkyields a closed-form, computable contraction region explicitlyparameterized by control gain and local smoothness constants.The formulation is extended to state-dependent control k(x),global radial bounds, and stochastic perturbations, leading tothe stability conditionQ(x) + N(x) < 1. The result provides an operational tool for stabilitycertification and control design without solving systemdynamics.