Recovery Dominance A Lyapunov Framework for Dynamic Nuclear Stability

Nuclear deterrence can be disturbed without failing, and nuclear capabilities can survive while the strategic system around them becomes dynamically unstable. This article treats that distinction as a stability problem. It models positive strategic coordinates, a normalized cross-escalation proxy, and a third-order crisis-momentum subsystem, then constructs a composite Lyapunov function whose decrease is a local certificate that disturbances are being absorbed rather than reproduced. The central claim is conditional: the modeled system is locally restoring when restorative production and crisis damping dominate the rate at which disturbance replenishes escalation pressure. That property is recovery dominance. It is not a theory of political intent and not a probability of nuclear use. It is a sign condition on an explicitly defined function. A worked illustration with declared parameters makes the condition visible. The same initial state remains inside the certificate under a short, dominated shock with adequate damping; stores oscillatory energy under weak damping; and leaves the certified region for as long as forcing exceeds restoration. Decaying warning-ambiguity forcing traces a certificate boundary in forcing memory versus damping. A discrete positivity-preserving correction, fired early or late, moves the peak of the same trajectory. The composite weight and the failure threshold are declared, not fitted.