This paper presents a formal control-theoretic analysis of recursively adaptive autonomous military systems operating under stochastic disturbance. It introduces the Recursive Strike Problem (RSP): the structural condition under which recursive policy reinforcement in delegated lethal architectures remains mean-square bounded.

Autonomous strike systems increasingly incorporate adaptive policy updates, reinforcement mechanisms, distributed coordination, and time-varying supervisory modulation. When recursive amplification exceeds corrective authority, escalation instability becomes structurally possible even if individual subsystems satisfy local safety constraints.

Using an Itô–Lyapunov framework, the paper derives a sufficient condition for mean-square ultimate boundedness of the internal policy state. The resulting dimensionless invariant — the Effective Policy Restraint (EPR) ratio — formalizes the dominance of corrective authority over recursive amplification. The analysis applies under explicit sector bounds, linear growth conditions, and uniformly bounded diffusion.

The result is structural rather than normative. It does not address ethical alignment, legal compliance, or strategic doctrine. It establishes a mathematically explicit escalation stability condition for recursively adaptive autonomous weapons architectures.

Simulation studies across three nonlinear system families illustrate empirical boundedness transitions while preserving the distinction between analytical sufficiency and model-specific behavior.

The work contributes a falsifiable structural invariant for stability in delegated lethal autonomy systems under bounded recursive dynamics.