Invariance of Interceptor Assignment Latency in Distributed Missile Defense via Hilbert–Krylov Decomposition | IJCT Volume 13 – Issue 2 | IJCT-V13I2P25

Modern missile defense systems face a critical scalability barrier: optimal interceptor– threat assignment degrades catastrophically under saturation attack. State-of-the-art meth- ods based on mixed-integer linear programming or auction-style assignment exhibit super- linear time complexity in the number of threats, rendering them unsuitable for hypersonic or swarm environments. We introduce a deterministic framework for Dynamic Kinetic Interdiction using Hilbert– Krylov Decomposition (HKD), treating the distributed defense grid as a modular space–time residue field. We prove that interceptor assignment latency is invariant to threat count, pro- vided a fixed lane-width coverage condition is satisfied. Empirical simulations demonstrate constant-time assignment behavior contrasted with the quadratic or cubic slowdown of con- ventional approaches. This result establishes a theoretical and practical foundation for real-time counter-battery and counter-hypersonic defense systems capable of operating under saturation without loss of responsiveness.