The Kinetic Singularity: Computational Saturation Points in Unregulated Autonomous Swarms

Current autonomous fleet protocols rely on decentralized “Sense and Avoid” (SAA) logic. While effective at low density, SAA scales with quadratic complexity (O(n²)). We present a theoretical model defining the “Kinetic Singularity”—a critical density threshold where the computational energy required for collision avoidance exceeds the energy available for propulsion. We argue that infinite-space assumptions embedded in legacy navigation stacks will lead to systemic gridlock in bounded urban airspaces. To maintain linear scaling (O(n)), we propose a shift from reactive avoidance to deterministic “Kinetic Scarcity” protocols. This short paper defines the "Kinetic Singularity" threshold where computational energy demands for collision avoidance paralyze autonomous drone swarms, forcing a halt cascade. It includes a simple energy-balance proof, a numerical example (N=1,000 agents → >120 ms compute latency vs. 50 ms physical reaction window), and a call for pre-allocated, deterministic protocols to restore linear scaling and prevent energy starvation in high-density operations.