The Recursive Damping Law: Stabilizing Recursive Self-Improvement in Adaptive AI Systems

This paper introduces the Recursive Damping Law (RDL), a formal stability condition for recursive self-improving AI systems. Framed through control-theoretic analysis, the law defines a dimensionless damping ratio (ζᵣ) that governs whether recursive optimization remains bounded or diverges. The paper derives a conservative stability threshold (ζᵣ ≥ 0.25) and validates it across 11,520 simulated system-years, 1,000,000 Monte Carlo configurations, and a Llama-3 auto-distillation prototype. Rather than treating recursive self-improvement as a speculative existential risk, this work reframes it as a measurable dynamical regime with computable stability margins. RDL v0.1 is released as an open working paper to invite replication, stress-testing, and formal critique.