Lyapunov Stability Envelopes for Speculative Decoding: Formalizing Rejection-Rate Compliance

Executive Summary: This technical specification applies Lyapunov stability analysis to the operational instability of speculative decoding in Large Language Models. It introduces the Speculative-Decoding Stability Envelope, a formal control barrier defined by the differential inequality.The Solution: Unlike existing heuristics, this framework treats the token rejection rate as a dynamical state variable. It guarantees:Bounded Recovery Time: Explicit exponential convergence of rejection cascades (proving the system recovers from instability within t∗ tokens).Side-Channel Mitigation: Enforces behavioral uniformity to defeat >90% accuracy timing fingerprinting attacks.Regulatory Robustness: Provides the mathematical "robustness" proof required by EU AI Act Article 15 and Basel / SR 11-7 for financial determinism.Verification Release: This document includes the complete derivation of the Gronwall bound, the Recovery Time Corollary, and reference implementation parameters for production serving systems