Safety Invariance in Stochastic AI Moderation Pipelines: A Physics-Informed Empirical Study

The deployment of Large Language Models (LLMs) in critical applications presents a fundamental tension between generative stochasticity and the requirement for deterministic safety guarantees. This work extends the physics-informed phenomenology of safety invariance—previously documented in physical control systems—to the domain of AI moderation pipelines. By framing semantic generation as a stochastic diffusion process, we analyze 2,735 samples within a prompt-filtering architecture to provide empirical evidence that safety emerges not merely as a statistical artifact, but as a dynamic forward invariant consistent with reflecting-boundary Fokker-Planck dynamics. This invariance is characterized by three robust phenomenological signatures: (1) strict distributional truncation with zero observed violations across all samples (Clopper-Pearson 95% upper bound: ), together with strong boundary-layer accumulation under crisis-level semantic pressure (242/560, 43.2%; ); (2) redirection dynamics consistent with Skorokhod-type reflection at the boundary; and (3) a scaling law in intervention intensity across 256 active correction events, revealing an effective repulsive response near the safety boundary. These findings support the hypothesis that forward-invariant safety manifolds are substrate-independent and provide a phenomenological basis for informing certification frameworks for stochastic AI systems through deterministic boundary enforcement.