The Stateful Isolation Law: Formal Contamination Bounds for Multi-Principal AI Systems

Executive Summary: Modern AI inference transforms Large Language Models (LLMs) into probabilistic databases, creating a new class of stateful security vulnerabilities that classical isolation frameworks (Bell-LaPadula, Noninterference) cannot address.The Threat Landscape: This document catalogs 25+ demonstrated attacks, including:PROMPTPEEK: 99% prompt reconstruction via timing side-channels.LeftoverLocals: 181 MB/query data leakage via GPU memory residue.Agentic Confused Deputy: 82.4% inter-agent compromise rates.The Solution: The Stateful Isolation Law (SIL) A unified formal framework comprising:The General Principle: A contamination functional parameterized by Rényi divergence.Six Enforceable Clauses: Covering KV-drift, Attention Spatial Isolation, Timing Channels, and Hardware Hygiene.Compliance Tiers: A graduated framework mapping Tier 0 (Development) through Tier 3 (Sovereign) directly to GDPR, EU AI Act, and FedRAMP requirements.