White paper - Runtime Stability and Governance for Artificial Intelligence Systems- V1.0

Abstract The Law-E framework introduces a thermodynamic perspective on the observability and governance of artificial intelligence systems. Modern AI architectures such as large language models, multi-agent systems and automated decision pipelines may exhibit unstable behaviors during execution, including hallucinated outputs, informational drift, or cascading reasoning errors. Current mitigation mechanisms are generally reactive and operate after outputs are generated. The Law-E framework proposes an alternative approach by modeling AI systems as informational dynamical systems whose stability can be evaluated at runtime. The framework introduces a latent thermodynamic coherence variable G(x)G(x)G(x) describing the informational stability of an artificial intelligence system. Because this quantity cannot be directly measured, the framework defines an operational estimator called the Energy Stability Index (ESI). The ESI aggregates several runtime signals related to system behavior, including historical stability, relative energy efficiency, measurement quality and computational reliability. The index is defined as: ESI = 100 × (β₁S + β₂P + β₃Q + β₄C) where the coefficients satisfy Σβᵢ = 1 and ESI ∈ [0,100]. This formulation enables a stability interpretation compatible with dynamical systems analysis through the function: V(x) = 100 − ESI(x) which can be interpreted as a Lyapunov-like stability function for AI systems. A reference implementation is provided through the Neomundi sandbox environment, allowing experimental observation of runtime stability signals for AI inference sessions. Preliminary experiments performed using the TruthfulQA benchmark indicate promising results, with approximately 79.5% detection of informational instability correlated with incorrect or hallucinated responses. The Law-E framework aims to provide a foundation for runtime observability and thermodynamic governance of artificial intelligence systems. Description Artificial intelligence systems increasingly operate as complex distributed infrastructures integrating large language models, autonomous agents and multi-model pipelines. As these systems scale, ensuring stability and reliability during execution becomes a fundamental engineering challenge. Many current approaches to AI safety and governance rely on post-generation validation mechanisms such as guardrails, heuristic filters or reinforcement learning based alignment techniques. While effective in certain contexts, these approaches remain reactive and often operate after unstable system behaviors have already occurred. The Law-E framework proposes a complementary paradigm by interpreting artificial intelligence systems as informational dynamical systems whose stability can be evaluated during execution. The framework introduces a thermodynamic interpretation of informational processing in artificial intelligence systems. Within this interpretation, AI systems are characterized by a latent thermodynamic coherence variable G(x)G(x)G(x) representing the global informational stability of the system. Because this latent variable cannot be directly measured, the framework defines an operational estimator called the Energy Stability Index (ESI). The ESI aggregates several observable signals describing the energetic and informational behavior of the system, including historical stability of execution energy patterns, relative energy efficiency, quality of measurement and computational reliability. The index provides a normalized stability score bounded between 0 and 100. Higher values correspond to more stable informational regimes during system execution. The framework also introduces a stability function: V(x) = 100 − ESI(x) which allows the stability of AI systems to be analyzed using concepts derived from Lyapunov stability theory. In addition to the conceptual framework, a reference implementation has been developed in the form of an experimental sandbox environment. This implementation allows runtime signals to be collected and analyzed in order to observe stability dynamics during AI inference sessions. Preliminary experiments conducted using the TruthfulQA benchmark dataset show promising results in detecting informational instability correlated with hallucinated outputs. The Law-E framework is intended as a foundation for future research and engineering work on runtime observability, thermodynamic governance and stability regulation of artificial intelligence systems.