Empirical evidence for a forward-invariant safety law across diverse control domains

We report the observation of a macroscopic safety invariant in learning-based control systems, analogous to conservation laws in physics. Across five heterogeneous domainsspanning thermal, electrical, physiological, and financial systems-and timescales differing by six orders of magnitude, we document a universal empirical regularity: the strict conservation of the safety indicator. This phenomenon is characterized by three robust signatures: complete distributional truncation at safety boundaries, redirection dynamics resembling reflecting boundary conditions, and a systematic scaling of intervention intensity near the boundary. Prospective validation in live financial markets confirms the causal nature of this invariant, demonstrating that the safety manifold functions not merely as a filter, but as a hard physical barrier. These findings provide phenomenological evidence for forward-invariant manifolds in constrained learning systems, offering a new perspective for the certification of safety-critical autonomous agents.