Discoveries Have Lifetimes: E-Values for Autonomous Discovery in Adversarial Environments

Open-ended discovery systems search for unexpected structure, generate candidate proposals and gather evidence, instead of only answering questions or validating supplied hypotheses. However, in real-world adversarial environments, discoveries have lifetimes. A fraud strategy emerges, becomes detectable, triggers an intervention, and then disappears. The relevant unit is therefore not ``$H$ is true,'' but ``$H$ describes the world during this specific time interval.'' To address that, we propose a simple framework: a generator proposes candidate regimes, an e-process certifies that a proposed regime is currently present, and an e-detector detects when it subsequently ceases to be current.