Information Set Emulation: Causal Certificates for AI Derived EHR Features

AI and large language models can recover clinically meaningful features from electronic health records (EHRs), but predictive usefulness does not establish admissibility for causal inference. We introduce information set emulation: an AI typed lift attaches source evidence, clinical and recording times, decision-time availability, representation version, proposed causal roles, and unresolved ambiguity to extracted features under a locked target trial. Causal certificates record auditable evidence for those roles. Features with unresolved downstream roles are routed to compatible reporting or separate analyses. Typed evidence defines an observational fiber of causal worlds consistent with the observed law. The locked scalar estimand maps this fiber to a compatible image whose squared Chebyshev radius equals the residual minimax mean squared error when the image is nonempty and compact. This classical identity provides a target-specific measure of information ambiguity. The contribution is its integration with a joint EHR observation map and an auditable certificate architecture. Under explicit exchangeability, positivity, and nuisance-consistency conditions, we give identification and cross-fitted augmented inverse probability weighted estimation, distinguishing empirical and population targets. An EHR compression-drift identity separates the roles of frame presence, treatment assignment, and outcome observation. Artificial simulations and a common-law finite-world example illustrate estimation failures and information-radius reduction. Synthetic Phase 0 notes demonstrate audit diagnostics; a separate role-specific analysis spread illustrates routing and is not an exact fiber radius. All experiments are synthetic. The framework specifies when reconstructed information can support a point claim and when compatible reporting is required.