Epistemic Interface Autogenesis in Controlled Open Worlds

This paper presents a formal framework for evaluating when an embedded system appears to generate a new epistemic interface: an executable mechanism for obtaining observations, issuing requests, interpreting records, testing claims, or invoking protected services. Instead of treating novelty or autonomy as a single score, the framework separates four questions: what the interface makes physically executable; whether the same operational behavior can be generated from inherited components and services; whether observed improvements are caused by deployment; and what remains unresolved because models, construction paths, channels, or interventions are not covered. The theory represents interfaces as stateful stochastic protocols on standard Borel spaces, with separate stopping times for decision and physical closure. Requests, delivered actions, physical effects, recovery processes, and lifecycle resources are kept distinct. A physical causal compiler is defined as a model-blind online transducer that preserves physical strategic laws and composes systems only through declared exposed boundary states. Its certificates report physical marginals, protected-action and task errors, plan and model coverage, lifecycle resource refinement, and a joint audit probability guarantee. Inherited capability is defined through the denotation of complete feasible construction graphs under a frozen context that specifies available models, services, horizons, resource rules, operational equivalence, and assessment procedures. The paper distinguishes exact semantic construction, operational reproducibility, metric approximation, and robust separation. Its principal results include a boundary-exposed compiler gluing theorem, a set-wise information–actuation obstruction, and a partial-identification result showing what incomplete construction coverage can and cannot establish. The framework also keeps provenance, source-replacement effects, architecture capability, fixed-policy deployment effects, recursive policy effects, actor equivariance, qualification, eligibility, and authority as separate certificate fields. Finite examples show how delayed information, hidden private state, premature stopping, graph sharing, metric mismatch, and incomplete coverage can create misleading claims. The intended output is a typed certificate, a refutation, or explicit evidence debt—not an intrinsic autonomy label. The framework is relevant to generated research interfaces, robotic laboratories, monitored services, and other embedded systems in which timing, physical delivery, resource use, and evidence boundaries matter.