The Gate Between Constraint and Identification

Abstract This paper develops a methodological account of bounded inference. It distinguishes generation, constraint, and identification, arguing that finite observation can constrain possible generators without uniquely identifying one. The boundary between strong constraint and unique identification is called the gate. The paper is presented as an epistemic companion to the identity–persistence forcing theorem: the forcing theorem asks what structure must exist for a persistence claim to be coherent, while this paper asks what bounded observers can infer about such structure from finite evidence. The central claim is not ontological closure but disciplined boundary-location. Recurrence permits persistence, persistence permits accumulation, accumulation permits constraint, and constraint permits invariant discovery, yet identification may remain gated. The paper illustrates this structure through induction, realism, free will, identity, verification, meaning, and scientific explanation while explicitly leaving determinism, final ontology, and metaphysical free will open. The result is a framework for locating where inference stops licensing stronger conclusions and for distinguishing what evidence requires from what it leaves unresolved.