The Boundary of Knowledge: A Framework for Learning the Limits of Identifiability in Artificial Intelligence Inference

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Predictive systems are typically trained to produce an answer for every query, even when the available evidence is compatible with more than one true state of the world. Existing safeguards against this failure mode largely act at the level of a single model's output distribution: calibration, selective prediction, and conformal prediction all summarize uncertainty as a scalar or a set derived from one fitted model, rather than asking whether the evidence could, in principle, ever determine the target. Separately, the causal-inference literature has long formalized identifiability—whether a query is a well-defined function of the available distribution—and has recently begun to study which additional experiments would tighten partial-identification bounds. These two literatures have developed largely independently, and neither, to the best of our knowledge, packages the result as an explicit, three-way, auditable classification (identifiable / conditionally identifiable / non-identifiable) with a machine-checkable ambiguity certificate that a downstream system can act on. We formalize this problem, introduce definitions that separate structural non-identifiability from model uncertainty, data uncertainty, and computational difficulty, and propose the Identifiability Boundary Framework (IBF): a fourteen-module architecture that represents competing explanations of the evidence as explicit “worlds,” certifies when two such worlds are observationally indistinguishable yet target-divergent, selects the minimum-cost additional observation or intervention that would separate them, and re-evaluates the boundary after acquisition. We give a formal problem statement, precise definitions, a minimum-information acquisition objective, and a full algorithm. We position the contribution carefully against the closest prior work—in particular recent work on ex-ante experiment selection for partial causal-effect identification—and are explicit that the individual mechanisms are not new in isolation; the contribution is a general, cross-domain formalization, an auditable certificate object, a sequential re-evaluation loop, and an evaluation protocol spanning causal, generative, and dynamical-system testbeds. We report a complete experimental design, baseline suite, metric set, and ablation plan; no results are claimed, and all reported numbers in this paper are explicitly marked as illustrative templates for the expected reporting format, not experimental findings.