Beyond Experimental Design: Empirical Reach and the Minimum-Cost Expansion of Scientific Observability

Modern experimental design asks which admissible experiment is most informative, but this question can be ill-posed when the current experimental repertoire itself collapses worlds that matter. We develop Empirical Reach, a framework for detecting this failure and for identifying the minimum-cost admissible expansion of scientific observability. Two possible worlds are empirically equivalent when every experiment constructible from the current repertoire induces the same response law; they are consequentially discordant when a target outcome differs despite that equivalence. We prove a closure-obstruction result: no adaptive policy restricted to the existing experimental closure can distinguish such worlds, regardless of computation, repetition, or decision rule. We then define reliable evidence cost using finite-sample discrimination bounds and show that the cheapest measurement can differ sharply from the cheapest experiment that establishes a consequential distinction. A reproducible software artifact implements empirical partitions, Blackwell controls, information-gain baselines, exact minimum-cost witness search, finite-sample costs, compositional experiment genesis, and continuous probe synthesis. In a controlled benchmark, supplied-model information gain can be maximal while consequential ambiguity remains unchanged; a new interaction with zero information about the supplied model label can eliminate that ambiguity. The contribution is deliberately bounded: finite candidate selection reduces to classical test-cover structure, and probe synthesis is defined relative to an explicit admissible interaction model rather than assumption-free invention. The framework therefore targets a different question from ordinary optimal experimental design: when is science optimizing experiments inside the wrong empirical alphabet?