Beyond Outcome Attainment: Resolution-Based Education and the Certification–Assessment Resolution Gap in the Generative-AI Era

Generative artificial intelligence can produce polished academic artifacts while leaving uncertain which learner capabilities those artifacts support. We formalize the resulting decision problem as the Certification–Assessment Resolution Gap (CARG): an assessment protocol may leave certification-relevant learner worlds observationally equivalent even though the intended credential requires different decisions. A necessary condition for universally correct certification is therefore that each assessment-equivalence class be homogeneous with respect to the certification rule. Building on this condition, we formulate the scientific foundation of Resolution-Based Education (RBE) as a conservative extension of outcome-based education: existing performance evidence is reused, additional burden is zero whenever current evidence is already resolution-adequate, and otherwise a finite adaptive policy seeks the least-burdensome admissible evidence needed to resolve the remaining decision. We formalize Resolvable Capability Outcomes, distinguish one-step discriminating probes from complete Minimum Resolution-Restoring Perturbations, define positive resolved attainment and explicit AR/AU/RN/NA/Deferred states, and derive course- and programme-level metrics including RNR. Reproducible tests include deterministic and probabilistic mechanisms, a policy-tree case, 20,000 Monte Carlo episodes, and retrospective analysis of 32,593 Open University student-module records. Falsification controls reject a broad predictive-superiority claim. The surviving empirical result is narrower: under the declared retrospective proxy setup, selective adaptive acquisition reduces evidence burden while strong fixed-confidence controls remain competitive on risk.