When Sufficient Representations Fail under Deployment

Exact sufficiency on a current support does not guarantee sufficiency for the same target after actions selected through the representation. We call the missing property deployment closure. For every K ≥ 2, two minimum-cardinality K-state representations can agree on the certified support and induce the same deployment, while only one remains sufficient afterward. Repair changes the quantifier: one target-distinct collision refutes closure, whereas interface repair must resolve every such collision under the information actually available to the decision maker. In ABIDES, identical public books hide ownership distinctions that become consequential after a public-book-selected trade; a prospective 128-pair study yields a graded evidence–risk frontier, while reanalysis without pair identity shows that repairing designated pairs need not repair the retained interface. In a controlled learned-world-model assay, recurrent state retains a payload distinction that the native transition fails to use; a transition repair fixed before testing reduces real regret to 0.0044 of a q-only baseline on 128 fresh matched pairs, with history-erasure and carrier-transplant controls. Together, the results separate current certification, reached-support sufficiency, and access to decision-relevant repair information.