Self-Certification of Representation Adequacy: Sequential Certification at Minimum Task Loss

A new arXiv paper (2608.02267v1) introduces a four-layer theory for self-certification of representation adequacy in agents that act on compressed histories. The static layer defines decision-theoretic adequacy via a Bayes-risk grouping identity and prices one-shot external verification using an exact total-variation threshold. The sequential layer frames certification as an optimal-stopping problem in terms of task loss, defining an environment-wise certification complexity constant through a covering linear program. The paper proves an information-task-loss lower bound for every delta-correct strategy and presents a Certification Track-and-Stop policy whose cost matches the bound asymptotically. This work addresses structural risks when representations alias histories with different optimal actions, potentially enabling agents to detect inadequacy from their own transcripts.