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

In the big-world regime, agents cannot be universally capable and their ability is inevitably specialized across a world model in pieces. Consequently, standard uniform guarantees fail to distinguish between the understanding of critical bottlenecks and irrelevant failures. We first formalize this limitation by proving that general agents are not universal, rendering standard worst-case analysis uninformative. To overcome this, we introduce structural certification, a transition-local framework that maps bounded goal-conditioned performance to entry-wise guarantees on the agent's internal world model. Our main contribution is constructive. We provide algorithms that filter specific transitions using deep compositional goals and prove that a general agent on these goals has a structural world model with a $\mathcal{O}(1/n) + \mathcal{O}(δ)$ error bound. Conversely, this bound is tight in the small-$δ$ regime, whose existence is explicitly guaranteed by our certification. These results enable the certifiable deployment of general agents by localizing the specific transitions where long-horizon planning is reliable.

Self-improving agents accumulate capability by repeatedly rewriting procedural policies, controllers, or heuristic rules. They typically rely on self-authored tests or metrics to decide whether to accept subsequent edits. The agent controls both the optimized object and its verifier. As a result, self-assigned scores can remain near perfect while real deployment performance degrades or stays low. We study this problem through the verifier--deployment gap. This gap refers to the discrepancy between an agent's self-authored verification signal and a sealed deployment evaluation that the agent cannot observe or access. We ask how self-authored verification fails under iterative policy-and-test rewriting, how the failure changes with capability, and how little exogenous trust is sufficient to prevent real regressions from being deployed. To address this problem, we introduce a Sealed Exogenous Acceptance Loop (SEAL). SEAL retains self-authored tests but compares each candidate with the incumbent through a fixed harness-side audit. The agent cannot author or inspect the audit, receives only accept/reject, and the whole incumbent state is retained after a clear regression. Our experiments show that this problem often appears in heuristic learning settings. These settings require trial-and-error discovery of the target objective. We further find that failures of self-written verification are stratified by capability. Weaker agents tend to damage previously acquired strategies behind easy self-tests. Stronger agents are more stable, but they still mismeasure the deployment distribution. Standard self-written constraints do not reliably close this gap. In contrast, SEAL outperforms unprotected baselines across six models and three random seeds. Reliable self-improvement need not abandon self-verification, but it requires at least one deployment-acceptance signal outside the agent's control.

Self-evolving agents violate the assumption behind most learning-theoretic guarantees: the data, evaluator, components, and hypothesis space are produced by the policy being updated. We present \textbf{SEA}, an architecture that confines self-modification to a small steering adapter and a versioned harness around a \emph{frozen} base model and admits each modification only through an anytime-valid gate that emits an auditable certificate against a fixed error budget. Five loop controllers compose published guarantees; because such gates can only \emph{select} among behaviors the frozen base already produces, five verifier-in-the-loop mechanisms -- best-of-$N$, micro-step search, self-authored reproduction oracles, search-layer control, and self-repair -- supply the dense, grader-free signal the gates require, computed from the issue text alone. On a $52$-instance SWE-bench Verified subset across four base models, base capability is the dominant, confound-free effect, and on two strong base models a deliberate no-op-composite control isolates the suite's contribution at $+4$ and $+5$ (\textsc{Glm}~5.2 $24\to28$; \textsc{Gpt} $29\to34$, the $65\%$ best), with event logs confirming that its mechanisms fire and prevent regressions. Results are single-run on expensive evaluations; confirming run-to-run variance and adapting the per-task algorithm mix are future work.