Assertion–Deferral Control Under Fixed Semantic Verification Constraints

This paper develops a formal decision-theoretic framework for assertion–deferral control in autonomous systems operating under fixed semantic verification constraints.

Building on prior work that established the existence, measurability, and identifiability limits of uncertifiable input mass (UIM) under finite auditing resources, this paper addresses the remaining open question: how a system should act optimally when a nonzero fraction of deployment inputs cannot be externally certified.

Under an explicit non-recognizability assumption, the paper proves that uncertifiability is not merely a lower bound on achievable reliability but an equality constraint governing all implementable policies. The feasible policy space collapses from an oracle-level input selection problem to a one-dimensional rate-control frontier, where no internal strategy, retraining procedure, or confidence heuristic can improve certified performance at a fixed assertion rate unless the verification boundary itself is modified.

Key contributions include:

• A proof of the implementability gap, showing that boundary-induced non-recognizability eliminates input-level selectivity and reduces control to assertion rate selection.

• Derivation of rate-optimal assertion–deferral policies under both constrained and cost-based objectives.

• Extension to robust control when uncertifiable input mass is only interval-identified due to noisy or partial audits, yielding minimax-safe operating guarantees.

• A formal demonstration that reliability improvements which do not alter the semantic verification boundary are structurally illusory at deployment scale.

The results clarify the limits of internal optimization and recast reliability as an environmental and verification-access property rather than a purely learning-based one. The paper completes the grounding-limited reliability program’s analysis of optimal action, characterizing the full set of implementable assertion–deferral policies once grounding limits and audit uncertainty are taken as fixed, and motivates boundary-first system architectures in which expanding or restructuring verification resources is the primary lever for improving certifiable behavior.