arXiv:2609.06036v1 Announce Type: new
Abstract: Proposal-based controllers—learned policies, language-model planners, and other black-box \emph{generators}—are increasingly deployed behind runtime verification gates. We ask when the closed-loop safety guarantee decouples from the generator. The prevailing per-candidate certification pattern does not compose: under retry or best-of-$k$ selection a per-candidate false-admission level $\alpha$ can inflate to $1-(1-\alpha)^{k}$. Our main theorem shows that \emph{simultaneous setwise soundness}—certifying a set of admissible proposals containing no nonviable action—is necessary and sufficient for generator-independent \emph{admission soundness}, the worst case over all generators of executing a nonviable proposal equalling the probability of setwise failure; together with a design-time certificate and a no-bypass rule it is sufficient for \emph{contract safety}, with violation bound $\Gamma+\sum_t\varepsilon_t+\eta$ invariant under arbitrary, even adversarial, replacement of the generator. A second theorem bounds every admission mechanism under partial observation: for a fixed probing and admission policy, if two state hypotheses whose information laws lie within total-variation distance $\delta$ require different safe decisions, then $\abar+\beta+\delta\ge1$. A sequential risk ledger makes the guarantee implementable with time-uniform confidence tubes, and shows that deterministic admission computations concentrate all statistical risk in state estimation. Simplex-style runtime assurance and control-barrier-function filtering are recovered as degenerate cases.
Abstract: Proposal-based controllers—learned policies, language-model planners, and other black-box \emph{generators}—are increasingly deployed behind runtime verification gates. We ask when the closed-loop safety guarantee decouples from the generator. The prevailing per-candidate certification pattern does not compose: under retry or best-of-$k$ selection a per-candidate false-admission level $\alpha$ can inflate to $1-(1-\alpha)^{k}$. Our main theorem shows that \emph{simultaneous setwise soundness}—certifying a set of admissible proposals containing no nonviable action—is necessary and sufficient for generator-independent \emph{admission soundness}, the worst case over all generators of executing a nonviable proposal equalling the probability of setwise failure; together with a design-time certificate and a no-bypass rule it is sufficient for \emph{contract safety}, with violation bound $\Gamma+\sum_t\varepsilon_t+\eta$ invariant under arbitrary, even adversarial, replacement of the generator. A second theorem bounds every admission mechanism under partial observation: for a fixed probing and admission policy, if two state hypotheses whose information laws lie within total-variation distance $\delta$ require different safe decisions, then $\abar+\beta+\delta\ge1$. A sequential risk ledger makes the guarantee implementable with time-uniform confidence tubes, and shows that deterministic admission computations concentrate all statistical risk in state estimation. Simplex-style runtime assurance and control-barrier-function filtering are recovered as degenerate cases.
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