When Can an Underspecified Language Agent Act? Certain-Action Verification via Outcome Invariance

Tool-using language agents must decide whether to act, clarify, or declare a request non-actionable under underspecification. Existing confidence and clarification methods focus on recovering a likely intent, but action safety depends on whether feasible interpretations induce different policy-relevant outcomes. We introduce CAVI, a contract-relative framework that represents interface-feasible task completions and certifies action only when all represented completions collapse to one outcome class. Otherwise, it returns outcome-distinguishing counterexamples or a machine-checkable non-actionability certificate. Under conservative completion coverage, faithful outcome abstraction, exact verification, and transaction-stable execution, CAVI certificates are sound for atomic or transaction-scoped actions. At the verifier level, across 120,000 requests in 12 domain-distribution cells, CAVI reaches the matched zero-false-action frontier while certifying 36.42% of requests; independent enumerative and symbolic implementations agree on all labels, and 1.2 million metamorphic checks produce no label failure. A frozen 2,160-call cross-domain parser confirmation yields 0 false actions and 0 false certificates among 533 certificates while certifying 24.68% of calls, and exposes high completion under-approximation and low clarification recall as the remaining parser boundary. We then test the same decision principle end-to-end: in a blind executable validation on held-out tasks in local state-mutating application sandboxes, CAVI operates as a consequential-action gate inside an LLM agent loop, reducing the false action rate to versus for direct execution while cutting unnecessary clarification to versus under conservative always-clarify interaction. Conservative completion coverage remains an important boundary; a mechanical semantic audit found one proposal–task mismatch among 83 CERTAIN_ACTION certificates, exposing proposal faithfulness as an additional agent-integration boundary. CAVI thus converts model-proposed task hypotheses into conditional, auditable action guarantees rather than relying on confidence alone.