Beyond Idle Compliance: The Claim–State Gap in Long-Horizon LLM Agents

An LLM agent may continue acting without progress, announce completion without a verified effect, produce a technically successful but unauthorized outcome, mistake locally completed subtasks for global closure, or preserve a success report after its evidentiary basis expires. These are distinct failure conditions even when fluent narrative, legitimate tool responses, and apparently successful component actions coexist. This conceptual paper develops an axiomatic claim–state account derived from the separation of operational regimes: intention, invocation, effect, independent observation, admissibility, authority, composition, and time. It formalizes a three-valued judgment of completion claims, proves bounded non-entailment and indistinguishability propositions, and derives five central archetypes—Loop of Death, Delusion of Done, Forbidden Success, Fractured Done, and Zombie Success—within a broader candidate taxonomy. Each archetype is assigned a failure condition, evidence discriminator, negative control, and defeater. A prospective research protocol specifies independent state oracles, evidence-matched conventional baselines, explicit abstention, temporal adjudication, and preregistered tests of prospective prediction. The manuscript reports no new LLM experiment and does not claim empirical prevalence, causal superiority, or an ontologically distinct Large Language Field. Its contribution is a falsifiable boundary-based research program for separating successful execution, warranted reporting, and legitimate closure across long-horizon agent trajectories.