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A central question is how such a system should route among specialists when execution does not simply succeed or fail, but fails in qualitatively different ways. Existing tool-augmented and multi-agent LLM systems typically leave this routing decision implicit in language generation, making recovery ad hoc, difficult to interpret, and hard to optimize. This paper presents STAR (Spatio-Temporal Agent Router), a failure-aware routing framework that externalizes inter-agent control as a state-conditioned transition policy over the current agent, task type, and typed execution status. At the center of STARis an agent routing matrix that combines expert-specified nominal routes with recovery transitions learned from execution traces. 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