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The paper introduces RouteFM, a foundation model for LLM routing that learns reusable routing capabilities via episodic pretraining across heterogeneous environments, allowing a frozen router to adapt to new domains, modalities, and candidate pools through behavioral context alone. RouteFM outperforms the strongest baseline by 2.23 quality points on MMR-Bench with only eight observations per candidate, supporting a 'pretrain once, route anywhere' paradigm.