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At the intersection of these paradigms lies the task of Open-Vocabulary Audio Event Grounding: predicting all time intervals of a target sound event described by an arbitrary natural language query. While this task is crucial for real-world audio understanding and LALM adaptation, it is bottlenecked by data scarcity. Few large-scale resources provide open-vocabulary onset/offset supervision, and manual temporal annotation is prohibitively expensive. To address this, we introduce Auto-AEG, a scalable pipeline that constructs such supervision by automatic data construction and model fine-tuning. 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