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While existing compression methods are effective in specific settings, most are either weakly query-aware or apply a fixed compression policy across frames, proving suboptimal when visual evidence is unevenly distributed over time. To address this, we present VideoRouter, a query-adaptive dual-router framework built on InternVL for budgeted evidence allocation. The Semantic Router predicts the dominant allocation policy, choosing between broad temporal coverage and adaptive high-resolution preservation, while the Image Router uses early LLM layers to score frame relevance. This enables aggressive compression on less relevant frames while preserving detail on critical evidence frames. 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