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Visual token pruning offers a natural solution, yet existing methods are imperfect: attention-based criteria tend to retain redundant tokens, while diversity-based criteria are often agnostic to user instructions. Even methods that combine multiple criteria still lack a principled formulation of the intrinsic objective of token pruning. In this paper, we revisit visual token pruning from a first-principles perspective and formulate it as constructing Token Optimal Preservation Sets. Through a top-down information-theoretic analysis, we identify three fundamental principles for effective token selection: Task Relevance, Information Coverage, and Semantic Diversity. 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