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We conduct a comprehensive empirical comparison between model and human reasoning across all 30 problems from AIME 2025, exhaustively annotating 10,247 reasoning steps into five functional categories: Analysis, Inference, Branch, Backtrace, and Reflection. We find a clear structural difference. Human solutions maintain a compact alternation between analysis and deduction, whereas DeepSeek-R1 frequently revisits intermediate results, performs shallow and often unnecessary verification, and loops through local checks without meaningful logical progress. We describe this as topological mimicry: reproducing the surface form of reasoning without its functional role. Despite this, we identify two signals of genuine reasoning. 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