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This improves the best known lower bound of $(1/4+o(1))k^2/\\log k$ due, independently, to Bohman and Keevash, and Fiz Pontiveros, Griffiths and Morris, resulting from their celebrated analysis of the triangle-free process. 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This improves the best known lower bound of $(1/4+o(1))k^2/\\log k$ due, independently, to Bohman and Keevash, and Fiz Pontiveros, Griffiths and Morris, resulting from their celebrated analysis of the triangle-free process. 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