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Our main result is that $L_n^f$ is a compactly central localisation.\n  A map $\\alpha: 1 \\to A$ in a presentably symmetric monoidal $\\infty$-category $\\mathscr{C}$ is central if there exists a homotopy $\\alpha \\otimes id_A \\simeq id_A \\otimes \\alpha: A \\to A \\otimes A$. 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Our main result is that $L_n^f$ is a compactly central localisation.\n  A map $\\alpha: 1 \\to A$ in a presentably symmetric monoidal $\\infty$-category $\\mathscr{C}$ is central if there exists a homotopy $\\alpha \\otimes id_A \\simeq id_A \\otimes \\alpha: A \\to A \\otimes A$. 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