Claims

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1946_01_01_erdos: Erdős proves that an additive function that never decreases from n to n plus one, or whose consecutive differences tend to zero, is a constant multiple of the logarithm; refereed, the case of an empty set of decreases.

2021_08_27_mangerel: Mangerel proves that a completely additive function with no outsized prime values, whose decreases up to X number at most X over a power of log X above two, is a constant multiple of the logarithm; refereed.

2026_09_08_gu: A 2026 Zenodo manuscript credited to GPT-6 Astra asserts that an additive function decreasing from n to n plus one only on a density-zero set is a nonnegative multiple of the logarithm; a full claim, pending review.

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