Claims

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1963_01_01_davenport_erdos: The 1963 theorem that the multiples of almost every real are uniformly distributed relative to a sequence with at most N^(2 - delta) terms below N; a partial positive case, containing every set of integers; refereed.

1969_01_01_schmidt: Schmidt's Theorem 1 of 1969: a real sequence with consecutive ratios tending to one along which the multiples of almost every real are not uniformly distributed, which disproves the problem.

2026_08_20_alexeev: A Lean theorem in Alexeev's repository, written by Codex and GPT-5.6 Sol, proves the problem for integer sequences, a case inside the Davenport–Erdős sparse case; not built or audited here.

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