Claims

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1989_03_01_hegyvari: Hegyvári (1989) proves that the two doubling floor sequences form a complete sequence when one coefficient is a dyadic rational and the other is not, answering the first question yes in that case; refereed.

2026_09_05_kitamura: Kitamura's unreviewed Lean proof of September 2026 that at the square root of the golden ratio one floor sequence is already complete, proving the catalog's existential form of the second question of Problem 354; disputed.

2026_09_11_jenw1n: Lean 4 proof credited to the solver handle JenW1N, certified and paid by the bounty site Conjectures.io in September 2026, that the doubling floors of two reals with irrational ratio form a complete sequence; the first question.

2026_09_13_yu_chen: Yu and Chen's unrefereed manuscript of September 2026, with its own Lean formalization, claims that the nonzero dyadic floors of two reals with irrational ratio stay complete after any finite deletion; unreviewed.

2026_09_20_geneson: Geneson's unrefereed preprint of September 2026 gives a Salem base between 6/5 and 13/10 and two coefficients with irrational ratio whose interleaved floors are all even, so not complete; a no to the every-base second question.

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