Claims

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1964_01_01_graham: Graham (1964) determines exactly which pairs (t, alpha) with 0 < t < 1 and 1 < alpha < 2 give a complete sequence of floors of t alpha to the n, a region of area about 0.85, refuting Erdős's conjecture; refereed.

2025_09_08_van_doorn: Van Doorn's 2026 preprint settles, with Graham's results, every base at or above the golden ratio, classifies entire completeness for bases up to the cube root of five, and proves completeness regions below the golden ratio.

2026_03_09_sothanaphan: Nat Sothanaphan's note of March 2026, written with GPT-5.2 Thinking, sharpens van Doorn's infinite-area completeness region by a bounded amount and certifies further rectangles of pairs (alpha, t) as complete.

2026_06_10_cepadugato: Lean proofs in a fork of formal-conjectures, contributed under the account cepadugato in June 2026, that no pair with base above 2 or at most 1 is complete and that positive integer pairs are complete only for (1, 2).

2026_09_05_kitamura: Kenta Kitamura's unreviewed Lean theorem of September 2026 that at the square root of the golden ratio the floor sequence is complete for every positive coefficient, settling one base of Problem 349 under every reading.

2026_09_06_geneson: Jesse Geneson's 2026 note and preprint claim that at one Salem number in (6/5, 13/10) arbitrarily large t make every floor of t times its powers even, refuting the conjectured completeness for all t > 0 below the golden ratio.

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