Claims

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1999_06_14_katz_tao: Katz and Tao's sums-differences bound N^(2-1/6) gives, through an elementary embedding, at most n^(11/6) common differences of three-term progressions in a set of n integers.

2014_04_14_lemm: Lemm's counterexample to the sums-differences statement with exponent above 1.77898 gives, through an elementary embedding, sets with more than n^1.77898 common differences, so O(n^(3/2)) does not always suffice.

2026_05_28_firsching: A self-contained Lean 4 proof in Moritz Firsching's fork of formal-conjectures that no constant C bounds the number of common differences by C n^(3/2), answering the second question no; claimed.

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