Claims

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1991_12_01_furstenberg_katznelson: The density Hales–Jewett theorem of Furstenberg and Katznelson (1991) puts an axis-parallel square in every dense enough subset of a large grid, answering the question yes without a bound; accepted, refereed and credited.

2004_03_01_solymosi: Theorem 1.1 of Solymosi (2004) proves that every dense enough subset of a large grid contains an axis-parallel square, with a bound at best of tower type, answering the question yes; accepted, refereed and credited.

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