Claims

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2017_03_31_tsaturian: Every red-blue coloring of the plane has a red unit pair or a blue five-term progression with unit step, so the least avoiding length is at least 6.

2017_05_05_conlon_fox: Conlon and Fox's line corollary gives a red-blue coloring of the plane with no red unit pair and no blue unit progression of 10^10 terms, so the least avoiding length is at most 10^10.

2026_06_15_currier_mody_xie_zhang: Theorem 1.2 of the preprint gives a red-blue coloring of the plane with no red unit pair and no blue unit progression of 6330 terms, so the least avoiding length is at most 6330.

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