Claims

../

1964_01_01_roth: Roth's 1964 theorem: a set of integers up to N with density strictly between 0 and 1 has a progression of difference at most N^{1/2} with discrepancy of order N^{1/4}; refereed, Acta Arith. 9 (1964), 257-260.

1966_01_01_cantor_erdos_schreiber_straus: Erdős's 1966 report that Cantor, Schreiber, Straus and he built a sign function with bounded partial sums along every single arithmetic progression, the bound L(d) < c^d d!; a journal publication, Mat. Lapok 17.

2017_05_30_beck: Beck's 2017 chapter proves a plus-minus-one coloring of the integers whose partial sums along every arithmetic progression of common difference d are at most d^{8+epsilon} for every epsilon > 0; an edited-volume chapter.

2026_09_19_korsky: A 2026 manuscript claiming a plus-minus-one coloring of the integers whose discrepancy on every finite arithmetic progression of common difference d is at most a constant times d to the power 5/2 plus twice the root of 2.

---