Open-problem statements, with their sources attached.

$W(3, 24) \ge 593$ from [AKS14, Table 2].

$W(3, 25) \ge 656$ from [AKS14, Table 2].

$W(3, 26) \ge 727$ from [AKS14, Table 2].

$W(3, 27) \ge 770$ from [AKS14, Table 2].

$W(3, 28) \ge 827$ from [AKS14, Table 2].

$W(3, 29) \ge 868$ from [AKS14, Table 2].

$W(3, 30) \ge 903$ from [AKS14, Table 2].

$W(3, 31) > 930$ from [AKS14, Table 3].

$W(3, 32) > 1006$ from [AKS14, Table 3].

$W(3, 33) > 1063$ from [AKS14, Table 3].

$W(3, 34) > 1143$ from [AKS14, Table 3].

$W(3, 35) > 1204$ from [AKS14, Table 3].

$W(3, 36) > 1257$ from [AKS14, Table 3].

$W(3, 37) > 1338$ from [AKS14, Table 3].

$W(3, 38) > 1378$ from [AKS14, Table 3].

$W(3, 39) > 1418$ from [AKS14, Table 3].

Does there exist a Lipschitz function $f : \mathbb{N} \to \mathbb{Z}$ whose graph $\Gamma = \{(n, f(n)) : n \in \mathbb{N}\} \subseteq \mathbb{Z}^2$ is free of 3-term progressions?

What is the largest subset of $[N]$ with no solution to $x + 3y = 2z + 2w$ in distinct integers $x, y, z, w$?

From [Ruzsa] $f(N) \gg N^{1/2}$.

From [Schoen and Sisask] $f(N) \ll N \cdot e^{-c(\log N)^{1/7}}$.