What is $C$, the infimum of all exponents $c$ for which the following is true, uniformly for
$0 < \alpha < 1$? Suppose that $A \subset \mathbb{F}_2^n \times \mathbb{F}_2^n$ is a set of density
$\alpha$. Write $N := 2^n$. Then there is some $d \neq 0$ such that $A$ contains $\gg \alpha^c N^2$
corners $(x,y), (x,y+d), (x+d,y)$.
This question has been resolved by [FSS20], showing that $C = 4$.
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