The single-point modification conjecture for APN functions

Let $F \colon \mathbb{F}_2^n \to \mathbb{F}_2^n$ be an almost perfect nonlinear (APN) function, meaning that for every $a\ne 0$ and every $b$, the equation $F(x+a)+F(x)=b$ has either $0$ or $2$ solutions. Let $G$ be obtained from $F$ by changing its value at one point.

Single-point modification conjecture. The function $G$ is not APN.

The paper states that this conjecture follows if the algebraic-degree conjecture holds, and identifies it with the assertion that graphs of all APN functions are maximal Sidon sets. Its general status is not specified in the supplied text.