McDonald–Sahay–Wyman's conjecture on the VC-dimension of Paley graphs

Let $N$ be prime, and let $b[?2004l\Gamma=\Gamma(N)$ be the Paley (di)graph on $\mathbb{Z}/N\mathbb{Z}$. The VC-dimension $\operatorname{VCdim}(\Gamma)$ is the maximum cardinality of a set shattered by the neighborhoods of $\Gamma$.

McDonald–Sahay–Wyman's conjecture. As $N\to\infty$ through the primes,

$$\operatorname{VCdim}(\Gamma)=(1+o(1))\log_2 N.$$

This conjecture is motivated by the analogous asymptotic behavior of random Cayley graphs and by the pseudorandomness of Paley graphs. The source mentions partial progress and numerical evidence, but does not state a resolution.