Godsil's controllability conjecture for random graphs

Let $G(n,1/2)$ be the Erdős–Rényi random graph on $n$ vertices, and let $G$ be controllable and minimally controllable when it has the corresponding controllability properties for its adjacency matrix. Godsil's conjecture. The probability that $G(n,1/2)$ is controllable and minimally controllable approaches $1$ as $n\to\infty$. This conjecture concerns the typical controllability of simple graphs; the source states that it was recently proven, so it is no longer open.