The congruence subgroup property for mapping class groups of genus at least 3

Let $\Sigma$ be a surface of genus at least $3$. A finite-index subgroup of $\operatorname{Mcg}(\Sigma)$ is a subgroup of finite index containing the kernel of the action on a finite quotient of $\pi_1(\Sigma)$; such a subgroup is called a congruence subgroup. The congruence subgroup conjecture. Every finite-index subgroup of $\operatorname{Mcg}(\Sigma)$ is a congruence subgroup. The congruence subgroup property is known in genus $0$, genus $1$ with punctures, and genus $2$, while the case of genus at least $3$ is open and is connected to questions about profinite rigidity of $3$-manifold groups.