Simpson's oper stratum conjecture

Let $M_{\rm dR}(X,r)$ be the de Rham moduli space with its stratification, and let $G_u^1$ denote the oper stratum. The source identifies $G_u^1$ as the highest stratum. Simpson's oper stratum conjecture. The oper stratum $G_u^1$ is the unique closed stratum and the unique stratum with minimal dimension. The conjecture is motivated by the rank-$2$ case of the nestedness conjecture, where the oper stratum has minimal dimension; the source does not state whether the general conjecture has been resolved.