Oper Stratum Conjecture

Let the de Rham moduli space $\mathbb{M}_{\mathrm{dR}}(X,r)$ be equipped with its oper stratification, whose strata are indexed by $\alpha$. Oper Stratum Conjecture. The oper stratum is the unique closed stratum and the unique stratum of minimal dimension. The claim concerns the distinguished oper stratum in Simpson's oper stratification. The supplied context says that many oper-stratification conjectures remain open, while the supplied status evidence only explicitly records a proof of the foliation conjecture; the resolution of this claim should be checked separately.