Cohen–Macaulayness conjecture for closed electroid varieties

Let $\chi$ be the electroid space equipped with the Frobenius splitting under consideration, and let closed electroid varieties be its closed electroid subvarieties. Cohen–Macaulayness conjecture. Closed electroid varieties are Cohen–Macaulay. Thus, they are normal and are the only compatibly Frobenius split subvarieties in the electroid space $\chi$ under our splitting. The paper establishes regularity in codimension one and compatible Frobenius splitting, hence semi-normality. Cohen–Macaulayness would imply normality by Serre's criterion; normality would imply the assertion about compatibly split subvarieties using the stated stratification and regularity of the open electroids.