Proper stratification conjecture for KLR algebras of affine quivers

Let $Q$) be an affine quiver without oriented cycles, let $\vecn$ be a dimension vector, and let $A_0(\vecn)$ be the corresponding KLR algebra. The preorder of~ is a preorder on the relevant strata.

Proper stratification conjecture. The preorder of~ is properly stratifying for $A_0(\vecn)$ in arbitrary characteristic.

A properly stratified structure in affine type was previously constructed under a restriction on the characteristic. The conjecture asserts that this characteristic assumption can be removed.