The arbitrary-type affine quasiheredity conjecture for KLR algebras

Let ${\tt C}$ be a generalized Cartan matrix and let $\alpha$ belong to the non-negative part of the corresponding root lattice. The KLR algebra $R_\alpha({\tt C})$ is defined for this data. Affine quasiheredity conjecture. The KLR algebra $R_\alpha({\tt C})$ is affine quasihereditary for an arbitrary generalized Cartan matrix ${\tt C}$. The finite-type case is known, while the case of a generalized Cartan matrix that is not of finite type is stated to be open and may require a more general notion of a stratified algebra.