Finite generation of canonical rings for projective log canonical pairs

Let $(X,\Delta)$ be a projective log canonical pair. Define the canonical ring by

$$R(X,K_X+\Delta)=\bigoplus_{m\in\mathbb{N}}H^0\bigl(X,\mathcal{O}_X(\lfloor m(K_X+\Delta)\rfloor)\bigr).$$

Canonical ring finite-generation conjecture. The canonical ring $R(X,K_X+\Delta)$ is finitely generated.

Finite generation would imply existence of the associated canonical model and, in the relative setting, existence of flips. The source presents this as a central question in higher-dimensional birational geometry; its status is not resolved in the supplied text.