The finite generation conjecture for log canonical algebras

Let $(X/Z,B)$ be a log canonical (lc) pair such that $K_X+B$ is a $\mathbb Q$-divisor, and let $f\colon X\to Z$ be the given morphism. Define the log canonical algebra by

$$\mathcal R(X/Z,K_X+B):=\bigoplus_{m\ge 0}f_*\mathcal O_X\left(\left\lfloor m(K_X+B)\right\rfloor\right).$$

Finite generation conjecture. The algebra $\mathcal R(X/Z,K_X+B)$ is a finitely generated $\mathcal O_Z$-algebra. The source explains that this is closely related to the minimal model and abundance conjectures and is expected to be essentially equivalent to them together. Its general status is not resolved in the supplied text.