The relative finite generation conjecture for log canonical rings

Let $f\colon X\to S$ be a proper surjective morphism between normal varieties, and let $B$ be a $\mathbb Q$-divisor on $X$ such that $(X,B)$ is log canonical. Relative finite generation conjecture. The relative log canonical ring

$$R(X/S,K_X+B)=\bigoplus_{m\geq 0}f_*\mathcal O_X(\lfloor m(K_X+B)\rfloor)$$

is a finitely generated $\mathcal O_S$-algebra. This is the more general relative form of finite generation and, in the source, implies the log flip existence conjecture. It is proved in dimensions at most four according to the surrounding discussion, but remains open in general.