Convergence of the Mabuchi functional on canonical approximants

Let $(X,B;L)$ be a polarized pair, let $R(X,L)$ be its section ring, and let $$ be a rational divisorial norm. For sufficiently divisible $d$, let $_d$ be the norm on $R(X,dL)$ generated in degree $1$ by the restriction of $$ to $R_d$. Canonical-approximant convergence conjecture. If $( _d)$ is the sequence of canonical approximants, then

$$\operatorname{M}( _d)\longrightarrow\operatorname{M}.$$

The source presents this convergence as a sufficient condition for the equality of divisorial and K-stability thresholds. It is therefore a more precise approximation statement underlying the preceding threshold conjecture.