Donaldson's conjecture on the Calabi functional and non-Archimedean K-energy

Let $(X,L)$ be a polarized manifold. Let $\mathcal{H}$ be the space of Kähler metrics in the class $c_1(L)$, let $\mathcal{H}^{\operatorname{NA}}$ be the space of smooth non-Archimedean metrics, let $\operatorname{Cal}(\omega)$ denote the Calabi functional, let $M^{\operatorname{NA}}(\Phi)$ denote the non-Archimedean K-energy, and let $\|\Phi\|_2$ be the non-Archimedean $L^2$-norm. Donald's conjecture. One has

$$\inf_{\omega\in\mathcal{H}}\operatorname{Cal}(\omega)=\sup_{\Phi\in\mathcal{H}^{\operatorname{NA}}}\frac{-M^{\operatorname{NA}}(\Phi)}{\|\Phi\|_2}.$$

This is the non-Archimedean formulation of Donaldson's conjecture relating the infimum of the Calabi functional to destabilizing non-Archimedean metrics; no resolution is given in the supplied text.