Li's slope formula for entropy

Let $(X,L)$ be a polarized variety and let $\varphi\in\mathcal{E}_{\mathrm{NA}}^2(X,L)$ subordinate to its maximal geodesic ray $\{\ell_{\varphi,t}\}_{t\in[0,\infty)}$. The entropy slope

$$\lim_{t\to\infty}t^{-1}\int_X\log\frac{\operatorname{MA}(\ell_{\varphi,t})}{\operatorname{MA}(\ell_{\varphi,0})}\operatorname{MA}(\ell_{\varphi,t})$$

should equal the non-archimedean entropy

$$\int_{X^{\mathrm{NA}}}A_X\operatorname{MA}(\varphi).$$

This formula would directly identify the ray and non-archimedean Calabi-energy descriptions; the source attributes it to Li and notes it follows from the regularization conjecture, but it remains unproved in the stated generality.