Entropy slope formula conjecture for maximal geodesic rays

Let $\Phi$ be a maximal geodesic ray, with non-Archimedean limit $\Phi_{\rm NA}$, and let ${\bf H}'^\infty(\Phi)$ and ${\bf H}^{\rm NA}(\Phi_{\rm NA})$ denote respectively the asymptotic Archimedean entropy slope and the non-Archimedean entropy. Entropy slope formula conjecture. For any maximal geodesic ray $\Phi$,

$${\bf H}'^\infty(\Phi)={\bf H}^{\rm NA}(\Phi_{\rm NA}).$$

The inequality ${\bf H}'^\infty(\Phi)\geq {\bf H}^{\rm NA}(\Phi_{\rm NA})$ is known for every geodesic ray, and equality is known for rays associated to ample test configurations. The conjecture remains open for general maximal geodesic rays.