Darvas–Di Nezza–Lu ceiling-envelope conjecture

Let $(X,\omega)$ be a compact Kähler manifold, and let $\theta$ be a smooth closed real $(1,1)$-form representing a big class. For $u\in\operatorname{PSH}(X,\theta)$, let $\mathscr C_\theta(u)$ denote the ceiling operator and $P_\theta[u]$ the singularity envelope. Darvas–Di Nezza–Lu's ceiling-envelope conjecture. For every $u\in\operatorname{PSH}(X,\theta)$,

$$\mathscr C_\theta(u)=P_\theta[u].$$

Darvas, Di Nezza, and Lu proved this identity in positive mass and conjectured that it holds in general, including classes of arbitrary mass. The status of the general identity is not resolved in the supplied text.