Symplectic compactification conjecture for polarized toric degenerations

Let $\mathcal{X}\rightarrow D$ be a polarized toric degeneration with intersection complex $(\check B,\check{\mathcal P})$. Let $\omega_t$ be a Kähler form on $\mathcal{X}_t$ representing the first Chern class of the polarization. Let $\Gamma$ denote the discriminant locus of $\check B$. Symplectic compactification conjecture. There is an open set $\check U\subseteq\check B$ such that $\check B\setminus\check U$ retracts onto $\Gamma$, and $\mathcal{X}_t$ is a symplectic compactification of $\check X(\check U)$ for any $t$. This predicts a symplectic realization of the intersection complex away from its discriminant locus and is part of the proposed geometric description of toric degenerations.