The topological mirror partner conjecture for toric degenerations

Let $Y$ be a smooth complete algebraic variety that is the generic fiber of a flat family with special fiber $Y_0$, where $Y_0$ is a complete intersection in a complete toric variety determined by a calibrated nef-partitioned framing. Let $Y_0^\vee$ be the corresponding $f$-mirror partner, and write $k_Z$ and $m_Z$ for the relevant topological invariants. Topological mirror partner conjecture. There exists a partitioned ftv $(X,\mathbf{a}=\sum_k\mathbf{a}_k)$ and a suitable resolution $\widehat{Y}_0^\vee\longrightarrow Y_0^\vee$ such that $Y_0^\vee$ is a topological mirror partner of $Y$, namely

$$k_{\widehat{Y}_0^\vee}=m_Y\quad\text{and}\quad k_Y=m_{Y_0^\vee}.$$

The conjecture extends $f$-mirror duality from toric complete intersections to varieties admitting toric degenerations. The source gives no resolution status or supporting theorem for these equalities.