The toric degeneration conjecture for large complex structure limits

Let $f:\mathcal{X}\rightarrow D$ be a large complex structure limit degeneration. A toric degeneration is a degeneration whose central fibre and associated structure have the toric form used in the paper.

Toric degeneration conjecture. The degeneration $f$ is birationally equivalent to a toric degeneration

$$f':\mathcal{X}'\rightarrow D.$$

This conjecture asks whether toric degenerations capture all large complex structure limit degenerations up to birational equivalence, which would substantially broaden the reach of the toric mirror-symmetry construction. The source does not establish the claim, so its status remains open.