Birational functoriality conjecture for destabilising test configurations

Let $(X,L)$ be a pair destabilised by a test configuration $(\mathcal X,\mathcal L)$, and let $\pi\colon X'\rightarrow X$ be a projective birational morphism.

Birational functoriality conjecture. There is a K-unstable pair $(X”,L”)$ destabilized by a test configuration $(\mathcal X”,\mathcal L”)$, a birational map $\phi\colon X\dashrightarrow X”$, a birational morphism $\psi\colon X'\rightarrow X”$ satisfying $\psi=\phi\circ\pi$ and $\psi(L')=L”$, and a morphism $f\colon \mathcal X'\rightarrow \mathcal X”$ such that $\mathcal L”=f_*(\mathcal L)$ and $f|_F=\psi$, where $F$ is the general fibre of $\mathcal X'$.

This conjecture proposes that a destabilising test configuration can be transferred through a projective birational morphism while preserving a compatible birational relationship between the fibres and total spaces. The supplied source does not state that it is solved or refuted.