Donaldson's asymptotic conjecture for the twisted Calabi flow

Let $(M,\omega,\chi,J)$ be the initial twisted Kähler data, and suppose that the twisted Calabi flows have global existence. The transformed data along the flow may be written $(M,[\omega_t],\chi_t,J_t)$. Donaldson's asymptotic conjecture. The asymptotic behavior of the twisted Calabi flow falls into one of the following possibilities: (1) the flow converges to a twisted cscK metric on the same complex manifold $(M,J)$; (2) the flow converges, up to a diffeomorphism, to a twisted extremal Kähler metric; or (3) if the manifold admits neither a twisted cscK metric nor a twisted extremal metric, the transformed flow converges to $(Y,[\omega_\infty],\chi',J')$, which carries a twisted extremal Kähler metric, possibly with singularities of at least codimension $2$. This is a proposed compactification picture for the long-time behavior of the flow, and the source gives no proof in the twisted setting.