Uniform lower bound conjecture for the Ricci potential before finite-time singularities

Let $X$ be the compact Kähler manifold equipped with the Kähler–Ricci flow

$$\frac{\partial \omega}{\partial t}=-\operatorname{Ric}(\omega),$$

and let $u$ be the normalized Ricci potential associated with the flow. Suppose the flow develops a singularity at a finite time $T<\infty$.

Uniform lower bound conjecture. There is a constant $C$ such that

$$u\geqslant -C$$

for all $t\in[0,T)$.

The conjecture concerns the finite-time, noncollapsing behavior of the scalar potential and is contrasted in the paper with the possible uniform decay of the potential in infinite-time collapsing cases. The supplied text gives heuristic evidence but no resolution.