Conjectural unboundedness of third covariant Ricci derivatives along Kähler–Ricci flow

Let $X$ be a compact Kähler manifold with semiample canonical bundle, and let $\omega^\bullet(t)$ be an immortal normalized Kähler–Ricci flow on $X$. Let $f:X\to B$ be the associated Iitaka fibration, let $S$ denote its singular-fiber locus, and let $K\Subset X\setminus S$ be compact. Write $\nabla^{\omega^\bullet(t),3}\operatorname{Ric}(\omega^\bullet(t))$ for the third covariant derivative of the Ricci curvature with respect to $\omega^\bullet(t)$.

Unboundedness conjecture. Under the assumptions above, the quantity

$$\left|\nabla^{\omega^\bullet(t),3}\operatorname{Ric}(\omega^\bullet(t))\right|_{\omega^\bullet(t)}$$

is in general not bounded over $K\times[0,+\infty)$.

The conjecture concerns the failure of uniform higher-order Ricci estimates away from singular fibers. The source explicitly identifies the boundedness question near singular fibers as open, but does not state a general resolution of this conjecture.