Conjecture on lengths of extremal rational curves

Let $(X,\Delta)$ be the dlt pair and setup of Theorem 1.6(iii), with a contraction morphism $iphi_{R_j}$ associated to a $(K_X+\Delta)$-negative extremal ray $R_j$, and suppose $iphi_{R_j}\colon U_j\to iphi_{R_j}(U_j)$ is proper. Define

$$d_j=\min_E\dim E,$$

where $E$ ranges over positive-dimensional irreducible components of $(iphi_{R_j}|_{U_j})^{-1}(P)$ for all $P\in iphi_{R_j}(U_j)$. Conjecture on lengths of extremal rational curves. There exists a possibly singular rational curve $C_j\subset U_j$ spanning $R_j$ in $N_1(X/S)$ and satisfying

$$0<-\omega\cdot C_j\leq d_j+1.$$

This is presented as a conjectural length bound for extremal rational curves, related to the cited question in Matsuki; no resolution is specified in the source.