Boundedness of minimal log discrepancies of Kollár components

Let $n\in\mathbb{N}^*$ and let $I\subseteq [0,1]\cap\mathbb{Q}$ be a DCC set. For a klt pair $(X,\Delta)$ with $\operatorname{Coef}(\Delta)\subseteq I$ and a point $\eta\in X$ of codimension $n$, define $\operatorname{mld}^{\mathrm{K}}(\eta,X,\Delta)$ as the smallest log discrepancy among Kollár components over $\eta$.

Boundedness conjecture. There exists a constant $A=A(n,I)$, depending only on $n$ and $I$, such that

$$\operatorname{mld}^{\mathrm{K}}(\eta,X,\Delta)\leq A.$$

This is proposed as a stronger analogue of the boundedness conjecture for minimal log discrepancies. The paper verifies related special cases, including codimension two, but the general assertion remains open.