Boundedness conjecture for minimal dlt centers

Let $c$ and $N$ be positive integers. A minimal dlt center of a log Calabi–Yau pair is a minimal log canonical center on a dlt modification of that pair. Boundedness conjecture for minimal dlt centers. There exists a birationally bounded family $\mathcal{M}_{c,N}$ of algebraic varieties such that, whenever $X$ is a Fano type variety of coregularity $c$ and $(X,B)$ is an $N$-complement of $X$ computing the coregularity, the minimal dlt centers of $(X,B)$ belong to $\mathcal{M}_{c,N}$.

This conjecture would bound the birational types of the minimal centers that are invisible in the dual complex alone. Their birational class is well-defined because any two minimal dlt centers of the same dimension are $\mathbb{P}^1$-linked; the proposed boundedness remains open.