The BCM-rationality characterization of rational singularities

Let $(R,\mathfrak{m})$ be a local ring essentially of finite type over a field of characteristic $0$. Here, $R$ is BCM-rational when it satisfies the big Cohen–Macaulay rationality condition used in the paper.

BCM-rationality conjecture. $R$ is BCM-rational if and only if $R$ has rational singularities.

This conjecture seeks to characterize rational singularities in characteristic zero through big Cohen–Macaulay algebras, extending the comparison established in the paper between BCM-rationality and other rationality notions. Its resolution is not supplied in the source.