Log canonicity of normal Q-Gorenstein lim-perfectoid pure singularities

Let $R$ be a normal $\mathbf{Q}$-Gorenstein ring. The lim-perfectoid log-canonicity conjecture. If $R$ is lim-perfectoid pure, then $R$ is log canonical. The paper proves the corresponding assertion for perfectoid pure rings when the $\mathbf{Q}$-Gorenstein index is not divisible by the residue characteristic, and conjectures that the index restriction can be removed, possibly after weakening perfectoid purity to lim-perfectoid purity.