Inversion of adjunction for arbitrary-codimension subvarieties

Let $X$ be a nonsingular variety over a field of characteristic zero, and let $Y=\sum_{i=1}^k t_iY_i$ be a formal combination where $t_i>0$ are real numbers and each $Y_i\subsetneq X$ is a closed subscheme. Let $Z\subsetneq X$ be a normal $\mathbb{Q}$-Gorenstein closed subvariety of codimension $r>0$ such that $Z\not\subset\bigcup_{i=1}^kY_i$. Inversion-of-adjunction conjecture. If the pair $(X,Y+rZ)$ is plt (respectively, lc) near $Z$, then the pair $(Z,Y|_Z)$ is klt (respectively, lc). This proposes an inversion-of-adjunction principle for arbitrary codimension, extending the known local-complete-intersection case; the paper presents it as suggested by the relationship between dense F-pure type and lc pairs, and between purely F-regular type and plt pairs.