Inversion of adjunction conjecture for foliations

Let $X$ be a normal variety, let $\mathcal F$ be a foliation on $X$, let $S$ be a prime divisor on $X$ and let $B \ge 0$ be a $\mathbb Q$-divisor such that $m_SB = \varepsilon(S)$ and such that $K_{\mathcal F}+B$ is $\mathbb Q$-Cartier. Let $n\colon T \rightarrow S$ be the normalisation and define foliation adjunction by

$$n^*(K_{\mathcal F}+B)=K_{\mathcal F_T}+B_T.$$

If $(\mathcal F_T,B_T)$ is log canonical, then $(\mathcal F,B)$ is log canonical in a neighbourhood of $S$.

Inversion of adjunction. Log canonicity of the induced foliated pair on the normalisation of $S$ should imply log canonicity of the original foliated pair near $S$.

This conjecture is closely related to the deformation conjecture for semi-log canonical foliation singularities and is motivated by inversion of adjunction in the birational study of pairs. The source presents it as an open conjecture.