MJ-canonicity conjecture for intersections under generic linkage

Let $X$ be a variety in a nonsingular affine space $A$, and let $Y$ be a generic link of $X$. Set

$$Z=X\cap Y.$$

Assume that $X$ is MJ-canonical. MJ-canonicity conjecture. Then $Z$ is also MJ-canonical.

This conjecture proposes that MJ-canonicity is inherited by the intersection with a generic link. The preceding results establish inequalities for minimal MJ-log discrepancies under linkage, but the stated preservation of MJ-canonicity is left as a conjecture.