Jet-density conjecture for separatrices of non-dicritical foliations

Let $X$ be a quasi-compact complex manifold, let $\mathcal{F}$ be a codimension-$1$ foliation on $X$, let $\mathfrak{V}(\mathcal{F})$ denote the set of hypersurfaces that are smooth, reduced, irreducible, non-tangent to $\mathcal{F}$, and whose restriction foliation is saturated, and let $Z$ be the union of the separatrices of $\mathcal{F}$. Jet-density conjecture. If $\mathcal{F}$ is non-dicritical, then for every $m\in\mathbb{N}$, the set

$$\bigcup_{V\in\mathfrak{V}(\mathcal{F})}J_m(Z)\cap J_m(V)$$

is dense in $J_m(Z)$. This is proposed as a possible route to proving the strong tangency conjecture; the source does not state that it has been proved or disproved.