Resolution conjecture for reduced analytic vector fields in dimension three

Let $\chi$ be a reduced analytic vector field on a real analytic manifold $M$ without boundary, and let $U\subset M$ be relatively compact. Write $L_\chi|_U$ for the line field induced by $\chi$ on $U$, and let $\mathbb{M}_0=(U,\varnothing,\varnothing,L_\chi|_U)$. A weighted blowing-up is a blow-up operation of the type used to transform singularly foliated manifolds. Resolution conjecture. There exists a finite sequence of weighted blowing-ups

$$\mathbb{M}_0\stackrel{\Phi_1}{\longleftarrow}\mathbb{M}_1\stackrel{\Phi_2}{\longleftarrow}\cdots\stackrel{\Phi_n}{\longleftarrow}\mathbb{M}_n$$

such that the resulting singularly foliated manifold $\mathbb{M}_n$ is strongly elementary. This proposes resolution of the singularities of reduced analytic vector fields by finitely many weighted blow-ups; the supplied text does not state whether the conjecture has been proved or disproved.