Formality conjecture for isotropy Lie infinity-algebras of singular foliations

Let $\mathcal F$ be a singular foliation admitting a geometric resolution, and let its isotropy Lie $\infty$-algebra at a point be the corresponding homotopy-theoretic isotropy object. Formality conjecture. At every point, the isotropy Lie $\infty$-algebra of $\mathcal F$ is homotopy equivalent to a finite-dimensional differential graded Lie algebra. This conjecture concerns whether the higher homotopy structure of isotropy can be represented by a finite-dimensional differential graded Lie algebra; the supplied context does not indicate whether it is known or open.