Convergence conjecture for the associated formal differential operator

Let $F$ be an analytic map defined in an open neighborhood of $0\in{\mathbb C}^n$, and let $a(z)$ denote the formal series associated with $F$ through the formal differential operator construction. Convergence conjecture. If $F$ is convergent near $0\in{\mathbb C}^n$, then $a(z)$ is also convergent near $0\in{\mathbb C}^n$. The source states that this is unknown even in one variable and for polynomial maps with Jacobian identically $1$, and explicitly presents it as a conjecture with little evidence.