Formal principle with convergence for general bracket-generating families of rational curves

Let $X$ be a complex manifold and let ${\mathcal K}$ be a connected family of smooth rational curves on $X$ with semipositive normal bundles. The family is bracket-generating when the natural distribution ${\mathcal D}\subset\Theta_{\mathcal K}$, whose fiber at $[C]$ corresponds to $H^0(C,N^+_{C/X})\subset H^0(C,N_{C/X})$, is bracket-generating. Here $N_{C/X}\cong N^+_{C/X}\oplus{\mathcal O}_C^q$ and a distribution is bracket-generating when its iterated Lie-bracket spans the tangent sheaf. Formal principle with convergence conjecture. A general member of ${\mathcal K}$ satisfies the formal principle with convergence: every formal equivalence between the curve and another relevant germ is convergent. This generalizes the case of families whose members have positive normal bundles, for which the result is known, and strengthens the corresponding theorem of Hwang; the conjecture remains open in the stated generality.