Mendson–Pereira jet-splitting conjecture for foliations on projective space

Let $\mathcal F$ be a codimension one foliation on $\mathbb P^n$, with $n\ge 3$, and let $N^*_{\mathcal F}$ be its conormal sheaf. Let $\nabla_B$ be the Bott connection on $N^*_{\mathcal F}$, and let $\mathcal{P}^1_{\mathbb P^n/\mathcal F}(\nabla_B)$ denote the first sheaf of transverse jets of this connection. A flat partial connection is a flat connection along the tangent directions of $\mathcal F$. Mendson–Pereira jet-splitting conjecture. If

$$H^0(\mathbb P^n,\Omega^1_{\mathcal F})=0,$$

then $\mathcal{P}^1_{\mathbb P^n/\mathcal F}(\nabla_B)$ is isomorphic to the direct sum of two flat partial connections on line bundles. This is presented as a reformulation of Mendson and Pereira's conjecture; the source does not specify whether it has been resolved.