Algebraicity conjecture for foliations with a stable algebraic leaf

Let $\mathcal{F}$ be a holomorphic foliation of dimension one with non-degenerate singularities in the complex projective space $\mathbb{C}\mathbb{P}^{3}$, admitting a stable graph $\Gamma(L)$, where $L\in\mathcal{F}$ is a stable algebraic leaf of $\mathcal{F}$. Algebraicity conjecture. All leaves of $\mathcal{F}$ are algebraic. The conjecture proposes that, under the stated non-degeneracy and stable-graph hypotheses, one stable algebraic leaf forces algebraicity of every leaf; the supplied material gives no resolution.