The lowness conjecture for lattice initial segments of the Turing degrees

Let $\mathbf a\in\mathcal D$, let $\mathbf x\geq\mathbf a”$ or $\mathbf x=\mathbf a'$, and let $\mathbf g\leq\mathbf x$. Suppose that $[\mathbf a,\mathbf g]$ is a lattice and that $\mathbf g$ is generalized low over $\mathbf a$ of level one, meaning

$$\mathbf g'=\mathbf g\cup\mathbf a'.$$

Lowness conjecture. Under these assumptions, $[\mathbf a,\mathbf g]$ is $\Sigma^0_1(\mathbf x)$-presentable.

This concerns the complexity of presentations of lattice intervals in the Turing degrees. The supplied text does not state whether the conjecture has been proved or refuted.