Boyd's conjecture on the closedness of Mahler measures

For each non-zero polynomial $P\in\mathbb{Z}[z_1,\ldots,z_n]$ with $n\geq 1$, let $M(P)$ denote its Mahler measure, and define

$$L^\sharp\coloneqq\{M(P)\mid P\in\mathbb{Z}[z_1,\ldots,z_n]\setminus\{0\},\ n\geq 1\}.$$

Boyd's conjecture. The set $L^\sharp$ is closed with respect to the Euclidean topology.

This conjecture concerns the topological structure of the set of Mahler measures of non-zero integral multivariate polynomials. The source attributes it to Boyd and does not state whether it has been resolved.