Quaternionic Lehmer conjecture

Let $P(x)\in\mathbb{Z}[x]$ be a monic irreducible polynomial, and let $m_{\mathbb{H}}(P)$ denote its quaternionic Mahler measure. Quaternionic Lehmer conjecture. There is a constant $c$ such that, for every monic irreducible polynomial $P(x)\in\mathbb{Z}[x]$,

$$m_{\mathbb{H}}(P)\geq c.$$

This is the quaternionic analogue of Lehmer's question about a positive lower bound for the Mahler measures of monic irreducible integer polynomials. The supplied source does not indicate whether the conjecture has been resolved.