Wu–Zhang's conjecture on extremal reciprocal algebraic integers

Let $\alpha$ be a reciprocal algebraic integer that is not a root of unity, and let $d=\deg(\alpha)\geq 2$. Let $\mathrm{mr}^d(d)$ denote the relevant degree-$d$ extremal reciprocal house quantity used in the source. Wu–Zhang's conjecture.

$$\mathrm{mr}^d(d)\geq \mathrm{mr}^{20}(20),$$

and, if $10\nmid d$,

$$\mathrm{mr}^d(d)\geq \mathrm{mr}^{12}(12).$$

The conjecture is presented as being supported by the paper's computed tables and is attributed to Wu and Zhang. No proof or disproof is supplied here.