Composite-degree extremal reciprocal polynomial conjecture

Let $\mathrm{mr}(d)$ be the minimum of the houses of reciprocal algebraic integers of degree $d$ that are not roots of unity, and let $R_d(x)$ be the minimal polynomial of an extremal reciprocal algebraic integer. Let $d$ be composite, and let $p_1,\ldots,p_k$ be odd prime divisors of $d$ or elements of $\{s,t\}$, where $s=9$ and

$$t=1;\qquad t=4\text{ if }8\mid d\text{ and }12\nmid d;\qquad t=6\text{ if }12\mid d.$$

Suppose

$$\mathrm{mr}^{2p_1}(2p_1)<\mathrm{mr}^{2p_2}(2p_2)<\cdots<\mathrm{mr}^{2p_k}(2p_k).$$

Composite-degree extremal reciprocal polynomial conjecture. If $R_{2p_i}(x)$ is the minimal polynomial of the extremal reciprocal algebraic integer of degree $2p_i$, then

$$R_d(x)=R_{2p_1}(x^{d/(2p_1)})$$

and

$$\mathrm{mr}(d)=\lvert R_{2p_1}(x^{d/(2p_1)})\rvert.$$

The conjecture is motivated by the computed smallest houses of reciprocal polynomials and would reduce composite-degree reciprocal cases to selected lower-degree cases. No resolution status is given in the source.