Conjecture on minimizers of the body-centred-orthorhombic theta energy

Let $\alpha>0$ and $t>0$, and let $\tilde{E}_t(y;\alpha)$ be the reduced theta energy for the body-centred-orthorhombic family, with $t_0(\alpha)$ defined by the preceding lemma. Conjecture. For any $\alpha>0$ and any $t>t_0(\alpha)$, the function $y\mapsto\tilde{E}_t(y;\alpha)$ is increasing on $(1,\sqrt{3}]$. Consequently, $y=1$ is the only minimizer of $\tilde{E}_t(\cdot;\alpha)$. This is justified only by numerical investigations in the source; it concerns the global minimization of the reduced energy and remains unproved there.