Global minimum conjecture for the theta series ratio of unimodular lattices

Let $\Lambda$ be a unimodular lattice, let $\Theta_{\Lambda}$ denote its theta series, and define

$$\Delta_{\Lambda}(\tau)=\frac{\Theta_{\Lambda}(i\tau)}{\Theta_{\mathbb{Z}^n}(i\tau)}.$$

Global-minimum conjecture. The theta series ratio achieves its global minimum at $\tau=1$:

$$\operatorname*{argmin}_{\tau>0}\Delta_{\Lambda}(\tau)=1.$$

The claim is related to the symmetry point at $\tau=1$ for unimodular lattices and would give the lower bound $\Delta_{\Lambda}(\tau)\geq\Delta_{\Lambda}(1)$ for all $\tau>0$. The source reports substantial supporting evidence but does not state that the conjecture has been resolved.