Rademacher's conjecture on the extremal lattice for Landau's constant

Let $\Gamma \subset \mathbb{C}$ be discrete and $f_\Gamma \in \mathcal{U}$, where $\mathcal{U}$ is the class of universal covering maps of $\mathbb{D}$ onto $\mathbb{C} \backslash \Gamma$. Let $\ell(f_\Gamma)$ be the covering radius defined by

$$\ell(f_\Gamma)=\sup\{r\in\mathbb{R}_+\mid D_r\subset f_\Gamma(\mathbb{D})\}.$$

Then define $\mathcal{L}_\Gamma^{-1}=|f_\Gamma'(0)|/\ell(f_\Gamma)$. Rademacher's conjecture. The quantity

$$\mathcal{L}_\Gamma^{-1}=\frac{|f_\Gamma'(0)|}{\ell(f_\Gamma)}$$

is maximal for the hexagonal lattice.

This is the lattice formulation of the conjectural extremal description of Landau's constant. The supplied status evidence treats the conjecture as resolved, although the surrounding text in the source says that it is still open; this status should be checked against the cited literature.