Bogomolny–Schmit nodal domain conjecture for even Maass cusp forms

Let $\Gamma=SL_2(\mathbb{Z})$ be the full modular group, let $\mathbb{X}=\Gamma\backslash\mathbb{H}$ be the modular surface, and let $\phi$ be an even Hecke–Maass cusp form with eigenvalue $\lambda_{\phi}=t_{\phi}^2+\frac{1}{4}$. If $k_{\phi}$ denotes its position in the ordering by eigenvalue and $N(\phi)$ the number of connected components of $\mathbb{X}\setminus Z_{\phi}$, where $Z_{\phi}=\\{z\in\mathbb{X}:\phi(z)=0\\}$, then Bogomolny–Schmit's conjecture.

$$N(\phi)\sim\frac{2}{\pi}\left(3\sqrt{3}-5\right)k_{\phi},\qquad k_{\phi}\to\infty.$$

This predicts the asymptotic number of nodal domains for high-energy even Maass cusp forms, refining the expected linear growth suggested by random-wave models. The source presents it as a suggestion of Bogomolny and Schmit and gives no resolution status.