The GL corner energy conjecture

Let $E_{\mathrm{corner},\beta}$ denote the effective Ginzburg–Landau energy associated with a boundary corner of opening angle $\beta$, and let $E_{\mathrm{corr}}$ be the correction energy for the smooth boundary. For any $1<b<\Theta_0^{-1}$ and $\beta\in(0,2\pi)$, GL corner energy conjecture.

$$E_{\mathrm{corner},\beta}=-(\pi-\beta)E_{\mathrm{corr}}.$$

The conjecture gives an explicit linear dependence of the corner contribution on the opening angle, despite the effective energy being defined only implicitly. Its status is not established in the supplied source context.