The one-dimensional formula conjecture for the Ginzburg–Landau energy

Let $E(L)$ be the limiting energy defined by

$$E(L)=\lim_{R\to\infty}\frac{\mathfrak{e}_{\rm gs}(L;R)}{2R},$$

and let $\lambda$ be the function introduced in the source. For $b>0$, define $E^{\rm 1D}(b)=\mathfrak{b}(\alpha_0,b)$, where $\mathfrak{b}(\alpha_0,b)$ is defined in the source. One-dimensional energy formula. If

$$\lambda_0<L^{-2/3}<\lambda(0),$$

then

$$E(L)=E^{\rm 1D}(L^{-2/3}).$$

This would give a simpler expression for the limiting energy in the intermediate regime between the thresholds $\lambda(0)^{-3/2}$ and $\lambda_0^{-3/2}$. The supplied text does not state whether the formula has been proved or remains open.