The strong diamagnetism conjecture for the magnetic ground-state eigenvalue

Let $\lambda(\beta)$ denote the lowest eigenvalue of the Neumann magnetic Laplacian in the unit disk as a function of the magnetic-field parameter $\beta\geq0$. Strong diamagnetism conjecture. The map

$$\beta\mapsto\lambda(\beta)$$

is monotonically increasing on $[0,+\infty)$. This is the strong diamagnetism question for the disk: unlike ordinary diamagnetic inequalities, it asks for monotonicity of the lowest Neumann magnetic eigenvalue with respect to field strength. The supplied excerpt does not state whether the conjecture has been resolved.