Laugesen–Siudeja's sharp area-perimeter eigenvalue conjecture for triangles

Let $\triangle$ be a triangle, with area $|\triangle|$, perimeter $|\partial\triangle|$, and first Dirichlet eigenvalue $\lambda_1(\triangle)$. Define

$$\mathcal{F}(\triangle):=\lambda_1(\triangle)|\triangle|-\frac{\pi^2}{16}\frac{|\partial\triangle|^2}{|\triangle|}.$$

Laugesen–Siudeja's conjecture. The functional $\mathcal{F}(\triangle)$ is minimized uniquely by the equilateral triangle, and its minimum value is $7\sqrt{3}\pi^2/12$. This is a sharp quantitative refinement of Makai's inequality for triangles; the source gives no evidence that the conjecture has been resolved.