de Lima–Oliveira–de Abreu–Nikiforov lower-bound conjecture for the least signless Laplacian eigenvalue

Let $G$ be a graph with order $n$ and size $m$. de Lima–Oliveira–de Abreu–Nikiforov conjecture.

$$\lambda_n(A_{\frac{1}{2}}(G))\geq\frac{m}{n-1}-\frac{n-2}{2}.$$

The source presents this as a conjectured lower bound for the least signless Laplacian eigenvalue. No resolution is stated in the supplied text.