Elphick–Wocjan positive square-energy strengthening of Wilf's inequality

Let $G$ be a graph on $n\ge 1$ vertices, let $\omega(G)$ be its clique number, and let $\lambda_1,\ldots,\lambda_n$ be the adjacency eigenvalues. Define the positive square energy by

$$s^+(G)=\sum_{\lambda_i>0}\lambda_i^2.$$

Elphick–Wocjan conjecture. For every graph $G$ on $n\ge 1$ vertices,

$$\frac{n}{n-\sqrt{s^+(G)}}\le \omega(G).$$

This conjecture asks whether Wilf's spectral clique bound remains valid after replacing the largest eigenvalue by the square root of the positive square energy; the supplied source does not state whether it has been resolved.