The $6/7$ positive square-energy exponent conjecture

Let $G$ be a graph with $m$ edges, and let $s^+(G)$ denote its positive square energy. Positive square-energy exponent conjecture.

$$s^+(G)=\Omega(m^{6/7}).$$

The paper proves the same lower bound with a double-logarithmic loss, while the conjectured bound without that loss remains open.