Akbari–Elphick–Kumar–Pragada–Tang order–inertia conjecture

Let $G$ be a graph of order $n$, and let $n^+(G)$ denote the number of positive eigenvalues of its adjacency matrix, counted with multiplicity. Akbari–Elphick–Kumar–Pragada–Tang's order–inertia conjecture. Every graph $G$ satisfies

$$2n\leqslant (n-n^+(G))(n-n^+(G)+3).$$

This conjecture is another proposed extension of the absolute bound for strongly regular graphs, expressed in terms of the graph order and positive inertia. The supplied material does not state whether it has been resolved; because the paper is titled as giving counterexamples to a conjecture on graph inertia, its status should be checked against the paper's results.