AGX's square-root lower bound for the independence number

Let $G$ be a graph, let $\alpha(G)$ be its independence number, let $v$ be the number of vertices of $G$, and let $\Delta$ be its maximum degree. AGX's square-root conjecture.

$$\alpha(G)\geq\lceil 2\sqrt{v}\rceil-\Delta$$

The source attributes this conjecture to AGX conjecture-making software and verifies it for the graph classes studied there; it does not claim a general resolution.