The lower general position product bound

Let $G$ and $H$ be graphs, and let $\operatorname{gp}^-(G)$ denote the lower general position number of $G$.

The lower general position product bound.

$$\operatorname{gp}^-(G \operatorname{\,\square\,} H) \geq \min \{ \operatorname{gp}^-(G),\operatorname{gp}^-(H)\}.$$

This conjectured bound relates the lower general position number of a Cartesian product to those of its factors. It has been verified computationally for all pairs of graphs whose orders are at most six, but remains open in general.