Negative curvature from nonpositive factors in Cartesian graph products

Let $G^{(1)}$ and $G^{(2)}$ be graphs. For vertices indexed by $i$ and $j$, let ${\boldsymbol p}_i^{(1)}$ and ${\boldsymbol p}_j^{(2)}$ denote their node resistance curvatures, and let ${\boldsymbol p}_{i\otimes j}$ denote the node resistance curvature at the corresponding vertex of the Cartesian product. Cartesian-product negativity conjecture. If

$${\boldsymbol p}_i^{(1)},{\boldsymbol p}_j^{(2)}\le 0,$$

then

$${\boldsymbol p}_{i\otimes j}<0.$$

This is presented as the most general conjectured implication for Cartesian graph products and is intended to capture the emergence of negative curvature at product vertices whose two factor curvatures are nonpositive. Its resolution is not indicated in the source.