The non-negative curvature obstruction for increasing regular expander families

Let $D\in\mathbb{N}$ be fixed. An increasing $D$-regular expander graph family is a sequence of $D$-regular expander graphs $\{G_k\}_{k\in\mathbb{N}}$ whose sizes increase with $k$, and a graph is non-negatively curved when every vertex has non-negative curvature. Non-negative curvature obstruction conjecture. There do not exist increasing $D$-regular expander graphs $\{G_k\}_{k\in\mathbb{N}}$ which are non-negatively curved in all vertices. The conjecture would rule out expander families with uniformly non-negative curvature, linking curvature constraints in graph geometry to the combinatorial expansion property. The source attributes it to Conjecture 9.11 of Chung, Lin and Yau; its status is not resolved by the supplied text.