Condensed Ricci curvature conjecture for strongly regular conference graphs

Let $G=(V,E)$ be a strongly regular conference graph with parameters

$$(4\beta+1,2\beta,\beta-1,\beta)$$

where $\beta\geq 2$. The condensed Ricci curvature conjecture. The condensed Ricci curvature satisfies

$$\Bbbk(x,y)=\frac{1}{2}+\frac{1}{2\beta}$$

for every edge $xy\in E$. In particular, every strongly regular conference graph has positive condensed Ricci curvature strictly greater than $\frac{1}{2}$. The conjecture is expected to follow from the matching criterion in the cited theorem if the neighbor sets of every adjacent pair admit perfect matchings; the paper states that this is left for future work.