Devriendt–Ottolini–Steinerberger minimum constant resistance curvature conjecture

Let $G$ be a connected graph on $n\geq 3$ vertices. For each vertex $v_i$, let $\kappa_i$ be its resistance curvature, defined by the unique solution $\kappa$ of

$$R_G\kappa=\mathbf{1},$$

where $R_G$ is the resistance matrix and $\mathbf{1}$ is the all-one vector. If all vertices have the same resistance curvature, write the common value as $\mathcal{K}_G$. Devriendt–Ottolini–Steinerberger's conjecture.

$$\mathcal{K}_G\geq\frac{6}{n^2-1},$$

with equality if and only if $G=C_n$. This conjecture gives the expected sharp lower bound for constant resistance curvature, improving the previously known bound $\mathcal{K}_G\geq 1/(n(n-1))$; the supplied text does not establish whether the conjecture itself is resolved.