Kernel–diadem inequality for graphs

Let $G$ be a finite graph. Write $\ker(G)$ for its kernel, $\diadem(G)$ for its diadem, and $\alpha(G)$ for its independence number. Kernel–diadem conjecture. For every graph $G$,

$$\left\lvert \mathrm{ker}(G)\right\rvert+\left\lvert \mathrm{diadem}(G)\right\rvert\leq 2\alpha(G).$$

This is a universal inequality concerning two families of critical independent-set vertices. The supplied text gives no resolution evidence for this claim, so its status remains open.