The all-charge multicenter Dirac lower-bound conjecture

Let $M\geqslant2$, let $R_1,\ldots,R_M\in\mathbb{R}^3$, and let $\nu_m\geqslant0$ satisfy $\sum_{m=1}^M\nu_m\leqslant1$. Let $D_0$ be the free Dirac operator and let $\lambda_1$ denote the first min-max level of the multicenter Dirac-Coulomb operator. The all-charge multicenter Dirac lower-bound conjecture. For every such choice of positions and charges,

$$\lambda_1\left(D_0-\sum_{m=1}^M\frac{\nu_m}{|x-R_m|}\right)\geqslant\lambda_1\left(D_0-\frac{\sum_{m=1}^M\nu_m}{|x|}\right)=\sqrt{1-\left(\sum_{m=1}^M\nu_m\right)^2}.$$

The inequality asserts that separating the nuclei cannot lower the first level below the merged point-charge value. The supplied status evidence says that this conjecture has been proved in the nonrelativistic case; the relativistic assertion is presented here as a conjecture.