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Recently announced results from the KATRIN collaboration imply an upper boundon the effective electron anti-neutrino mass $m_{\nu_{e}}$, $m_{\nu_{e}}<0.8~{\rm eV}/c^{2}$. Here we explore the implications of combining the KATRINupper bound using a previously inferred lower bound on the smallest neutrinomass state, $m_{i,{\rm min}}\gtrsim 0.4~{\rm eV}/c^{2}$ implied by thestability of white dwarfs and neutron stars in the presence of long-rangemany-body neutrino-exchange forces. By combining a revised lower bound estimatewith the expected final upper bound from KATRIN, we find that the availableparameter space for $m_{\nu_{e}}$ may be closed completely within the next fewyears. We then extend the argument when a single light sterile neutrino flavoris present to set a lower mass limit on sterile neutrinos.

Implications of Recent KATRIN Results for Lower-Limits on Neutrino Masses