What is the mass of the lightest neutrino?
In plain words
Oscillations measure only differences of neutrino masses. The overall scale must come from precise $\beta$ decay spectra or from how neutrinos affected the growth of cosmic structure.
Precise statement
Determine $m_{\mathrm{lightest}}$, or equivalently $m_{\beta}=(\operatorname{sum}\left|U_{ei}\right|^{2}m_i^{2})^{1/2}$ and $\operatorname{sum} m_{\nu}$. KATRIN (2025) gives $m_{\beta}<0.45\ \mathrm{eV}$ (90 percent CL); oscillations require $\operatorname{sum} m_{\nu}\ge \sim 0.059\ \mathrm{eV}$ (normal) or $\sim 0.10\ \mathrm{eV}$ (inverted). An answer is a nonzero value with $\sim 20\ \mathrm{percent}$ uncertainty or a consistent upper limit across laboratory and cosmology.
What would settle it
Cosmological detection of sum $m_{\nu}$ at $\ge 3\sigma$ (DESI, Euclid, CMB-S4) cross-checked by a laboratory direct measurement (Project 8 or successors) reaching $m_{\beta} \sim 40\,\mathrm{meV}$.
Status in the literature
Unverified note
DESI DR2 plus CMB (2025) gives sum $m_{\nu} < 0.064\,\mathrm{eV}$ (95 percent, LCDM), in tension with the oscillation minimum; the tension relaxes in evolving dark energy fits.