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The overall scale must come from precise $\\beta$ decay spectra or from how neutrinos affected the growth of cosmic structure.","posed_since":"","precise":"Determine $m_{\\mathrm{lightest}}$, or equivalently $m_{\\beta}=(\\sum\\left|U_{ei}\\right|^{2}m_i^{2})^{1/2}$ and $\\sum m_{\\nu}$. KATRIN (2025) gives $m_{\\beta}<0.45\\ \\mathrm{eV}$ (90 percent CL); oscillations require $\\sum m_{\\nu}\\ge \\sim 0.059\\ \\mathrm{eV}$ (normal) or $\\sim 0.10\\ \\mathrm{eV}$ (inverted). An answer is a nonzero value with $\\sim 20\\%$ uncertainty or a consistent upper limit across laboratory and cosmology.","problem_ref":"02ea08734e6f7503d0222ff513d71aa481eb674b5da50e563ee8a8a626fb168a","references":"","settled_by":"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_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.","title":"What is the mass of the lightest 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