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It would show up as extra appearance and disappearance at short distances.","posed_since":"","precise":"Determine whether a fourth mass state with $\\Delta m^2_{41} \\sim 0.1 \\text{ to } 10\\,\\mathrm{eV}^2$ and mixings |U_e4|, |U_mu4| large enough to produce sin^2(2 theta_mue) $\\sim 10^{-3}$ exists. An answer is a $5\\,\\sigma$ oscillation signal or exclusion of the region preferred by LSND and gallium in both appearance and disappearance.","problem_ref":"3cb42522eb6acd43f0f0debf98bbcae131552215be6acdb523466bccb80da689","references":"","settled_by":"Combined SBN-program oscillation fits with near and far detectors, plus reactor (PROSPECT, STEREO) and atmospheric (IceCube) disappearance limits.","status_note":"Appearance-disappearance tension in global fits and the 2025 MicroBooNE result disfavor the simple 3+1 model.","title":"Does an eV-scale sterile neutrino 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