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Such particles could be made at accelerators and seen decaying.","posed_since":"1998","precise":"Determine whether heavy neutral leptons N with $M_N \\sim 0.1\\ \\text{to}\\ 100\\ \\mathrm{GeV}$ and active-sterile mixing $U^2$ in the range where resonant or oscillation-based (ARS) leptogenesis gives $\\eta_B \\sim 6 \\times 10^{-10}$ exist. An answer is a discovery with measured $M_N$, $U_e^2$, $U_{\\mu}^2$, $U_{\\tau}^2$ consistent with that region, or its exclusion.","problem_ref":"fd602f9520e23e8ccda77f556d7530d9cbd43adee92892c80a35603985f614ba","references":"","settled_by":"Beam-dump and collider searches (SHiP, displaced-vertex searches at LHC, FCC-ee at the Z pole) covering the leptogenesis region.","status_note":"SHiP was approved at CERN in 2024 for operation in the 2030s.","title":"Do GeV-scale heavy neutral leptons realize low-scale 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