Point sources of ultra-high-energy neutrinos: Minimalist predictions for near-future discovery

The discovery of ultra-high-energy neutrinos, with energies above 100 PeV, may soon be within reach of upcoming neutrino telescopes. We present a robust framework to compute the statistical significance of point-source discovery via the detection of neutrino multiplets. We apply it to the radio array component of IceCube-Gen2. To identify a source with 3\sigma3σ significance, IceCube-Gen2 will need to detect a triplet, at best, and an octuplet, at worst, depending on whether the source is steady-state or transient, and on its position in the sky. The discovery, or absence, of sources significantly constrains the properties of the source population.