Neutrinos are the most abundant fundamental matter particles in the Universe and play a crucial part in particle physics and cosmology. Neutrino oscillation, discovered about 25 years ago, shows that the three known species mix with each other. Anomalous results from reactor and radioactive-source experiments1 suggest a possible fourth neutrino state, the sterile neutrino, which does not interact through the weak force. The Karlsruhe Tritium Neutrino (KATRIN) experiment2, primarily designed to measure the neutrino mass using tritium β-decay, also searches for sterile neutrinos suggested by these anomalies. A sterile-neutrino signal would appear as a distortion in the β-decay energy spectrum, characterized by a discontinuity in curvature (kink) related to the sterile-neutrino mass. This signature, which depends only on the shape of the spectrum rather than its absolute normalization, offers a robust, complementary approach to reactor experiments. Here we report the analysis of the energy spectrum of 36 million tritium β-decay electrons recorded in 259 measurement days within the last 40 eV below the endpoint. The results exclude a substantial part of the parameter space suggested by the gallium anomaly and challenge the Neutrino-4 claim. Together with other neutrino-disappearance experiments, KATRIN probes sterile-to-active mass splittings from a fraction of an eV2 to several hundred eV2, excluding light sterile neutrinos with mixing angles above a few per cent.
