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Electrical recordings from a large array of electrodes give us access to neural population activity with single-cell, single-spike resolution. These recordings contain extracellular spikes which must be correctly detected and assigned to individual neurons. Despite numerous spike-sorting techniques developed in the past, a lack of high-quality ground-truth datasets hinders the validation of spike-sorting approaches. Furthermore, existing approaches requiring manual corrections are not scalable for hours of recordings exceeding 100 channels. To address these issues, we built a comprehensive spike-sorting pipeline that performs reliably under noise and probe drift by incorporating a channel-covariance feature and a clustering based on fast density-peak finding. We validated performance of our workflow using multiple ground-truth datasets that recently became available. Our software scales linearly and processes a 1000-channel recording in real-time using a single workstation. Accurate, real-time spike sorting from large recording arrays will enable more precise control of closed-loop feedback experiments and brain-computer interfaces.