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Rejecting cosmic rays (CRs) is essential for the scientific interpretation of CCD-captured data, but detecting CRs in single-exposure images has remained challenging. Conventional CR detectors require experimental parameter tuning for different instruments, and recent deep-learning methods only produce instrument-specific models that suffer from performance loss on telescopes not included in the training data. We present Cosmic-CoNN, a generic CR detector deployed for 24 telescopes at the Las Cumbres Observatory, which has been made possible by the three contributions in this work: (1) We build a large and diverse ground-based CR data set leveraging thousands of images from a global telescope network. (2) We propose a novel loss function and a neural network optimized for telescope imaging data to train generic CR-detection models. At 95% recall, our model achieves a precision of 93.70% on Las Cumbres imaging data and maintains a consistent performance on new ground-based instruments never used for training. Specifically, the Cosmic-CoNN model trained on the Las Cumbres CR data set maintains high precisions of 92.03% and 96.69% on Gemini GMOS-N/S 1 × 1 and 2 × 2 binning images, respectively. (3) We build a suite of tools including an interactive CR mask visualization and editing interface, consolemore »commands, and Python APIs to make automatic, robust CR detection widely accessible by the community of astronomers. Our data set, open-source code base, and trained models are available athttps://github.com/cy-xu/cosmic-conn.