Resolving closely-spaced small targets in dense clusters presents a significant challenge in infrared imaging, as the overlapping signals hinder precise determination of their quantity, sub-pixel positions, and radiation intensities. While deep learning has advanced the field of infrared small target detection, its application to closely-spaced infrared small targets has not yet been explored. This gap exists primarily due to the complexity of separating superimposed characteristics and the lack of an open-source infrastructure.In this work, we propose the Dynamic Iterative Shrinkage Thresholding Network (DISTA-Net), which reconceptualizes traditional sparse reconstruction within a dynamic framework.DISTA-Net adaptively generates convolution weights and thresholding parameters to tailor the reconstruction process in real time.To the best of our knowledge, DISTA-Net is the first deep learning model designed specifically for the unmixing of closely-spaced infrared small targets, achieving superior sub-pixel detection accuracy.Moreover, we have established the first open-source ecosystem to foster further research in this field. This ecosystem comprises three key components: (1) CSIST-100K, a publicly available benchmark dataset; (2) CSO-mAP, a custom evaluation metric for sub-pixel detection; and (3) GrokCSO, an open-source toolkit featuring DISTA-Net and other models, will be publicly available soon.