Assessing the green low-carbon innovation effect of digital-real integration in the Yangtze River Delta urban agglomeration

In the global pursuit of green low-carbon transition, green low-carbon innovation (GLCI) serves as a core driver, and the integration of the digital and real economy (IDR) holds transformative potential to accelerate this process. However, the spatio-temporal dynamics between IDR and GLCI, along with the nonlinear and heterogeneous impacts of IDR on GLCI, remain insufficiently explored. Focusing on the Yangtze River Delta (YRD), this study employs multidimensional spatio-temporal analysis methods, spatial simultaneous equation model, boosted regression tree, and geographically weighted random forest model to bridge existing research gaps and elucidate pathways to strengthen IDR-GLCI synergy. Key findings are as follows: (1) Both IDR and GLCI exhibited consistent upward trends across the YRD, yet displayed marked regional disparities, featuring a prominent Z-shaped high-value corridor alongside low-value clusters in less-developed peripheral areas. (2) A strengthening temporal synergy and predominantly positive spatial correlation characterized the IDR-GLCI relationship, with stronger correlations in central cities and weaker in northern peripheries. Stable spatio-temporal dependencies and and lock-in effects persisted, manifesting as HIDRHGLCI clusters in advanced cities and LIDRLGLCI clusters in less-developed regions. (3) IDR exerted a significant direct positive effect on GLCI, although its indirect effect remained positive yet insignificant. Green financial support, industrial intelligence transformation, and corporate ESG performance emerged as primary channels for this influence. Conversely, GLCI significantly promoted IDR while producing a notable negative indirect effect. (4) The impact of IDR on GLCI followed a nonlinear temporal trajectory of rapid early growth, mid-phase fluctuations, and later stabilization, coupled with pronounced spatial heterogeneity that favored developed core cities over underdeveloped northern and northwestern peripheries. These findings underscores the necessity of strengthening regional coordination, promoting cross-regional collaboration, and implementing tailored innovation policies to bridge developmental disparities and optimize DPI-GLCI synergy, thereby establishing the YRD as a leading exemplar for high-quality, sustainable green-digital development.