Abstract:Under the dual context of rapid urbanization and the push for low-carbon development, studying the synergistic development between spatial structure and carbon emissions in the Guanzhong Urban Agglomeration is crucial for promoting high-quality and stable regional growth. This study constructs a multidimensional compactness evaluation system based on population, economic, land use, transportation infrastructure, and ecological data from 2005 to 2025. Using the carbon emission intensity identity as a foundation, we applied multiple analytical methods—including the entropy method, standard deviation ellipse model, coupling coordination degree model, and geographical detector—to systematically examine the spatio-temporal dynamics and coordinated evolution of the two dimensions.The findings indicate that urban compactness showed a fluctuating upward trend during the study period, while carbon emission intensity declined significantly. The coupling coordination degree between the two increased from[1] 0.534 in 2005 to 0.763 in 2025, reflecting steady improvement in synergistic development and a shift from a state of imbalance to one of coordination. Spatially, a multi-center networked pattern has formed, with Xi"an–Xianyang as the core.Geographical detector analysis reveals that technological innovation capacity, population agglomeration, and urbanization progress are key drivers of coordinated development. The explanatory power of their interaction is significantly stronger than their individual effects, with two-factor interactions producing a non-linear enhancing effect.Therefore, the Guanzhong Urban Agglomeration should strengthen the combined role of technology and talent, and establish policies to promote urbanization in the region. This will support high-quality development in Guanzhong and similar areas, and provide theoretical insights and policy guidance for achieving low-carbon transition.