Research on the coupling coordination and spatial influence effect of the digital economy and carbon emission

• Examines digital economy-carbon emissions coupled coordination evolution. • Interaction verified via coupling coordination model and spatial effects. • Coordination between the two remains low, with marked regional disparities. • The spatial pattern of coordination level decreases from east to west. • Promote energy structure optimization and digital transformation. The digital economy serves as a pivotal driver of high-quality development, and investigating its coupled coordination with carbon emissions is essential for advancing carbon reduction strategies. Grounded in coupled coordination theory, this study establishes an evaluation framework for the digital economy and carbon emissions, and empirically examines their interactive dynamics using panel data from 30 Chinese provinces between 2011 and 2021. The key findings are as follows: First, the overall level of coupled coordination between the digital economy and carbon emissions has significantly advanced from a state of "mild imbalance" to "primary coordination," exhibiting a spatial pattern characterized by higher levels in the eastern region and lower levels in the western region—albeit with the latter demonstrating a catching-up trend driven by the radiating influence of the east. Second, inter-regional disparities constitute the primary source of overall coordination inequality, with an average contribution rate of 44.6 %; the eastern region displays polarization, while the western region exhibits the most rapid improvement. Third, the relationship between digital economy development and carbon emission intensity follows an inverted U-shaped nonlinear trajectory. This study contributes novel analytical insights into balancing digital economic growth with carbon emission mitigation and offers targeted policy recommendations for promoting regional coordination, optimizing energy structures, and accelerating industrial digital transformation.