Based on the coupled coordination development theory, the evaluation feature system of the coupled coordination system is first established according to the principle of feature selection, and the feature system of the digital economy subsystem is co...

Industrial digitalization reshapes production processes and can potentially improve carbon productivity by optimizing factor allocation and energy efficiency. Using panel data for 30 Chinese provinces from 2012 to 2022, this study constructs a comprehensive industrial digitalization index with four dimensions and 13 indicators using the entropy method and examines its impact on carbon productivity (GDP per unit of CO₂ emissions). We employ the Dagum Gini coefficient and kernel density estimation to describe regional disparities and their evolution, a dynamic panel threshold model to test the nonlinear role of industrial transformation and upgrading, and a spatial Durbin model to identify spatial spillover effects. The results indicate that industrial digitalization has risen nationwide but remains uneven; industrial digitalization significantly enhances carbon productivity, with stronger effects in the eastern and western regions and in plain areas; the effect exhibits a double-threshold pattern with respect to industrial transformation and upgrading, implying a U-shaped relationship; and industrial digitalization generates positive spatial spillovers. These findings suggest that policy should coordinate digital infrastructure investment with industrial upgrading and regional collaboration to accelerate low-carbon, high-efficiency growth.