Fig. 2

Kernel density estimation of rural revitalization, 2011–2022. Note: 1. Curve Shape and Temporal Trends: From 2011 to 2022, the rural revitalization kernel density curve consistently exhibited a multi-peak pattern, with the main peak gradually shifting to the right over the years. This indicates a steady improvement in China’s overall rural revitalization level, with prefecture-level cities at the intermediate development stage (corresponding to the main peak group) serving as the core driving force behind rural revitalization. 2. Multi-Peak and Gradient Effects: A distinct secondary peak emerged after 2016, further differentiating into second and third peaks post-2020. This reflects how some lagging prefecture-level cities gradually formed a second tier through targeted rural revitalization support policies, while a few developed eastern prefecture-level cities—benefiting from early digital financial penetration and robust infrastructure—established a third tier. This ultimately manifests as a “multi-tiered, multi-model” development landscape. 3. Distribution Dispersion: The peak values of the curve show a slight decline over time, indicating that while disparities exist in rural revitalization levels among prefecture-level cities, extreme polarization has not emerged. Overall, the pattern exhibits “steady improvement with graded convergence.”