## 2 Literature Review
### Research on Carbon Emission Efficiency
applied the all-element method to reflect the carbon emission efficiency around the region of the Yangtze River Delta [29]. Measurement methods commonly applied to quantify carbon emission efficiency include DEA and SFA. The former has been widely applied; for example, [PERSON] et al. used DEA to measure the carbon emission efficiency in the region of the Yangtze River Delta, Pearl River Delta, and Beijing-Tianjin-Hebei region [30]. [PERSON] et al. and [PERSON] et al. applied DEA to quantify the efficiency of China's regional carbon emissions [31; 32]. In regard to the application of SFA, [PERSON] et al. used this method to analyze the carbon emission efficiency in Tianjin [33], [PERSON] et al. applied SFA to quantify the carbon emission efficiency in Shandong Province [34], and [PERSON] et al. used SFA to calculate and analyze the carbon emission efficiency in Xinjiang [35]. Research on the Relationship between Carbon Emissions, Economic Development, and Environmental Protection  
There are few studies on the ternary relationship between carbon emissions, economic development, and environmental protection abroad. Instead, the focus is often on the dual relationship between carbon emissions and economic development, or between economic development and environmental protection, with a specific focus on the selection of appropriate measurement models. Commonly used measurement models include neoclassical growth models, endogenous growth models, input-output models, environmental computable general equilibrium (CGE) models, environmental Kuznets curve (EKC) models, and comprehensive assessment models [36; 37; 38]. For example, [PERSON] et al. proposed an inverted U-shaped relationship between carbon dioxide emissions and economic growth [39]. [PERSON] analyzed the relationships between per capita carbon emissions and per capita GDP across 137 countries [40]. [PERSON] et al. analyzed the level of the coordinated development of the economy and the environment in Scotland [41]. [PERSON] studied the relationship between global CO2 emissions and GDP growth [42], and [PERSON] et al. studied the relationship between CO2 emissions and economic growth across various countries [43]. In China, research on the relationship between carbon emissions, economic development, and environmental protection mainly focuses on binary relationship analysis and the selection of appropriate measurement models, including EKC, decoupling models, and coupling coordination models. For example, [PERSON] et al. used the EKC to analyze the relationship between carbon emissions and economic development in the Yangtze River Economic Zone [44]. [PERSON] quantified the EKC between carbon dioxide emissions and economic growth in China [45]. [PERSON] et al. analyzed the decoupling relationship between China's economic development and carbon emissions [46]. [PERSON] et al. quantified the relationship between China's carbon emissions and environmental protection by measuring the carbon carrying capacity [47]. By contrast, domestic research on the ternary relationship between carbon emissions, economic development, and environmental protection started late, with relatively few research results. Among the few related studies, the research focus is on the aspect of the measurement and quantification of the coordination degree of the 3E (energy-economy-environment) system. For example, [PERSON] et al. analyzed the coordination degree of China's 3E system [48], [PERSON] et al. quantified the coordination degree of Shanghai's 3E system [49] and [PERSON] et al. analyzed the coordination degree of the 3E system in Guangdong province [50]. Overall, although related research has achieved some fruitful results, a number of obvious shortcomings still persist. Firstly, research on the ternary coordination relationship between carbon emissions, economic development, and environmental protection is still lacking, and relevant research on the basis of the core perspective of carbon emissions is especially rare.