## 3 Method and Data  
### Measurement of RGTI, NQP, and CRCI  
Accurate quantification of the three key variables--RGTI, NQP, and CRCI--is the foundational step of this study. Based on a systematic review and evaluation of existing measurement methodologies, this study employed the annual number of utility model  
Figure 1: Research framework. patents and invention patents granted in each province as the metric for regional green technological innovation (RGTI). Compared to green total factor productivity indicators derived from input-output methods, patent data offer greater timeliness and comparability, providing a more direct reflection of a region's actual green technological innovation capacity [35]. For the assessment of NQP, a multi-dimensional composite index evaluation system was adopted. This system evaluates regional sustainable development capabilities and technological progress from various dimensions, including economic development level, human resource quality, infrastructure completeness, environmental protection intensity, energy industry structure, and digital economy development. This multi-dimensional framework captures the intrinsic characteristics of NQP, enhancing the comprehensiveness and reliability of the measurements. In measuring carbon reduction levels in the construction industry (CRCI), a comprehensive evaluation system was designed, encompassing total carbon emissions, carbon emissions intensity, the proportion of total industrial carbon emissions, and per capita carbon emissions. The specific calculation of carbon emissions follows the standard methodology proposed by the IPCC (2006), tailored to the characteristics of the construction industry. Carbon emissions are systematically measured across two dimensions: direct emissions and indirect emissions [36]. The detailed calculation formulas are provided in Equations (1) and (2). \[C_{dec}=\sum_{i=1}^{11}E_{i}\times\alpha_{i}\times f_{i},\ C_{icc}=\sum_{j=1}^{5 }M_{j}\times\beta_{j}\times(1-\varepsilon_{j}) \tag{1}\]  
\[C_{ce}=C_{dec}+C_{icc} \tag{2}\]  
In Equation (1), \(C_{dec}\) represents direct carbon emissions, while C\({}_{icc}\) denotes indirect carbon emissions. \(E_{i}\) represents the consumption of the \(i\)-th type of energy, \(\alpha_{i}\) is the average low calorific value of the \(i\)-th energy type, and \(fi\) is the default CO\({}_{2}\) emissions factor for the \(i\)-th energy type. \(M_{j}\) denotes the consumption of the \(j\)-th type of construction material, \(\beta_{j}\) represents the CO\({}_{2}\) emissions factor for the \(j\)-th construction material, and \(\varepsilon_{j}\) is the recycling coefficient of the \(j\)-th construction material. In Equation (2), \(C_{cc}\) represents the total carbon emissions of the construction industry. Taking into account the multidimensionality and complexity of measuring the RGTI, NQP, and CRCI indicator systems, as well as the significant heterogeneity in the dimensional characteristics, measurement units, and numerical attributes of the indicators, the entropy method was employed in this study for the standardization of indicator data to ensure an accurate assessment of the development levels of RGTI, NQP, and CRCI. The entropy method, as an objective weighting approach based on the principle of information entropy, determines weight coefficients by quantifying the information entropy values of each indicator, which effectively avoids any systematic biases that may arise from subjective weighting, thereby ensuring the scientific accuracy of the measurement results [37]. Specifically, this study applies range normalization to the raw data to eliminate dimensional differences, heterogeneity in scale characteristics, and disparities between positive and negative values among indicators. The specific formulas are presented in Equations (3)-(5).