## 2 Materials and Methods
### Analytical Framework and Indicator System  
The study constructed an analytical framework of SETS resilience, positioning TecR as equally significant as EcoR and SocR. The dimensions of these three subsystems were systematically conceptualized, and the underlying mechanisms were disentangled through an analysis of their spatiotemporal coupled interactions (Figure 2). SocR, EcoR, and TecR are interconnected components of urban systems. Ecosystems serve as the spatial carriers and material foundations for urban development. EcoR maintains the structure and function of ecosystems, thereby supporting the continuous provision of ecosystem services [47], which are fundamental for SocR and urban well-being. Social development and human activities profoundly impact EcoR by altering ecological structures, encroaching on natural spaces, and exploiting resources [48]. High SocR usually means more efficient resource allocation mechanisms, strong social organization capacity, and adaptive policies, so as to provide a guarantee for technological innovation and improve TecR. In turn, an improvement in TecR could help strengthen infrastructure, stabilize economic development, and improve public services, particularly in the digital age [49]. Smart technologies such as web-based platforms and smartphone apps can support evidence-based decision-making and offer learning and knowledge-sharing opportunities to enhance adaptive capacity [50]. In addition, TecR contributes to EcoR by enabling better monitoring, management, and restoration of ecosystems [51]. Adequate infrastructure and high technological performance in pollution control and energy saving help reduce human pressure on the well-being of ecosystems [52]. Correspondingly, EcoR provides a natural foundation for technological innovation by providing a variety of raw materials, serving as sources of inspiration, and creating a suitable environment. Figure 1: The location of the BTHUA. In this study, SocR was categorized into three dimensions: economic strength, public service, and social stability. Economic strength serves as the foundation for SocR, providing the necessary resources and financial support to withstand and recover from various external shocks. This ensures that communities can access essential goods and services even during crises. The per capita GDP and per capita disposable income of urban residents reflect the level of macroeconomic development, indicating that urban residents have an economic foundation to bear risk-related losses. A higher share of the tertiary industry signifies a more rational regional economic structure [53]. Effective public services, such as healthcare, education, basic insurance, and emergency response, help maintain social cohesion, promote social equity and inclusion, ensure that basic needs are met during and after disruptions, and enhance the capacity of communities to respond to crises [8]. These services are also essential for long-term resilience. Social stability involves strong social networks, effective governance, and a shared sense of identity, which help reduce vulnerability and foster collective action [54]. Human development serves as the foundation for social stability and drives overall social progress. A rational population growth rate and adequate financial investments in social security and employment can maintain basic urban functions, ensure a sufficient workforce, and support social development. The urban-rural  
Figure 2: Analytical framework of SETS resilience. gap is a critical factor affecting urban stability, as a narrower urban-rural income gap reduces social vulnerability and fosters more balanced urban-rural development [25]. EcoR was divided into three dimensions: resource endowment, landscape pattern, and ecological quality. The availability and distribution of natural resources form the material basis for ecosystem functioning and human well-being. Adequate resource endowments, particularly water, land, and forests, ensure that ecosystems can sustain their functions and support biodiversity.