A spatial-temporal evolution resilience estimation framework for low-carbon long-term performance and its network effects

• Reshaping the underlying logic of LCDs’ resilience performance evolutionary process. • Redefine the resilience temporal process descriptors by blocking, stability and potential (BSPs). • Redefine the resilience spatial process descriptor by performance relationship network (PRNet). • The descriptors of "BSP-PRNet" are designed systematically and verified better. • The paradigm of LCDs' resilience performance in China is characterized by macro polarization and micro differentiation, but supported by midscale resilient forces from band like connectivity and periodic spatial oscillation complementarity of circles. Evaluating the resilience performance(RP) of low-carbon development system (LCDs) and revealing their multi-scale spatio-temporal effects contributes to constructing sustainable long-term future development pattern. However, extensive research has only emphasized short-term decoupling economic efficiency objectives and static spatial distribution expression. Considering the long-term strategy for Sustainable Development Goals, this study constructed a novel spatial-temporal process estimation framework for LCDs' RP and its network effects. First, by defining a nonlinear logarithmic relationship, the "blocking, stability, and potential system (BSPs)" was proposed for evaluating the long-term resilience agent's temporal capacities. Further, a functional performance relationship network was created as the spatial resilience process descriptors. By computing the network changes' nodes-lines and intra-inter, it measured the multi-agent differentiation effects of the strip-like and ring-like patterns. Taking Chinese provinces as a case study, results showed that the smoothness and validity in BSPs models are remarkable. The evolution pattern of LCDs' RP were total improved, but with long-term agents imbalance on the "Southeast-Northwest" axis in macroscale. These imbalances commonly existed and counteracted the advantages of traditional economic provinces in microscale. A five-year cyclical resilience-supporting forces emerged in the midscale, driven by "inter adaptive equilibrium" and "intra polarization complementary". Overall, the resilience performance evalutaion model can better fit evolutionary processes, and the network diffusion effect operator can place greater emphasis on “point-to-point” interaction process information. This provides a new research paradigm for observing the multi-scale spatio-temporal evolution of long-term low-carbon performance. The positive evolutionary process we observed in China can provide a valuable reference for other regions.