Prioritizing Sustainable Development Goals under China’s carbon peaking across alternative socioeconomic pathways

2030 is a critical juncture for China, marking the deadline for the United Nations 2030 Agenda for Sustainable Development and China’s carbon peaking commitment under the Paris Agreement . Given limited time and resources, harmonizing decarbonization targets with Sustainable Development Goals (SDGs) is a core governance challenge. This study proposes a framework integrating Multi-spatial Convergence Cross-Mapping (MCCM), network analysis, and Graph Convolutional Network (GCN)-based scenario forecasting. By incorporating causal effects, structural importance, and evolutionary potential, the framework quantitatively derives SDG priority orders across Shared Socioeconomic Pathways (SSPs) under China’s carbon peaking. The results show that SDGs 7.2.L, 3.d.1, 1.1.L, 3.8.1, and 9.5.1 are core cross-pathway levers, yielding spillovers 60.7 %–91.5 % above system average. Targeted resource allocation to these indicators can catalyze SDG advancement. At the goal level, leveraging SDG 7 as a core driver (spillovers 57.3 % above mean) and addressing lagging SDG 15 constitute the backbone for cross-pathway synergy. Implementation sequences are path-dependent. In SSP1, SDG 4 and SDG 17 are the foundational pillars for harmonizing climate commitments with SDGs. Under SSP3 and SSP5, structural imbalances elevate the urgency of SDG 10 by 38.7 % and 37.3 % relative to SSP1, increasing its strategic priority. In SSP2 and SSP4, SDG 9 becomes pivotal, driven by lagging progress (10.7 % and 17.3 % behind SSP1) and amplified spillover effects (15.2 % above average). This study provides evidence-based guidance for China to optimize policies and maximize dual-goal synergies across pathways, while offering transferable insights for aligning sustainability and climate action globally.