## 1 Introduction  
In the past few years, the ground communication network has further expanded and developed with the increase in communication volume worldwide. However, the ground communication network cannot offer equal coverage to remote areas or the edge network due to insufficient resource planning, which leads to unassured communication service quality in these areas. At the same time, satellite communication systems leverage the benefits of high altitude and multicast/broadcast capabilities while complementing traditional ground networks to enable novel mobile communication networks [1]. Increasingly, organizations are initiating projects on the satellite-terrestrial hybrid network (STHN). Notably, OneWeb, O3b, SpaceX, and Telesat are among the companies proposing satellite-based Internet solutions [2]. As shown in Figure 1, owing to its intrinsic benefits encompassing wide scope, efficient processing capabilities, and versatile nature, STHN finds application across numerous practical domains, intelligent transportation systems [3], military tasks, disaster relief [4], etc. On the one hand, cloud-native computing inherits from the development of cloud computing and has the characteristics of Infrastructure as a Service (IaaS), Platform as a Service (PaaS), and Software as a Service (SaaS) [5]. Additionally, cloud-native computing achieves high reliability, elasticity, manageability, and observability of applications through means such as containerization, microservices architecture, declarative API, automateddeployment, dynamic configuration, and auto-scaling, better adapting to the rapid changes in and complexity of cloud environments. On the other hand, future universal computation requires an open and integrated network architecture that deeply integrates computing power, communication, and industry intelligence in a decentralized network. This new network architecture will transform traditional cloud AI into edge AI and then support network for AI (NET4 AI) [6], enabling a variety of AI applications such as multi-task transfer learning on edge devices [7] and the integration of edge cloud-native and intelligent wireless communication. Cloud-native and edge intelligence are the core parts of NET4 AI. Artificial intelligence can achieve better results in edges that are closer to data and have greater elasticity compared to single cloud computing. In this context, the trend of cloud-native computing in the telecommunications industry is on the rise. Compared to almost any other service, telecommunication services have higher requirements for resilience, security, and performance [8]. The Third Generation Partnership Project (3 GPP) initially introduced the Service-Based Architecture (SBA) paradigm [9] for 5G Core (5 GC). This paradigm involves the decomposition of monolithic Network Functions (NFs) into multiple microservices, offering finely grained functionalities. These microservices are designed for deployment as Virtual Machines (VMs) or lightweight containers (e.g., Docker) in a cloud-native fashion, making efficient use of cloud computing resources. Consequently, NFs can be dynamically scaled both horizontally (out/in) and vertically (up/down) to accommodate fluctuations in signaling traffic from a multitude of devices. The emergence of open-source core network platforms such as Open5 GS [10] and Free5 GC [11] further assists research in realizing cloud-native core network. While the emerging mobile core network can enhance deployment flexibility and scalability through cloud-native environments [12; 13], several challenges need to be addressed in practical deployments at multiple edge nodes close to users. First, due to limited computing and data storage resources at edge nodes, the cloud-native network functions (CNFs) should be distributed across multiple edge nodes and run in response to terminal service requests following communication protocol procedures. It is foreseeable that edge-distributed core networks will consume more communication resources than remote data center-based core networks.