As research in mobile networks is already transitioning from 5G to 6G, we identify a set of fundamental barriers in the current 5G architecture that limit efficient and global operations. We propose innovative architectural solutions that can remove such barriers and lay the foundation for 6G systems. Specifically, we introduce three novel architectural components: the Global Service-Based Architecture (GSBA), the Compute Continuum Layer (CCL), and the Zero-Trust Layer (ZTL). The ORIGAMI framework effectively overcomes existing network limitations, crucial for advancing to 6G. We introduce three key innovations: the Global SBA (GSBA), Compute Continuum Layer (CCL), and Zero-Trust Layer (ZTL), each addressing specific barriers in network efficiency, security, and scalability. Additionally, we show how integrating concrete Network Intelligence and Global Services into our framework enhances its capability to handle complex network demands.