The Authenticated Transfer Protocol (AT Protocol) does not use ActivityPub for a few reasons:
Design Philosophy: ActivityPub operates on a fundamentally different philosophy than the AT Protocol. ActivityPub is a protocol for creating, updating and deleting content on a distributed server-to-server network. It mainly handles the server to server interactions, but does not deal with how users and applications manage their data or how they should interact with this network. On the other hand, AT Protocol's design involves more granular control over data ownership and handling, federation, and interoperation with a larger focus on user control and privacy.
Different data model: AT Protocol and ActivityPub use different data models. AT Protocol uses a model where data is kept in signed data repositories that can be synced across different servers and provides a schema network called Lexicon to unify data across different servers. On the other hand, ActivityPub uses a model where data is distributed across servers using an inbox/outbox model and does not provide a global schema.
Different approaches to federation: ActivityPub has a single federation model where servers are peers and communicate using the ActivityPub protocol. AT Protocol uses a more complex federation model with Personal Data Servers (PDS) and Big Graph Services (BGS) to handle user data and events respectively. This distinction is meant to achieve scale and user choice.
Account portability: AT Protocol emphasizes account portability, allowing users to migrate their data to a new Personal Data Server without the server's involvement, using a system of DIDs and signed data repositories. This isn't a built-in feature of ActivityPub.
Algorithmic choice: AT Protocol is designed to allow users to choose their own algorithms for content discovery and search, which is not a feature provided by ActivityPub.
Overall, it's not so much that AT Protocol doesn't use ActivityPub; rather, AT Protocol was designed with different goals and philosophies in mind, leading to a different protocol architecture. ActivityPub is a wonderful tool for certain kinds of decentralized applications, but the designers of AT Protocol clearly had a different vision for what they wanted to achieve.