From an email I sent to some fellow XRI Editors:
The universe of XRI authorities forms a cloud of nodes, probably mostly connected, except for truly private communities. The “connections” between these nodes are pointers (e.g. Auth Res Service Service blocks) from XRDs handed out by the authorities. This cloud of nodes forms a directed graph (possibly cyclic, NOT a tree).
You can start from any node and follow a number of edges. You can identify this starting node using a cross reference or a GCS character.
This walk through the graph is a path (in graph terminology).
This “path” is serialized as an XRI (or more precisely the authority part of an XRI).
Important to note that any node can be the root of a tree. And the decision of where to start is a SOCIAL decision which is for a community to make. XDIORG is stepping up to bless three nodes as “community/global/sacred/royal” GRS nodes that make the GRS identifiers have more value. The idea is that XDIORG builds trust and respect and reputation so that the community makes the SOCIAL decision to use those nodes. But that’s again, a SOCIAL decision, not a TECHNICAL decision.