You got it on your edit. The inbox is generated dynamically from multiple outboxes. The time series data, however, is not able to fit in one server's memory; it's sharded over multiple non-communicating Redis instances, collectively known as a pool. And multiple pools (complete replica sets) constitute the system.
Weirdly enough I am implementing a CRDT list today (not a set). The TreeDoc example in the main paper has a problem I think, if two writes with same key go in, the disambiguator keeps an ordering. But if that occurs, you now can't insert between those two edits because the disambiguators are not dense.
