I think the "C" in ACID indeed refers to application-defined integrity constraints (or "invariants"). Referential integrity is just one example; unique key cons

I think the "C" in ACID indeed refers to application-defined integrity constraints (or "invariants"). Referential integrity is just one example; unique key constraints are another. This has nothing to do with the "C" in CAP, which is best interpreted (IMO) as linearizability. (Aside: IMO the "C" in ACID implies "I" and specifically serializability, because that is the only isolation level guaranteed to preserve arbitrary application invariants.)