This paper combines various self-stabilization techniques within a replication protocol that ensures eventual consistency in large-scale distributed systems subject to network partitions and asynchrony. A simulation study shows that the resulting protocol is scalable and achieves high throughput under load. Our protocol does not rely on any form of consensus, which would lead to block the replicas in case of partitions and asynchrony. Our protocol instead ensures that (1) updates are continuously applied to the replicas and (2) no two updates are ever performed in a different order. Gaps might occur during periods of unreliable communication. They are filled whenever connectivity is provided, and consistency is then eventually ensured, but without any conscious commitment. That is, there is no point in the computation when replicas know that consistency is achieved. This unconsciousness is the key to tolerating perpetual asynchrony with no consensus support.