> How does a replica know it isn’t missing a transaction from some other shard if that shard is offline come its turn to declare transactions in the log? It must at least receive a message saying no transactions involving it were declared by that shard, no?

A transaction is committed to the log with sufficient information necessary for the log (and each storage host) to know whether any particular host is involved in that transaction. There's no need for a message to prove a host's absence from that transaction - it has all it needs in the log to determine that it isn't involved. There is some complexity around how that information maps to the cluster's physical topology, but hosts which aren't involved in a transaction don't process that transaction and need not check with any other host to know that fact.

[ETA] That information is derived from the read set when constructing the transaction to propose to the log. Logical partitions that weren't a part of that read set don't need to know that they weren't involved - that fact is obvious from their absence.

> I think scalability is something that is a function of both theoretical expectations and practical demonstration.

I agree with you, though as a commercial product operated as a service, that practical demonstration is naturally limited in this forum.