[_nalply]

I am probably naive again, but it seems for me that you don't need to verify other transactions, only the one between A and B. You could ignore the shards/channels not affected by the transaction.

Another optimisation would be that for example an exchange tries to pull all its local transactions into the same channel. Or people join the retail's channel before paying. The idea is to avoid ascending as much as possible. In other words, a variant of Lightning Network!