All Ethereum blocks contain a stateRoot field - That is, the root hash of the world state trie. I have two questions about that.
From what I've understood through all the reading I've done on Casper CBC, there will be state changes occuring in parallel (that of each shard) so no one shard will have a correct global state (with regards to other shards) and be able to have a merkle proof of that state self-contained within the shard.
By this I mean, if I perform a state change in shard A, from block x - 1 to block x, and at the same time a state change occurs in shard b from block x - 1 to block x, the global state hashes of both shards would not match.
As such, does that mean cross-shard transactions are going to have to fit under the current tps rate? Considering they'd have to occur under a block that affects all shards, which would require every shard to temporarily join the main chain and then split back off?