This article (Link to article) explains the "fork choice rule".
The first figure after the section "Fork choice rule" is really confusing (along with its explanation).
The first question is that:
What is the "message" that has been transferred between shards? Is it a transaction? or something else?
What is the purpose of exchanging such messages between the shards?
What does distance between the shards mean? Since the shards are NOT the node. How to imagine a topology of the shards? The nodes maintaining the shards can leave the network at any arbitrary time. And why in this figure, the maximum distance between the block A2 and B2 is 2 ? Why not 1 or 3 ?
In the explanation of the mentioned figure (in the article) says that "each block includes the shard ID", whereas, in the figure, in both shard#1 and shard#2, the blocks do NOT include the shards IDs (that are #1 and #2).
And finally, Is there any more clear article about the "fork choice rule"?