I think Alice and Carol need knowledge of 2 tx with Bob to coordinate a common ancestor; that's it. If you imagine the ledger like a deck of cards, there is pr

I think Alice and Carol need knowledge of 2 tx with Bob to coordinate a common ancestor; that's it. If you imagine the ledger like a deck of cards, there is probably a point where all txo's are shuffled (and we can likely make a conjecture that after N shuffles, the position of any txo is unknown, it's just hard to gauge how many shuffles we need to do for real privacy guarantees. If you want 6 sigma privacy, you might need to wait a very long time).