but the example I made, when funds are transferred to a particular account on a particular blockchain, they are frozen there- in that one account- and the act of freezing them there is what gives you access to some proportional amount of value on another chain- until the time that you want to undo it, and you transfer them to some particular address on the 2nd chain to give you access back to you funds on the first chain- isn't that how it works?

that's the impression I got after reading those papers.