[gendal]

The actor wanting to reanimate the coins on the Bitcoin network provides a proof to the Bitcoin network that 1) the coins on the sidechain have been moved to a particular address that puts them out of reach, 2) that this transaction has been buried by sufficient blocks so that it's unlikely to be reversed, 3) that it was this actor that did it.

This is why the sidechains paper suggests a one-off change to Bitcoin might be needed: there's no out-of-the-box Bitcoin feature to validate this proof. The authors propose an interim measure where n-of-m "functionaries" are trusted to validate the proof.