I didn't read the paper yet, but I have some problems even understanding the basic concept.

If the idea is to also accept transaction in orphaned blocks (or forks), then how can one even be sure all nodes are aware of the transactions contained in the orphans? With the current longest-chain scheme this is easy: I can just walk back through all the blocks and get a list of all transaction which is exactly the list of all valid transactions. With the proposed change I don't see how I can get a provably complete list of all valid transactions.

Please someone enlighten me.