This is a very interesting topic. If a solution was found, a much better, easier, more convenient implementation of Bitcoin would be possible. Originally, a coin can be just a chain of signatures. With a timestamp service, the old ones could be dropped eventually before there's too much backtrace fan-out, or coins could be kept individually or in denominations. It's the need to check for the absence of double-spends that requires global knowledge of all transactions. The challenge is, how do you prove that no other spends exist? It seems a node must know about all transactions to be able to verify that. If it only knows the hash of the in/outpoints, it can't check the signatures to see if an outpoint has been spent before. Do you have any ideas on this? It's hard to think of how to apply zero-knowledge-proofs in this case. We're trying to prove the absence of something, which seems to require knowing about all and checking that the something isn't included.
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