> more about how consistency of state can be maintained across completely opaque commitments of transaction validity. I have the same confusion as you, and I'm

> more about how consistency of state can be maintained across completely opaque commitments of transaction validity. I have the same confusion as you, and I'm not sure I understood your last paragraph. The prover (person submitting a new transaction) can provide a ZKP that the transaction he is making is valid, and the blockchain will adopt it if indeed it's a valid proof. So then the onus of preventing the double-spend here effectively on the prover: he can only provide a valid ZKP for a valid transaction, and a double-spend would not be a valid transaction. But then at the end of the day, seems like the underlying balance needs to be accessed somehow (otherwise how would the prover even know if he has enough funds avaliable?). I guess the prover (and only the prover) can do this because he presumably has access to the right private keys?