The whole idea behind zkp is to prove correctness of the result of a computation without actually disclosing the inputs that you might want to keep secret. So why in the context of zk-rollups it is so important that all the calldata is stored somewhere (on-chain or off-chain)?

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The validity proof shows the state transition is valid, but you still need access to the state to do most kinds of transactions. Imagine if a powerful entity hid all the valid transactions from you and only submitted proofs of correct state transitions. You wouldn't even know what your own balance is.

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