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Accumulate is a network of networks. The networks are coordinated by a Directory Network that primarily collects cryptographic proofs of the other networks.
Since every account collects only information on transactions against the account itself, a wallet can sync with the Directory Networks core state and photographically prove the hashes of the current summary hash for the entire network. This is a small and fast proof.
Once an application has the proof of the current summary hash for the entire network of networks that make up Accumulate, and cryptographic proof of the state of a set of accounts is very fast and simple. In the case of a wallet, that means the wallet can quickly validate the set of transactions against an account and its balance. This only requires the transactions against that account and the state of the account.
Ultimately, it is easy to see that no blockchain can scale if users have to parse the entire state of the blockchain to have proof of a set of data like a definitive set of all transactions against an address or account. Accumulate is primarily designed to do this.
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