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The fundamental problem in digital record-keeping is establishing consensus on an update to a ledger, e.g., a payment. Consensus must be achieved in the presence of faults—situations in which some computers are offline or fail to function appropriately. Traditional centralized record-keeping systems rely on trust in a single entity to achieve consensus. Blockchains decentralize record-keeping, dispensing with the need for trust in a single entity, but some instead build a consensus based on the wasteful expenditure of computational resources (proof-of-work). An ideal method of consensus ...