Bitcoin, as well as many of its successors, require the whole transaction record to be reliably acquired by all nodes to prevent double-spending. Recently, many blockchains have been proposed to achieve scale-out throughput by letting nodes only acquire a fraction of the whole transaction set. However, these schemes, e.g., sharding and off-chain techniques, suffer from a degradation in decentralization or the capacity of fault tolerance. In this paper, we show that the complete set of transactions is not a necessity for the prevention of double-spending if the properties of value transfers is fully explored. In other words, we show that a value-transfer ledger like Bitcoin has the potential to scale-out by its nature without sacrificing security or decentralization. Firstly, we give a formal definition for the value-transfer ledger and its distinct features from a generic database. Then, we introduce an off-chain based scheme with a shared main chain for consensus and an individual chain for each node for recording transactions. A locally executable validation scheme is proposed with uncompromising validity and consistency. A beneficial consequence of our design is that nodes will spontaneously try to reduce their transmission cost by only providing the transactions needed to show that their transactions are double-spending-proof. As a result, the network is sharded as each node only acquires part of the transaction record and a scale-out throughput could be achieved, which we call "spontaneous sharding".