  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".
