Before revision:  We identify a structural property called one-endedness, which is desirable in any blockchain system . We prove that whenever the blockchain network model is stochastically stable, then a blockchain is one-ended .
After revision:  We identify a structural property called one-endedness, which is desirable in any blockchain system as it is directly related to distributed consensus among the peers. We show that the stochastic stability of the network is one-ended .