Before revision:  Our main theorem shows that a currency network, where agents can be members of more than one currency community, can achieve distributive justice globally across the network by joint egalitarian minting , where each agent mints one coin in only one community at each timestep.
After revision:  Our main theorem shows that a currency network, where agents can be members of more than one currency community, can achieve distributive justice globally across the network by joint egalitarian minting joint egalitarian minting, whereby each agent mints one coin in only one community at each timestep.