Bankers/miners competing for cash.
As a value net, the input is proof of stake, a centralized portion, and output is proof of work, the decentralized portion. The ledger system is all about making change efficiently.
The corner store has proof of stake purchase on inventory. He collects proof of work cash, his customers actually collect the cash, bring it to the owner and he aggregates it and it reenters the banking system.
The fiat ledger is hierarchical, perfect for this type of system. But bitcoin sharding makes this work also, one account shard a chunk of the ledger, and circulates that ledger entry as cash for a fee.
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