Let debt be a graph where the nodes are people (with ledgers) and the edges are all of the form "alice rents $x from bob for y% APR". Actions that resolve/relax graph are payments of the form "alice pays bob $z", that lead to all balances being 0. Let the edges decay to null when balance is 0, such that a 'resolved graph' is simply a list of nodes with no edges, meaning 'no one is in debt to anyone'.
From this we can infer:
1. There is only one logical 'debt graph' in the world since they can (and do) all join.
2. The people running the graph do not want the graph to die, ever.
3. The profit of the debt business is proportional to transactions over time,
which is proportional to edges of the debt graph.
4. They want to (add, prevent from decay) as many edges as possible.
I somehow feel like I've caught my first, hazy glimpse of something important.