Hi, thanks for the interest! Actually, there is no ledger (:
Every two nodes that setup mutual credit maintain the balance between them. This turns out to be enough to be able to send funds across a chain of nodes in a secure manner.
Some of the general idea can be found here:
https://offst.readthedocs.io/en/latest/theory/
It is a bit outdated given the modifications of the last few months, but I think it is still relevant enough to give you a better view of how things work.
