So, the bank can't flip a few bits in its databases and go "actually I have a quadrillion dollars now" because other people know how much money that bank should have based on transactions it has made? Do I have that right?
Seriously I have wondered about this for decades. I don't know why this would be obvious to anyone.
> other people know how much money that bank should have based on transactions it has made?
Approximately. Everyone keeps a running total of their bilateral transactions. This summing and sharding reduces information. But it also decentralizes accountability in a robust way.
Add occasional audits (which allow trusted persons to evaluate the transaction record), and some of those parties' books (in the aggregate) being public record, thereby permitting every party (including third parties) to compare their books to theirs, and you get a system which tends towards accuracy.
Seriously I have wondered about this for decades. I don't know why this would be obvious to anyone.