Let's say we only have one ledger block, or whatever, or UTXO commitment thing. If we don't know the blocks before that, other than just headers, we can't verify that people are building on valid blocks. Someone could have made a fraudulent ledger block, and built on top of it. If people don't catch this, and never check contents before that, they have successfully attacked the network.
(For any audience, "ledger block" is same thing as "rolling root".)
Thank you for the reply (and trying to address my questions)! I'm not convinced that is correct, however. How would this attacker create a convincing fraudulent ledger block that beats the ledger block of the honest nodes?
1. The ledger block of the honest nodes will contain transactions that
can be verified to have thousands of confirmations.
2. The ledger block of the honest nodes will be part of a longer chain than the fraudulent one for the same reasons described in the bitcoin paper.
If I'm wrong, I must be missing some subtle and would appreciate it if you (or anyone else) could explain what that is.