Interesting concept but I am not sure I would call this a “proof”. An attacker could easily create another “proof” showing different values (by just creating a new transaction). What I mean is that I can not just take this single transaction and show it to somebody who doesn’t know the current ledger state (like a syncing node), and he can tell if this is the correct balance.

And if I have to ask some kind of consensus mechanism, to check if the information that I have received is indeed the “correct” proof, then I can also just omit sending the “proof” and ask the consensus about the current balance of an address directly on a 2nd layer rather than wasting precious bandwidth for information that synced nodes can calculate anyway?