What is crypto-proof UTXO set?
In bitcoin, the UTXO set is derived independently by every full node by processing and verifying transactions in blocks. It is then stored on disk until it is spent. When a UTXO gets spent, it gets removed from the UTXO set so the UTXO set is definitely modifiable. When full nodes verify transactions, they also use the UTXO set on disk to check the validity of each transaction. Full nodes have to make sure that UTXOs consumed as inputs in a transaction actually do exist in the UTXO set, otherwise a transaction will be invalid.