How does everyone converge on a shared understanding in terms of who owns what?
first everyone has the whole blockchain, so everyone can compute what the UTXO should hash out to for any block height. no questions asked.
once we have this UTXO checkpoint we throw away all the history.
now everyone has a UTXO checkpoint and accumulates 10days of "real blocks", after 1440 blocks everyone computes another UTXO checkpoint and throws away all the history again.
no need to "converge" your node either is synced or not, can produce a UTXO or not. there is no ambiguity as to what the UTXO should hash out to, just like there is no ambiguity as to what is contained in the last 1440 blocks.
if you are a brand new node, (or maybe you've been offline and missed 300 blocks). you simply download the lastest UTXO checkpoint from other nodes, and make sure it hashes out to what every other node says the hash ought to be. ( maybe you can download this file in fragments from many nodes, downloading it in full from only 1 node might lead to a security hole )
i dont see a problem... no other node can try to fool me into downloading a bad UTXO checkpoint because the node checks its hash and makes sure its the same hash that everyone else is reporting. once the node is synced, it starts to compute and validate new "UTXO checkpoint hash" independently.
if you use a bad UTXO checkpoint your node will never compute the right hash for all subsequent "1440th block" and you'll fork off, but i'm sure it could easily be detected long before that.
