How does Kaspa verify that someone owns their coins?

Kaspa verifies ownership using the UTXO set — a complete, current record of every unspent coin on the network. UTXO stands for Unspent Transaction Output; the UTXO set is essentially a snapshot of who owns what right now. Full transaction history exists on the network as an audit trail, but it is not what determines ownership — the UTXO set alone is sufficient for that. Kaspa's UTXO set is complete, unpruned, and independently verifiable, so any participant can confirm ownership without trusting a third party.