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No, the covenant that holds your collateral requires you to burn it to redeem it. There is no trust involved in doing this.
The asset is minted cooperatively, between the user providing collateral UTXO and Fuji providing the reissuance token that grants power to issue: this process is like an atomic swap, so it either goes through or not.
Fuji can theoretically mints assets without collateral, but this being verifiable onchain by anybody if it happens.
I see. Let me guess the reason you have to do centralized minting instead of whatever DAI is doing: there's no Chainlink on Liquid so somebody needs to be the price oracle?
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Minting is a cooperative process. That could be made non-interactive, locking the re-issuance token in a covenant, but you would need an oracle attestation and make on-chain calculation to make the mint. We are going to explore that eventually but seems an over-kill, putting more pressure on oracle to be available at mint time also, besides liquidation.
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