So basically hedge against fiat the amount of sats you took out for something? And it involves a bit of trust placed in the mint on the other hand?

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That's right if you put in $10 of sats you'd get $10 stability against BTC collateral. And involves trust in mint, correct.

Ok, so how’s the balance upheld? Someone takes the opposite position?

That’s correct. The Stable Provider is taking the upside and downside risk for the Stable Receiver.

How is this achieved? Who's doing the settlement and is it done on daily basis? How can we be sure that the provider is not just bucketing trades?