Okay now we're on the same page.

Further on the topic of custodianship differences;

Can't I redeem my cashu tokens with another mint?

It seems like also being able to choose a mint or run your own mint is a major key difference between classical custodianship in Bitcoin land.

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Peep this disclaimer,

You can't redeem on another mint directly. You have to redeem on the first mint and then it forwards a lightning payment to the next mint that then issues them to you on it. If the first mint rugs you then your mint/next mint wouldn't credit you. This disclaimer is excellent as far as trust goes though.

Yes that part is clear to me, but you can swap mints if you feel like it - I think this is a major difference to traditional custodial options and why I prefer if we don't conflate the word with invariably different things.

1. A custodial exchange/wallet when you're banked by a single entity.

2. A protocol that has custody tradeoffs that can be chosen based on voluntary market forces.

Both Cashu mints and custodial exchange wallets are backed/banked by a single entity. I can slightly see the point of part two though because the protocol could be easier to swap from due to the mint not having as much information to limit redemption. They could still limit redemption by other methods like where the withdrawal is set to go. Similarly you can usually move via lightning based on very similar voluntary market forces if you realize the custodian isn't reliable.