I believe I heard Obi say that different Fedimints can send payments through each other. The underlying values are all pegged to BTC, thus the values aren't different. Is this functionality available?
Right now it's mostly through a Lightning gateway that fedimints achieve speedy interoperability. Eventually I believe it would be possible to have non-lightning based gateways that holds ecash from multiple federations and settles them instantly without dealing with lightning at all.
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I would expect lightning to the way forward af the default interoperability layer. Managing eCash from multiple federations in a gateway (which can be rugged and introduces extra complexity) scales poorly whereas lightning "just works". What would be the advantages of such a gateway?
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Lightning does not "just work"
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One way this could work is -- with support from your app that interacts with the federations -- the following:
Suppose you have 100 fmBTC in Federation 1 (we'll denote as F1), and your current balance in federation 2 is 0 or very low.
Now imagine that you wish to pay someone in federation 2 50 fmBTC eCash. Clearly you don't have enough balance in this federation, but you do in F1.
A smart wallet could at the time you attempt to pay your friend in F2 (where you have zero balance) perform a multi-mint swap transparently in the background: it would mint a 50 sat eCash token on F1, direct a lightning payment to the F2 gateway with your own F2 account as designated beneficiary, which would materialize a 50 sat eCash token in your F2 account, that can then be sent to your friend.
Although this capability is not present in the Fedi alpha app (AFAICT?), it is present in the eNuts client for Cash (a similar, but non-federated Chaumian eCash system)
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