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My two main questions are what kind of liveness assumption does one need to participate in a round

A lot. All senders and receivers have to be online, and the coinjoin round may take several attempts to get signatures from every participant. Payment finality requires the transaction to get confirmed on the blockchain.

and how does the previous owner of a credential "forget" it

When a sender passes a credential to another owner, the new owner reissues it with the coordinator for a new credential. The previous owner doesn't "forget" it, but they can't double spend it since the coordinator will recognize it and reject it.

I suspect they already have solutions in both cases, I just don't understand them.

When Kompaktor's credentials expire at the end of each round, they settle as onchain UTXOs. The solution for this limited lifespan is for participants to claim their coins as Ark VTXOs.

Thanks for the info. I saw that Ark was mentioned in it a number of times (and that the dev is an Arkade dev) but I didn't understand how the Ark part works. So this business of "one output" is one Ark VTXO?

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0 sats \ 0 replies \ @kruw 13h

The "one output" thing is basically reverse batching: Normally, an exchange will delay customer withdrawals for a few minutes and then send a bulk transaction with many outputs.

Instead, an exchange would delay deposits (which customers would send in the form of anonymous credentials) until the coinjoin round ends, and then accept a bulk transaction with many inputs.

Ark service providers can fill the UX gaps, allowing participants to "exit" from a different round than they "entered" from.

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