Follow-up question.
What would happen if the transaction gets stuck in the mempool. Can the ASP do an RBF on the transaction or would it require all participants in the coin-join to sign the transaction again.
The ASP cannot RBF, but could CPFP or pay a miner out of band to include a stuck coinjoin transaction.
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Eventually someone will need to use it as inputs and they're going to have to pay fees using CPFP, I suppose. Until then, Ark txs will be public so all participants in the round will have an incentive to keep it around to broadcast it if needed.
It does allow the ASP to double spend the input coins though as long as the tx is unconfirmed. Supposedly that can be mitigated by using one of the nonce-fixing strategies.