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I am interested in using the ripple network in conjunction with bitcoin transactions, but am curious as to interplay between the ripple ledger verification and the bitcoin blockchain verification.

I understand that the ripple network operates as essentially a series of IOUs and allows the ledger to be verified in an order of magnitude of seconds, however, a Bitcoin block takes on the order of magnitude of 10 minutes.

Does this mean that ripple transactions that involve bitcoin are entirely off the chain transactions or am I somehow missing something? I am just trying to get my head wrapped around the seemingly hand-wavy aspect that something that takes 10 minutes to verify can be used in a transaction that takes only 5 seconds to verify.

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As you already have described, Ripple transactions are based on exchanging IOUs. As such, when you trade bitcoins on the ripple network, you are trading IOUs denominated in Bitcoin owed to you by some party, e.g. BTC owed to you by Bitstamp. Therefore, as long as the transaction is between Ripple users, it is completely off-chain and can be confirmed within seconds.

However, there is at least one Ripple Bitcoin bridge which is offered by Bitstamp. This bridge allows Ripple transactions to directly end in on-chain Bitcoin payouts. It works by having a Ripple transaction send money to Bitstamp, who then converts the amount and sends Bitcoin to the recipient. The Ripple side takes the regular short time to confirm, the Bitcoin side is a regular on-chain transaction though, which will be confirmed as usual in the next Bitcoin block.

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