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Exactly once processing is possible with idempotence keys over an at least once delivery system.

You've just pushed the problem down to the system that checks idempotence keys.

If you're referring to the CAP theorem, it needs some clarification: https://www.infoq.com/articles/cap-twelve-years-later-how-th...

It's not impossible. You just pick CP from the CAP theorem (and give up availability).

i.e., the message will be delivered exactly once if the system makes progress.

If you want an existence proof, NFSv3 had this working back in the 1980's. I doubt it was the first.

It does say, _Imagine_. Not sure what you're quoting, I don't see this text in TFA and your comment is not a child of another.