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The protocol isn't finished yet, but there are implementations - I believe the primary one is Cyrus: https://github.com/cyrusimap/cyrus-imapd

Yes, in Cyrus IMAP we take care to follow the latest spec. It's the version that drives the JMAP backend at FastMail.

The JMAP website has a list of other clients and server: https://jmap.io/software.html