The purpose of a valid DKIM signature is to identify the party that
signed the message.
Here, you are completely correct.
Whether this is a first-party or third-party signature is largely
irrelevant.
Here, you are correct only if you restrict your vision to DKIM-BASE. Once we
start talking about DKIM-SSP, first-party vs third-party becomes extremely
relevant.
--
Arvel
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