Another thing I think people might mean when they say "I own the data" when they've only signed the data is that others can't "own" the data. But, they can.
The singular important thing that digital signatures provide wrt to data ownership is the ability to say "I own the means of authenticating my possession and intent to sign this data."
In my mind signing is identity.
if you sign a post you are saying the person who knows the secret to this public key posted this.
If we think about a repost or a retweet, signing it would by a way of endorsing it or proving that a certain person wanted to spread the info contained in the post.
When it comes to self referential data (like a will or a contract) signing makes a lot of sense and almost matches up with what seems to be the normie understanding of it.
With creative data (writing, thoughts, art) it probably isn't as useful. But then, the idea of needing to sign art has always been a little funny anyway.
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