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Maybe it would be more clear if I used some examples.

Identity: mjevans on news.ycombinator.com

Authentication: is allowed to post as (Identity), is allowed to vote on things, etc.

Identity alone should not imply authorization, when someone is asking for a proof of identity what they really want is a record that you are actually an identity (authorization).

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I think you may have authentication and authorization swapped.

You're correct in that I'm grouping authentication and authorization.

The three types of tuples would include:

An identity (E.G. a person at an address).

Proof that you are that person at that address.

A list of things you're allowed to do at that address (IRL laws, or for a computer account publishing as that address/etc).

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