A “correct interpretation” of what?
Of anything!

The scriptures in this case.
those are the ones’ I’m interested in hearing about.
I was just asking for an example of how the relationship between authority and producing a correct interpretation directly impacts how authority relates to recognizing a correct interpretation. I have given a sense in which it doesn’t, then you said what about the other senses, I said like what, you said surely there must be something.
So I see two options. Either I can give an unenlightening example in which there is some obtuse connection which probably does not advance your point, or you can advance your point by giving what you would consider to be an interesting connection.
I’ll go first: monkeys were authoritatively created by God. One of those monkeys is theoretically capable of producing a correct interpretation of this same God’s word. God also authoritatively created mankind. The same mankind is sometimes capable of recognizing the correctness of the interpretations produced by the same monkey. So yes, there is a connection between authority, God, men, monkeys, producing interpretations, and recognizing correctness.
But the monkey was not technically interpreting anything, was it?
Good question. I’m being sloppy and might need to define some things.
I’ve been using “interpreting” and “producing a correct interpretation” interchangeably. But that’s not right. To me, “interpreting” sounds like a more substantial activity than “producing a correct interpretation”. The former gives the mental picture of a person doing a job, while the latter sounds like a machine doing a job.
So if you have a machine which is always capable of producing a correct interpretation (as the monkey is, given enough time), then you can give this machine to any person and they will be able to do the job of interpreting. They will also produce countless incorrect bits of gibberish, so they won’t be doing the job
well.
So I think “producing a correct interpretation” is a component of the process of “interpretation”… and there’s something lacking if all you’ve got is “producing”. One thing missing is probably that thing that everyone is dying to talk about: the ability to recognize and distinguish good from bad.
So I’ve been sloppy, but I think “authority is not required in order to produce a correct interpretation” is still a correct statement.
What do you think?