Isn't the 401 for LLMs the same single undecidable token? Doesn't this basically go to the undecidable nature of math in CS?

Put another way, you have an excel roster corresponding to people with accounts where some need to have their account shutdown but you only have their first and last names as identifiers, and the pool is sufficiently large that there are more than one person per a given set of names.

You can't shut down all accounts with a given name, and there is no unique identifier. How do you solve this?

You have to ask and be given that unique identifier that differentiates between the undecidable. Without that, even the person can't do the task.

The person can make guesses, but those guesses are just hallucinations with a significant n probability towards a bad repeat outcome.

At a core level I don't think these type of issues are going to be solved. Quite a lot of people would be unable to solve this and struggle with this example (when not given the answer, or hinted at the solution in the framing of the task; ie when they just have a list of names and are told to do an impossible task).