That's not really possible. If you're writing a dissertation and find that some of the important foundational work you're building upon is wrong you can't just ignore it. If it's wrong, you need to say it's wrong in order to justify why you've chosen not to consider it in your dissertation. If you can't claim it's wrong, then you have to use it in your dissertation otherwise you're going to leave yourself open to criticsm that your dissertation ignores important prior work in the field. So the only choice you have left is to write your dissertation built upon work that you know is trash, and then if you do later choose to publish criticism of that work you're essentially trashing your own dissertation. And of course, none of that matters, because you're still going to face professional consequences when you choose to write the separate paper disputing the famous paper.

> Why not a) finish the dissertation as soon as humanly possible, and b) now that you're bona fide, publish a separate paper disputing the famous paper which your dissertation didn't rely on?

The last thing you want to do before pointing out that the emperor has no clothes is get a job at the palace.

(Re)-Read their story[1]-- they were fighting to publish the refutation as the first chapter of their dissertation. They wanted to publish no matter what.

Given that, choose your sword:

1. Grad Sword that must be approved by a dissertation committee

2. Master (well, PhD) Sword where you choose your own adventure

If you reply #1 then I'm logged in to a fake HN site.

1: https://www.theorgplumber.com/posts/statement/