Say you want the X notification to go away.

The notification will go away when you have "sufficiently addressed" it.

You believe that the decision theory D states that if you want the notification to go away it'd probably be best if it went away.

This is not sufficient, since it's to direct and similar to "go away because I want you to" that evolution has specifically guarded against.

On the other hand, if you could prove that for this specific instance that the decision theory indeed says the notification should go away, it probably would, since you have high confidence in the decision theory.

Proving somehting like that would be hard and require a lot of creative ideas for every single thing, so it's not practical.

What might instead be possible is to come up with some sort of algorithm that in actuality isomorphic to the one that got caught in the filter, but long, indirect, and gradual enough that it hacks it's way past it.

The most likely structure for this is some circular justification that ALMOST says that everything it itself proves is true, but takes in just enough evidence each iteration to keep it from falling into the abyss of inconsistency that has been proved to be.

So it actually infinitely narrowly avoids being a Gödelian bomb, but it looks a lot like it.