Does it matter whether any of this is correct?

(Mathematics at least has the potential for automated non-AI proof checking, although I don't think that's as widely used as you'd expect)

Does it matter if the Leiden Declaration is correct? To the humans, maybe but not in the bigger picture.

At scale, correctness and reward are becoming increasingly disconnected. Example: capital continues to compound regardless of whether it reflects underlying human welfare, just as information can spread regardless of whether it is true. Reality still matters, of course. If you want airplanes to stay in the air, somebody eventually has to be correct. The problem is that our economic and social systems are becoming less effective at distinguishing between what is true and what is merely rewarded.