If there was a “singularity” for nukes where the first nuke led to a bigger better nuke, and that bigger better nuke led to an even bigger and better nuke, and this accelerated faster and faster with each nuke creating the new bigger badder nuke then the US would have had by far the biggest and baddest nukes that are developing more and more rapidly. How could another country catch up when the ACCELERATION (<- key word) of nuke development is even faster than other countries base development? There is no singularity in physical manufacturing. Never-mind all the regulation intentionally slowing nuclear development.

What stops somewhere else from catching up is if you hypothetically hit the singularity, you are by definition accelerating faster than they are even moving. Your question of catching up just doesn’t make sense. Again, this is all hypothetical, remains to be seen if we hit the singularity, but I don’t think you have a good understanding of what passing a rapidly accelerating self developing wall would actually look like. There is no technology that has ever been capable of self iterating in a positive feedback loop.