I don't think "intellectual poisoning" is really the mechanism that harms the mathematics community.

The harm is if you have a community of mathematicians who are focused on expanding human understanding, then having instant access to a bunch of AI proved results muddies the water about who has contributed what. If someone could scoop any significant theorem at any time by pointing an AI at it, how do you really demonstrate that you have created new understanding? Or that your new understanding is about something important? How do you prove that the AI needed your new concepts to be able to solve it?

I do see how this is a problem in terms of assigning credit, but I think the cat is already out of the bag in terms of these models being capable. Even without AI labs spending millions of dollars to solve millennium prize problems, there are plenty of other people who will use them to pick low hanging fruit. I don't think any social solution is going to make things go back to the way they were, where you could share your progress towards a famous open problem without risking someone "scooping" you within a couple of days.

I think that the most likely outcomes are either mathematics becomes more secretive, or there is a more deliberative approach to assigning credit than who was "first" to solve some problem. In the former case, this may slow down progress, and in the latter case, this could mean that credit would become more subjective, and be a continual source of controversy.

It seems like restrictions on the model talking about non famous people might have been responsible for the appearance of the models being unable to do this.

I would really suggest you rewrite the README, to remove the cliches and make it clear how much effort you put in. You clearly are able to communicate well about this project on your own.

I hate to say this, but this submissions readme seems obviously AI generated.

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I am thinking of an example like constructing two incredibly large numbers (of the same sort as grahams number) where it is not known which is larger, and then e.g. doing x damage to a creature with y health. Ideally this happens in a way that nobody would object to the construction if x and y, since they are simple to describe and construct.

I understand that you can construct a turing machine to perform an arbitrary computation, but that defeats the spirit of this question. The question is whether there is a simpler way to construct such a paradox where you might follow along happily until you get to the end.