An experimental AI-math challenge: using tenth discriminant bounds to explore arguments ruling out Siegel zeroes

In the spirit of my recent “Math 2.0” talk on new ways to use AI assistance to enhance the human understanding of mathematics, rather than substitute for it, I am using this post to propose an experimental challenge, inspired by the recent activity around excluding Landau–Siegel zeroes, as discussed in this previous post. There is a well-known connection between Landau–Siegel zeroes and the tenth discriminant problem, which I will briefly recall here; an in-depth discussion on this problem can be found in this survey of Shafarevich. As far back as the work of Gauss, it was observed that there were nine discriminants whose rings of integers for the associated quadratic field enjoyed unique factorization, namely Gauss believed this list of nine to be the complete list of such discriminants (the “class number one problem”), but this was only proven by Heegner in 1952 by introducing the concept of a Heegner point on the modular curve; and the above numbers are now known as Heegner…