Advanced Mathematical Proof Prompt

I have to create a really hard math statement like graduate-level hard that requires a full proof. It has to be original, not copied from anywhere, and it needs to be difficult enough that AI models are likely to mess it up when trying to solve it. So basically Im designing a high-level math problem thats intentionally tricky but still mathematically correct

Pose a statement that needs graduate level mathematics to prove. You can leverage research papers, qualifying exams, part 3 exams and other open source materials as inspiration. DO NOT copy anything verbatim – be sure to create your own valid question. If your proof statement requires a reference graph or model, please upload the graph/model here. Note: Your statement must be incorrectly solved by the models to qualify for this project. Submit this block to generate the responses! Note: for topology tasks, always specify in the prompt whether manifolds can be manifolds with boundary or manifolds without boundary. This is important for the models to understand.