This may be a silly question, I'm no expert. But why not simply define as AGI any system that can answer a question that no human can. So for example, ask AGI to find out, from current knowledge, how to reconcile gravity and qed.
It's conceivable (though not likely) that given training enough training in symbolic mathematics and some experimental data, an LLM-style AI could figure out a neat reconciliation of the two theories. I wouldn't say that makes it AGI though. You could achieve that unification with an AI that was limted to mathematics rather than being something that can function in many domains like a human can.
But consider: technically AlphaTensor found new algorithms no human did before (https://en.wikipedia.org/wiki/Matrix_multiplication_algorith...). So isn't it AGI by your definition of answering a question no human could before: how to do 4x4 matrix multiplication in 47 steps?