Since all theories trying to unite and reconcile quantum theory with general relativity kind of failed, I wonder if one of the two theories doesn't have some structural errors.
At the time being we have no experimental access to the regime where quantum gravitational effects are relevant. So no theory of quantum gravity has been falsified experimentally. That is, none have failed because they didn't match the experiments. The experiments have not been carried out yet because we don't have the technological ability to do them or we haven't had the ingenuity to infer how to retrieve experimental data from available sourced.
The real problem is this: both QM and GR have been proven by experiments to be wrong. GR predicts entirely wrong results for the motion of electrons and other small particles. QM predicts wrong results at galactic scales.
However, they both work very very well at certain scales. So we don't want to get rid of them. Instead, we want to find some rule that tells us when to use the math of GR, and when to use the math of QM, so that we don't need to guess and just pretend that they are right.
You can find euclidian geometric proof of some standard arithmetic theorems, but geometry isn't the right tool to prove really complex arithmetic theorems.
Try to make euclidian geometry complete enough to resolve all arithmetic, and you will probably find yourself in front of contradictions (I stopped doing math after my bachelor, so I clearly might be wrong about that).
Why do we need to expand th9se theory? First correct the issues left within the defined context. Then find more contexts and see if you can define a new theory or use an old one?
To oversimplify, the fundamental lemma of the project posits a direct connection between the generalized fundamental representation of a finite field with its group extension to the automorphic forms under which it is invariant. This is accomplished through abstraction to higher dimensional integration, by an equivalence to a certain analytical group as an absolute extension of its algebra. Consequently, this allows an analytical functional construction of powerful invariance transformations for a number field to its own algebraic structure.