Razborov and Rudich, I just looked. The kind of paper where hand-waving arguments are dressed with impeccable technical proofs to arrive at a "rigorous" result which depends on a series of conjectures about NP. Haha, avoid, indeed. In fact, a "daunting" paper will often turn out to be something like this, so kudos to @Timothy Chow for "Do everything in your power to not read the paper."

This is not a good place to give strong justifications, unfortunately. But, logically, either 1) eventually teleparallel theory is brought to be exactly equivalent to GR or 2) GR is wrong and this one is right or else 3) it is nonsense.```` The consensus is on 3), I assure you.

I heard a senior person give a smashingly convincing argument about why exactly "GR CANNOT be described as a Yang-Mills gauge theory", too bad I cant remember the argument :-) You can read the paper by Pellegrini and Plebanski, it is available for download on researchgate. However, besides that opinion from the senior person about GR as gauge theory, there are other reasons to believe that ultimately the teleparallel gravity is nonsense.

Clever answer. The Fourier transform itself is used to obtain the Schroedinger propagator, by starting with $ U(t) = e^{-itk^2/2}$, then the Fourier gives the propagator $K = \frac{1}{{2\pi i t} e^{ix^2/t}$. And yes, $U(-t) * U(t) = 1$, but the Fourier transform itself not an example of this phenomenon as far as i can tell.