It's also very hard to verify the sources for some claims: I would expect the snag to be that many model theory results we have (Such as Gödel theorems) require quantifying over an infinite set, but that seems plausibly not possible to model in the physical universe. I quickly found this quote from the paper:
> Arithmetic expressiveness; LQG can internally model the natural numbers with
their basic operations. This is important as quantum gravity should reproduce calculations used for amplitudes, curvature scalars, entropy, etc in appropriate limits. Both string theory [34, 37] and LQG [35, 38] satisfy this by reproducing GR and QM in appropriate limits
Here the citations are four entire books. How am I supposed to very that LQG can model N with that?
> Arithmetic expressiveness; LQG can internally model the natural numbers with their basic operations. This is important as quantum gravity should reproduce calculations used for amplitudes, curvature scalars, entropy, etc in appropriate limits. Both string theory [34, 37] and LQG [35, 38] satisfy this by reproducing GR and QM in appropriate limits
Here the citations are four entire books. How am I supposed to very that LQG can model N with that?