

Actually, F_QG is itself an assumption which isn’t backed up. See the paragraph before the one you quote when defining it. The beauty of axioms is that we can assume whatever we want but we need to either show nothing goes underneath it (eg Peano axioms) or have a very compelling case to make them (eg non-Euclidean geometry like parallel lines meet at infinity). This is a metasumary of some similar research at best. It’s not a proof in the way you think it is. Just because you don’t understand what you’re responding to doesn’t mean you’re right.






You’re missing the initial step.
Both OP commenter and myself take umbrage with #1 (if I can speak for them; they make disagree with me). I assume that if we trace the sources for the letter that we’ll see the reasons we’re able to make all of these logical leaps using other results in the field that come out of these proposals. I also assume that, if one of these systems is the foundation for a fully consistent theory of quantum gravity, then its conclusions are valid. This paper doesn’t address that initial assumption though so things like the article summarizing it are begging the question.
There are many situations where we just have to agree to assume. If you read 14 and 36, you’ll find some of the core assumptions that go into this letter (both interesting ideas and the same authors so you can understand why they’d continue). An assumption Faisal makes is the rejection of objective observability which is one of those things you either believe or don’t believe. It’s analogous to the axiom of choice in that it could be contested but could be generally accepted.