I think I found the issue (Score 1)

I've plowed through the original paper and I think I found the part where (for me) it comes apart:

These technical results respect rather than undermine the principle of sufficient reason . The core demand of that principle is that every true fact must be grounded in
an adequate explanation. This forms the basis of science.

Here I think it goes off the rails. I think it is the other way around: the basis of science is for every explanation to be grounded in fact.
And you can debate this point all you want, but at the end of the day, you can't get around the simple fact that your explanation needs an explanation as well. The induction breaks down because there is no trivial case.
Observation has no such limitation: reality forces itself upon us. And whatever philosophers may claim: they do look left and right before crossing the street (the living ones do).

After this, the retreat continues:

Gödel incompleteness, Tarski undefinability, and Chaitin bounds do not negate this demand; they merely show that “adequate explanation’’ is broader than “derivable by a finite, mechanical procedure.’

Off the rails it is now! Faced with this gaping gap in the foundation, they are forced to redefine the foundation. Because they have no inductive basis they extend the induction to infinity! Turtles all the way down!

There is a contradiction and there are two ways out of it:
1. either the principle of sufficient reason doesn't hold
2. physics is doomed to the God machine T(x)

I have chosen mine, so have they.