Agreed. Lots of papers like this are submitted, but none have been right so far. Is there some reason to trust this one in particular? I'm not sufficiently familiar with this material to evaluate it.

This happened a few years ago when someone posted some code on GitHub that they claimed demonstrated P=NP, however it turned out not to.

This paper on the other hand is a more theoretical approach and appears to be more concrete than previous attempts that I'm aware of.

While it may or may not be correct, (experience hinting at the latter) it is interesting news, and an interesting paper nonetheless.

Actually, there appears to be nothing new, structurally or ideas-wise, and I don't think it is very interesting. The concreteness is all about creating a system of equations in terms of the bits in a multiplication. That's really trivial. Large and messy, but nothing new.

There's no concrete indication that I've found in this paper about how to solve those equations.

Yes, this is the implication of the paper, although it may be a bit of a jump from the main focus which is a little simpler.