From the abstract:

"Assuming [assumptions] we show that ... can in principle solve..."

Yeah, well, you know... that doesn't sound as promising as the title.

Assuming X is true, that implies Y. We don't think Y is true therefore we now doubt that X is true, is a very standard thing to do in math.

Yes, but the title suggests that "[method] solves NP-complete problems", and sounds kind of like "Quantum-Physics-related trick solves NP-complete problems".

Moreover - it doesn't even solve NPC problems conditionally, but that show that "in principle" they should be / would be solvable.

That's the whole point of the article:

"We show [Assuming {competing physics theory} then {P = NP}]"

(or something along the lines)

"But we actually think P != NP... so [Assuming {P != NP} then {competing physics theory} cant be true]"

[deleted]

Shocking..