I am not a theoretical physicist, but I can’t take this seriously since these constructions of fixed coordinates and distances trivially break special relativity and so doesn’t model nature. (The problem as I understand it is that these efforts are mostly entertained by mathematicians with a physics interest.)

Even less seriously since I note a double sleight of hand. I couldn’t find a reference for the claim that “add quantum mechanics and the spectral dimension at short distances goes down from four to two.” However I found an article that relates to this one by using spectral dimensions on CDT structures. And of course in that specific case of *geometry* — not by adding quantum mechanics as such or even at all — the dimensions go from our 4 to the imposed 2! [ https://arxiv.org/pdf/hep-th/0505113v2.pdf ]

I call triple foul.