Our real universe is macroscopically 4D. Hints come from every directions & show that it had to be so

In the multi-fold theory, spacetime results from 2D (fractal) processes at very small spatial scales then growing to 4D at larger spatial scales, where we naturally recovered a 4D macroscopic, and at large enough microscopic scales. So far, we invoked stability of GR reconstruction to justify 4D. In a recent paper, we argued that we have almost all the elements for a theory of everything, based on the multi-fold least action principle and multi-fold space time matter induction and scattering. There, we essentially assumed 4D at large enough scales, rather than deriving it.

This paper organizes past considerations before expanding and adding to them. The analysis is based both on conventional, and on multi-fold considerations. The conclusions are that the spacetime is 4D at large enough microscopic, and at macroscopic, scales, and only with 2D and 3D behaviors at the smallest spatial scales. At 4D, it can be continuous and equipped with notions of Hamiltonians, volume, areas or dot products / metrics / distances. It is not (asymptotic) AdS, and it has only one time dimensions.

In the course of our analysis, we encounter a few nuggets.  This paper provides a rigorous proof of why multi-fold spacetime reconstruction by random walk is 4D, and only 4D at large enough scales, and why (multi-fold) dark energy effects do not grow additional dimensions. Relying on random walks, and quantum cellular automata based on them, to model QFTs, we predict challenges in formulating QFTs at spacetime dimensions of 5 and above, except maybe for some CFTs, or when built using the random walks of extended objects like strings or branes in their AdS spacetime. This analysis extends to the QFT world. The case of dS universe is discussed.

Our analysis of Kaluza Klein (KK) dimensions leads us to propose that the Higgs presence in the multi-fold is also understandable as related to Higgs as dilaton in KK, and in the double copy between gravity and gauge fields..

We also explain why, on the other hand, AdS could be generated via the random walks of strings or extended objects, or non-conservative random walks, up to way higher dimensions, where one can still encounter (unphysical) supersymmetric or conformant fields. It infers why that story stops at 10D/11D, and fields misbehave at 26D for bosonic strings.

The paper includes some analyses of QCD and Electroweak interactions at spatial scales where spacetime appears 2D and 3D, and additional considerations on the mass gap in different dimensions.

Coupled with the Multi-fold Least Action principle, our universe has to be 4D at large enough spatial scales. No other physical solution is possible.