According to the Random Dynamics philosophy, chiral fermions may be more fundamental than geometry. And from the point of view of the Planck scale, all fermions are Weyl particles, thus Weyl equation is the basic equation ruling the world of matter.

By assigning this primacy to the Weyl equation, 3+1 dimensions are furthermore "derived". The argument is that in a non- Lorentz invariant world, the Weyl equation in 3+1 dimensions requires less finetuning than other equations. This means that the Weyl equation is especially stable, in the sense that even if general, non-Lorentz invariant terms are added, the Weyl equation is regained. In this scheme both 3+1 dimensions and Lorentz invariance thus eventually emerge.

Here is an explicit description of the derivation: "Lorentz invariance derivation for beginners".