> Why is (bent) space-time (1+3)-dimensional?
> Why is it an SU(2,2) which is the covering group of fully quantized General Relativity?
Only a handful of more or less evident postulates is needed in order to deduce that fundamental physics must be based on an atomistic model and that the number of degrees of freedom should be some small power of 8 in terms of a degeneracy expansion. Irreducibility, then, is slicing our world into separate bent universes orthogonal to each other.
After deriving Einstein's "World Formula" from first principles, its evaluation provides a consistent Quantum Gravity in fully quantized space-time on its first degeneracy level - as a singlet representation with respect to the Grand Unification (GUT). Its second degeneracy level adds "internal" forces as vector representations of the GUT. A particle (viewed from outside) and our universe (viewed from inside) are subject to identical equations.
Finally, the mechanism is derived how a particle is condensing out of Dark Matter.