history has a distinguished discrete foliation and an associated notion of (discrete) proper time, which ensures the presence of a well-defined causal structure globally (see [@cdtreviews; @physrep] for details on motivation, construction and results in CDT). Numerical simulations in 3+1 dimensions have shown that these modifications lead to a completely different quantum dynamics, compared to the earlier Euclidean DT model: CDT quantum gravity in 3+1 dimensions contains a phase whose nonperturbative ground state of geometry is extended, macroscopically four-dimensional and on large scales can be matched to a de Sitter universe [@cdt4d; @desitter]. Moreover, the theory has recently been shown to possess a second-order phase transition, which according to standard arguments is a prerequisite for the existence of a continuum limit [@trans].

The causal structure of CDT is realized by putting together its simplicial building blocks such that each CDT configuration has a product structure, not just at the level of topology – usually chosen as $[0,1]\times{}^{(3)}\Sigma$, for fixed three-topology ${}^{(3)}\Sigma$ – but [*as triangulations*]{}. A (3+1)-dimensional CDT geometry consists of a sequence of slabs or layers, each of thickness 1, which may be thought of as a single unit of proper time. The orientation of the light cones of 