while sticking to two types of links, one spacelike and one timelike, where we will continue to use the notation $\ell_s^2$ and $\ell_t^2\! =\!-\alpha \ell_s^2$ for their squared lengths. Fig. \[fig:fourtriangles\] shows the four types of triangles which can be built from these two link types. By calculating the metric inside the triangles one finds that there are exactly two which have Lorentzian signature $(-+)$, the two at the centre of the figure. We will call them the $sst$- and the $tts$-triangle respectively, in reference to the spacelike ($s$) and timelike ($t$) edges they contain. Note that in standard CDT in two dimensions only the $tts$-triangle is used.

The use of Lorentzian building blocks is not a sufficient condition for the triangulation to have a well-defined causal structure locally, we also need to check that we obtain well-defined light cones in points where triangles are glued together. If the gluing happens according to the standard rule of only identifying links of the same type (spacelike with spacelike, timelike with timelike), the only local causality violations[^6] can occur at the vertices of the triangulation. Counting past and future light cones separately, the point is that one may obtain more or fewer 