(Quantum) spacetime as a statistical geometry of lumps in random networks

In the following we undertake to describe how macroscopic space-time (orrather, a microscopic protoform of it) is supposed to emerge as asuperstructure of a web of lumps in a stochastic discrete network structure. Asin preceding work (mentioned below), our analysis is based on the workingphilosophy that both physics and the corresponding mathematics have to begenuinely discrete on the primordial (Planck scale) level. This strategy isconcretely implemented in the form of \{cellular networks} and \{randomgraphs}. One of our main themes is the development of the concept of\{physical (proto)points} or \{lumps} as densely entangled subcomplexesof the network and their respective web, establishing something like\{(proto)causality}. It may perhaps be said that certain parts of ourprogramme are realisations of some early ideas of Menger and more recent onessketched by Smolin a couple of years ago. We briefly indicate how this\{two-story-concept} of \{quantum} space-time can be used to encode the(at least in our view) existing non-local aspects of quantum theory withoutviolating macroscopic space-time causality.