The model is “top down” in its mathematical development, also.  That is, each mathematical postulate has consequences. Each consequence generates a new feature corresponding to physical phenomena.  Thus, the postulate that points are distinguishable one from the other is a consequence of the physical phenomena of fields.  The characteristics of the fields are consequences of constraints by which the points are distinguishable from a primordial set of indistinguishable points.  The constraints segregate different spacetimes.  The characteristic fields of a given spacetime are consequences of the number of dimensions, the metric signature, and the resultant symmetries.