What is space?
Space is a pattern in a tally of comparisons, with no container underneath it. Observers meet at shared boundaries, and distance is how many comparisons separate two of them. Each piece of the world has twelve readings, one per port, and repair splits them into bands that fade at different rates, and only the slowest band lasts long enough for two observers to compare a position in it. That band has three directions. An observer's position is six whole numbers, one per pair of opposite ports, each counting comparisons out through one port less those in through its opposite. Those points crowd in everywhere, and filling in their limits, as the real numbers fill the gaps between fractions, gives smooth continuous space. The only geometry put in was a list of which port is wired to which.
Also in Chapter 12: Why Is the World Made of Relations and Not of Things?, Appendix A: Eighteen Questions.
This answer comes from OPH, Observer Patch Holography. OPH is a rigorous, consistent and complete description of the unified, self-creating computational Universe we inhabit. Its consistency is machine-checked: the fixed point at its core is constructed explicitly, and a theory with a model contains no contradiction.
To understand OPH and check every step yourself, start with the free book Reverse Engineering Reality. It builds the theory from the ground up, and the OPH Notebook answers your questions while you read.
read the free bookask the notebookor ask sage:read chapter 15: Why Does Space Have Three Directions?watch a universe make its own particles