Space is a 3-surface which is produced by dynamic tensions between 'neighboring' space quanta
the phenomenon space. To explain that which manifests itself as space adequately, we must account for a few basic properties. Space is place. Two objects cannot be in the same place at the same time. We experience space as being 3-dimensional. It is distorted by gravity. The combined speed of objects through time and space is always equal to the speed of light. Nevertheless, whenever a wave function 'collapses', the results are expressed instantaneously regardless of distance.
Space has 3 spatial degrees of freedom
In QM, the number of degrees of freedom of a wave determines its very nature. It is a number which must be fixed before the wave can exist. So the answer to the question "Why does space appear to be 3-dimensional?" is that this was determined before space came to be, perhaps at the stage where natural purpose operated to choose a viable universe out of the countless possibilities for universes to exist. Note that we cannot rule out that there are more spatial dimensions, as string theory would have us believe, but choose not to pursue such possibilities whilst the explanations with lower Occam Scores have not been exhausted.
Space consists of quanta
If all that is arises from a single, ultimate quantum, the Occam method dictates that we explore the possibility that space arises by means of the same mechanisms as anything else, namely quantum mechanical processes. In these processes, quanta produce more quanta, and never something that is neither a quantum nor composed of quanta. In other words, space consists entirely of quantum phenomena. It is composed of discrete things – quanta of space.
There must first be space and only subsequently particles, because a combined genesis of particle quanta and space quanta would result in the particles having much more (positive) mass-energy than they produce in (negative) gravitational energy, giving the universe a net positive energy. But that would violate the principle of conservation of energy, which, in combination with QO, dictates that the net energy of the universe is zero at all times. Space quanta as such have no net energy, so they can be added without such problems. Space quanta split into more space quanta, which split into more space quanta, and so on, creating space.
The structure of space
Space is the result of space quanta splitting, whereby the new space quanta retain the edges that the parent quantum had with neighboring space , and connect to each other. These edges have a tension, which is the basis of gravitation and of the structure of space. The links are also the basis for distance. Essentially, the distance traversed is measured by the number of edges traversed.
Note that when a space quantum splits, space expands into itself. For the space that is not immediately adjacent to the split quantum are not affected directly. A circle around the split quantum will have the same number of edges and hence the same length as before. A surface enclosing the split quantum will have the same number of space quanta and hence area as before. But they will enclose more space quanta and hence have a higher volume. Regions of space which have a greater volume than their surface area dictates we call rich space. They are rich in the measure of the imbalance.
When regions of rich space are surrounded by regions of less rich space, there is a process of diffusion, evening out the difference in space richness.
The topology of space
Space does not have a boundary, because there is no reason to prefer one set of edges and nodes as a boundary as opposed to another. Space is more or less uniform, because it everywhere develops according to uniformly operating processes. We would therefore expect space to have a symmetric topology. The simplest topology which fits this criterium is the 3-surface of a 4-sphere.
Note that the assumption that space consists of quanta leads to the conclusion that singularities do not exist. No distance smaller than the distance between the centres of two space quanta is physically meaningful. Hence forces, energies and whatever other physical quantities there may be that tend to infinity as the distance between two points at which they operate tends to zero, are in practice limited to some finite value.
Space and the arrow of time
Note also that the expansion of space is irreversible. Space quanta can come into existence, and once they exist there is no process by means of which they cease to exist. This should not surprise us. All persistent quantum events are irreversible. Time has an arrow.
This explanation is a possible result of the QO assertion that everything that exists is a quantum, which is operationally credible. Any theory in which space is continuous depends on an account for the origin of the universe is at least two notches worse on the Occam Scale. However, we have not demonstrated that this explanation is the only possible explanation for space which is compatible with this assertion. There may be other explanations which are more credible, but unimagined and perhaps unimaginable. Therefore this explanation is tentatively credible.