There is some truth in Platonism: All that we observe are instantiations of concepts that exist of themselves, in other words they do not owe their existence to their instantiations. However, the interaction between concepts and their instantiations is a two-way street. And concepts which we invent have no existence except in our heads.
Space consists of space quanta: Space, like everything in the universe, consists of quanta. Space quanta connect to neighboring space quanta, dynamically, so that space behaves as a fluid. These connections produce a vector geometry.
Space is the 3-surface of a 4-ball: Space is the result of uniform processes and hence has a more or less uniform topology. It has 3 dimensions, no boundaries, and is finite. The simplest topology which fits this bill is the 3-surface of a 4-ball.
Mathematical truths are the result of quantum mechanical processes: When the initial quantum popped into existence out of absolute nothingness, there was no mathematics. It has developed stepwise ever since, by means of the standard quantum mechanical processes of quantum splitting and resonance of quantum systems.
A priori natural selection: the universe selects solutions before making them real, in the sense of existing absolutely rather than existing as one solution in a superposition of solutions. This applies to the laws of the universe, life itself, the building blocks of life, genera, species and mutations of species. Solutions are subsequently subject to a posteriori natural selection - survival of the fittest - but that determines which solutions are eliminated, rather than which solutions exist in the first place.