Dear Akinbo,
You ask interesting and deep questions! Is space purely mathematical, or is there such a thing as a physical space (independent from the processes that take place within it) that emerges from the math? What is a world and does it have a size?
I think there are always many different ways to look at the same thing (that's why I believe that we live simultaneously in an infinite number of different larger contexts), and I think that space is one of those things that can be seen either as physically real (so that space can bend or stretch according to relativity and Big Bang cosmology), or as "merely" a convenient mathematical construct to make sense of the phenomena that we observe. The concept of world also depends on your point of view: from one perspective, your world is the sum of all your sense impressions, from another, your world is all that lies within the cosmic horizon of the observable universe, from another, it is even larger, being the totality of what could potentially causally connect with you.
You ask if a world can perish. Once again, it depends on your point of view. I believe that capital-E Existence ("All that exists") exists in an "atemporal and eternal" way: I don't think it makes sense to say that it can be different at different times, because it would mean that there is a "time-counter" outside of capital-E Existence to make sense of this change, and this is impossible because capital-E Existence is all there is! On the other hand, when you look at a subset of reality, at a "local" world, it is quite possible to define a time-counter outside this world, and relative to this time-counter, this world can be born, evolve and perish.
The fact that worlds are born and perish is certainly one of many properties that worlds can have, but I don't see it as fundamental. For instance, I have no problems with eternal physical worlds, and mathematical structures are, by themselves, "atemporal and eternal". Of course, it is possible to define a mathematical structure that is related to another structure that acts as a time-counter, and relative to that time-counter, the first structure can evolve, even appear and disappear, so I think it is possible to define a structure made of geometric points (or extended geometric objects) that, in some sense, can be "born" and "perish". (That's why I have no problem in believing that a physical universe that is born, evolves and ultimately perish can be thought as nothing more than a mathematical structure.)
I've read you essay and I know that "perishable geometry" is a crucial part of the theory you propose, and I will soon post my comments about your essay on your forum.
Marc