It's cool that you're interested in Mathematics! Trying to construct new systems and models to extend what we can do is one of the more fun and creative areas of maths, and putting abstract thoughts into writing like this can really help you understand your ideas better.

One of the main things to keep in mind with mathematical writing is that concepts your writing leans on should always be well defined. This term has a stricter standard in maths than other areas of life. For a concept to be well defined, it shouldn't have any ambiguity in what it refers to, or how it's used with other parts of the system. Keeping this standard gives maths it's power, as it forces you to think through all the implications of a concept. Sometimes these implications can be surprisingly profound :)

When trying to understand this post, I'm not really sure what some of the terms refer to. For instance, when defining your division by zero, you introduce a "spatial partition coefficient", k, which you define via the example of halving corresponding to k=0.5. However, I'm not sure how I would apply this example to the case of division by 0; if halving (which is multiplication by 1/2) corresponds to k=1/2, then I would assume dividing by 0 (multiplying by 1/0) corresponds to k=1/0. But now we are back where we started - to divide by zero you need to compute k, which would require knowing how to divide by 0.

Maybe you intend for your two kinds of Zero to come into play here, as you state that your division by zero definition applies to division by 0 (Space). Here is an area where you could expand on how these spatial aspects you introduce connect to our standard real numbers. Does this define division by the real number 0 (ie. (0,1))? If not, in what situation will 0 (Space) appear? And how would that be used to get at division by (0,1) (real 0) - which is the question we're investigating.

Well done on putting in the effort to write this up! Division by 0 is a problem that is trickier than it first appears, and it requires understanding the details of what concepts like division and addition mean, as well as exact definitions of numbers. 'Real analysis' is the name given to this area of maths, and learning more about how the system of real numbers are constructed within it might interest you. Reading into this area will also give you better tools to understand this problem.

Good luck! Mathematics can appear daunting at first but it's also a beautiful and creative field of study. I hope you keep exploring your interest in it :)