Hi Tejinder, I like your essay very much.
Although your classification into categories of of things and laws works, I think the names themselves might be ambiguous and cause confusion if this is used elsewhere. At first I didn't like the use of 'thing' as it seemed to belong to objects but I see that it can be extended to related ideas. Space would be thing-where, time thing-when, motion thing-happening, object thing-exists. All sorts of 'thingness', which is a term you use later on. Law too seems, at first, to belong to specific kinds of prediction or decrees of how things should be. Yet, the contents of the set of law such as qualia and measurables are (to some extent) predictable consequences. At first you have all of mathematics in there but later it seems there is a question of the whereabouts of maths' natural home.
The separation of motion, thing(-happening), from law, velocity, is useful. Distilling thing(-exists) into quantity is a mental process. Taking your example of a brick, without the mind there is just the brick and not the distilled quantity. Distilling thing(-happening) into a singular measurable involves some kind of measurement process, which need not be entirely mental treatment of sensory input but also some kind of interaction with the measured. Yet, the outcome of the process and any additional treatment such as calculation does end up with a mental 'product' that is known. Which is distinct from the thing. Taking the example of velocity, without the decision of how it is to be measured, that is 'relative to what?' the motion is undefined, not distilled into a singular value .
Up until you start to blur the separation of mind-brain and consciousness law, and thing, I am in broad agreement. The spacetime you propose I can see relates to your previous work, in references. Certainly time needs to be non commutative because when things happen is very important. Such as the building of the sequence of a protein chain. Having a sequential, non commutative time does not, as I see it, mean that "everything happens at once" but merely that it is the same time everywhere, yet things still happen over the passage of time. Nevertheless, I realize you are talking about your own specific model.
Mathematics can be 'distilled' from observations of nature and then be used to compare similar circumstances or objects. That there is similarity or sameness of the mathematics seems to me to likely be a consequence of the similarity of what is compared rather than the mathematics being causal. All exponential growth of what ever kind is mathematically similar not because the 'numerical pattern distillation' is causing it to be but because of the similarity of the happening; hence the 'distillations' are the same. I think that is agreeing with your idea that the mathematical answers are in the things themselves (bricks example). Which it seems is true for quantities but not measurables which are relational.
Good thought provoking read. Kind regards Georgina
