Vladimir,
It is a very thoughtful and well written essay. The problem is that I dispute the central premise. An ideal is not an absolute and that is the core of your argument. The absolute is a universal state. Shapes are definition, delineation, form. Absolute zero is not a point, line, circle, sphere, etc. It is the complete absence of energy and thus the interactive connectivity which builds complex reality out of the most elemental energies arising from that absolute state of the formless vacuum. Zero is not a point, but empty space. All of physical nature, even the biggest galaxies and galaxy clusters, are little more than minor fluctuations in the infinite vastness of space. When we measure time, we are only measuring action, while point, location, distance, area and volume are all aspects of space, not the basis for it, as geometry presumptively assumes. Like Roman numerals, geometry doesn't even have a proper zero, because it treats the center point as zero. A real zero would be the absence of any actual mark. Empty space/the blank sheet of paper.
We exist as an effective point in space, so we describe reality from the perspective of the point. Thus space becomes this three dimensional coordinate system, located on the center point, while time is the sequence of events, from past ones to future ones, rather than the underlaying physical dynamic which forms and erases these events, taking them from future potential to past circumstance.
You inductively distill out these ideal forms as being essential, but consider how nature actually creates them. There are much more spheres in nature, than square boxes, even though both are basic ideals. That is because it is much easier for nature to produce a sphere by congregating energy around a point, while a box requires much fairly precise interaction of different energies pushing against each other.
The fact is that if you have nothing, you don't need any laws or forms to govern or define it. No energy, no information. When you start to have the most basic energies, pulling against/pushing against each other, etc, then you start to have the most basic forms/laws defining their actions and interactions. The more complex things get, the more complex the principles arising from them get.
Physics creates math. Not the other way around.
I score you well for clarity, it's just that what you present so clearly is incomplete.
Regards,
John