Hi Domenico,
First my contestant pledge: goo.gl/KCCujt
You make a good point very succinctly: There is something about our universe that encourages both the preexistence (in physics) and emergent formation (in language) of "compact description[s] of ... knowledge and fundamental objects."
Thus your answer to the FQXi challenge question is (I think) that "fundamental" means any mathematical or linguistic description that compactly captures a large body of behavior or knowledge. That is pretty much how I also define it in my essay "Fundamental as Fewer Bits". I just used up a lot more bits -- I was less compact! -- in my essay.
Structurally, though, the top half of your essay is hard to read and has many assertions that are highly debatable. I think for example that you are trying to say that the ancient concept of defining units of measure (mene, mene, tekel, upharsin comes to mind) is itself an recognition of compact conservation rules, that is, an explicit recognition that certain quantities of the physical universe persist over time without either increasing or decreasing, and so can be measured in a uniform way. But if that is your point, it's hard to extract from the essay
Also, further down you you make assertions about physics that are very hard to interpret. For example, your essay asserts that the experimentally very well-grounded and readily lab-accessible special theory of relativity has postulates that are "unprovable laws". You then rather mysteriously assert that the general theory of relativity, which is hugely less accessible since it operates more at that astrophysics level, is composed of "physical laws". That is very hard logic to follow, whatever your intent may have been.
So, overall: I think you have made and excellent point about the importance of compactness to a rule or description being "fundamental." It makes me feel a bit dumb for taking so long to say the same thing in my own essay. But the essay itself, even in such a short form, is tricky to understand and asserts too many things that are at best dubious assertions. That aspect of your essay distracts from your main point.
And I do I like the boldness of your brevity!
Cheers,
Terry