***Why should we demand that any "stuff" we want to label already has some special properties to be called "principle" (not to say "holy principle").***
Remember where we are in your ontology. Anything physical behaves mathematically because it exists as a result of mathematics. Well, what do we have before mathematics? We have boolean logic. What do we have before boolean logic? We have "something" that we haven't defined yet what it is (i.e., it is undefined). Physical matter, vacuum, etc is defined according to mathematics, and therefore can only exist after mathematics exists (i.e., after boolean logic gives birth to mathematics - btw, I am not saying I agree with this but am giving your view the benefit of the doubt). So, in order for your ontology to be consistent this "something" would not be mathematical (e.g., false vacuum, matter fields, etc), rather it would be some holy principle that causes boolean algebra, mathematics, etc.
***"Something" may have very little features (say, vacuum, or time, or space) to assume that it may correspond to something else.***
Any properties in your view would need to be reduced to mathematics, but this is something that hasn't been defined yet. You can't have mathematical properties before you've defined mathematics.
***Or we then have to agree on what we mean by "principle" first (because I understand by word "principle" some relationship between two or more objects or phenomena, or classes of objects/phenomena). Say, symmetry principle (unchange under transformation): right=left, before=after. Or equivalency principle: gravity = acceleration.***
By first principle I mean an axiom that there is nothing more fundamental and that everything else in the world follows in some particular manner.
***So, I think, word "principle" is not proper word to describe labeling, or naming objects (or phenomena). It suggests, that there is something more than just an object itself.***
The problem here is that you think objects and phenomena are not only described by mathematics but is also dictated and exists because of math. Therefore, math is more fundamental. What makes math true then? According to your ontological model it is "something", but this "something" can't have mathematical properties (that's cart before the horse).
Warm regards, Harv