I'm somewhat in sympathy with Jonathan Burdick's pithy response, but of course in ten pages you do more that say that the map is not the territory. I take you also to say that the territory (reality) is not mathematical. I suppose that as a positivist, albeit I think you are too influenced by the post-positivists to really claim the name, you might accept that Physics is the systematic description of reproducible experimental results. Whatever systematization we use would then seem to be a part of mathematics, which leaves me wondering what principle or postulate you are proposing, or critiquing, to speak to the theme of the competition? [An empirical principle is, I take it by definition, a systematic view of some large body of experience, which to be successful must allow the construction of a tractable mathematics, whereas a postulate is something more in the realms of convention. Interesting that the competition is phrased in terms of postulates rather than principles.]
It is true that there are some parts of Physics that are apparently less systematized --more empirical or phenomenological, one might say-- than other parts, but where there is chaos there is the presumption that a better systematization might be possible if a good enough mathematician comes along. What is left to do is very hard, in the usual story of all the low-hanging fruit having been picked, but we have made better tools than our forebears. It is also possible that there is some part of the territory that only ever happens once, so that it cannot be subject of Physics taken to be a repeatable experimental subject. Indeed, the irreproducibility of quantum mechanical phenomena at the finest level of detail precisely underlies the turn to statistics, where there is reproducibility, and the idealization of statistics as probability.
In any case, there has been a constant interplay between Mathematics and Physics, a "battle" that has recently been going relatively less well for the Platonists, which I think many creative theoretically-inclined Physicists continually renegotiate in their attempts to construct new models, sometimes stepping into high theory, sometimes stepping into phenomenology, anything that helps in the construction of a new systematization of experimental data.