Understanding the place and use of probability theory in the submicroscopic is critical. The reasons, conceptually, why it is necessary to describe phenomena observed as particulate/wavelike in terms of probabilities are very valid. The H principle is experimentally verified, and rock solid. It is not in any way "untenable". Mathematics is not used as a "proof", not in this universe anyway. We use math to describe and model reality. The fact that the universe can be comfortably, if not perfectly mathematically described is a fact scientists take to have great significance. We can extrapolate from mathematical models, but we always do so with caution, keeping our eye on field observations...and realizing we are in uncharted territory, and on theoretical ground.

I'm not particularly impressed with your "reinterpretation" of experimental results either. I would honestly suggest you carefully rethink your work before you challenge a concept with such veracity.

Best wishes in your quest!

Sam Cox