Your claim was "A classical apparatus is part of the QM framework."
I just pointed out it is not, and gave you axioms that define QM, and asked where the classical part is. You ignored, as expected.
>But physics is not (and has never been) "pure math,
This is not clear. I pointed out three pretty solid places that seem to disagree. In fact, a huge chunk of advances over the past 150 years came from where? Pure math. Electron oribital structure - forced by spherical harmonics (we didn't measure the orbits, then write equations - we looked for harmonics, the math game them all, then we experimented and found them all). Spin, forced by the math (relativity + qm had no solutions - to get them forced the representations to have a spin component, forced by pure math, then we found them). Positrons and anti-particles - forced by the math (the equation for electrons had two roots, pure math, at first people ignored the second root, then they decided to look, and found anti-matter). Relativity - forced by the math (the underlying Riemannian geometry is extremely forced - and the "pure math" of it led to a century of predictions, all from the pure math, that later became observed). Noether's theorem underlying all conservation principles - forced by the math (and it's an astounding, very general priciple, devoid of any physical content, but once applied, out pops all sorts of conservation laws, some we had not even observed, all forced by pure math). Quarks, Higgs Boson, nearly all of modern physics - forced by the math, not the other way around.
This list is incredibly extensive, far beyond what is here.
This is why physicists reached the "Unreasonable effectiveness of mathematics" and "It from Bit." More and more of physics is being recast as information theory and computation, since it is becoming more clear that a significant amount of what we call physics and nature is forced by math. Some, like Tegmark as I pointed out, go so far as to claim all math is physics and we just don't see some yet, because our inputs, timeframe, and objervations of multi-verse things are so small. So to claim physics is not math (another of your claims that is too hand wavy and short-sighted to believe) is not demonstrable - it's your belief, one that is slowly but surely giving way to realizing how intertwined they are.
The idea that we simply observe nature than add more terms to model it is long gone. What to look for as pointed to by math, not observation, has led to so many physical discoveries that it is why physicists (and mathematicians, and philosophers) deeply question why is math directing nature, not nature directing math.
Since I provided axioms for QM without your requirement of a "classical apparatus," and you cannot show where in those axioms your "classical apparatus" resides, I guess that part is done now too.