Oh I see what you mean, the dome is a little bit pointy at the top, so the first derivative is not continuous. I missed that at first. Sorry. Still though, t

Oh I see what you mean, the dome is a little bit pointy at the top, so the first derivative is not continuous. I missed that at first. Sorry. Still though, this seems like a typical situation in physics where you get superposed solutions to a DE and then throw out the nonphysical ones. Someone else just created a new thread about the dome problem, and web search shows a vast literature about it (like there is for the Monty Hall problem). I guess you're already familiar with the literature so there's not much I can add. Superdeterminism isn't classical determinism, it's a specific idea in the interpretation of quantum mechanics. It's based on the idea that not only is it fully determined which box the particle ends up in, but it's also determined which box the experimenter will look in, and those forced choices conspire to make the experimenter think the particle is actually following the Born rule. At least that's my best understanding of it: physics isn't my thing. See: https://en.wikipedia.org/wiki/Superdeterminism https://en.wikipedia.org/wiki/Superdeterminism Besides the people mentioned in that article, I believe Gerard 't Hooft is an adherent. He has a bunch of articles on his site about a possible classical mechanism underneath QM. But, I think most physicists think that is unlikely. You might like John Baez's article "Struggles with the continuum", which is about various annoying singularities that come up in areas of physics including classical mechanics: https://math.ucr.edu/home//baez/continuum.pdf https://math.ucr.edu/home//baez/continuum.pdf