Redux: (∃ Stochastic Natural Latent) Implies (∃ Deterministic Natural Latent)

Once upon a time, John Wentworth and I thought we had a proof of a very useful looking theorem. We did not have that proof. An important intermediate step was shown[1] to be invalid and the whole thing crumbled and disappeared, never to see the light of day again...[2]Until now! I'd love to say that we came up with an ingenious fix to the old erroneous proof, but unfortunately it turned out to be a really infuriatingly hard nut to crack. Instead I spent the last ~month experimenting with various...