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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