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@SebastianMeznaric: This is usually deterministic--- the "mixed state" stops being mixed as the time-steps become small, as the probability of deviating from the eigenvector path goes as "epsilon squared", while the number of timesteps only goes as 1/epsilon, so that in the continuous measurement limit, you have deterministic evolution. This only fails when the eigenvalues collide, which is measure zero, but at this point, you get a definite stochastic splitting depending only on the eigenvectors of the Hamiltonian just after and just before the collision.
@Mariano Suárez-Alvarez: I thought it's noncircular for sufficiently large n, that's why I phrased the example the way I did. It is probably circular for n=5. I am aware that this can be proved using "any subgraph of a planar graph is planar", and "K5 is nonplanar" or "Euler's theorem", all of which are preliminary results to 4-color-theorem, but it was not clear to me that this consistutes a circularity, as this is a statement with a quantifier, just a ridiculously easy one to prove. I was testing the limits of the question, in a sense. I agree it's not 100% in the spirit.
