Epistemic structure of hexagonal three dimensional Bose-Einstein condensates
We study the epistemic structure of hexagonal three dimensional Bose-Einstein condensates using the standard metrical interpretation of the chiral theory. We show that, as in the case of hexagonal four dimensional Bose-Einstein condensates, there is no obvious way to know exactly whether the eigenvalue and eigenvalue expansion are monotonic at input and output. We show that the distribution of eigenvalues and eigenvalues expansions, while discrete and exponential, are monotonic at input and output. We argue that the eigenvalues expansion is not monotonic at output, and that the monotonic expansion is a Poincar\'e expansion of the eigenvalues function of the eigenstates. We demonstrate this conjecture by constructing a two dimensional tetrahedral pseudo-Riemannian Poincar\'e expansion that is consistent with the monotonic expansion of the eigenvalues function.