Oh, speaking of brainfizzles on my part, may as well disregard my hunch above about relations being the "real" configuration space. The intuition that led me to that was based on a really really bad mental miscalculation of the number of degrees of freedom, confusing the dimensionality of the configuration space with the dimensionality of the associated hilbert space, and basically a whole bunch of mental booboos. So while the notion of 'violations' of some identities and inequalities might fit with curvature is still interesting to me, I'm, well, unbetting on that model. eye eeeeesh shtuuupid. :)