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I am aware that curvature is a complicated thing and I am simplifying a lot. Also, we need to be very careful about what are we calling dimension. As we are considering a (hyper)graph model instead of a vector space we do not have a natural concept...
With my limited knowledge on the subject I think the basic features to check are [dimension][1] (as we know our three classical dimensions), [curvature][2] (but I think we have some doubts on our universe's curvature), and the several conservation...
I think a general procedure would be directly in conflict with the computational irreducibility principle.