The symmetric-cone representation theorem

This excludes the stated geometric realizations. It does not prove that the underlying event posets admit no unrelated nonlinear embedding into a Lorentzian order. Nor does it prohibit Euclidean-ball sections of a Lorentz cone. The compact affine bases emphasize the presence of boundary segments in the orthant base and their absence in the Lorentz-cone base (Figure fig:bases).