Proposition: Alexandrov–Zeeman classification, conditional

For $D\ge 2$, C7${}^{\mathrm{cal}}$ implies that every group element is an orthochronous Poincare map. If the theory also has the sharp boundary relays, its maximal operational speed is frame invariant.

Proof. The causal-automorphism theorem gives $g(p)=a+\lambda Lp$, $\lambda >0$, with $L$ orthochronous Lorentz Alexandrov,Zeeman. Its spacetime volume multiplier is ${\lambda }^{D+1}$. Calibration forces $\lambda =1$. Operational preservation and transitivity then transfer the upper bound and its boundary attainment between admitted frames.