Proposition: No global conical Cauchy inference

The regular conical product is not globally hyperbolic. The finite instrument construction does not require a global conical inverse.

Proof. Fix a radial ray, $r_0>0$, and $z_0$. For $A>r_0/c_{\mathrm{h}}$, the causal diamond between $(-A,r_0,{\phi }_0,z_0)$ and $(A,r_0,{\phi }_0,z_0)$ contains

The sequence approaches the excluded apex and has no convergent subsequence in ${\mathcal{M}}^{\circ }$. The diamond is not compact.

Every new calculation below concerns finite-dimensional operators and explicitly located finite ports.