Certificate theorem and intrinsic slice geometry

The exchange has the four-region incidence of the type-A exchange in tHooft1993. Its scope is:

Type-A incidence only. Not the transition catalogue. Not a particle hop. Not a field equation. Collar subdivisions are declared interface, not a minimal polygon gauge.

Although the patch has trivial ambient holonomy, its marked slice is not intrinsically flat at every vertex. The calculation in app:angles gives the event defect

Each incoming triple junction and each outgoing triple junction has defect ${\kappa }_0/2$. Thus the exchange redistributes the central intrinsic angle defect while leaving the spacetime solution unchanged.

The event can be used in thm:spectators only with ass:blind. To use thm:locality, a computational metric and a block-diameter certificate must additionally be supplied. Physical patch size alone is not such a certificate.