Necessary limitations of the geometric claim

The admitted faces may be nonconvex and regular vertices need not be trivalent. This certificate is not an admission theorem for every stricter polygon calculus. The simultaneous three-to-six expansion is not claimed generic in the space of all slicings, and is not identified with one universal elementary transition catalogue.

In $3+1$ dimensions there is one event parameter and an axial event locus, not an isolated singular event point. Only a transverse section has the finite vertex/edge/face counts. The axial product is stated explicitly; no compact axial taper or additional event-free interpolation is inferred.