Abstract

The regular conical product prescribed in I-B is not globally hyperbolic. Consequently, an intrinsic wave evolution requires an additional choice at the missing apex. We construct retarded and advanced inverses of the Klein–Gordon equation from a specified semibounded self-adjoint spatial extension, including flat complex line bundles with prescribed holonomy. We classify the rotation-diagonal, spatial-product extensions considered here and give their exact positivity criterion, distinguishing transverse bound states from the continuous bands they generate after adding the longitudinal direction.

For the Friedrichs extension we prove two-sided Green identities, an exact sequence on the extension-dependent spectral smooth domain, and finite propagation with respect to the intrinsic spatial distance. We derive a Sommerfeld–Carslaw–Dowker representation consisting of finitely many geometric terms and an apex-diffracted term. The latter begins at the broken-path length through the apex. Angular lift factors, local parallel trivialisations, image boundaries, and the advanced sign are specified explicitly.

A supported transfer theorem identifies the intrinsic scalar operator with the flat-completion operator before the first additional arrival. Its use in the Enter companion sheets also requires their independent retained-shadow and laboratory-margin hypotheses. A finite supplied-report catalogue is constructed without interpreting finite numerical agreement as a distributional identity or as acquisition of a continuum field. The reported numerical discrepancies from the supplied draft are retained separately as unverified numerical data. General non-Friedrichs propagation, non-diagonal extension families, spinor and gauge constraints, uniform flat limits, states, and interacting products are not constructed.