Output wavefront theorem

After a defined joint distribution and actual proper pushforward, the required output is a compact degree-two residual-field kernel.

A sufficient target bound is

under the fixed Minkowski cotangent identifications.

This is an output bound on the residual field variables, not an intermediate attachment-kernel bound. Equation (eq:referenceWF) is not that output theorem: its attachments have not undergone the missing joint construction and pushforward.

Properness of the inherited tree datum supplies support control only. It cannot establish this wavefront theorem for an absent coefficient.

The branches and species channels outside the retained germ also remain part of the global pair. A successful local characteristic construction would still require the appropriate global compatibility before admission of the full coefficient.