Self-contained setting and relation to predecessors

The equations printed below define the mathematical instance studied in this paper. Identifying that instance with a predecessor's frozen graph requires the same source-output conversion, component pairings, constant map $\mathsf{D}$, crossed array, and vertex normalization. Those identifications are not consequences of notation alone.

The source specification follows XII-C XIIC. The internal formulas follow the displayed retained architecture in Em01-B-v3, XIV-H, and XIV-J Em01B,XIVH,XIVJ. All operations used in the new calculations are either defined below or used with explicitly stated hypotheses.

Distributions have complex-bilinear pairings. Unless indicated otherwise, they are represented using flat coordinate densities. A smooth coordinate-density conversion is displayed explicitly or absorbed into a test or coefficient.

For tests supported in $L⋐U$, write

Strong distributional convergence means uniform convergence on bounded test sets. Such sets have a common compact support and bounds on all test derivatives.

For wavefront-constrained operations we use the normal topology: pullback and suitably supported pushforward are continuous, whereas the relevant bilinear operations are hypocontinuous BDH (Sections 3–6). Fixed compact tensor products and their pushforwards below are defined independently of a characteristic coincident-point product.