Abstract

We enter the joint-map obligation left unresolved by XIV-I. The internal retarded amplitude module, including both $K_5$ placements, is a copied prerequisite. It is not identified with the required composition against the grouped quantum cross-lines.

Two additional interfaces are established. First, a joint map on reconstructed kernels must annihilate the kernel of internal reconstruction. An explicit normal-distribution identity shows that the highest polynomial degree of an amplitude presentation need not descend to an intrinsic symbol of its reconstructed kernel.

Second, the supported response sector $K_6+K_8+K_9$ is put into an exact finite normal-jet form on the codimension-five response incidence. Its grouped cross-line composition is constructed on the local complement of the codimension-eight characteristic locus. The construction retains every normal derivative and both terms of the scalar root, and has an explicit wavefront bound. It is a reference theorem for that sector, not a composition theorem for the full six-branch sum.

A conditional normal-jet extension interface identifies the additional coefficient distributions that a supported realization would require. None is selected or constructed across the characteristic locus. No generalized joint composition for the full sum, complete joint section, transverse estimate, contact gluing, or output admission is supplied. The first unresolved gate remains J2. No ${R_1}^{(1)}$ is admitted in ${\mathcal{E}}_H$, and XV-B remains closed.