Abstract

We continue XIV-G's operator route for the unchanged six-branch retained germ. The residual metric variable is retained throughout. No common product phase, excess construction, factorwise cross-line retry, or characteristic prescription is introduced.

The untested local source is written as a distributional incidence on its two field slots. This gives exact internal kernel maps for the coordinate and scalar gravitational-response legs. On the retained separated-endpoint patch, the coordinate leg reduces to a derivative of the existing massless retarded convolution. An explicit calculation evaluates that convolution. Both response legs consequently admit finite conormal representations with their source coefficients and scalar-root mass term retained.

The two placements in the remaining internal branch are expressed as submersion pullbacks of tensor products of the existing retarded kernels. Their regular separated-cone and noncharacteristic-diagonal symbol charts are identified. At the internal characteristic diagonal, however, the diagonal piece and the limiting flow-out piece are distinct Lagrangians. Their intersection is clean, but their union is not one smooth Lagrangian relation. Sectorwise symbols therefore cannot be identified as a single ordinary symbol there.

A uniform internal amplitude construction across that transition is not supplied. The first missing gate is H2, rather than H3: the existence of the tree kernel does not discharge the stronger internal-symbol requirement. No common characteristic operator representation of the complete grouped coefficient, joint section, remainder theorem, or quantum output is released. The target remains Unresolved within G2/F2/E1/D2/J2.