Abstract

We continue the operator route at XIV-H's missing internal amplitude theorem. The frozen pair, source, inverse coefficient, switches, width, and partial-diagonal ambiguity class are unchanged. The residual metric variable is retained.

For the two internal placements of $K_5$, we define a finite distribution-valued Fourier-amplitude module. It is not a classical symbol space on one ordinary Lagrangian. The fixed massless retarded multiplier has an explicit simple-pole decomposition near either nonzero characteristic sheet. This decomposition relates the noncharacteristic multiplier to the separated light-cone kernel, with its retarded normalization fixed by the already existing distribution.

We prove uniform annular estimates across the pole, continuity of the reconstruction map, and an exact finite decomposition into the highest normal-frequency degree and its lower-degree remainder. Both placements are reconstructed in their actual coordinates, with uniform control on compact sets of all untested variables.

This constructs the named internal amplitude map at I2. It does not construct the joint characteristic multiplication required for the grouped six-branch coefficient. A common precomposition presentation is supplied, but the operator map composing it with the grouped cross-lines on the retained characteristic locus is missing. The first unresolved gate is therefore I3. No joint section, characteristic prescription, transverse degree, gluing theorem, or output admission is released. In particular, no ${R_1}^{(1)}$ is admitted in ${\mathcal{E}}_H$, and XV-B remains closed.