Abstract

We continue XIV-D's unresolved characteristic composition problem for the unchanged binary pair. The first calculation concerns the complete six-branch smooth-slot expression, not the temporal component of one branch.

An exact regrouping removes the explicit second derivative of the scalar test from the combined $B_4+B_7$ expression and retains its remaining first-derivative terms. The coordinate-response branches $B_5+B_6+B_8$ combine into one divergence with all source coefficients present. The scalar-response branch $B_9$ is expressed through the complete advanced observation root. These are identities of existing tree kernels, not definitions of their joint contraction with the cross-lines.

We then identify the ambient spaces relevant to a common symbol calculation. The copied characteristic stratum has codimension four in the three-vertex space. Its intersection with the residual metric attachment diagonal has codimension eight in the common sixteen-dimensional space. The elementary sum of the three selected line phases and the attachment phase has differential rank six, rather than seven, while its critical set has codimension eight. It is neither a nondegenerate nor a clean phase. An exact quadratic identity exhibits the two transverse directions invisible to the linearized light-cone equations.

These results do not provide a different common phase, a joint symbol of the complete coefficient, or lower-order microlocal control. No complete cancellation or failure-of-cancellation theorem is obtained, and no characteristic prescription is constructed. The exact ending is Unresolved at E1, within D2/J2. J3–J5 and the quantum Ward-defect question remain unopened.