Abstract

This manuscript continues XIII-C's joint-extension problem on the unchanged polynomial carrier. It does not continue XIV-B's relative antifield complex.

We freeze the switched metric–scalar vertex and the complete displayed second-order coefficient, including its scalar-sourced slot once. The eleven-branch decomposition, 48 labelled matchings, partial-diagonal ambiguity class, and elementary parallel-line extensions are copied. Individual line derivative orders distinguish those primitive results from the remaining joint problem.

The first new calculation is performed at a retained, noncoincident, null-collinear configuration. The three light-cone defining functions have differentials of rank two along a smooth characteristic stratum of codimension four. Their oriented conormals admit an explicit positive relation, reproducing the failure of the sufficient product criterion throughout this stratum. A retained component of the actual incidence has nonzero coefficient and nonvanishing differential symbols there. This does not determine whether the complete tensor and branch sum cancels the configuration.

A separate support lemma shows that the frozen collision contacts cannot alter any neighborhood disjoint from the collision loci. They therefore cannot supply an unnamed characteristic prescription. No uniform cancellation of the complete selected pair, and no prescription with the required ambiguity and wavefront control, is constructed. The first unresolved gate remains J2. The subsequent transverse, gluing, and output obligations are recorded but not opened.

The complete coefficient of $\lambda \hslash$ remains Unresolved. No nonexistence theorem, admitted quantum coefficient, residue subtraction, or Ward defect is asserted.