E3: downstream gates and the Ward-defect boundary

J3 opens only for a distribution supplied by a successful E1 or E2 construction. The copied parallel-line degree eight is a collision degree, not a degree along ${\mathcal{N}}^{\circ }$.

The exact integrations by parts in Theorem thm:regroup do not supply uniform transverse bounds for the unresolved characteristic product, larger collision strata, or their intersections.

J4 remains closed: no characteristic prescription has been composed with the singular spectators and compatible partial contacts.

J5 remains closed: inherited properness applies to an existing distribution. It does not construct (eq:target) or prove the required output wavefront bound.

The intermediate attachment-kernel bound of Proposition prop:kernels is not the J5 theorem for the degree-two residual-field output.

No $s_{\mathrm{ext}}$, $s_{\Psi }$, or $s_0$ is applied to ${R_1}^{(1)}$. No binary Ward defect is formed. The already constructed tree coefficient is not substituted for the missing quantum coefficient.

The classical breaking density from XIV-A and the relative complex of XIV-B remain separate from this analytic problem. Neither the value $-8I$ nor a classical evaluation identity normalizes the graph.