Scope, the two gates, and the corrections

XI-E closed three routes and left one object outside all of them: the cubic Einstein response $u_3$ and its insertion ${\mathcal{C}}_3$ XIE. XI-E computed the classical variation of ${\mathcal{C}}_3$ on a witness and found a second nonzero number $I$, distinct from the $I$ that its split cancellation had already removed. It did not admit ${\mathcal{C}}_3$ to its Hadamard algebra, and it did not compute the gauge-fixing companion of the cubic variation. Those are the two gates here.

1. Admit ${\mathcal{C}}_3$ into the polynomial on-shell Hadamard algebra ${\mathcal{E}}_H$ of XI-E, or exhibit a wavefront direction that leaves its polynomial microcausal class.

2. Compute the order-$\kappa$ variation of the de Donder term under the single-field transformation law, from XI-B's gauge fermion, and its retarded response through ${G_{\mathrm{gr}}}^{\mathrm{R}}=-\mathcal{P}{{\mathsf{E}}_0}^{\mathrm{R}}$.

3. Assemble the second-order variations on the XI-E witness and decide whether their sum vanishes on the plateau, with the off-plateau support stated.

4. Say what the result is not.

The three endings of the series apply to each gate: Constructed, Proved obstructed, Unresolved. The worst ending governs the release.