Scope, the four gates, and the corrections

XI-F released two gates for the cubic Einstein response and stopped at a third XIF. Gate F1 proved the frozen representative of ${\mathcal{C}}_3$ obstructed: zero Cauchy data for the second coefficient together with an unswitched, unramped cubic source produce a sharp onset $\theta (y^0)$ in a metric slot, and $\pm \mathrm{d}t\in \mathrm{WF}$ at $\Sigma$. Gates F2–F3 constructed the classical plateau sum with ledger $-I+I+0=0$. The on-shell class was left open. This paper decides it, and nothing else.

1. Restrict both metric slots to the gauge-fixed free shell and write the boundary pairing produced by $\theta (y^0)$ explicitly in Cauchy data.

2. Prove that agreement with $u$ on the free shell is a bulk equation term, identify the class invariant, and show that no bulk term removes what the shell sees.

3. Either construct $\tilde{u}\in {\mathcal{F}}_{\mathrm{mc},\mathrm{pol}}$ agreeing with $u$ on the shell, or prove that every reproducing distribution meets a forbidden covector, or record the missing estimate.

4. Say what the result is not.

Three endings apply to each gate: Constructed, Proved obstructed, Unresolved. The worst governs the release. A missing representative is not a no-go; obstruction of the frozen kernel is not obstruction of the class. The theorems below are stated with the quantifier written out.