Release: two gates, three endings, worst ending governs

: two gates, three endings, worst ending governs{

Gate 1 (F1, admission): Proved obstructed.

The frozen representative of ${\mathcal{C}}_3$ has a timelike conormal covector at $\Sigma$ in a metric slot and is not in ${\mathcal{F}}_{\mathrm{mc},\mathrm{pol}}$. XI-E's admission map does not apply. The on-shell class question is open.

Gate 2 (F2–F3, plateau sum): Constructed.

The de Donder companion is computed from XI-B's fermion with the coefficient $-1$; the finite transformation of $u_3$ is the X-A second-order law with $\zeta ={\zeta }_{\mathrm{gf}}$; the plateau sum is zero when $A\gamma =0$ on $U$, with the off-plateau remainder a switching term supported in $(\mathrm{supp}\mathrm{d}g\cup \mathrm{supp}((1-g)f))\cap J^{+}(\mathrm{supp}\xi )$.

Overall ending: Proved obstructed (Gate 1). No quantum version of the plateau sum exists in ${\mathcal{E}}_H$, because ${\mathcal{C}}_3$ is not admitted. No ${\hat{s}}_{\mathrm{int}}$, loop, $\epsilon \to 0$ limit, or repair of ${\mathcal{J}}_g({\varphi }_m)$.}