Handoff list

If X-B is opened, it receives only:

• the coefficients ${\mathcal{O}}^{(0)},{\mathcal{O}}^{(1)},{\mathcal{O}}^{(2)}$ of Definition def:observable with Lemma lem:Phiexp, and the derivative kernels of Proposition prop:kernels;

• the configuration space $\mathcal{C}$ and the test space ${C_c}^{\infty }({M_T}^{\circ };\mathbb{R})$ in label space;

• the support statement ${\mathcal{D}}_f=J^{-}(\mathrm{supp}f)\cap M_T$ of Proposition prop:continuity(a);

• the fixed-$\epsilon$ continuity statements of Proposition prop:continuity(b);

• the classical gauge identity of Theorem thm:main(iv)–(vi), together with the retained defect terms (eq:varied) and (eq:firstorder) for parameters leaving the plateau, and the edge-zone defect (eq:edgegap);

• the single interaction selected for a later retarded product: the first-order switched scalar vertex

  $$V_{1,g}[h,\varphi ]={\int }_{M_T}g{\mathfrak{L}}^{(1)}[h,\varphi ]{\mathrm{d}}^{4}x=\frac{1}{2}{\int }_{M_T}g({a_1}^{\mu \nu }[h]{\partial }_{\mu }\varphi {\partial }_{\nu }\varphi -m^2{b}_1[h]{\varphi }^2){\mathrm{d}}^{4}x,$$

  whose scalar Hessian is ${\mathsf{V}}_{1,g}[h]$ of (eq:V1g).