Assumption: Unchanged supported presentation

Retain the instance already declared in X-A-ST and used by X-E-ST, X-F-ST, and X-G-ST:

1. the regular time-oriented conical product $({\mathcal{M}}^{\circ },G)$, its stipulated worldsheet $\mathcal{W}$, and its prescribed future relation;

2. an injective supported developing chart

   $$\iota :\mathcal{L}⟶{\mathcal{M}}^{\circ }$$

   with the retained compact reserve disjoint from $\mathcal{W}$;

3. the independent analytical completion

   $$\hat{M}={\mathbb{R}}^{1+3},\eta =\mathrm{diag}(1,-1,-1,-1),M_{T_{\ast }}=[0,T_{\ast }]\times {\mathbb{R}}^3,\Sigma =\{t=0\};$$

4. the signature and time ledger

   $${\iota }^{\ast }G=-\eta ,t=c_{\mathrm{host}}(T-T_{\Sigma });$$

5. a nonempty observation region

   $$\mathcal{O}⋐(0,T_{\ast })\times {\mathbb{R}}^3,J_{\eta }^{-}(\overline{\mathcal{O}})\cap M_{T_{\ast }}⋐\mathcal{L}.$$

Every global Green operator and free field below belongs to $\hat{M}$. The regular conical product is not used as a globally hyperbolic Cauchy spacetime.