Assumption: Inherited supported presentation

Retain exactly the host instance fixed by X-A-ST:

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

2. its supported injective developing chart

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

   whose retained compact subsets stay off $\mathcal{W}$;

3. the declared flat completion

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

4. the signature ledger

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

   The host has signature $(-,+,+,+)$, while all analytical equations in this manuscript retain $(+,-,-,-)$;

5. a retained observation region $\mathcal{O}⋐(0,T_{\ast })\times {\mathbb{R}}^3$, with

   $$D_{\ast }:=J_{\eta }^{-}(\overline{\mathcal{O}})\cap M_{T_{\ast }}⋐\mathcal{L}.$$

   Compact laboratory tests are transported to $\hat{M}$ and extended by zero.

The regular host is not assumed globally hyperbolic. The global free field and all Green distributions below live on $\hat{M}$, not on that regular product.