Requirement: Retarded interface I ret

A proposed retarded system must specify:

1. The vertex and observable roles and the off-shell subtraction convention. These are not inferred from the letters $B,W$.

2. The causal Green operator and kernel convention. A first-order vanishing requirement is

   $$\mathsf{R}(V;O)=0\text{if}{\mathrm{supp}}_{\mathrm{fun}}O\cap J^{+}({\mathrm{supp}}_{\mathrm{fun}}V)=\varnothing .$$

   A stronger distributional argument-slot support statement must name those slots and be separately proved.

3. Exact agreement with declared old retarded maps and specified smooth classical comparison coefficients.

4. Preservation of every fixed old product; no subtraction may change an already fixed regular coefficient.

5. Admission and actual-functional descent of every nonconstant coefficient and required descendant.

6. A named continuity domain and proof, including the additional domain obligations of any higher retarded formula.