What a family would require, and why the sheet stops

A family of time-ordered maps in the sense of DF,BF,FR consists of multilinear maps $T_n$ on $n$-tuples of admissible functionals, satisfying at least

1. symmetry in the entries;

2. causal factorization: $T_{n+k}(A,B)=T_n(A)\star T_k(B)$ whenever the support of $A$ is disjoint from the causal past of that of $B$;

3. a Wick-type expansion in which the $j$-contraction term of $T_2(A,B)$ is $\frac{{\hslash }^j}{j!}⟨A^{(j)},{{\Delta }_{\mathrm{F}}}^{\otimes j}{B}^{(j)}⟩$ wherever this is defined, with a specified extension where it is not;

4. $T_1=\mathrm{id}$, and normalization conditions for the extensions in (T3).

A retarded product is then $R(A;B)=\frac{i}{\hslash }(T_2(A,B)-A\star B)$.