Assumption: Future time-ordered lift

For the implication below only, suppose:

1. a symmetric actual map ${\mathsf{T}}_2:D_2\to {\mathcal{P}}_{\Sigma }{\otimes }_{\mathbb{C}}\mathbb{C}[\hslash ]/({\hslash }^4)$ is constructed, with $\sigma ,\gamma$-stable comparison domain $E_2=D_2\cap D_{\mathrm{cmp}}$;

2. all its coefficients and required descendants are admitted, and actual-presentation descent holds;

3. its classical coefficient is multiplication, and ${\mathsf{T}}_2(F,G)=S(F\otimes G)$ whenever $F\gtrsim G$;

4. (eq:antitime) holds;

5. all claimed old time-ordered and retarded overlaps are supplied and agree exactly, with old unnormalized retarded convention $i({\mathsf{T}}_2-S)$;

6. any claimed continuity is proved on the same named comparison interfaces.

None of these new time-ordering hypotheses is discharged by this assumption's declaration.