Requirement: Time-ordered interface I TO

A proposed bosonic causal construction must provide:

1. actual tensor domains $D_2$, and any required $D_3$, with all necessary flips, conjugates, and intermediate domains specified;

2. a symmetric linear map

   $${\mathsf{T}}_2:D_2⟶{\mathcal{P}}_{\Sigma }{\otimes }_{\mathbb{C}}\mathbb{C}[\hslash ]/({\hslash }^4),T_0(F,G)=FG,{T_1}^{\mathrm{arity}}(F)=F;$$

   the last normalization concerns arity one, not $\hslash$-order one;

3. admitted coefficients and all required descendants, with actual-presentation independence;

4. causal factorization on every retained comparison pair:

   $${\mathsf{T}}_2(F,G)=S(F\otimes G)\text{if }F\gtrsim G;$$

5. exact values on every separately supplied old time-ordered overlap, and a specified admissible contact class;

6. anti-time ordering and involution:

   $${\overline{\mathsf{T}}}_2(d)=S(d)+S(\sigma d)-{\mathsf{T}}_2(d),{\mathsf{T}}_2(d{)}^{\ast }={\overline{\mathsf{T}}}_2(\gamma d);$$

7. a continuity theorem on named domains at a specified strength.

Outside $D_{\mathrm{cmp}}$, every additional free comparator must be independently constructed. Higher causal factorization must name every product it uses.