Theorem: IX-D revised interface package

Relative to the explicitly inherited carrier, calibration, and IX-Free-2 premises, this manuscript establishes:

1. Separate time-ordered and retarded interfaces with actual-domain requirements.

2. Configuration-support bounds for all displayed constructed free outputs, including the one-edge terms and the classical word.

3. Identification of ${\mathcal{N}}_c(f,g,f^{\prime })$ as the constant projection of the constructed free association, together with its non-lift to a causal map definition.

4. An explicit separation of free wordwise coherence from causal factorization.

5. The source-contact contradiction under the simultaneous hypotheses of Assumption ass:source.

6. The conditional admitted subtraction, causal vanishing, old-overlap, and involution implication of Proposition prop:conditionalret.

7. The precise normalized $\hslash$-order limitation.

8. Persistence of the copied first-order switch witness against corrections beginning at order ${\kappa }^2$.

It constructs no sharp ${\mathsf{T}}_2$, normalized $R_1$, or $R_2$ on the requested sector.

The causal-product release is Unresolved. The live stop is the time-ordered extension and its remaining causal, admission, and overlap obligations, not degree-four descent of the inherited free word.

Proof. The statements follow from Requirements req:TO–req:ret, Theorem thm:support, Theorem thm:nonlift, Lemma lem:separation, Proposition prop:contact, Proposition prop:conditionalret, Lemma lem:hbaraudit, and Proposition prop:switch.

Assumption ass:free2 supplies the named free sector. No result here constructs the separate time-ordering hypotheses of Assumption ass:future. Its conditional consequence therefore does not release a sharp retarded map.

The source contradiction excludes only its stated simultaneous prescription. The switch result retains its copied first-order hypotheses. Neither is a universal obstruction to every possible causal extension.