Abstract

We revise the causal-support interface for the ordered word $B_f,W_g,B_{f^{\prime }}$ using the constructed free sector of IX-Free-2 as an explicit inherited premise. Relative to its stated prerequisites, IX-Free-2 supplies degree-four descent, simultaneous overlap agreement, a truncated partial product ${\star }_c$ on a named tensor domain, and agreement of the two associations through order ${\hslash }^3$. It does not supply a time-ordered or retarded product.

We establish configuration-support bounds for the constructed outputs, including all one-edge terms and the classical word. We identify the calibrated scalar as the constant projection of an existing free word, while proving that this projection still does not define a causal map. An explicit algebraic separation argument shows that wordwise free coherence, even together with an admitted symmetric auxiliary multiplication, does not imply causal factorization.

Separate time-ordered and retarded interfaces are stated with actual tensor domains, old-product overlaps, order-reversing involution, and continuity boundaries. We retain the conditional source-contact incompatibility and prove the conditional retarded-subtraction implication on a domain where every required free product exists. The normalization audit shows that numerator data through ${\hslash }^3$ determine a quotient by $\hslash$ only through ${\hslash }^2$.

The interface and separation analysis is complete. The sharp causal-product release remains unresolved at the unconstructed time-ordered extension and its causal compatibility proofs. The free gate for this word is no longer the live stop. Neither a general free-product enlargement nor a G2-compatible interacting construction is asserted.