Conclusion

The first-stage commutator is controlled by the imaginary part of the locked kernel, not by full support or injectivity. Double ordering means causal disjointness of functional supports. A nonzero commutator on any retained two-way pair is a universal obstruction on the fixed domain, and no contact can remove that contradiction without changing prescribed free data.

If the prescribed values instead satisfy all actual relations, Theorem thm:algebraic supplies an algebraic extension criterion. Its arbitrary linear extension is not a substitute for a sharp distributional construction or continuity proof. Admission, contacts, old overlap, and continuity must still be established at the declared analytical strength.

Once those obligations are discharged, Theorem thm:subtraction supplies the unnormalized binary retarded difference through ${\hslash }^3$. Normalization shifts the determined order to ${\hslash }^2$. With the information presently supplied, the honest release remains Unresolved; the free-sector descent and every stated external boundary remain unchanged.