Abstract

We evaluate the imaginary part of the locked mixed Cauchy kernel and apply it to the first-stage commutator on the fixed comparison domain of IX-E. A common Abel regulator gives an exact distributional decomposition into a direct sine contribution and two cosine contributions. Away from the spatial apex, the imaginary part consists of a direct null-cone delta distribution and a locally integrable contribution in the observation-spacelike region between the direct and reflected cones. The direct and reflected cosine tails cancel outside the reflected cone.

Consequently, the commutator vanishes identically on IX-E's entire strongly separated two-way witness class. An explicit observation-spacelike control has nonzero commutator, but is not certified as a two-way pair of actual functional supports. The remaining domain-wide obligation is therefore an actual functional-support bridge, not another evaluation of the kernel on the settled witness class.

The release remains Unresolved. No time-ordered replacement, contact classification, normalized retarded product, or fixed-domain obstruction is claimed. The inherited free-sector results and external non-identification boundaries are unchanged.