Theorem: IX-E-2-ST stage release

Part III proves the exact imaginary part, its full positive-time distributional support, vanishing on the entire strongly separated two-way class, and a nonzero observation-spacelike control.

The retained-pair obstruction criterion remains valid, but no nonzero pair satisfying both actual orderings has been certified. The release is Unresolved at the actual support bridge. No time-ordered replacement is constructed.

Proof. The positive results are Theorem thm:imag, Corollary cor:imagsupport, Theorem thm:strongzero, and Proposition prop:control. Proposition prop:uppernotlower identifies the missing inference.