Theorem: IX-E-ST stage release

Part II proves the double-ordering geometry, a nonempty strong-separation criterion, the commutator identity, fixed-domain obstruction criterion, and algebraic extension criterion. Its subtraction theorem is conditional.

At this stage the necessary restriction of $K-\overline{K}$ has not been evaluated on the intended two-way sector, no nonzero old time-ordered map is supplied, and no sharp analytical extension is constructed. The release is Unresolved, not a universal obstruction.

Proof. The positive statements are proved above. Neither an analytical candidate nor a certified violating two-way pair has been produced in Part II. These are distinct missing discharges.