Retained obstruction boundaries

The supplied IX-C records the VII-C obstruction under (E1)–(E4): preservation of the old Wick algebra, exact sharp admission, normal-topology sequential admission continuity, and hypocontinuous multiplication with continuous coefficient extraction. That conditional obstruction is retained, not independently reproved here.

Likewise, the reported separated witness excludes removal of the selected logarithm by observation-diagonal counterterms. The VII-D numerical subtraction does not restore unchanged regular-product convergence or invalidate the original obstruction hypotheses.

No positive-cutoff old product has been subtracted or redefined in this manuscript. No claim contradicts $B_{f,\epsilon }\nrightarrow B_f$ in ${\tau }_{\Sigma }$. Numerical calibration and bulk-relative value preservation are not normal-topology admission continuity.

The external $R_{1,1}$, oscillator coefficient, and Newton–wave cubic identified in V are different objects. No theorem from V enters a proof here. No retarded, interacting, switched, gravitational, or all-graph construction is begun.