What remains unchanged

IX-B's separated witness proves that observation-diagonal counterterms cannot remove the selected logarithm IXB (thm:diagonal). The unchanged regularized coefficient remains divergent on that witness. The normal-topology extension obstruction of VII-C, under its declared hypotheses including (E1)–(E4), remains valid VIIC (thm:coefficient, ass:extension, cor:noalgebra).

IX-A explicitly proves

for nonzero real $f$ IXA (thm:IX1, cor:compatibility). No opposite continuity requirement is introduced here.

A numerical subtraction from ${T_{\epsilon }}^{\rho }$ is not a change inside the unchanged old product. Subtracting old regular coefficients would change those products; assigning only a sharp value would not restore the forbidden normal continuity IXB (rem:subtraction, Section “Continuity reconciliation”).

The separate G2 condition is untouched. Where IX-A's stated switch-gap hypotheses apply, its first-order incompatibility continues to apply IXA (prop:G2). No unconditional gauge theorem outside those hypotheses is inferred.