Conjugate transfer and fixed-domain obstruction

Let $S(d)={\star }_c(d)$ and

The inherited reversal identity gives

Conjugation preserves actual functional support on the unrestricted real configuration space: a dependence vanishes exactly when its conjugate vanishes.

Consequently any proved original-sector bridge clears the double-ordering commutator test on the declared conjugates and flips. For the real-coefficient flat realization, $B_f^{\ast }=B_{\overline{f}}$ and $W_g^{\ast }=W_{\overline{g}}$; the distributional statement itself also applies directly to those tests.

This transfer does not prove the bridge on the original pairs. It also does not evaluate relations among sums of actual tensors.