Proposition: Flip and conjugate transfer

Let $J(d)=S(d)-S(\sigma d)$. Then

Conjugation preserves functional support, so a proved original-sector bridge transfers to retained flips and conjugates. This does not evaluate arbitrary relations among sums of actual tensors.

Proof. Free reversal gives $S(\gamma d)=S(\sigma d{)}^{\ast }$ and $S(\sigma \gamma d)=S(d{)}^{\ast }$. Subtract. A functional changes under a local perturbation exactly when its complex conjugate changes, proving support invariance.