Proof: Proof of the zeros

Proof. On the $47$, $5a$, and response scalar seeds, $q_R=0$, so $a_{R,\delta }=1$ and ${\theta }_{0R,\delta }=0$. The response seeds have $r=0$, where ${\theta }_{\mathrm{away}}=0$. Because the partition is inserted after the adjoints, no derivative of these vanishing factors has been generated.