Odd-level pole cancellation in the symmetric Veneziano amplitude ($\mathrm{Res}{A}_{\mathrm{sym}}\propto [1+(-1{)}^n]{\prod }_{j=1}^n({\alpha }^{\prime }t+j+1)$)

For identical open-string tachyons, $s+t+u=-4/{\alpha }^{\prime }$. At ${\alpha }^{\prime }s=n-1$, the ordered Veneziano amplitude residues in the $s,t$ and $s,u$ terms differ by $(-1{)}^n$, so their symmetric sum cancels odd-level $s$-channel poles at generic $t$. In particular the massless vector does not couple to this identical-scalar singlet amplitude. It remains a state of the open-string spectrum and is visible in suitable ordered or color-dependent amplitudes. Pole absence due to an external-state selection rule must not be interpreted as absence of the exchanged state from the theory.