Let $\Psi$ be a virtual support function. We will write $((L_{\Psi},z_{\Psi}),s_{\Psi})$ for the toric line bundle with toric section associated to the $\mathbb{T}$-Cartier divisor $D_{\Psi}$ by Theorem 4.22. When we do not need to make explicit the vector $z_{\Psi}$, we will simply write $(L_{\Psi},s_{\Psi})$.