\] The $0$-forms $\omega^{+,+}$, $\omega^{+,-}$, $\omega^{-,+}$ and $\omega^{-,-}$ determine smooth, closed $0$-forms on the compactified configuration space $\mathcal C_{0,0}^+$, which enjoy the following properties:  -   $$\omega^{+,+}\vert_\alpha=\mathrm d\varphi,\ \omega^{+,-}\vert_\alpha=\mathrm d\varphi-\mathrm d\eta,\  \omega^{-,+}\vert_\alpha=\mathrm d\varphi-\mathrm d\eta,\ \omega^{-,-}\vert_\alpha=\mathrm d\varphi,$$ where $\mathrm d\varphi$ is the normalized volume form of $\mathcal C_0\cong S^0$.  -   $$\begin{aligned}     \omega^{+,+}\vert_\beta&=\omega^+,\ & \omega^{+,-}\vert_\beta&=\omega^+,\ & \omega^{-,+}\vert_\beta&=\omega^-,\ & \omega^{-,-}\vert_\beta&=\omega^-\quad \text{and}\\     \omega^{+,+}\vert_\gamma&=\omega^+,\ & \omega^{+,-}\vert_\gamma&=\omega^-,\ & \omega^{-,+}\vert_\gamma&=\omega^+,\ & \omega^{-,-}\vert_\gamma&=\omega^-,     \end{aligned}$$ where $\omega^\pm$ have to be understood on $\mathcal C_{0,0}^+$.  -   $$\begin{aligned}     &\omega^{+,+}\vert_\delta=\omega^{+,-}\vert_\delta=\omega^{-,+}\vert_\delta=0,\\     &\omega^{+,-}\vert_\varepsilon=\omega^{-,+}\vert_\varepsilon=\omega^{-,-}\vert_\varepsilon=0.     \end{aligned}$$  -   $$\begin{aligned}     &\omega^{+,-}\vert_\eta=\omega^{-,-}\vert_\eta=0,\ & &\omega^{+,+}\vert_\theta=\omega^{-,+}\vert_\theta=0,\\     &\omega^{-,+}\vert_\zeta=\omega^{-,-}\vert_\zeta=0,\ & &\omega^{+,+}\vert_\xi=\omega^{+,-}\vert_\xi=0.     \end{aligned}$$  ### The $0$-colored propagators on $\mathcal C_{0,0