Non-degeneracy conjecture for the pulled-back Goldman symplectic form

Let $P(\Theta)$ be the space of circle patterns with a fixed Delaunay angle structure $\Theta$, let $P(S_g)$ be the space of marked complex projective structures, and let $f:P(\Theta)\to P(S_g)$ be the forgetful map. Let $\omega_G$ denote Goldman's complex symplectic form and let $\omega_P$ denote the corresponding pullback form on $P(\Theta)$. Non-degeneracy conjecture. The bilinear form

$$\operatorname{Re}\omega_G=\frac{1}{2}\omega_P$$

over $P(\Theta)$ is non-degenerate. This would give a symplectic structure on the circle-pattern space once the conjectural smoothness and even-dimensionality are established; the paper states it as a further conjecture.