The full-symmetric monodromy conjecture for optimal triangulation

Let $\mathcal{P}_\bullet=(P_1,\ldots,P_n)$ be a generic arrangement of $n\ge 2$ cameras, let $\mathcal{M}_{\mathcal{P}_\bullet}\subset\mathbb{C}^{2n}$ be its affine multiview variety, and let $\pi:\mathcal{E}_{\mathcal{M}_{\mathcal{P}_\bullet}}\to\mathbb{C}^{2n}$ be the Euclidean distance cover. Its degree is

$$\operatorname{ED}(\mathcal{M}_{\mathcal{P}_\bullet})=\frac{9}{2}n^3-\frac{21}{2}n^2+8n-4.$$

Full-symmetric monodromy conjecture. The cover $\pi$ has full-symmetric Galois/monodromy group, and consequently

$$\operatorname{gw}(\pi)=\frac{9}{2}n^3-\frac{21}{2}n^2+8n-4.$$

This is proposed as a refinement of the known Euclidean-distance-degree formula for generic camera arrangements. The supplied text does not state that the full-symmetric-group assertion has been proved or disproved.