The minimal-generation conjecture for rigid multiview ideals

Let $A=(A_1,\ldots,A_n)$ be a generic configuration of $n$ cameras, and let $J_A$ denote its rigid multiview ideal. The displayed degree classes record the multidegrees of the generators, with a class such as $(110..000..)$ indicating the corresponding multidegree in the $\mathbb{Z}^n$-grading.

Minimal-generation conjecture. The rigid multiview ideal $J_A$ is minimally generated by

$$\frac{4}{9}n^6-\frac{2}{3}n^5+\frac{1}{36}n^4+\frac{1}{2}n^3+\frac{1}{36}n^2-\frac{1}{3}n$$

polynomials. These polynomials come from two triples of cameras, and the numbers in the eight degree classes are

$$\begin{array}{rlrl} (110..000..):&1\cdot 2\binom{n}{2} &(220..111..):&3\cdot 2\binom{n}{2}\binom{n}{3}\\ (220..220..):&9\cdot\binom{n}{2}^2 &(211..211..):&n^2\binom{n-1}{2}^2\\ (111..000..):&2\binom{n}{3} &(211..111..):&2n\binom{n-1}{2}\binom{n}{3}\\ (220..211..):&6n\binom{n}{2}\binom{n-1}{2} &(111..111..):&\binom{n}{3}^2. \end{array}$$

This conjecture extends the explicitly verified $n=2$ case and predicts the minimal generators for arbitrary numbers of cameras; the source gives no proof or resolution for $n\geq3$.