Radical-generation conjecture for the three-factor model

Let $I_{p,3}$ be the prime ideal of invariants of the three-factor model. Let $J_{p,3}$ be the ideal generated by all off-diagonal $4\times4$-minors of the covariance matrix $\Psi$ and all septad linear eliminants.

Three-factor radical-generation conjecture. The radical of $J_{p,3}$ is the prime ideal $I_{p,3}$:

$$\sqrt{J_{p,3}}=I_{p,3}.$$

The paper observes that the minors and septads determine the parameter space set-theoretically in all computed examples, although they do not generate the entire ideal. The conjecture formalizes this observed set-theoretic generation and remains unproved in the source.