Semistable-net conjecture for nondegenerate quadrics

Let $\gamma$ be a net of quadrics, meaning a three-dimensional linear system of quadratic forms, and suppose that $\gamma$ is semistable. Semistable-net conjecture. If $\gamma$ is a semistable net of quadrics, then a generic quadric in the net is nondegenerate. The claim is proposed as a reinterpretation of the generic non-jumping conjecture for instantonic nets; its validity is not established in the supplied text.