SD-degree conjecture for Chow threefolds and secant surfaces

Let $\mathcal{C}\subset\mathbb{P}^3$ be a curve, and let the Chow threefold and secant surface associated with $\mathcal{C}$ have Grassmannian-distance degree ${\rm GDdegree}$ and square-data degree ${\rm SDdegree}$. SD-degree conjecture. One has

$${\rm SDdegree}=2\cdot{\rm GDdegree}$$

for the Chow threefold, while

$${\rm SDdegree}={\rm GDdegree}$$

for the secant surface. These identities are based on the computations reported in the paper and are not proved in the supplied text.