Strong Delta Conjecture for the SAP maximum nullity parameter

Let $G$ be a simple graph, and let $\delta(G)$ denote its minimum degree. Write $\nu(G)$ for the greatest codimension of a faithful orthogonal representation whose Gram matrix has the Strong Arnold Property (SAP). Strong Delta Conjecture. For every simple graph $G$,

$$\delta(G) \le \nu(G).$$

This conjecture would strengthen Maehara's conjecture because $\nu(G)\leq \mathrm{M}_+(G)$. The source introduces it as a possible stronger conjecture and does not report a resolution.