Excellent connections for degenerate forms

Let $\varphi$ be a degenerate anisotropic form, let $X$ be its associated variety, and let $d_X$ denote the relevant dimension parameter. Let $r$ be the parameter used in the theorem on excellent connections. A pair $(a,b)$ is excellent when it satisfies the excellence condition defined in the paper; write $a_{\mathrm{lo}}$ and $b^{\mathrm{up}}$ for the corresponding lower and upper elements of $\Lambda(X)$, and say that they are connected when they lie in the same connection relation in $\Lambda(X)$.

Excellent-connections conjecture. For integers $a,b$ with $0\leq a,d_X-b<r$, if $(a,b)$ is excellent, then $a_{\mathrm{lo}}$ and $b^{\mathrm{up}}$ are connected in $\Lambda(X)$.

This conjectures that the theorem on excellent connections for nondegenerate forms extends to degenerate forms. The source presents the extension as unresolved and as the concluding conjecture of the paper.