The CVR dimension conjecture for hierarchical T-mesh spline spaces

Let $\mathscr{T}$ be a hierarchical T-mesh, and let $\mathscr{C}$ be its CVR (cross-vertex relationship) graph. For a spline space with the highest order of smoothness, write $\bar{S}_d(\mathscr{T})$ and $\bar{S}_{d-2}(\mathscr{C})$ for the corresponding spline spaces. CVR conjecture. For $d\ge 2$, one has

$$\dim\bar{S}_d(\mathscr{T})=\dim\bar{S}_{d-2}(\mathscr{C}).$$

This conjecture concerns the relationship between spline spaces on a hierarchical T-mesh and its CVR graph; the equality would identify the original space's dimension with that of a lower-degree space on the graph. The source presents it as a conjecture and gives no resolution status beyond the results discussed in the paper.