Dimensional absolute stability implies diagonalizability for T-meshes

Let $\mathscr{T}$ be a T-mesh. A T-mesh is called dimensionally absolutely stable when its spline-space dimension is stable under the relevant local modifications, and it is called diagonalizable when it admits the diagonalization property considered in the paper.

Dimensional absolute stability conjecture. $\mathscr{T}$ is dimensionally absolutely stable if and only if it is diagonalizable.

This conjecture proposes that diagonalizability exactly characterizes the absolute-stability subclass among dimensionally stable T-meshes. The preceding discussion motivates it through unstable ranks of minors associated with minimal simple cycles in the CNDC; its resolution is not established in the supplied text.