The Schumaker formula equality conjecture for planar splines

For a simplicial complex $\Delta\subseteq\mathbb{R}^2$, let $S^r_d(\Delta)$ be the real vector space of splines whose polynomial pieces have degree at most $d$ and whose smoothness is $r$. Write $f_1^0$ and $f_0^0$ for the numbers of interior edges and vertices, respectively, and let $\sigma_i$ denote the correction terms in Schumaker's dimension lower bound. The Schumaker formula equality conjecture. The Schumaker dimension formula holds with equality if $d\geq 2r+1$. Earlier work establishes equality under stronger degree bounds, but the conjectured bound remains part of the open planar spline-dimension problem.