Normality conjecture for Boij–Söderberg coefficients of Veronese surfaces

For the $d$-uple Veronese embedding of $\mathbb P^2$, let $\beta(\mathbb P^2,b;d)$ denote its Betti table with twist parameter $b$, and let its Boij–Söderberg coefficients be the coefficients in its decomposition into pure Betti diagrams. Boij–Söderberg unimodality conjecture. For any $b,d$, the Boij–Söderberg coefficients of $\beta(\mathbb P^2,b;d)$ are unimodal. The conjecture predicts a regular distribution of these coefficients; the paper says that its limited data suggests this behavior but does not prove it.