Smallest classical weight conjecture for boundary slope seeds

Let $V\in\{U_p,U_{\mathfrak p}\}$, let $\kappa_{\min,\chi\tau^t}$ be the smallest classical weight associated with the character $\chi\tau^t$, and let $t\in(\mathbb{Z}/T\mathbb{Z})^g$. Smallest classical weight conjecture. The seed set in the boundary slope generation formula is

$$B_{\kappa,r}(t,V)=\mathcal{S}^{\mathrm{cl}}_{\kappa_{\min,\chi\tau^t}}(V),$$

where $\chi$ is as in the definition of the smallest classical weight, $\tau$ is the character defined in the source, and $T$ is the period from the boundary slope generation conjecture. Thus the boundary slopes should be determined by classical slopes at the smallest available classical weights. This is motivated by the computed examples and would give a stronger control theorem for weights near the boundary, but it is not proved in the source.