Degree-independence conjecture for sums of indecomposable parabolic structures

Let $\boldsymbol{\mu}\in(\mathcal{P}_n)^l$, let $\boldsymbol{\lambda}\in\mathcal{P}_{\boldsymbol{\mu}}$, and let $D$ be a reduced divisor on $\mathbb{P}^1_k$ compatible with $\boldsymbol{\lambda}$. For each $({\bf b};\mathbf{m})$, set $\mathcal{E}^{{\bf b};\mathbf{m}}=\bigoplus_i\mathcal{O}(b_i)^{m_i}$ and let $\deg({\bf b};\mathbf{m})$ be its degree.

Degree-independence conjecture. For every integer $d$, the sum

$$\sum_{\deg({\bf b};\mathbf{m})=d,\,\sum_{i=1}^f m_i=n}\mathcal{A}^{{\mathcal{E}^{{\bf b};\mathbf{m}}}}_{\boldsymbol{\mu},\boldsymbol{\lambda},D}(q)$$

is independent of $d$.

This conjecture asserts degree-independence after summing over all splitting types of fixed rank. The source supplies no resolution.