Natural-definition problem for non-full-flag Higgs bundle moduli spaces

Let $p_i$ be punctures with parabolic weights $\boldsymbol{\alpha}=(\alpha_i)$, and call the flags not all full when, for some $p_i$, the corresponding weight satisfies $4\alpha_i \in \\{0, \frac{1}{2}\\}\4$. Natural-definition problem. There is a more natural definition of the Higgs bundle moduli space when the flags are not all full. The current definition can lead to a drop in dimension, so the resulting moduli spaces need not be four-dimensional or ALG-$D_4$; the proposed natural definition is intended to address this discrepancy.