Conjecture on dessins corresponding to families of conformal blocks

Let a dessin satisfy the conditions in the proposition preceding the conjecture, namely that its gauge-theory parameters obey

$$m_1=\pm/\mp k_1m_0,\quad m_2=\pm/\mp k_2m_0,\quad m_3=\pm/\mp k_3m_0,\quad a=\pm/\mp k_{\mathrm{int}}m_0,$$

where $k_{i,\mathrm{int}}>0$. The associated states are 4-point conformal blocks (CBs) in minimal models whose allowed cases and conditions are those listed in the source's table.

General dessin conformal-block conjecture. For a dessin satisfying the proposition's conditions, it corresponds to a family of 4-point CBs whose states follow the stated table.

This conjecture extends the preceding proposition from the existence of possible conformal blocks to a family-level correspondence for every dessin satisfying its parameter conditions. The source provides no evidence of resolution.