The non-admissible collapsing isomorphism conjectures for exceptional W-algebras

Let $E_6$, $E_7$, $E_8$, and $F_4$ denote the corresponding simple exceptional Lie algebras, and let the labels such as $2A_2$, $A_2+3A_1$, $E_6$, and $\widetilde A_2$ denote nilpotent orbits. Non-admissible collapsing isomorphism conjectures. The following isomorphisms are conjectured:

$$\mathscr{W}_{-9}(E_6,2A_2)\cong L_{-3}(G_2),\qquad \mathscr{W}_{-6}(E_6,2A_1)\cong L_{-2}(B_3).$$ $$\mathscr{W}_{-12}(E_7,A_2+3A_1)\cong L_{-2}(G_2).$$ $$\mathscr{W}_{-30+32/12}(E_8,E_6)\cong L_{-4+2/3}(G_2),\qquad \mathscr{W}_{-24}(E_8,E_6(a_3))\cong L_{-2}(G_2),$$ $$\mathscr{W}_{-45/2}(E_8,A_4+2A_1)\cong\mathbb{C},\qquad \mathscr{W}_{-70/3}(E_8,A_4+A_2+A_1)\cong\mathbb{C}.$$ $$\mathscr{W}_{-15/2}(F_4,\widetilde A_2)\cong L_{-7/2}(G_2),\qquad \mathscr{W}_{-6}(F_4,\widetilde A_2)\cong L_{-2}(G_2).$$

These conjectures concern collapsing levels that are not admissible; the source motivates them using coincidences of central charges, asymptotic growths, dimensions, and associated-variety data. Their general validity remains open.