The conjecture on obstructions to desingularizing Ricci solitons

Let $(M_o,g_o)$ be a Ricci soliton that is compact or has controlled asymptotics, such as cylindrical or conical asymptotics. Let $\overline{e{R}}^+$ denote the relevant obstruction matrix, and suppose

$$\mathop{\rm \det}\nolimits\overline{e{R}}^+\neq 0.$$

Ricci-soliton obstruction conjecture. Such $(M_o,g_o)$ cannot be the limit of smooth Ricci solitons in the pointed Gromov--Hausdorff sense.

This is proposed by analogy with known Einstein desingularization obstructions and would extend obstruction results to many Ricci solitons.