The inner mantle non-definability conjecture for limit ordinals

Let $\gamma$ be a limit ordinal, and let $(\mathrm{M}^{\alpha})_{\alpha\in\mathrm{Ord}}$ denote the sequence of inner mantles, with $\mathrm{M}^{\alpha}$ its stage at index $\alpha$. Inner mantle non-definability conjecture. For any limit ordinal $\gamma$, it is consistent that the sequence of inner mantles does not stabilize before $\gamma$ and that $\mathrm{M}^{\gamma}$ fails to be a definable class. This is a further proposed behavior for the transfinite sequence of inner mantles; the source gives no evidence that the conjecture has been resolved.