The inner mantle conjecture for limit ordinals

Let $d702$ 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 conjecture. For any limit ordinal $\gamma$, it is consistent that the sequence of inner mantles does not stabilize before $\gamma$ and that $\mathrm{M}^{\gamma}$ is a definable inner model of $\mathsf{ZF}+\neg\mathsf{AC}$. This asks how far the sequence of inner mantles can continue to change while a limit-stage mantle remains definable and satisfies choice-free set theory; the source provides no resolution.