The LST-hod mouse equiconsistency conjecture

An $LST$-hod premouse is a premouse $\mathcal P=L[\mathcal P|\delta]$ with cardinals $\kappa,\delta$ such that, in $\mathcal P$, $\delta$ is Woodin, $\kappa$ is $<\delta$-strong, and $\kappa$ is a limit of Woodin cardinals.

LST-hod mouse equiconsistency conjecture. The following theories are equiconsistent:

$$\begin{array}{ll} \text{ZFC+there is an $LST$-hod premouse},\\ \text{ZFC+there is a Woodin limit of Woodin cardinals}. \end{array}$$

The source proves upper and lower consistency bounds around $LST$-hod premice and presents this equiconsistency as the remaining conjectural identification of their exact strength.