The PFA-to-superstrong-cardinal conjecture in the uB derived model

Assume that the Proper Forcing Axiom $\operatorname{PFA}$ holds. Let $\kappa\geq\omega_2$, and let $g$ be $\operatorname{Col}(\omega,\kappa)$-generic over $V$. Then

$$\text{there is a superstrong cardinal in }\operatorname{HOD}^{L({{\sf{uB}}}_g,\mathbb{R}_g)}.$$

PFA-to-superstrong-cardinal conjecture. Under these hypotheses, there is a superstrong cardinal in $\operatorname{HOD}^{L({{\sf{uB}}}_g,\mathbb{R}_g)}$.

This is a typical target of the core model induction, connecting forcing axioms with large-cardinal strength in canonical determinacy models. The source states that the conjecture is currently open even when a Woodin limit of Woodin cardinals is assumed instead of a superstrong cardinal.