Covering with Chang models

Assume ${\sf{NLE}}$ and suppose there are unboundedly many Woodin cardinals and strong cardinals. Let $\kappa$ be a limit of Woodin cardinals and strong cardinals such that either $\kappa$ is a measurable cardinal or $\operatorname{cf}(\kappa)=\omega$. Covering with Chang Models. There is a transitive model $M$ of ${\sf{ZFC-Powerset}}$ such that

$$\operatorname{Ord}\cap M=\kappa^+,$$

$M$ has a largest cardinal $\nu$, and for any $g\subseteq\operatorname{Coll}(\omega,<\kappa)$, defining

$$\mathbb{R}^*=\bigcup_{\alpha<\kappa}\mathbb{R}^{V[g\cap\operatorname{Coll}(\omega,\alpha)]}$$

and

$$\Gamma^*=\{A^g\cap\mathbb{R}^*: \exists\alpha<\kappa\,(A\in\Gamma^\infty_{g\cap\operatorname{Coll}(\omega,\alpha)})\},$$

then, in $V(\mathbb{R}^*)$,

$$L\left(M,\bigcup_{\alpha<\nu}\alpha^\omega,\Gamma^*,\mathbb{R}^*\right)\vDash{\sf{AD}}.$$

If in addition there is no inner model with a subcompact cardinal, then

$$L(M)\vDash {\sf{ZFC}}+\wp(\nu)=\wp(\nu)^M+\square_\nu.$$

The result gives a covering model with Chang-model-like structural properties from strong large-cardinal hypotheses, while also producing a model of determinacy after the indicated collapse. The supplied text does not state whether this result is intended as a conjecture, theorem, or open problem, so its database status remains open.