The cofinality and Sealing conjecture for $\mathcal{B}^\infty$

Suppose $\kappa$ is a supercompact cardinal and there is a proper class of inaccessible limits of Woodin cardinals. Let $g\subseteq\operatorname{Col}(\omega,2^{2^\kappa})$ be $V$-generic, and set

$$\eta^\infty_g=(\Theta_{\Gamma^\infty_g})^{L(\Gamma^\infty_g,\mathbb{R}_g)}.$$

Let $\mathcal{B}^\infty=L((\eta^\infty)^\omega,\mathcal{A}^\infty)$. Cofinality and Sealing conjecture.

$$\operatorname{cf}(\eta^\infty_g)=\omega.$$

Moreover, the Sealing Theorem holds for $\mathcal{B}^\infty$ in $V[g]$. This conjecture seeks a stronger canonical determinacy model obtained from $\mathcal{A}^\infty$; the source gives no resolution.