In his Midrasha Mathematicae lectures ("In Search of Ultimate $L$", BSL 23 [2017]: 1–109), Woodin notes that $V = \textit{Ultimate }L$ implies $\textrm{CH}$ (Theorem 7.26, p.103). Is it known whether $V = \textit{Ultimate }L$ implies $\textrm{GCH}$? 



Does $V = \textit{Ultimate }L$ imply GCH?
In his slide [Absolutely ordinal definable sets](http://logic.berkeley.edu/logic@UCB/Steel_logic@UCB.pdf) John Steel writes: 



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> At the same time, one hopes that V = ultimate L will yield a detailed ﬁne structure theory for V, removing the incompleteness that large cardinal hypotheses by themselves can never remove. It is known that V = ultimate L implies the CH, and many instances of the GCH. Whether it implies the full GCH is a crucial open problem
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