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Jan 30 at 12:11 comment added Satan's Minion @Z.M. I omitted the obligatory discussion of the berthelot generic fiber. I stand by everything I wrote.
Jan 30 at 11:52 comment added Z. M Note that $A$ and $B$ are subtler than the one in the linked question. For example, $\mathbb Z_p[\![t]\!][p^{-1}]$ corresponds to the open unit disk over $\mathbb Q_p$, and it does not seem to be an "affinoid $\mathbb Q_p$-algebra" in the usual sense (it is not a Huber ring, and even not qcqs as an adic space, cf. Scholze–Weinstein §4.2).
Jan 30 at 9:14 history answered Satan's Minion CC BY-SA 4.0