Integral locality conjecture for perfectoid affinoid algebras

Let $K$ be a perfectoid field, let $(A,A^+)$ be a complete affinoid $K$-algebra for which $A^+$ has the $p$-adic topology, and set $X=\operatorname{Spa}(A,A^+)$. Assume that $X$ has a cover by rational subsets $U_i\subset X$ for which the completion $\widehat{\mathcal{O}_X(U_i)}$, taken with respect to the topology giving $\mathcal{O}_X^+(U_i)$ the $p$-adic topology, is a perfectoid $K$-algebra. Integral locality conjecture. Then $(A,A^+)$ is a perfectoid affinoid $K$-algebra. This is a foundational locality question for perfectoid spaces, posed as a variant of the preceding conjecture and presented as open.