I should point out that Joshi's paper does not falsify Remark 9 of our paper.

In Joshi's Theorem 4.8 (which he claims to falsify our Remark 9) the curve $X/E$ stays the same (and hence of course its tempered fundamental group stays the same). The only thing that changes is how $E$ is embedded into an untilt $K$ of an auxiliary characteristic $p$ perfectoid field $F$. But this extra data also doesn't have anything to do whatsoever with the situation -- of course one can't reconstruct it from the tempered fundamental group, as the latter doesn't even know about this extra data...

I should point out that Joshi's paper does not falsify Remark 9 of our note.

In Joshi's Theorem 4.8 (which he claims to falsify our Remark 9) the curve $X/E$ stays the same (and hence of course its tempered fundamental group stays the same). The only thing that changes is how $E$ is embedded into an untilt $K$ of an auxiliary characteristic $p$ perfectoid field $F$. But this extra data also doesn't have anything to do whatsoever with the situation -- of course one can't reconstruct it from the tempered fundamental group, as the latter doesn't even know about this extra data...