We study the plus-pure threshold ( \({{\,\textrm{ppt}\,}}\) ) of hypersurfaces in mixed characteristic. We show that the \({{\,\textrm{ppt}\,}}\) limits to the F-pure threshold (fpt) as we ramify the base DVR. Additionally, we show that analogs of some positive characteristic extremal singularities cannot attain the same ‘extremal’ \({{\,\textrm{ppt}\,}}\) values in the unramified setting. We also study equations which have controlled ramification when we adjoin their p-th roots as well as equations which admit p-th roots modulo \(p^2\) (or modulo other values), bounding their \({{\,\textrm{ppt}\,}}\) s. In particular, given a complete unramified regular local ring of mixed characteristic \(p>0\) , \(f^p + p^2 g\) does not define a perfectoid pure singularity for any f and g. Finally, we compute bounds on the \({{\,\textrm{ppt}\,}}\) of hypersurfaces related to elliptic curves. This gives examples where the \({{\,\textrm{ppt}\,}}\) is neither the corresponding \({{\,\textrm{fpt}\,}}\) in characteristic \(p > 0\) nor the \({{\,\textrm{lct}\,}}\) in characteristic zero. This also provides examples where p times the \({{\,\textrm{ppt}\,}}\) is not a jumping number, in stark contrast with the characteristic \(p > 0\) picture.
