We show that the recent result of Castañeda and Wu regarding the ramification filtration in certain $p$-extensions of function fields of prime characteristic $p$ is equally valid over local fields of mixed characteristic $(0,p)$. Apart from being applicable to both equicharacteristic and mixed characteristic cases, our method is local, conceptual, natural, and shorter.
"The ramification filtration in certain $p$-extensions." Rocky Mountain J. Math. 49 (2) 487 - 492, 2019. https://doi.org/10.1216/RMJ-2019-49-2-487