The Gersten conjecture for $p$-adic étale Tate twists and the $p$-adic cycle class map

We prove the Gersten conjecture for $p$-adic étale Tate twists for a smooth scheme $X$ in mixed characteristic in the Nisnevich topology. Our main observation is that, while $p$-adic étale Tate twists are not $\mathbb A^1$-invariant, for the proof of the Gersten conjecture it suffices that they sati