Logarithmic Kummer pro-étale Poincaré lemma

Let $X$ be a smooth logarithmic rigid analytic space over $k/\mathbb{Q}_p$, and consider the projective maps

$$g:X_{\text{Kummer-pro-étale}}\rightarrow X_{\text{Kummer-ét}},\qquad f:X_{\text{Kummer-pro-étale}}\rightarrow X.$$

Logarithmic Kummer Poincaré conjecture. The logarithmic versions of the strictly exact long exact sequences in the Poincaré lemma for the rigid-analytic situation should hold for these maps.

This is proposed as the logarithmic analogue of the rigid-analytic Poincaré lemma. The supplied text does not specify the complexes in the sequences or establish the assertion.