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In this note, we prove the logarithmic 
$p$-adic comparison theorem for open rigid analytic varieties. We prove that a smooth rigid analytic variety with a strict simple normal crossing divisor is locally 
$K(\unicode[STIX]{x1D70B},1)$ (in a certain sense) with respect to 
$\mathbb{F}_{p}$-local systems and ramified coverings along the divisor. We follow Scholze’s method to produce a pro-version of the Faltings site and use this site to prove a primitive comparison theorem in our setting. After introducing period sheaves in our setting, we prove aforesaid comparison theorem.
