  Let $K$ be a discrete valuation field with perfect residue field, we study
the functor from weakly admissible filtered $(\varphi,N,G_K)$-modules over $K$
to the isogeny category of Breuil-Kisin-Fargues $G_K$-modules. This functor is
the composition of a functor defined by Fargues-Fontaine from weakly admissible
filtered $(\varphi,N,G_K)$-modules to $G_K$-equivariant modifications of vector
bundles over the Fargues-Fontaine curve $X_{FF}$, with the functor of
Fargues-Scholze that between the category of admissible modifications of vector
bundles over $X_{FF}$ and the isogeny category of Breuil-Kisin-Fargues modules.
We study those objects appear in the essential image of the above functor and
call them arithmetic BKF modules. We show certain rigidity result of arithmetic
BKF modules and use it to compare existing $p$-adic Hodge theories at
${A}_{\mathrm{inf}}$ level.
