Compatibility of semisimple local Langlands parameters with parahoric Satake parameters

In this paper, we prove that there is at most one correspondence between parahoric-spherical representations and semisimple local Langlands parameters which satisfies certain natural properties. Our proof of uniqueness statement very formal. particular, the constructed by Fargues Scholze yield unique candidate for such representations. As a corollary, conjecture posits compatibility with parahoric Satake parameters.