The moduli of semisimple generic L-parameters, introduced by Hansen, is a dense open substack of the moduli stack of L-parameters, and it is expected to be the largest open substack for which Fargues-Scholze’s categorical local Langlands correspondence can be understood reasonably explicitly. In this talk we show that much of the correspondence over this locus can indeed be made explicit, assuming certain properties of the correspondence such as geometric Eisenstein compatibility (currently known for GL(2)).