De Rham epsilon factors for flat connections on higher local fields

This note is a companion to the author's "Higher de Rham epsilon factors". Using Grayson's binary complexes and the formalism of $n$-Tate spaces we develop a formalism of graded epsilon lines, associated to flat connections on a higher local field of characteristic $0$. The definition is based on comparing a Higgs complex with a de Rham complex on the same underlying vector bundle.