  One can compute the local $\mathbb{A}^1$-degree at points with separable
residue field by base changing, working rationally, and post-composing with the
field trace. We show that for endomorphisms of the affine line, one can compute
the local $\mathbb{A}^1$-degree at points with inseparable residue field by
taking a suitable lift of the polynomial and transferring its local degree. We
also discuss the general set-up and strategy in terms of the six functor
formalism. As an application, we show that trace forms of number fields are
local $\mathbb{A}^1$-degrees.
