  Clausen has constructed a homotopical enrichment of the Artin reciprocity
symbol in class field theory. On the Galois side, Selmer K-homology replaces
the abelianized Galois group, while on the automorphic side the K-theory of
locally compact vector spaces replaces classical idelic objects. We supply
proofs for some predictions of Clausen regarding the automorphic side.
