  This is the first in a series of papers where scissor congruence and
K-theoretical invariants are related to cobordism groups of foams in various
dimensions. A model example is provided where the cobordism group of weighted
one-foams is identified, via the Sah-Arnoux-Fathi invariant, with the first
homology of the group of interval exchange automorphisms and with the
Zakharevich first K-group of the corresponding assembler. Several variations on
this cobordism group are computed as well.
