With Rob van Glabbeek as second author.

A cornerstone of the theory of proof nets for unit-free multiplicative
linear logic (MLL) is the abstract representation of cut-free proofs
modulo inessential rule commutation. The only known extension to
additives, based on monomial weights, fails to preserve this key
feature: a host of cut-free monomial proof nets can correspond to the
same cut-free proof. Thus the problem of finding a satisfactory
notion of proof net for unit-free multiplicative-additive linear logic
(MALL) has remained open since the inception of linear logic in 1986.
We present a new definition of MALL proof net which remains faithful
to the cornerstone of the MLL theory.