  We classify all additive invariants of open Petri nets: these are
$\mathbb{N}$-valued invariants which are additive with respect to sequential
and parallel composition of open Petri nets. In particular, we prove two
classification theorems: one for open Petri nets and one for monically open
Petri nets (i.e. open Petri nets whose interfaces are specified by monic maps).
Our results can be summarized as follows. The additive invariants of open Petri
nets are completely determined by their values on a particular class of
single-transition Petri nets. However, for monically open Petri nets, the
additive invariants are determined by their values on transitionless Petri nets
and all single-transition Petri nets. Our results confirm a conjecture of John
Baez (stated during the AMS' 2022 Mathematical Research Communities workshop).
