  This paper examines networks of $n$ measuring parties sharing $m$ independent
nonsignaling resources that can be locally wired together: that is, each party
follows a scheme to measure the resources in a cascaded fashion with inputs to
later resources possibly depending on outputs of earlier-measured ones. A
specific framework is provided for studying probability distributions arising
in such networks, and this framework is used to directly prove some accepted,
but often only implicitly invoked, facts: there is a uniquely determined and
well-defined joint probability distribution for the outputs of all resources
shared by the parties, and this joint distribution is nonsignaling. It is
furthermore shown that is often sufficient to restrict consideration to only
extremal nonsignaling resources when considering features and properties of
such networks. Finally, the framework illustrates how the physical theory of
nonsignaling boxes and local wirings is causal, supporting the applicability of
the inflation technique to constrain such models.
  For an application, we probe the example of (3,2,2) inequalities that witness
genuine three-party nonlocality according to the
local-operations-shared-randomness definition, and show how all other examples
can be derived from that of Mao et al. [Phys. Rev. Lett. 129:150401 (2022)]
