  Understanding the nonlocality of many-body systems offers valuable insights
into the behaviors of these systems and may have practical applications in
quantum simulation and quantum computing. Gisin's Theorem establishes the
equivalence of three types of quantum correlations: Bell nonlocality,
EPR-steering, and entanglement for isolated systems. No similar result exists
with regard to genuine multipartite correlations. We answer this open problem
by proposing a new network-inflation method. Our approach demonstrates that
genuine multipartite nonlocality, genuine multipartite EPR-steering, and
genuine multipartite entanglement are equivalent for any isolated many-body
system. This is achieved through an extended Bell test on an inflated network
consisting of multiple copies of the given sources. The device-independent
method is also robust against noise.
