  We show that some tripartite quantum correlations are inexplicable by any
causal theory involving bipartite nonclassical common causes and unlimited
shared randomness. This constitutes a device-independent proof that Nature's
nonlocality is fundamentally at least tripartite in every conceivable physical
theory - no matter how exotic. To formalize this claim we are compelled to
substitute Svetlichny's historical definition of genuine tripartite nonlocality
with a novel theory-agnostic definition tied to the framework of Local
Operations and Shared Randomness (LOSR). A companion article [PRA. 104, 052207
(2021)] generalizes these concepts to any number of parties, providing
experimentally amenable device-independent inequality constraints along with
quantum correlations violating them, thereby certifying that Nature's
nonlocality must be boundlessly multipartite.
