  In a joint work with D. Bennequin, we suggested that the (negative) minima of
the 3-way multivariate mutual information correspond to Borromean links, paving
the way for providing probabilistic analogs of linking numbers. This short note
generalizes the correspondence of the minima of k-multivariate interaction
information with k Brunnian links in the binary variable case. Following
Jakulin and Bratko, the negativity of the associated K-L divergence of the
joint probability law with its Kirkwood approximation implies an obstruction to
local decomposition into lower order interactions than k, defining a local
decomposition inconsistency that reverses Abramsky's contextuality local-global
relation. Those negative k-links provide a straightforward definition of
collective emergence in complex k-body interacting systems or dataset.
